Handbook of Natural Resource and Energy, Volume 3 (Handbooks in Economics)

HANDBOOK OF NATURAL RESOURCE AND ENERGY ECONOMICS VOLUME Ill HANDBOOKS IN ECONOMICS Series Editors KENNETH J. ARROW...

Author: A.V. Kneese | J. Sweeney

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HANDBOOK OF NATURAL RESOURCE AND ENERGY ECONOMICS VOLUME Ill

HANDBOOKS IN ECONOMICS

Series Editors

KENNETH J. ARROW

MICHAEL D. INTRIUGATOR

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HANDBOOK OF NATURAL RESOURCE AND ENERGY ECONOMICS VOLUME 3 Edited by

ALLEN V. KNEESE and

JAMES b. SWEENEY Stanford University

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Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands First edition 1993 Reprinted 2004, 2005, 2006 Copyright © 1993 Elsevier Ltd. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (44) (0) 1865 843830; fax: (44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data (Revised for Volume 3) Handbook of Natural Resource and energy economics. (Handbooks in economics; 6) Includes bibliographics and indexes 1. Energy Industries. 2. Natural Resources. 3. Conservation of natural resources. 4. Power resources. 5. Environmental protection. I. Kneese, Allen V. II. Sweeney, James L. III. Series: Handbooks in economics; bk. 6. HD9502.A2H257 1985 333.7 85-10322 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN–13: 978-0-444-87800-7 ISBN–10: 0-444-87800-9 For information on all Elsevier publications visit our website at books.elsevier.com Printed and bound in Great Britain 06 07 08 09 10 10 9 8 7 6

INTRODUCTION TO THE SERIES

The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics. KENNETH J. ARROW and MICHAEL D. INTRILIGATOR

This Page Intentionally Left Blank

CONTENTS OF THE HANDBOOK

VOLUME I Preface to the Handbook ALLEN V. KNEESE and JAMES L. SWEENEY

PART 1 - SOME BASIC CONCEPTS Chapter 1

Welfare Economics and the Environment KARL-GORAN MALER

Chapter 2

Bioeconomics of Renewable Resource Use JAMES E. WILEN

Chapter 3

Spatial Aspects of Environmental Economics HORST SIEBERT

Chapter 4

Economics of Nature Preservation ANTHONY C. FISHER and JOHN V. KRUTILLA

Chapter 5

Ethics and Environmental Economics ALLEN V. KNEESE and WILLIAM D. SCHULZE

PART 2 - SELECTED METHODS AND APPLICATIONS O F ECONOMICS T O ENVIRONMENTAL PROBLEMS Chapter 6

Methods for Assessing the Benefits of Environmental Programs A. MYRICK FREEMAN, I11

...

VIII

Contents of the Handbook

Chapter 7

Environmental Economics, Industrial Process Models, and Regional-Residuals Management Models DAVID JAMES Chapter 8

Input-Output Models, National Economic Models, and the Environment FINN R. FBRSUND

PART 3 - T H E ECONOMICS O F ENVIRONMENTAL POLICY Chapter 9

Distributional and Macroeconomic Aspects of Environmental Policy G.B. CHRISTAINSEN and T.H. TIETENBERG Chapter 10

Comparative Analysis of Alternative Policy Instruments PETER BOHM and CLIFFORD S. RUSSELL

VOLUME I1 Preface to the Handbook ALLEN V. KNEESE and JAMES L. SWEENEY

PART 4 - THE ECONOMICS O F RENEWABLE RESOURCE USE Chapter 1 I

Economics of Water Resources: A Survey ROBERT A. YOUNG and ROBERT H. HAVEMAN Chapter 12

Multiple Use Management of Public Forestlands MICHAEL D. BOWES and JOHN V. KRUTILLA Chapter 13

Land Resources and Land Markets ALAN RANDALL and EMERY N. CASTLE

PART 5 - T H E ECONOMICS O F PROVIDlNG RENEWABLE RESOURCE GOODS AND SERVICES Chapter 14

The Economics of Fisheries Management GORDON R. MUNRO and ANTHONY D. S C O X

Contents of the Handbook Chapter 15

The Economics of Outdoor Recreation KENNETH E. McCONNELL

PART 6 - ENVIRONMENT AND RENEWABLE RESOURCES IN SOCIALIST SYSTEMS Chapter 16

Economics of Environment and Renewable Resources in Socialist Systems Part 1: Russia MARSHALL I. GOLDMAN

Part 2: China SHIGETO TSURU

VOLUME I11 Preface to the Handbook ALLEN V. KNEESE and JAMES L. SWEENEY

PART 1 - SOME BASIC CONCEPTS Chapter 17

Economic Theory of Depletable Resources: An Introduction JAMES L. SWEENEY Chapter 18

The Optimal Use of Exhaustible Resources GEOFFREY M. HEAL Chapter 19

Intertemporal Consistency Issues in Depletable Resources LARRY KARP and DAVID M. NEWBERY

PART 2 - ANALYTICAL TOOLS Chapter 20

Buying Energy and Nonfuel Minerals: Final, Derived, and Speculative Demand MARGARET E. SLADE, CHARLES D. KOLSTAD and ROBERT J. WEINER Chapter 21

Mineral Resource Stocks and Information

DeVERLE P. HARRIS

x


Chapter 22

Strategies for Modeling Exhaustible Resource Supply DENNIS EPPLE and JOHN LONDREGAN

PART 3 - APPLICATIONS TO POLICY AND FORECASTING ISSUES Chapter 23

Natural Resources in an Age of Substitutability PARTHA DASGUPTA Chapter 24

Natural Resource Cartels DAVID J. TEECE, DAVID SUNDING and ELAINE MOSAKOWSKI Chapter 25

The Economics of Energy Security: Theory, Evidence, and Policy MICHAEL A. TOMAN Chapter 26

Natural Resource Use and the Environment CHARLES D. KOLSTAD and JEFFREY A. KRAUTKRAEMER Chapter 27

Energy, the Environment, and Economic Growth DALE W. JORGENSON and PETER J. WILCOXEN

PREFACE TO THE HANDBOOK

Natural resources have been studied by economists from the earliest days of the profession. They have been seen as providing a basis for national prosperity, power, and wealth. The ability to harness energy in new ways has been recognized as a major, if not the major, factor underlying the industrial revolution. Because forests, fisheries, and agricultural land are fundamental to food supplies, these resources have been long studied. Yet only relatively recently have there been developed broad theories specific to the fields of natural resources and energy economics. Previously, examination of these fields relied upon the general economic theories being utilized for analysis of other commodities. More recently, however, it has been recognized by economists that certain special characteristics of natural resources require theories which explicitly account for these characteristics. Agricultural land, forest, and fisheries have been seen only in the last generation to be usefully described as renewable resources. Such resources are self-renewing at a limited rate which may itself depend upon the size of the stock in existence at any given time and upon the extent and nature of human intervention into the stock dynamics. Minerals and many energy commodities are now seen as depletable or nonrenewable resources. These are resources for which only a limited concentrated stock exists for allocation over all time. For these resources, a central issue involves when they should be extracted, since a decision to utilize a given portion of the stock at one moment of time precludes the opportunity of using that portion at another time. Even more recently have the environmental resources - air, water, open space - also been seen as renewable or even in some cases depletable resources. The image of environmental resources, fisheries, and wild animal stocks as common property resources owned by everyone and hence by no one is also of relatively recent development. And even more recently, economists have systematically incorporated concepts of materials balance into theories of the flow of physical materials from the natural environment, through the economy, and back into the natural environment.

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Preface to the Handbook

And it has been only since the early 1970s that energy resources have been given particular attention as a matter for theorizing, empirical testing, and policy-making. Thus, there now exists a set of concepts which unite the field of natural resource economics. While these concepts are also finding application in other branches of economics, their formalization has been motivated by the need to better understand natural resource issues. Also uniting the study of natural resource issues is the growing realization that most important energy and natural resource issues are inherently interdisciplinary. The interdisciplinary nature requires applied work to integrate information from some combination of physics, engineering, chemistry, biology, ecology, political science, and law. To a lesser extent the current theories also reflect this interdisciplinary reality. Materials balance concepts from physics are now fundamental to economic theories of the environment. Population dynamics concepts from biology and ecology are intertwined with economic concepts in renewable resources theories. Thermodynamic concepts and concepts of energy conservation are fundamental to theoretical work on energy economics. Legal concepts of property rights and ownership greatly influence analysis of environmental economics. The study of resource economics has thus required and motivated researchers to reach out beyond their own disciplines and to integrate ideas from other fields into their own disciplines. Presumably this integration will influence not only resource economics but also other areas within economics. The three volumes comprising the Handbook of Natural Resource and Energy Economics examine the current theory and sample current application methods for natural resource and energy economics. Volumes I and I1 deal with the economics of environmental and renewable resources. Volume 111, completed well after the first two volumes were published, deals with the economics of energy and minerals. Volumes I and I1 are divided into six parts. Part 1, which deals with basic concepts, consists of five chapters. The first chapter discusses environmental issues and welfare economics. Among the more penetrating developments in the short history of environmental economics is a wedding of the concepts of economic general equilibrium, materials balance, and common property resources into a single unified theory. This model offers a systematic explanation of the occurrence of pollution-type environmental problems and an opportunity to explore the welfare economics of suggested remedies. In chapter 1, Karl-Goran Maler uses a version of this model to provide a general theoretical framework for the field of environmental economics. Chapter 2 attests to the interdisciplinary character of both environmental and renewable resource economics. In it James Wilen explains the bioeconomic models pertinent to these fields. The response of biological systems both to insults and to management actions is a central concern in many natural resource problems. Often, models simulating these responses are an integral part of the economic analysis of


xiii

such problems. In much of economics the spatial relationships among economic activities can be safely ignored. In environmental economics these relationships can rarely be ignored. Environmental effects of human action occur in and through space; neglect of this fact can lead to serious error. Space is involved in such matters as the degradation of residuals in the environment, the effects of airborne residuals on visibility, and the efficiency of alternative environmental policies. Moreover, environmental economics must address problems of interregional and international trade. In chapter 3, Horst Siebert explores the spatial aspects of environmental economics. Conservation of natural resources is a long-standing human concern. But in the last two decades there has been active economics research addressing the problems related not to scarcity of resource commodities, but rather to the protection of natural areas. This research has concerned itself with such issues as irreversibility, option values, and asymmetric technological change. In chapter 4, Anthony Fisher and John Krutilla address these new conservation issues. The final chapter in Part 1 deals with ethics and environmental economics. The theoretical underpinning of benefit-cost analysis, one of the basic tools of natural resource economics, is welfare economics. Welfare economics, in turn, can be viewed as an enormous elaboration and adaptation of an ethical theory: classical utilitarianism. But there are other valid ethical systems. And these other systems might imply quite different outcomes if applied to natural resource problems. For example, issues such as the long-term storage of nuclear waste and changes in climate resulting from resource use raise ethical issues perhaps more strongly than is usual in economics. These concerns are addressed in chapter 5 by Allen Kneese and William Schulze. Part 2 deals with methods and applications of economics to environmental problems. In chapter 6, A. Myrick Freeman reviews methods for assessing the benefits of environmental programs. One of the most challenging areas of environmental economics, development of methods for estimating benefits of environmental improvements, has also been one of the most active areas of research in recent years. The interest results, in part at least, from increased pressure to demonstrate benefits from the costly environmental improvement and protection programs put into place by governments of industrialized countries in recent years. Another major area of environmental economics, pursued especially actively in the 1970s, is the application of quantitative (usually linear) economic models to environmental questions. Such models have been applied to analyze effects of alternative policies on residuals generation and on control cost at both the industrial and regional level of detail. For regional analysis, transfer functions, which translate emissions at various points into ambient concentration at other receptor - points, are often embedded directly into economic models. David James reviews both industrial and regional models and their applications in chapter 7.

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An important class of linear models applied to environmental problems is that of national input-output models. When outfitted with residuals generation coefficients and residuals control options such models can be utilized to analyze indirect, as well as direct, effects on the environment of economics growth, changes in product mix, and alteration of other variables of interest. In chapter 8, Finn Forsund describes the use of national input-output models, with special application to the economy of Norway. Part 3 of the Handbook includes two chapters on the economics of environmental policy. Chapter 9, by Gregory Christainsen and Tom Tietenberg, reviews what is known about the distributional and macroeconomic consequences of environmental policy. How, if at all, does environmental policy contribute to inflation or to unemployment? How are the costs and benefits of environmental policy distributed among income groups? This chapter describes methods of addressing such questions and offers a set of conclusions. Chapter 10, by Peter Bohm and Clifford Russell, provides a comparative analysis of environmental policy instruments. While the idea of effluent fees as a policy instrument flows naturally from abstract economic reasoning, most governments have chosen not to follow economists' advice and have resorted to command and control strategies. Also advocated by some economists, and partially implemented, are tradeable permits to emit residuals. Deposit-and-return systems are also applied to some environmental problems and may have potential for dealing with others. This chapter reviews what the last twenty years of economic research have shown about the strength and weaknesses of these various approaches. Part 4 deals with uses of renewable resources other than simply as recipients of residuals. Water resource development and use has probably received more attention from economists than any other natural resources subject except agriculture. There are at least three reasons for this attention. Because US federal water resources agencies have long practiced benefit-cost analysis in the evaluation of water resources, there has been much opportunity for economists to develop and use theoretical concepts, methods, and data for such evaluations. Second, the development of river systems for multiple purposes has provided interesting opportunities for the application of systems analysis, that close relative of microeconomics. Third, market processes have played some role in the allocation of scarce western water. Chapter 11, by Robert Young and Robert Haveman, reviews economic and institutional aspects of water development. The remaining two chapters in this part, chapter 12 by Michael Bowes and John Krutilla, and chapter 13 by Alan Randall and Emery Castle, deal with land use, although not in the traditional manner as a factor of production in agriculture or yielder of a single product, wood, in forestry. Chapter 12 deals with the management of wildlands. Recognizing that wildlands yield not only timber but also recreational and aesthetic values, this chapter integrates theory derived from the forestry literature with that from the multipurpose


xv

firm literature. Chapter 13 also departs from the conventional view of land, using an asset pricing model to analyze land markets. The chapter includes an in-depth study of rent determination, examining influences of macroeconomic changes and of growing alternative demand for land on land prices, and in turn examines the reaction of land prices to increasing rents. The chapter also explores implications for land use planning and regulation and examines the role of land in the evolution of economic thinking. Part 5 deals with the economics of renewable resource goods or services provision. Chapter 14, by Gordon Munro and Anthony Scott, treats commercial fishery economics. Commercial fishing has fascinated natural resources economists because this activity uses a common property resource as an essential input. The common property nature of the resource in a free market leads to decisions which produce economic inefficiency. Free access can lead to excessive depletion of the resource and to excess investment, both phenomena eliminating any net economic returns that would, under optimal management, be available from this resource. The chapter reviews these issues and spells out implications for public policy and international cooperation. Chapter 15, the final one in this part, by Kenneth McConnell, treats the economics of outdoor recreation. It surveys conceptual and empirical approaches, problems, and solutions encountered in applying economics to the provision of natural resources for recreational purposes. It also shows how the evolution of the economics of outdoor recreation was influenced by the distinctive nature of markets for outdoor recreation. Part 6 concludes Volumes I and I1 with two case studies dealing with environmental and renewable resources in socialist systems. The first, by Marshall Goldman, focuses upon the Soviet Union, and the second, dealing with China, is by Shigeto Tsuru. Since in socialist states all means of production are owned by the state, a superficial view might suggest that all externalities would be internalized and that, therefore, there would be no incentive to generate excessive residuals or overuse renewable resources. Goldman, in his study, shows that for the Soviet Union this impression is very,far from the truth. He argues that the incentives for abusing resources are at least as large as in market economies and, possibly, much larger. Tsuru's study of China suggests that the situation may be somewhat different there. China is a developing economy and resources for environmental protection are accordingly limited. There is, however, explicit recognition of the environmental problem, and there is a public policy aimed at the comprehensive recycling of wastes. Presumably, this recycling is motivated by the scarcity of resource inputs as well as by a desire for control of residuals. Volume 111 focuses on the economics of energy, minerals, and depletable resources. This volume was delayed greatly in its preparation. As a result, the configuration of chapters and authors was changed significantly from that

xvi


appearing in the table of contents published in the first two volumes. Volume I11 includes three parts. Three chapters dealing with basic concepts comprise Part 1. Chapter 17, by James Sweeney, introduces the positive theory of depletable resources, focusing on deterministic models of optimal extraction from individual resource deposits (for price trajectories exogenously determined) and of price and quantity determination in either competitive or monopolistic markets. A time-varying opportunity cost associated with the depletability constraint emerges from these analysis, providing an organizing concept linking the theories. This concept is also at the core of analysis of comparative dynamics under various extraction cost functions, ranging f r ~ mthe simplest Hotelling assumption through the complex assumption that extraction costs depend on stock of remaining resources as well as on extraction rate. Chapter 18, by Geoffrey M. Heal, examines key analytical questions underlying normative theories of the optimal use of exhaustible resources. A central normative issue is how to strike the correct balance between present and future generations. This balance is at issue not only as depletable resources are extracted, but also as society invests resources to research and development intended to produce substitutes for exhaustible resources and as society chooses the overall rate of capital formation in an economy. A main thrust of the discussion elucidates the role and implications of discounting, reflecting the central role the discount rate plays in determining the appropriate intertemporal balance. The final chapter of Part 1, by Larry Karp and David Newbery, addresses a central conceptual issue which arises when the resource is controlled by agents with market power who would like to make promises - implicit or explicit -which they subsequently wish to break. When such problems of dynamic inconsistency arise, unless some mechanism exists to bind agents to their promises, such promises are not credible and cannot form the basis for a rational expectations equilibrium. Dynamic inconsistency typically involves three key ingredients: the future affects the present, at least one agent has market power and can influence the future, and the agent with market power cannot credibly commit to future actions. These ingredients and their game-theoretical implications provide the focus for chapter 19. Part 2, consisting of three chapters, presents a set of analytical tools for empirical analysis of depletable resource supply and demand. Chapter 20, by Margaret Slade, Charles Kolstad, and Robert Weiner, addresses lnethodological issues important for analyzing the demand side of energy and nonfuel minerals markets. The record of empirical work applied to these markets is impressive but there are many areas in which the coverage is incomplete and tools are inadequate. Insights into expectations formation in highly uncertain markets appear in literature on rational expectations but have yet to be adequately incorporated into mineral demand studies. Aggregation problems are endemic and empirical responses to these


xvii

problems are underdeveloped. Disequilibrium and rationing have characterized such markets from time to time, yet techniques for incorporating these problems into demand studies have not been fully exploited. Market power by resource buyers may help shape demand relationships, yet the common duality techniques assume price-taking behavior. Speculatation in the face of rapid changes implies that observed purchases may differ greatly from final demand so that data issues must be more fully addressed. This chapter encourages modelers to address more fully these fundamental empirical difficulties. The last two chapters of Part 2 address the supply side of minerals markets. Chapter 21, by DeVerle Harris, illustrates the interdisciplinary issues relevant for description and estimation of mineral resource stocks. Such resource stocks cannot be directly observed but must be estimated through models and data deriving from geological and economic perspectives. The challenge to modelers is to merge theory and empirical observations from several disciplines so as to construct models consistent with both economic and geological insights. Sueh approaches could help estimate the magnitude and the size distribution of the resource base, could provide improved extraction cost models, and could improve exploration process models. Such improvements are needed in order to test, expand, and possibly refute theoretical conclusions derived for depletable resources. The third and final chapter in Part 2 also addresses the supply side of minerals markets, with hfocus on extraction costs and rates. Chapter 22, by Dennis Epple and John Londregan, examines and assesses strategies for quantitative modeling of exhaustible resource supply, addressing the extent to which theory has been used and found to be a satisfactory foundation for applied modeling of resource supply. Their review of the applied literature suggests that room for considerable additional work remains. In particular, their examination of empirical research into cost functions suggests great potential pitfalls in aggregating across deposits found at different points in time. And although econometric methods and computational equilibrium methods have both advanced greatly, the distinction between these classes of models remains and their use has not yet been integrated. Thus fruitful roles for both approaches remain and can be expected to remain indefinitely. Part 3, which discusses applications to policy and forecasting issues, includes five chapters. Chapter 23, by Partha Dasgupta, considers natural resources in an age of substitutability. Mineral demand is normally derived from demand for final goods and services. While minerals provide desired characteristics of these goods, technological advances eventually allow other means or materials to provide these characteristics. Dasgupta argues that the key mechanism is a process whereby lower-grade resources are systematically substituted for vanishing highgrade resources; economic forces provide incentives for technological discoveries which allow future generations to exploit currently unusable resources. Thus, he argues, with the exception of phosphorus, a few trace elements, and fossil fuels, essential raw materials are in effect available in infinite supply. The key issue is one

xviii


of using technology to substitute currently unusable or uneconomic resources for those currently being depleted. Chapter 24, by David Teece, David Sunding, and Elaine Mosakowski, provides a conceptual and empirical discussion of the durability of natural resource cartels and of their welfare effects. Conventional theory teaches that difficulties of sharing, detecting, and punishing make cartels inherently unstable, but modern gametheoretical approaches show that in theory, cartels can achieve a high degree of cooperation. In fact, some cartels have solved their problems enough to survive for significant periods of time. The OPEC oil cartel, the world mercury cartel, the international uranium cartel, and the De Beers diamond cartel have had important impacts on prices and availability of their respective commodities. The history of these cartels suggests that success of a natural resource cartel depends on both the external market environment and on the internal structure of the organization. The interplay between the external environment and the internal structure provides the central focus of this chapter. Trade-offs among three objectives - energy security, environmental protection, and economic growth - have been dominant concerns in energy policymaking for the last two decades. In chapter 25, Michael Toman discusses economic issues of energy security, presenting theory, evidence, and resulting policy questions. The nature, and even the existence, of the energy security problem, depends on two central issues: the relationships between energy (especially oil) imports and economic well-being and the nature and severity of economic adjustment costs imposed by rapid energy price changes. These two issues, within an analytical framework of market failure for imported energy, provide the central focus of chapter 25. Although possible economic consequences of energy insecurity will continue to be large and current understanding of appropriate policies is far from complete, additional policy analysis needs are dominated by fundamental uncertainties about the nature of world energy markets and about the importance of spill-overs from energy markets to the rest of the economy. Many major environmental problems stem from natural resource extraction and use; policies to protect the environment often have significant effects on natural resource industries. Chapter 26, by Charles Kolstad and Jeffrey Krautkraemer, address theoretical, empirical, and policy questions of relationships between natural resource use and the environment, placing existing research within a common framework. Most existing theoretical work is dynamic in nature, examining relationships between natural resource use, environmental change, and economic growth. Theoretical literature focuses on interactions between resource depletion, irreversibility of environmental effects, and intergenerational equity and efficiency, stressing the great uncertainty. In contrast, the vast bulk of empirical work is static. This rich body of work concentrates largely on energy development and the environment. The spatial nature of resource markets provides a major focus


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as does work attempting to value negative externalities of resource use, especially use which impacts on air quality. Impacts of natural resource and environmental policies on economic growth provide the focus of the final chapter. In Chapter 27, Dale Jorgenson and Peter Wilcoxen discuss quantitative general equilibrium models, focusing particular attention on impacts of environmentally motivated restrictions and of energy price increases on economic growth. Prominent among these models is the econometrically estimated Jorgenson-Wilcoxen intertemporal general equilibrium model of the US economy. This model's integration of detailed econometric studies into a neo-classical framework allows the wealth of historical experience to be systematically interpreted so as to provide guidance for future policy making. This ability is demonstrated by estimating economic growth consequences of (1) environmental regulations introduced in the 1970s and early 1980s, (2) the temporary oil price increases of the 1970s and 1980s, and (3) prospective impacts of proposed future carbon taxes. Taken together, the twenty-seven chapters of the Handbook of Natural Resource and Energy Economics are meant to provide in depth examination of the economic concepts uniting the field of natural resource economics, the analytical tools applicable to natural resource and energy issues, and a set of illustrative examples of economic analysis directed toward the most important current issues of natural resources economics. Creation of this Handbook included efforts of many people. We would particularly like to thank the authors whose chapter writing and advice on the overall document was so invaluable, and Fabrizio Carlevaro and Sandra Archibald for their assistance in reviewing chapters in Volume 111. The series editors, Kenneth Arrow and Michael Intriligator, provided many valuable inputs from the beginning to the end of the preparation process. ALLEN V. KNEESE Resources for the Future, Inc.

JAMES L. SWEENEY Stanford University


CONTENTS OF VOLUME I11

Introduction to the Series

v


vii

Preface to the Handbook PART 1 - SOME BASIC CONCEPTS Chapter 17

Economic Theory of Depletable Resources: An Introduction JAMES L. SWEENEY

1. Background 1.1. 1.2.

2.

Extraction with prices determined exogenously 2.1. 2.2. 2.3.

3.

5.

General problem formulation Optimizing models without stock effects Optimizing models with stock effects

Extraction with prices determined endogenously 3.1. 3.2. 3.3.

4.

A classification of resources The depletability concept

Competitive equilibrium Depletable resource monopoly Comparative dynamics and intertemporal bias

In conclusion Appendix: proofs 5.1.

5.2.

References

Marginal cost for a discrete time cost function (eq. 10) Intertemporal bias result

Contents of Volume 111

Chapter 18

The Optimal Use of Exhaustible Resources GEOFFREY M. HEAL

1. Introduction 2. Characterizing optimal depletion 2.1. 2.2. 2.3. 2.4.

Pure depletion Depletion and capital accumulation Depletion, capital accumulation and technical progress through R&D Depletion with a backstop

3. Perspectives on discounting 4. Existence of optimal policies 5. Discounting utility versus discounting consumption 6. Geometric explanation of the role of discounting References Cllapter 19

Intertemporal Consistency Issues in Depletable Resources LARRY KARP and DAVID M. NEWBERY

1. 2.

Introduction A framework 2.1. Time consistency and perfection 2.2. Markov equilibria ' 2.3. Consistency and the principle of optimality 2.4. Concluding comments

3.

Strategic buyers, competitive sellers 3.1. A pure monopsonist 3.2. Monopsonist with fringe buyers 3.3. Oligopsonistic buyers

4.

Strategic sellers, competitive buyers 4.1. 4.2. 4.3.

Dominant seller facing competitive fringe: Open-loop equilibria Perfect Stackelberg equilibria Endogenous market structure

5. The period of commitment 6. Conclusions References

Contents of Volrlrne 111

PART 2 - ANALYTICAL TOOLS Chapter 20

Buying Energy and Nonfuel Minerals: Final, Derived, and Speculative Demand MARGARET E. SLADE, CHARLES D. KOLSTAD and ROBERT J. WEINER

1.

Introduction 1.l. 1.2. 1.3. 1.4. 1.5.

2.

Theoretical background 2.1. 2.2. 2.3.

3.

Classical period Neoclassical period Laissez-faire and conservation Recent events Organization of the chapter Derived demand Consumer demand Aggregation and separability

Types of econometric demand models 3.1. Estimation 3.2. Single-commodity models 3.3. Multicommodity models

4.

Issues treated by demand models 4.1. 4.2. 4.3. 4.4. 4.5. 4.6. 4.7.

Capital-energy substitutability Technical change Scale effects Dynamics Disequilibrium and rationing Discrete choice Durability and secondary markets 4.8. Imperfect competition 4.9. Time-of-day, seasonal, and block pricing 4.10. Uncertainty

5.

Demand by hedgers and speculators 5.1. Background 5.2. The purchase and sale of energy commodities 5.3. The purchase and sale of metals 5.4. Hedging and speculative demand

Contents of Volrirne I11

6.

Concluding remarks 6.1. 6.2. 6.3. 6.4. 6.5. 6.6. 6.7.

The treatment of uncertainty From individual to aggregate relationships Temporary equilibrium and rationing Demanders with price power Speculative dynamics Model validation Summing up

References C/~apter21

Mineral Resource Stocks and Information DeVERLE P. HARRIS

1. 2.

Introduction Motivations for appraisal of mineral resources 2.1. Resource adequacy 2.2. Anticipating scarcity 2.3. Land management and economic development

3.

Notions of supply 3.1. 3.2. 3.3. 3.4.

4.

Stock concepts and measures 4.1. 4.2. 4.3. 4.4. 4.5.

5.

Reserve Resource Potential supply Additional stocks: Endowment and resource base A formal statement of stock measures and determinants

Perspective on resource information 5.1. 5.2. 5.3. 5.4.

6.

Supply as a flow Supply as a stock Future flows Dynamic supply

General The time dimension Estimation issues Resource, information, and policy

Geology of mineral occurrence 6.1. Crustal abundance of elements - A gross feature of mineral stocks 6.2. Across elements relations 6.3. Geologic environments and deposit types - A basis for increasing resource information 6.4. Features of deposits vary by environment and deposit type

Contents of Vohtrne III

7. A generalized model of resource by deposit type - A conceptual reference 7.1. 7.2.

8.

Deposit models 8.1. 8.2. 8.3.

9.

Kinds of models Contamination of geologic data by economics The size bias effect with economic truncation

Cost models 9.1. 9.2.

9.3. 9.4.

10.

Perspective Model components

Perspective Zimmerman's analysis of coal cost and resources Response function of a cost estimation system Cost model for gold in gold-quartz vein deposits - A case study

Exploration models 10.1. General 10.2. Discoverability, information gain, and depletion 10.3. Sequential decisions and valuation of exploration information using capital markets 10.4. The Arps-Roberts exploration process model

11.

Geologic endowment models 11.1. 11.2. 11.3. 11.4. 11.5. 11.6.

Perspective Institutional use of subjective estimates by experts NURE - A massive national resource program Heuristics, hedging, and bias in subjective estimation Purposeful hedging - motivational bias The Arizona appraisal system -An expert-like system

12. Concluding remarks References Chapter 22

Strategies for Modeling Exhaustible Resource Supply DENNIS EPPLE and JOHN LONDREGAN

1. 2. 3.

Introduction Cost functions for exhaustible resources Cost functions for non-renewable resources: specification issues 3.1. Cumulative cost functions 3.2. Issues in specification 3.3. More flexible formulations of the cost function 3.4. Aggregation

m i

Contents of Volurne III

4.

Equilibrium models 4.1. 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. 4.8. 4.9. 4.10.

Models with price-taking present-value-maximizing producers Non-traditional price-taking models Market power Monopoly models Dominant-firm models Cartel models The time-inconsistency problem Treatment of uncertainty in computational models Long-run versus short-run analysis Concluding remarks on computational models

5.

Econometric models 6. Conclusion References PART 3 - APPLICATIONS TO POLICY AND FORECASTING ISSUES Chapter 23

Natural Resources in an Age of Substitutability PARTHA DASGUPTA

1. 2. 3. 4. 5.

Introduction History Resource substitution as the key process Analysis of resource prices Royalties as a measure of resource scarcity 6. Transition from exhaustible to durable resource base 7. Prospects for transition to the age of substitutability References Chapter 24

Natural Resource Cartels DAVID J. TEECE, DAVID SUNDING and ELAINE MOSAKOWSKI

1. Introduction 2. The cartel problem 2.1. 2.2.

3. 4.

Monopoly Target revenue models

The durability of cartels Welfare implications of cartels 4.1. 4.2.

The coordination of complementary and competitive investments Price stabilization cartels

Contents of Volzrme III

5.

A synopsis of some natural resource cartels Cartel issues raised with respect to world oil in the immediate post-embargo period 5.2. Cartel experience in the world mercury market 5.3. Cartel experience in the world uranlum markets 5.4. The diamond cartel

xxvii

1145

5.1.

6. Conclusion References Clzapter 25

The Economics of Energy Security: Theory, Evidence, Policy MICHAEL A. TOMAN

1.

Introduction 1.1.

1.2. 1.3.

2. 3.

Recent experience with oil shocks Oil market behavior 3.1. 3.2. 3.3.

4.

World oil supply and OPEC decisionmaking Changes in market institutions Short-run market reactions to a market disturbance

Possible energy security externalities 4.1. 4.2. 4.3. 4.4. 4.5.

5.

Overview of the energy securlty problem Energy security reconsidered: Lessons from the 1980s Plan of the chapter

Oil imports and the monopsony wedge Other possible costs of long-term oil Import dependence Macroeconomic costs of oil price shocks Cost of risk-bearlng Policy coordination spill-overs

Policy issues 5.1. 5.2. 5.3.

Long-term oil import constraints Strategic oil stocks International policy coordination

6. Concluding remarks References Chapter 26

Natural Resource Use and the Environment CHARLES D. KOLSTAD and JEFFREY A. KRAUTKRAEMER

1. Introduction 2. Resource-environmental interactions

1145 1152 1155 1160 1164 1164

Contents o f Volume 111

3.

Static resource-environmental interactions 3.1. 3.2. 3.3.

4.

Direct costs of environmental regulation Environmental damage Costbenefit analysis

Intertemporal resource-environmental interactions 4.1. 4.2.

Dynamic models of resource-environmental interactions Intertemporal efficiency and intergenerational equity

5. Conclusions References Clzcrpter.27

Energy, the Environment, and Economic Growth DALE W. JORGENSON and PETER J. WILCOXEN

1. Introduction 2. An overview of the model 2.1. 2.2. 2.3. 2.4. 2.5.

3.

The impact of environmental regulation 3.1. 3.2. 3.3. 3.4.

4.

Operating costs Investment in pollution control equipment Motor vehicle emissions control The overall impact of environmental regulation

The impact of higher energy prices 4.1. 4.2. 4.3.

5.

Producer behavior Consumer behavior Investment and capital formation Government and foreign trade Constructing the base case

Effects on the steady state Dynamic effects Summary

The impact of carbon taxes 5.1. 5.2. 5.3. 5.4.

Computing carbon emissions Carbon dioxide emissions policies Long-run effects Intertemporal results

6. Conclusion References

Subject index

PART 1

SOME BASIC CONCEPTS


ECONOMIC THEORY OF DEPLETABLE RESOURCES: AN INTRODUCTION JAMES L. SWEENEY * Deparfment of Enginee~ing-EconomicSystems, Stanford University, Terman Engineering Centel; Stanford, CA 94305-4025, USA

1. Background

I . I . A classijication of resources

One can think of a two-way classification of natural resources, based on (1) physical properties of the resource and (2) the time scale of the relevant adjustment processes. Based on physical characteristics, we can divide resources into biological, nonenergy mineral, energy, and environmental resources. Each of these categories could be broken down further if useful for purposes of analysis or information collection. As examples, biological resources would include fish, wild animals, flowers, whales, insects, and most agricultural products. Non-energy minerals could include gold, iron ore, salt, or soil. Energy would include solar radiation, wood used for burning, and natural gas. Environmental resources could include air, water, forests, the ozone layer, or a virgin wilderness. Based on the time scale of the relevant adjustment processes, we can also classify resources as expendable, renewable, or depletable. Depletable resources are those whose adjustment speed is so slow that we can meaningfully model them as made available once and only once by nature. Crude oil or natural gas deposits provide prototypical examples, but a virgin wilderness, an endangered species, or top soil also can well be viewed as depletable resources. Renewable resources adjust more rapidly so that they are self renewing within a time scale important for economic decisionmaking. But actions in one time period which alter the stock of the resource can be expected to have consequences in subsequent time periods. For example, * I would like to acknowledge and thank Robert Patrick for his helpful reading of several drafts of this chapter and for offering helpful suggestions. All errors of course remain the responsibility of the author. Flnanciai assistance underlying the research was provided by the Exxon Education Foundation through the Stanford University Center for Economic Policy Research Handbook of Natural Resource and Energy Economics, vol. III, edited by A. K Kneese and J.L. Sweeney 01993 Elsevier Science Publishers B. K AN rights reserved

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populations of fish or wild animals can well be viewed as renewable as can be water in reservoirs or in many ground water deposits. Expendable resources are those whose adjustment speed is so fast that impacts on the resource in one time period have little or no effects in subsequent periods. For example, noise pollution and particulates in the air, solar radiation, as well as much agricultural production can be thought of as expendable. Although there is a correlation between the physical properties and the time scale of adjustment, the correlation is far from perfect. Table 1 illustrates the two-way categorization, giving examples of resources based on both classifications. Each physical class of resources includes examples of each adjustment speed. For example, while most non-energy mineral resources can be viewed as depletable, salt evaporated from the San Francisco Bay can be viewed as expendable since the cordoning off of an area of seawater has no perceptible impact on the total availability of seawater in the Bay. Energy resources include solar radiation (expendable), hydropower and wood (renewable), and petroleum (depletable). Volumes I and I1 of the Handbook of Energy and Natural Resource Economics dealt with the economics of renewable and environmental resources, including biological resources. Volume 111 focuses attention on depletable resources and energy resources. While particular attention is given to desirable, depletable, energy resources in Volume 111, we focus attention on the bottom row - depletable resources - and on the third column - energy resources. This chapter focuses on the bottom row, providing an introduction to the economic theory of depletable resources. The introduction is designed to make accessible fundamental theoretical models of depletable resource supply and of market equilibrium and to provide the reader with an understanding of basic methods underlying the theory. It is meant to present theoretical economic models in a self contained document and to provide a background useful for the articles that follow.

1.2. The depletability concept The depletable resources indicated in Table 1 all have adjustment speeds so slow that we can think of them as made available once and only once by nature. Their consumptive ' use can be allocated over time, but once they are used up, they are gone forever, or for such a long time that the possibility of their eventual renewal has no current economic significance. In particular, there initially exists some stock (or stocks) of the resource in various deposits. As the resource in a given deposit is There can be both consumptive and non-consumptive uses of many resources. Unless otherwise indicated, by "use", we refer to consumptive use.

Ch. 17: Economic Theory of Depletable Resources - Introduction Table 1 Examples of natural resources Availability

Physical properties Biological

Non-energy, Mineral

Energy

Environmental

Expendable

Most agricultural Salt products, e.g., corn, grains

Solar radiation; Hydropower; Ethanol

Noise pollution; Non-persistent, e.g., air pollution (NO,, SOx, particulates), water pollution

Renewable

Forest products; Fish; Livestock; Harvested wild animals; Wood; Whales; Flowers; Insects

Wood for burning; Hydropower; Geothermal

Ground Water; Air; Persistent, e.g., air pollution, water pollution (C02, toxics); Animal populations; Forests

Depletable

Endangered species Most minerals, e.g., gold, iron ore, bauxite, salt; Top soil

Petroleum; Natural gas; Coal; Uranium; Oil shale

Virgin wilderness; Ozone layer; Water in some aquifers

used, stock declines. The greater the consumptive use, the more rapid the decline in remaining resource stock. No processes increase the stock in any deposit, although the number of deposits available for use could increase. If stock ever declines to zero, then no further use is possible and for some positive stock level, further use may be uneconomic. These characteristics will be taken to define depletable resources. Definition: Depletable resource. A resource is depletable if (1) its stock decreases over time whenever the resource is being used, (2) the stock never increases over time, (3) the rate of stock decrease is a monotonically increasing function of the rate of resource use, and (4) no use is possible without a positive stock. Let St denote stock at the end of time period t for the particular deposit and let Et denote the quantity of the resource extracted from that deposit during time period t . Et is generally referred to as the "extraction rate7',but its units are physical quantities, such as tons or barrels, and not physical quantities per unit of time. Then the depletable resource definition implies the following relationships in a discretetime model:

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h(Et)3 0 and Et> 0 + h(Et)> 0,

(2)

Several examples can illustrate the underlying concept. A deposit of natural gas or oil many remain under the ground with its stock unchanged until the resource is discovered. Then as it is extracted, the stock declines at the rate of one Btu for every Btu of natural gas or oil extracted from the deposit. In this case, h(Et)= E,. However, if oil is extracted very rapidly, some is left trapped in the mineral media and that oil cannot be extracted. Thus the resource available for extraction may decline by more than one Btu for each Btu extracted. In this case, h(Et)> Et.If extraction stops, the stock will remain constant, unless there is some leakage from the deposit, in which case the stock will continue to decline. Once there is nothing left in the deposit, no more can be extracted. However, it may become virtually impossible to extract any more of the stock once the pressure driving the resource to the well declines enough, that is, once stock is below some critical level. A virgin wilderness can remain unspoiled forever, absent human intervention, although its precise composition will change over time. We can consider many different uses of the resource, only some of which would be the consumptive use envisioned under the definition above. At one extreme of non-consumptive use, small groups can backpack through the wilderness, having no more impact than that of grazing deer. At the other extreme of consumptive use, the forest can be clear cut for timber. It is the latter type of activity - consumptive use - that would be considered "use" under the depletable resource definition. The greater the area that was used by clear cutting in each decade, the less the remaining stock of virgin wilderness, and the more rapid the rate of stock decrease. Top soil may be eroded as a result of agricultural activity and differing crops may lead to differing rates of top soil erosion from cultivated lands. In this case we may have a vector of agricultural activities, E,,with the amount of annual erosion as a complex function of this vector of activities. The function h(E,)would indicate the amount of top soil eroded away as a function of this vector of agricultural activities. The variable Stwould measure the remaining quantity of top soil remaining at the end of time t . Note that none of these examples, in fact, none of the resources characterized as depletable in Table 1, perfectly meets the definition, but that each approximately British Thermal Unit, a measure of the energy content of energy commodities.

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763

meets it. Oil and natural gas are derived from the transformation of organic material underground. This process continues today, so that strictly, the stock of oil in some locations is increasing, although at an infinitesimally small rate. Leakage from a deposit may involve migration to another deposit, which then may be increasing over time. If we were to harvest a virgin forest but then allowed the land to remain undisturbed for 10000 years, the forest would revert to a virgin state. We can reinject natural gas back into a well and thereby increase stock of natural gas in that deposit. Thus the definition must be viewed as a mathematical abstraction, but an abstraction that approximates many situations so closely that it is a useful analytical construct. For most analysis, we will not require as much generality as allowed in eqs. (2) and (3).In particular, it will normally be appropriate to assume that every unit of the resource extracted reduces the remaining stock by a single unit. We will refer to such an assumption as "linear stock dynamics". Although the assumption of linear stock dynamics is not always valid, most insights from depletable resource theory can be developed without requiring the greater generality allowed in eqs. (2) and (3). Assumption: Linear stock dynamics. The stock is reduced by one unit for every unit of the resource extracted. This reduction is independent of the rate of extraction and of the remaining stock:

h(Et) = Et. Under the assumption of linear stock dynamics, eqs. (1)-(3)translate to St = S t - , - E,.

(5)

Equations (1)through (4)describe the most fundamental constraints underlying a theory of depletable resources. In addition, linear stock dynamics will be assumed, so that eq. (5)will be used as a more specific form of relationships (1)-(3). Therefore, eqs. (4)and (5) will provide the fundamental mathematical constraints underlying depletable resource theory in this chapter. Under the assumption of linear dynamics, eqs. (4)and (5) can be combined to imply a simple form of the depletability condition. The following equation (6)will always hold, but includes less information than obtainable from eqs. (4)and (5):

These examples suggest that depletable resources can be viewed a limiting case of renewable resources, a case in which the renewal rate has been reduced to zero. This interpretation will not be used here, but it can link the theory of depletable resources and that of renewable resources.

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The total extraction of the resource over all time can be no larger than the initial stock of that resource, or more generally, the total extraction of that resource over all time beginning from an arbitrary starting point can be no greater than the stock remaining at that starting point. Each equation presented above has assumed a discrete-time representation. We will use such discrete-time representations throughout this chapter, although a continuous-time formulation could be utilized, as in most published theoretical literature. Continuous-time formulations can be seen as discrete-time formulations in which the length of each time interval converges to zero. As such all equations presented in this chapter can be readily translated to their continuous-time counterparts. Our discrete-time models can have arbitrarily short intervals, so no loss of generality is entailed by using discrete-time representations. And whenever empirical work is conducted or computational models are constructed, discretetime formulations are the only ones possible. In addition, discrete-time models allow the analyst to avoid some mathematical subtleties of infinite-dimensional spaces at points required by continuous-time market models. For these reasons we have chosen to use discrete-time representations. Even though a discrete-time representation is used, we can envision an underlying continuous-time model such that the discrete-time variables are equal to integrals of the corresponding continuous-time variables. Let the continuoustime extraction rate be denoted by ~ ( t and ) let the length of each time interval be denoted by L. Then the discrete-time extraction rate, El, and ~ ( twould ) be related as

E t will be roughly proportional to L, in the sense that if each interval were partioned into smaller intervals, the sum of the Et over these smaller intervals would equal the original E,. For the underlying continuous-time model, let stock be denoted by S or by S(t). Then eq. (5) would become dSldt = - ~ ( t ) . Other variables and functions to be presented can be related to underlying continuous-time models in a like manner. At a later point we will show that the existence of an underlying continuous-time model imposes constraints on the functions in the discrete-time model. For depletable resources such as energy and other mineral resources, there is a typical sequence of activities, each governed by economic considerations. Initially there may be preliminary exploration of a broad geological area and later of specific tracts. At some point the land may be offered for leasing, perhaps through a competitive bidding process. After a period of more focused exploration the deposit may be discovered. Only then can extraction begin. Further activities may be devoted to delineating the extent of the resource and these activities may lead to further discoveries. The resource, once extracted, is then transported to some

Ch. 17: Economic Theory of Depletable Resources -Introduction

765

location for further processing and then to final users. Some resources might be recycled for further rounds of processing and consumption. The timing and magnitude of each process is governed by human decisions and typically by economic forces. But the amount and quality of the deposit discovered and ultimately extracted are constrained by the natural endowment. Thus the basic patterns of depletable resource use are governed by an interplay of economic forces and natural constraints. The combination of processes can be very complex. Yet economic models of depletable resources - including those discussed in this chapter - typically abstract away from most processes and focus attention on the elements in the definition: the rate of use (extraction) of the resource and the resultant change in the quantity of the resource stock. This abstraction allows insights about the economic forces, insights which may not be available from more detailed analyses. But the abstraction does present a fairly bare-bones image of a complex set of processes, an image which could well be usefully expanded. For example, Harris, in this volume (ch. 21), brings in a richer understanding of the interplay between physical constraints and human choices. Depletable resource theory typically addresses several broad classes of questions, either in a normative manner ("should") or in a positive manner ("would") for a particular set of economic conditions: Should a specific resource ever be extracted? Would it under competitive markets? How much of that resource should or would ultimately be extracted? What would be the timing of extraction with competitive markets? What would be market price pattern over time under competitive forces? What timing of extraction should be best for society as a whole? How do market-determined and socially optimal rates compare? Can we expect overuse, underuse, or correct use with competitive markets? Under monopolistic conditions? How would various market changes - higher interest rates, changed expectations, varying market structures, taxes - change patterns of extraction? What is the nature of the supply function for depletable resources? This chapter will address positive questions in the context of a sequence of depletable resource models. Heal addresses normative questions in ch. 18. Section 2 presents a sequences of models of extraction from one resource stock when prices are exogenously determined. Section 3 presents intertemporal market equilibrium conditions and analyzes markets in which prices are determined endogenously from the interplay of supply and demand. Finally, Section 4 provides concluding thoughts.

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2. Extraction with prices determined exogenously

The simplest depletable resource models are those applicable to the competitive owner of a resource stock as that owner chooses the time path of its extraction. We address such models in this section. We assume that the firm takes selling prices of the extracted commodity as fixed in the marketplace, not influenced by his or her actions. These prices may be varying over time but their future path is assumed to be known with certainty. Although the assumption of uncertainty is very strong, particularly when we consider the long-term future evolution of economic parameters, we will not address uncertainty per se within this chapter.

2.1. Generalproblem formulation 2.1.1. Objective and constraints

If Pt and Et represent price and extraction rate at time t , the revenue at time t (R,) obtained from selling the extracted commodity is a linear function of extraction rate:

Total cost incurred by the resource owner during a time period will depend upon total extraction during that period, perhaps upon the stock remaining from the last period, and on time: C t ( E t , S t - I ) .We will assume that this time-dependent cost function will be known to the resource owner with perfect certainty. Given revenue and cost functions plus constraints defined by resource depletability, the resource owner will be assumed to choose a time path of extraction so as to maximize present value of profit. Equivalently, the owner is assumed to select an extraction path so as to maximize the deposit value, where value is determined as a discounted present value of revenues minus costs. For our analysis we will assume a finite time horizon of T, where T is arbitrarily long4. If I7 denotes discounted present value of profit, the firm faces the following maximization problem, where r represents the instantaneous interest rate facing the owner of the resource deposit:

We use finite, but arbitrarily long time periods to avoid the mathematical complications associated with an infinite time horizon model.

Ch. 17: Economic Theory of Depletable Resources - Introduction

T

Max IT =

[PtEt - C t ( E t ,S t - l ) ]e-" t= l

Under : St = St-1 - Et for all t ,

I

2.1.2. Characteristics of the discrete-time cost function

The cost function in such a discrete-time model should in principle be derivable as the integral of cost in an underlying continuous-time representation. Let g ( r ( y ) ,S ( y ) ) be the underlying continuous-time cost function. Then the discretetime cost function will be the minimum feasible integral of cost5 over the interval from t to t + L , given that total extraction is Et and stock at t is

1

Jt

t+L

such that

1

(9)

7

r ( y )d+ = E,

and S(+) = S t P l -

r(0)dQ.

The discrete-time cost function depends on properties of g ( ~ ( y S) ,( y ) ) , and on L, St-,, and E,. Properties of C t ( E t , S t - , )must derive from the optimization problem (9). First, C t ( E t , S t - l )must be roughly proportional to L in the sense that if the interval L were partitioned into N intervals, the N costs must add to the value of the original Ct(Et,St-l). This could be a minimization of the discounted present value of g(~(y),S(y)).However it is envisioned that L is short enough that discounting within a time period is irrelevant. If a discounted present value is used, none of the subsequent conclusions are modified. Under the formulation as stated here, the necessary condition for optimization is

+

where P is a constant independent of y and each of the partial derivatives is evaluated at time t y within the time interval. Theory for solving this optimization is identical to that for solving the overall optimization problems discussed in this chapter. This equation leads directly to eq. (10) in the body of the chapter.

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The existence of an underlying continuous-time representation implies restrictions on the partial derivatives of allowable discrete-time cost functions. Consider first the partial derivative of cost with respect to initial stock 6 :

where ag/aS is evaluated at some point between t and t +L. The partial derivative of cost with respect to initial stock must be approximately proportional to the length of the underlying time interval and must have the same sign as ag/aS. The existence of an underlying continuous-time representation imposes more rigid restrictions on the marginal extraction cost, aC,/aE,. As El varies, the instantaneous extraction rates, ~ ( y )must , vary so that their sum remains equal to E,. aC,/aE, then is the integral of the changes in costs associated with the changes in the ~ ( y )accounting , for the changes in S(y) induced by the changes in ~ ( y )Because . C,(Et, St-,) is defined as the result of an optimization, the impact on total cost for a small increase in ~ ( ywill ) be the same for all y.Thus, in order to assess the integral, we can evaluate the marginal cost of a change in instantaneous extraction rates at any time, including at y = t. Evaluating at y = t , the partial derivative aC,/aEt is thus:

This equation is derived more rigorously in the Appendix. By eq. (lo), marginal cost of extraction during a discrete interval consists of two components. The first, aglae, is simply the additional cost directly associated with additional extraction at t. The second term captures the incremental cost of lower stock for the rest of the interval, associated with more extraction at the beginning of the period. The second term in eq. (10) is identically equal to the derivative of cost with respect to initial stock. Thus eq. (10) can be combined with the previous equation to show:

ac,+ - act -aEt

-ag

as,-, a&> 0,

where a g / a ~is evaluated at y = t. Equation (1 1) imposes an important restriction on the specification of a discretetime cost function. The restriction must hold even if no analogous restrictions exist Because Cr( E r ,S,-,) is defined based on the result of an optimization, the impact on cost for a small variation in E(Y) will be zero as long as the total of all ~ ( y is) unchanged.


769

for the underlying continuous cost function. Thus in using discrete-time models, it is important to recognize that continuous-time underlying cost functions do not translate precisely to discrete-time cost functions hrcing the same functional form, and that not all cost functions appropriate for a continuous-time model are also appropriate for a discrete-time model. Equation (11) can be differentiated with respect to E, in order to derive an expression relating second partial derivatives:

Expression (12) implies that the derivative of marginal cost with respect to extraction rate will be the sum of two effects. Increasing total extraction during the interval ( E l )increases the instantaneous extraction rate for all time, including at t, and an increase in instantaneous extraction rate increases marginal cost [right-hand side of eq. (12)l. Thus the right-hand side of the equation is positive. In addition, increasing extraction rate at the beginning of the time period reduces stock during the remainder of the period. This stock reduction further increases marginal cost if a2Clas3E is negative [on the left-hand side of eq. (12)l. Many discrete-time models improperly start with a discrete-time cost function without so restricting its properties. For this chapter, however, we will always assume that the discrete cost function is consistent with the existence of an underlying continuous cost function and will thus always assume that eqs. (11) and (12) will be valid'.

'

The inequality of eq. (12) might not apply to the underlying continuous-time model, yet it must apply to the discrete-time model. To illustrate, assume that the inequality were reversed in a discrete-time model. Consider two cases in which P and opportunity costs were unchanged between the two cases (see the discussion of first-order necessary conditions for optimality at a later point in this chapter.) In the first, the initial stock was higher by 6SlP1.As a result the optimal extraction rate in the first case is increased by 6E1,where

Consider the change in stock after time period t: 6S1 = 6StT1- 6EI < 0. Higher stock at the beginning of a time period would lead to lower stock at the end of the period! This could not happen in a continuous-time model even if the inequality were likewise reversed. Assume that a 2 g / a ~ 3< e -a2g/ae2 and that the initial stock were higher by 6Sl-1. Instantaneous extraction rate would increase by 6e = -6Sl-I [a2g/aSas]/[a2g/ae2] > 6Sl-1. Therefore the rate of stock decline over time would increase by an amount larger than 6S,-1. The stock increase SS would decline over time. But in so doing, it would reduce the magnitude of S E and hence of the rate of decline of 6s. It would never be possible for 6S to become negative because as 6S converged to zero, so would be. Thus if 6Sl-, > 0, then 6Sl-l > 0, even if the inequality were reversed. Hence if the discrete-time model is consistent with l -> 1 - a 2 c I / a ~ ;even , if an underlying continuous-time model, then it must be true that ~ 2 ~ l l a ~aE, a2g/as8~ < -a2g/ae2.

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Assumption: Dominance of extraction rate on marginal cost. Marginal cost is more sensitive to extraction rate than to stock level:

Even meeting the necessary restrictions, the cost function in problem (8) could have many different characteristics. The marginal cost of extraction (aCIIaEt) could be decreasing, constant, or increasing in extraction rate. Similarly, the marginal extraction cost and the total cost could be increasing or decreasing in remaining stock or it could be independent of stock remaining from the last period. The characteristics of the optimal solution will depend upon which of these combinations is appropriate for a given problem. Much depletable resource literature assumes that the cost function at each time is independent of the remaining stock of the resource. The initial works by Hotelling (1931) and by Gray (1912-1914) assumed, in addition, that marginal extraction cost was independent of extraction rate. And this set of assumptions has been followed by many researchers. Other work maintains the assumption that the extraction cost function is independent of the remaining stock but assumes that the marginal extraction cost is an increasing function of extraction rate. Alternatively, one might assume that marginal extraction costs do vary with remaining stock. Typically one might expect marginal extraction cost to increase as the resource is depleted. This relationship could hold for physical reasons. For example, as oil or natural gas deposits are depleted, the driving pressure in the deposit declines and extraction rates decline. Re-establishing the previous extraction rate could be very costly. In addition, it will typically be optimal to extract high-quality low-cost portions of deposits before low-quality, higher-cost grades 8. In that case, the smaller the remaining stock, the higher the unit extraction costs. But the reverse situation can occur, at least in early stages of extraction. The extraction process itself can lead to technological improvements which reduce extraction costs. This "learning by doing" phenomenon would imply that for a range of stock levels, the lower the stock, the lower the marginal cost. Another common approach reflects these possibilities in a simple way. Marginal extraction cost of the underlying continuous-time cost function might be assumed to depend on remaining stock, but not on extraction rate. Total cost would be linear in extraction rate for the underlying continuous-time model. However, these linearity assumptions for a continuous-time model lead to a discrete-time model in which marginal extraction cost is an increasing function of extraction rate and a decreasing function of the remaining stock. Total extraction cost could be an increasing or decreasing function of remaining stock independent of whether marginal cost increased or decreased with stock. For This ordering by extraction cost will be discussed more fully in a later section of this chapter.

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example, subsidence of land overlying an aquifer may be a function of the stock of water in the aquifer and not a function of the extraction rate. Total environmental costs associated with clear-cutting a virgin forest depend upon the amount of the forest which has been clear-cut although the marginal costs of additional harvest may be virtually independent of the remaining stock. The costs of global climate change may depend upon the cumulative extraction of fossil fuels and thus upon the remaining stock. In this chapter, we do not seek full generality. Although we will examine several different derivatives of total cost with respect to stock and several different derivatives of marginal costs with respect to stock, we will always assume that the cost function is weakly convex in its arguments. Therefore the second-order conditions for optimality will be satisfied, the set of optimal choices must be convex, and multiple local unconnected optima cannot exist 9. Assumption: Weak convexity. We assume that the cost function is weakly convex. A function is weakly convex if and only if the Hessian matrix - the matrix of second partial derivatives - is positive semidefinite at every point. A matrix is positive semidefinite if and only if its principal minor determinants are all positive or zero. The principal minor determinants of the Hessian matrix from the cost function are

all of which must be non-negative everywhere, given the convexity assumption. With this background, we can now turn to simplified versions of these models, versions useful for deriving insight into the behavior of optimizing suppliers of depletable resources. We will examine various cost assumptions in turn, starting with models in which extraction rate is independent of remaining stock. We will discuss the Hotelling assumption that marginal cost is independent of both stock and extraction rate as a special case of the more general model in which marginal cost is non-decreasing in extraction rate. We will only then turn to models in which remaining stock influences marginal extraction cost. 2.2. Optimizing models without stock effects

A fundamental distinction among depletable resource models is whether the remaining stock influences cost of extraction from a given deposit. The initial Convexity of the cost function and linearity of the revenue function together imply that the objective function is weakly concave. The constraints define a convex set. The set of optimal points for a concave function, constrained to a convex set, must always be convex. Hence for this problem, while the optimal point may not be unique, the set of optimal points will be convex.

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stock may typically influence the cost structure. However, the distinction is whether current extraction decisions influence future costs through their impacts on stock remaining at those future times. We will refer to such impacts as "stock effects". In this section we deal with models in which there are no stock effects: here the remaining stock has no influence on extraction costs. Assumption: No stock effects. The remaining stock does not appear as an argument in the cost function.

Under the assumption that total (and marginal) extraction cost is independent of the remaining stock of the resource, problem (8) reduces to T

Max LT =

[PIE, - C,(E,)] eCrt t=l

Under : Sf = St- - E, for all t ,

1 1

Several different optimization methods can be used to solve problem (13). In what follows we use the Kuhn-Tucker conditions to develop first order necessary conditions for optimality. In addition, we show that the same conditions can be obtained in a more insightful manner by examining feasible variations from the optimal path. 2.2.1. Necessary conditions for optimality: Kuhn-Tucker conditions 2.2.1.1. Kuhn-Tucker theorem The Kuhn-Tucker theorem aids solution of constrained optimization problems by providing first-order necessary conditions for optimalityI0. Consider the optimization problem max f (x) under Gi(x) < 0,

i = 1,. . . ,k ,

(MI

where x is a vector of variables to be selected, f (x) is the objective function, and Gi(x) is one of k inequality constraints on the components of x. Let x* denote the optimum value of the x vector and let VGi(x*) denote the gradient of Gi(x) evaluated atx*. Number the constraints so that constraints 1throughn are binding, where n k. The constraint qualification will be said to hold if the set of gradients VGi(x*), for i = I,. . . , n is linearly independent.

0 (for example, with learning by doing), then the current value opportunity cost growth rate is faster than r and the present value will increase over time. Equation (26), which provides a boundary condition for the difference equation, is identical to eq. (16). Both show that the current value opportunity cost is equal to zero at time T unless the stock is totally depleted by the time horizon. Positive final stock may well be the norm, not the exception for depletable resources with stock effects. In those situations in which final opportunity cost is zero, the current value of opportunity cost must be shrinking, not growing, as the time horizon is reached. Although these equations can be solved in principle, in practice their solution typically involves numerical simulations based upon explicit cost functions and price trajectories. Such solutions generally involve iterative procedures to guess the initial value of the opportunity cost, to calculate the adjustments of stock and opportunity cost to the time horizon, and to compare the final opportunity cost and stock to the conditions required by eq. (26). If the final opportunity cost is too high, the initial opportunity cost can be decreased for the next iteration and conversely if the final opportunity cost is too low. In this way iterative procedures can find explicit solutions, given explicit cost functions and price trajectories. For this chapter, however, we are more concerned with properties of the equations and solutions. Interpretation of the opportunity cost for depletable resources with stock effects will be the focus of the following section.

2.3.2. Inteipretations of opportunity costs When stock effects exist, the concept of opportunity cost is no longer dependent upon absolute limits to resource availability. An opportunity cost will exist even if the resource is not ultimately depleted. This conclusion is in sharp contrast with results from models without stock effects. In particular, opportunity cost can be interpreted as the present value (discounted to time t) of future cost increases due to additional extraction at time t if the resource is not ultimately depleted. To examine this interpretation of opportunity cost, consider a resource deposit that will not ultimately be totally depleted. For such a resource q 5 ~= 0, by eq. (26), where T is the time horizon. For such a resource there is no absolute limit on availability; the owner could extract more of the resource without extracting less at another time.


793

To calculate the opportunity cost, we rearrange eq. (25) and solve it recursively, beginning from t = T - 1 and working backward. Rearranging gives:

The boundary condition c $ = ~ 0 allows eq. (28) to be solved, at least conceptually. The general solution to this recursive equation gives the current value opportunity cost and the present value opportunity cost as follows:

Equation (29) shows that the opportunity cost at time t is simply the present value, discounted to time t, of future incremental costs accruing as a result of extracting one more unit of the resource at time t. An additional unit extraction at time t requires no compensating extraction reduction. Yet it does lead to one unit stock reduction for all subsequent times. At time 7 , that stock reduction causes a cost change of -aCT/aST-l. The cost change is discounted by a factor ecr('-') to time t and by a factor e-" to time 0. Summing terms over all subsequent time gives the opportunity cost as being equal to the present value of future costs stemming from additional current extraction, as shown in eqs. (29) and (30). Equations (25) and (26) do provide for an opportunity cost component which derives from absolute limits to resource extraction if the deposit ultimately is totally depleted. This component rises at the interest rate, just as in models without stock effects. If the resource ultimately is totally depleted, the final value of the opportunity cost can be positive, say equal to cPT.By eq. (28), the opportunity cost at time t will include a term equal to c$Te-r(T-').If we choose a constant X equal to c$Te+", this opportunity cost component would equal Xer', the same form as obtained in models without stock effects 14. Because eq. (25) is a linear equation, opportunity cost can be determined as the sum of the two separately derived and conceptually separate components. Therefore the total opportunity cost will be the present value of incremental future costs (eq. 29) plus an exponentially rising term deriving from resource limits:

l4 The basic theory of difference equations shows that the solutions to equations such as (28) will in general be the sum of a homogeneous solution and a particular solution. The homogeneous solution must grow at the interest rate and can always be written as Xert.The particular solution is just eq. (29).

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Equations (29) or (31) may well give opportunity costs which are small initially, which rise over time as the deposit is depleted, but which then ultimately decrease if the time horizon is ever approached. This pattern occurs if extraction costs are relatively insensitive to remaining stock when St is large but are very sensitive to St as the deposit approaches an economic shutdown. A limiting case would occur if aC,/aS,-, = 0 for large stock. Then during early years when stock is large, all nonzero terms on the right-hand side of eq. (29) would remain from one year to the next, and the discount factor would be multiplied by e r each year. During this time, opportunity cost would grow annually at the interest rate. But once aCT/aST-l varied from zero, opportunity cost would stop growing at the interest rate because the number of non-zero terms in the summation would decrease from year to year while those that remained would grow at exactly the interest rate. In summary, opportunity cost for depletable resource deposits stems from two conceptually separate phenomena. Pure depletion leads to an opportunity cost which rises at the rate of interest. But if resource deposits are not fully depleted, but rather shut down due to economic conditions, then this component is always zero. The second component stems directly from stock effects. If current extraction leads to future costs through reduced future stock levels, then the discounted present value of these additional costs is a component, and perhaps the only component of the opportunity cost.

2.3.3. Steady-state conditions

Without stock effects, steady-state conditions were straight forward: extraction stops when stock is reduced to zero. From that time onward there would be no further extraction. For depletable resources with stock effects, extraction likewise ceases in steady state, but the deposit need not be totally depleted. We explore here the steady stock level at which extraction permanently ceases. To so do we make the further assumption that the external conditions - price, cost functions, interest rate - are time invariant. Furthermore, we assume that the time horizon T is so far in the distant future that it is irrelevant for current decisions. Under these assumptions we can examine depletable resource steady state conditions. Assumption: Time invariance. Prices, interest rate, and cost functions are independent of time. The time horizon is so long that its existence has virtually no impact on the optimal choices.

Under the time-invariance assumption, eqs. (24) and (25) or (25') can define a steady-state stock level at which opportunity cost remains constant, extraction stops, and stock remains constant. Steady-state stock will depend upon prices, possibly upon the interest rate, and upon the cost function.

Ch. 17: Economic Theovy of Depletable Resources - Introduction

Fig. 7. Steady-state and final equilibrium stocks.

In steady state, opportunity cost remains constant from one time period to the next. We denote steady-state opportunity cost as = 4, = $,+, . By eq. (25'):

4

where costs are evaluated at E = 0, since in steady state all extraction ceasesI5. Steady-state opportunity cost is the present value of a perpetual stream of incremental costs -aC/aS. This interpretation can make the time-horizon condition in the assumption clear. A stream of -aC/aS for (T - t ) years would have a discounted present value of [I - e ~ ' ( ~ - ' ) ]However, . for sufficiently large values of (T - t ) , this discounted present value can be made arbitrarily close to The time horizon is assumed to be distant enough that e-r(T-t) is virtually zero. Combining eqs. (24) and (32) in steady state gives a condition defining steadystate stock:

4

4.

Each term on the right-hand side of eq. (33) is evaluated at E = 0. Since extraction rate is not a variable for that equation, steady-state stock, 3, is the only variable, and thus 3 can be determined from eq. (33). Figure 7 illustrates eq. (33). The righthand side of eq. (33) consists of two terms, both typically decreasing functions of stock. 3 is determined as that stock level at which price is just equal to the Note that the steady-state opportunity cost is independent of the length of a time interval (L), since both the numerator and the denominator are roughly proportional to L.

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marginal extraction cost plus the steady-state opportunity cost, both evaluated at zero extraction rate. Equation (33) implies that the higher the price, the lower the steady-state stock and the greater the quantity extracted before steady state is reached, as easily seen in Figure 7. Figure 7 identifies S M as that stock level for which marginal cost, evaluated at E = 0, equals price. If stock exceed S M when time reaches T, then extraction will occur at the time horizon. However, if total cost is a decreasing function of stock at zero extraction, and hence > 0, then the steady-state stock exceeds S M . In this case, a deposit may converge to steady state before the time horizon but may then be reopened for extraction as time approaches the horizon. Extraction may terminate and then be reinitiated even with no change of price or cost function. In many circumstances, if there is no extraction, there will be zero cost or some fixed shutdown cost, independent of the remaining stock. For example, the costs to plug and abandon an oil or natural gas well will typically not depend upon the amount of the resource remaining at the time of abandonment. In this situation = 0 and the two curves in Figure 7 would be identical. Once extraction is halted, it will remain stopped forever, unless prices or costs were to change over time. But there are many situations in which > 0 because there remains a stockdependent cost after all extraction ceases. These situations tend to be related to environmental consequences of resource extraction or use. For example, if a virgin forest is harvested, even after all harvesting has ceased, there will be longterm environmental consequences. The less forested area remaining, the higher the environmental cost. Similarly, the more coal is strip-mined in a region, the higher the environmental costs or the one-time restoration costs. Subsidence of overlying land may occur as resources are extracted and the amount of subsidence may depend upon the total stock of the resource ultimately depleted. The greater the cumulative use of carbon-based resources, the gleater the accumulation of C 0 2 in the atmosphere even after use of such fuel stops. In such situations, aC/aS < 0 atE = 0and$>0. In summary, the total resource quantity ultimately extracted will be less than the initial stock if marginal extraction cost increases enough as stock declines toward zero. If price does not correspondingly rise, then economic shutdown will occur. Stock remaining at economic shutdown will depend on the marginal extraction cost (at E = O), the price of the extracted commodity, the magnitude of the stockdependent environmental or other costs, and the interest rate. We turn now to analysis of trajectories toward the steady state.

4

4

6

2.3.4. Phase diagrams for dynamic analysis Under the time-invariance assumption, phase diagrams provide convenient tools for comparative dynamic analysis of adjustment toward the steady state as well as

Ch. 17: Economic Theoy of Depletable Resources -Introduction

Fig. 8. Phase diagram for depletable resources.

for comparative static analysis of the steady state. Phase diagrams can also be used to gain insights into analysis of markets with time-varying parameters. A phase diagram is a graph in a space of S vs $, divided into four regions, based upon the directions of movement of $ and S. Boundaries are defined by two loci: (1) the locus of points at which E is just reduced to zero and at which stock remains constant (the S-constant locus), and (2) the locus of points at which $ remains constant over time (the $-constant locus). The S-constant locus is defined by

Along or above the S-constant locus, S remains constant over time, while for lower values of 4, E > 0 and stock declines over time 16. To the right of the 4-constant locus (higher values of S), opportunity cost increases over time, while to the left of that locus, opportunity cost decreases over time 1 7 . Figure 8 illustrates such a l 6 This relationship can be seen from eq. (24).If E = 0 for one value of 4, then if 4 increases, E remains equal to zero. If 4 decreases below the minimum level which gives E = 0, then extraction rate will become positive. l 7 This result can be shown from eq. (25).From the 4-constant locus, if S increases, the first term on the right-hand side of eq. (25)remains unchanged. The second term increases (or remains constant) under the convexity assumption, as will be shown in what follows. If S increases by SS, where 15sis infinitesimally 6s + a2c/asi3E 6E. Byeq. (24)the change small, then the change in aC/aS will be 6[aC/aS]= a2~/as2 in E will be 6E = -[(a2c/as ~ E ) I ( ~ ~ c 6s. / ~ Combining E ~ ) ] these two equations gives:

Thus the right-hand side of eq. (25) increases or remains constant when S increases. Therefore 4 must increase in time or, in the limit, be constant over time, to the right of the $-constant locus.

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phase diagram for depletable resources with stock effects. The arrows indicate the direction of movement of opportunity cost and stock. In Figure 8, the S-constant locus slopes upward as long as BCIaE is a decreasing function of S, as normally is the case absent learning by doing. The S-constant locus slopes downward for those stock levels at which a2ClaE a S < 0 as may be the case with learning by doing. The &constant locus is defined by

where aClaS is evaluated at the extraction rate consistent with the 4 defined in eq. (35). This locus is downward-sloping, as has been drawn in Figure 8, if a2ClaE as < 0 (or not much greater than zero) 18. This expression can be totally differentiated, recognizing that aClaS depends on S and on E , which itself depends on S and 4, to calculate d4/dS as non-positive l9 as long as a2ClaSaE < a 2 C / a ~ 2 . Steady state of the system can be illustrated as that portion of the 4-constant locus on which stock remains constant. The S-constant and the &constant loci intersect at $, 3 . Steady state of the system can occur at any portion of the 9constant locus for which S < 3 . At any such combinations of S and 4, extraction rate is zero, stock remains constant, as does opportunity cost. For the time horizon extremely far in the future (or infinite), the system either starts at one of these points (for So < 3) or converges to 4, 3. For So < 3, the resource is never extracted at all. Figure 8 has been drawn with steady state opportunity cost positive, under the assumption that there exist environmental or other costs that lead to positive incremental costs of reduced stock even after extraction ceases. Conversely, if l 8 Differentiating p4 = -aC/aS gives the following for infinitesimally small changes in 4 , S and E : pq5 = - a 2 ~ / i 3 ~6s2 - t 1 2 ~ laE a ~SE. Differentiating P = aCItlE + 4 gives: a2C18E as SS a ' C / a ~SE~ + 64 = 0. Combining these two expressions gives

+

Convexity of the cost function implies that the expression in brackets on the right-hand side of this expression is non-negative. The first term in parentheses on the left-hand side of this expression is aE < 0. This establishes the result always positive and the second term is positive as long as a2c/as ~ <pa2~la~2. that q5 is a decreasing function of S as long as a 2 C l a aE l9 Notice that this condition will be independent of the length of the interval in the discrete model. In particular, as L increases, p would increase in proportion to L, as would t12Cltl~ aE, and a 2 ~ l awould ~2 be roughly independent of L.


/

LOCUS

Fig. 9. Phase diagram with convergent locus.

aC/aS = 0 when E = 0, then the steady state would occur along the horizontal axis, with 4 = 0. The difference equations determining changes of 4 and S can be solved to give a unique optimal path of stock and opportunity cost from any initial stock to the final state. In the time-invariant case, this unique optimal path must converge to the steady state. Under the time-invariance assumption, the optimal extraction rate and opportunity cost given stock must be independent of time and must be independent of the initial stock. This implies that for every S there is a unique q5 on its optimal extraction path, independent of the history of extraction. Such a mapping from S to 4 defines a third locus of points in the phase diagram: the "convergent trajectory". The convergent trajectory provides a closed-loop feedback control under the time-invariance assumption in which: (1) 4 is a function of S, (2) E is a function of 4 and S, and thus (3) E is a function of S. Figure 9 adds the convergent trajectory to the phase diagram of Figure 8. The convergent trajectory is indicated by the line with arrowheads indicating the direction of convergence toward the steady state. For a finite time horizon problem, eq. (26) determines conditions at the final time horizon. At time T, the final state of the system must be along either the horizontal or the vertical axis. Figure 8 has been drawn under the normal case in which the Sconstant locus intersects the horizontal axis at some positive stock, SM,the same SM as in Figure 7. For a finite time horizon problem ST 2 SM and q5T = 0 (unless the system starts with initial stock below SM.)For the system to terminate on the horizontal axis, the entire path of opportunity cost must lie below the convergent trajectory. For any given stock, opportunity cost will be smaller, extraction will be larger, and stock will decline more rapidly than in the convergent trajectory. This finite time horizon trajectory is illustrated in Figure 10. For very long time horizon, the actual path lies very close to the convergent trajectory and the system

J.L. Sweeney

Fig. 10. Finite-time vs. infinite-time trajectories.

state remains very close to the steady state for many time periods. Only as the time horizon is approached does the system trajectory diverge from the convergent trajectory. The preceding discussion and graphs assumed that marginal cost and total cost were both decreasing functions of remaining stock at all stock levels. However, in early phases of development of a deposit, stock reductions may lead to reductions in costs rather than cost increases. In this case the S-constant locus may bend downward for high stock levels. In addition, as S increases in the region in which a 2 C l a as ~ > 0, the slope of the S-constant locus approaches minus infinity. This locus cuts through the S-axis to give negative values of q5 along the &constant locus. The locus never slopes upward. Rather 4 gets negative enough and extraction rate gets positive enough that either a 2 C l a ~increases 2 so that a2ClaSaE < p a 2 C l a ~ 2 everywhere on the @constant locus or the locus does not exist for some values of S. A phase diagram for such "learning-by-doing" cost functions appears in Figure 11. Figure 11 shows that the initial opportunity cost may be negative if learning-by doing is significant for high stock levels. In this case, the anticipation of future cost reductions would cause the firm to extract more rapidly than it would absent the incentive to reduce future costs. Phase diagrams are particularly valuable for examining comparative dynamics of the optimal trajectories. It is such analyses to which we now move, utilizing phase diagrams whenever the system is time invariant or can be treated as such. Whenever the time-invariance assumption is inappropriate, we will use eqs. (24)-(26) directly.

The analysis can be illustrated with a specific numerical example, in which extraction costs are quadratic in extraction rate and are inversely proportional to


S-Constant Locus

Fig. 11. Phase diagram with "learning by doing".

the remaining stock and where environmental cost is zero if stock equals the initial level but increases as stock is depleted:

The constant K is positive and the constant M is non-negative20.The first term of the cost function is homogeneous of degree 1 and thus is only weakly convex, but the second term makes the cost function strongly convex when M is positive. It can easily be seen that the second derivatives with respect to extraction rate and with respect to stock are both positive. The determinant of the Hessian matrix is always positive when M is positive and zero when M is zero. The second cross partial derivatives are negative. When M is zero, this is a limiting case of a weakly convex cost function and in that case the slopes of the S-constant locus and the &constant locus will also be limiting cases of the slopes discussed above. Equation (24) can be solved to calculate the optimal extraction rate as a function of price and opportunity cost for P, 2 4,:

This equation allows us to calculate the S-constant locus easily. The S-constant locus is exactly equal to price, independent of the remaining stock. Stock remains constant if the opportunity cost is greater than or equal to price and stock declines for lower values of the opportunity cost. Additional limits are placed on these parameters by the requirements of eq. (11). In using this equation, we choose parameters so that eq. (11) is valid for all values of the variables in the optimal solution.

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Equation (25) can be rewritten based upon the optimal extraction rates:

Note that for this example, the evolution of the opportunity cost depends on the interest rate, price, cost function, and remaining stock. If we know the final time and the final value of the opportunity cost, these equations can always be solved (at least numerically) starting from the last time period and working backward in time to calculate the opportunity cost over time. This calculation can be made even if prices vary over time. For this part of our analysis we will adopt the time-invariance assumption and treat the terminal time as arbitrarily far in the future and assume that the price remains constant over time. Therefore we can drop the t subscript on price and focus attention on the convergent trajectory. At a later point we will return to this model in a time-varying case. The steady-state opportunity cost can be calculated from the above equation by asking the value of 4 that would make 4, equal to $,-I. The resulting quadratic equation has a closed-form solution:

The $-constant locus is a decreasing function of remaining stock and lies below the S-constant locus for S > ( M I ~ P ) " ~In. steady state, extraction rate will be zero and , it would take infinite time to reach steady state. stock will be equal to ( M I ~ P ) " ~but In steady state, = P . Optimal extraction along the convergent trajectory can be calculated to be

6

Along the convergent trajectory for very large stock or small value of M , both the stock and the extraction rate decline approximately geometrically, with extraction rate a virtually fixed proportion of remaining stock. However, for smaller values of stock and/or larger values of M , the fraction of the remaining stock extracted each period shrinks as S declines. The rate of extraction, and thus the rate of geometric decline is an increasing function of both price and interest rate and a decreasing function of the extraction cost. For a finite but long-distant time horizon, opportunity cost is slightly below that calculated above and extraction rate is slightly above the rate calculated here. We turn now to more general properties of solutions for more general cases.


2.3.6. Optimal trajectories and comparative dynamics The models can be used to examine characteristics of the optimal extraction path for a depletable resource with stock effects. We will present many of the same examples as examined previously to illustrate methods of analysis and conclusions that can be derived. In all the discussions that follow, we assume that the initial stock exceeds 3 so that some extraction will occur. 2.3.6.1. Extraction path under time-invariant conditions

The phase diagrams of Figures 9 or 11 can be used to illustrate the optimal trajectory. In the optimal trajectory, if the &constant locus is downward-sloping everywhere, the opportunity cost must begin in the region in which is increasing and S is decreasing over time, and must converge to the crossing point of these two loci 2 1 . If the system began in any other region it could never converge to the steady state. Characteristics of the time pattern of extraction are influenced by the derivative of marginal cost with respect to stock. In the absence of learning by doing or other phenomena which lead to positive values of a2C/aEa s , extraction rate must decline over time; opportunity cost grows and as stock decreases, marginal cost for any extraction rate must increase. The basic pattern of extraction rates declining over time is similar to the pattern absent stock effects. With learning by doing, two effects work in opposite directions: the rapid increase in the opportunity cost implies declining extraction, but the decline in the marginal extraction cost as stock declines would have the opposite effect. Either effect could dominate and the extraction rate could increase or decrease over time. 2.3.6.2. Extraction path for prices vaying: vey long time horizon When price varies over time, phase diagrams do not provide as decisive a conclusion as that outlined in the previous section, even when a2ClaEaS < 0. If price is increasing over time, extraction rate may grow or decline, depending upon the increase of price relative to the change in the opportunity cost. For rapidly increasing price, extraction rate will grow from one period to the next, while for slowly increasing price, extraction rate will decline. If price declines from t - 1 to t , the S-constant locus will shift upward and the $-constant locus downward from t - 1 to t. Thus a decline in price could move the $-constant locus from above the current value of $ to below the current value, If the initial stock was below the steady-state level, however, this pattern would be impossible and therefore no extraction at all would occur. However this possibility has been ruled out by assumption.

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allowing a convergence to the steady state. Thus an essential part of the argument of the previous section is not valid if prices ever decline. However, if we adc! an assumption that - aC/aS is itself convex in extraction rate, maintaining assumptions that any time horizon is far in the future, that a * C / a as ~ < 0 for all stock levels, and that the cost function is time invariant, we can establish that if Pt 6 PtPIthen Et < El-,. The maintained assumption that the cost function is convex does not imply that - aC/aS is itself convex in E , unless additional structure is imposed on the cost function. For example, if the cost function is separable into two multiplicative or additive factors, one dependent only on S and the other only on E , then cost function convexity implies 22 that - aC/aS is convex in E. With such additional assumptions, declining price implies a declining extraction rate. Assume then that - aC/aS is convex in E , that Pt < P,-,, but that E, 2 We will show that this leads to a contradiction, thus implying that E, < El-,. By eq. (24), if Pt < P,-, :

where the marginal costs on the right-hand side are evaluated at St-2 and St-, respectively. The right-hand side can be expanded, recognizing that St-2 - St-1 = EtW1and incorporating the dominance of extraction rate on marginal cost assumption:

and St-l The derilrative on the right-hand side is evaluated at stock between and extraction rate between E, and Et-1. A second limit can be placed on the change in the opportunity cost using eq. (29) under the assumption that the time horizon is very far in the future:

The first derivative on the right-hand side is evaluated at Sf-, and E, while the second term is evaluated at St-, and E=O. Under the assumption that - aC/aS is convex in E , this inequality becomes

I would like to thank Robert Patrick for for pointing out this result about multiplicatively separable functions.

22


Extraction Rate

~ce,Oppottunlty Cost

1000

800

600

400

200

Time

Fig. 12. Price, opportunity cost and extraction rate approaching the time horizon.

The two inequalities for the change in opportunity cost are inconsistent with one another. Thus the contradiction implies that whenever P, 6 P,_,, then E, < E,-1 for very long time horizon situations under the assumptions outlined here. 2.3.6.3. Extraction path as time approaches the horizon

Results from the previous section cannot be generalized as time approaches the horizon. If the cost function is time invariant, a 2 C I X a E < 0, and - aC/aS is convex in E , extraction rate can increase over time even while prices are declining. As time approaches the horizon, opportunity cost must decline and may decline faster than price. As stock declines, marginal cost of extraction from a given rate increases. If this marginal cost increase is not sufficient to compensate for the drop in opportunity cost, extraction will grow over time. This possibility is illustrated with calculations based upon the numeric example presented above. We use the cost function of our example, with So = 105units, M = lo1', K = lo3, and p = 0.1. Price begins at $10/unit and declines by $O.l/unit each year over 21 years. Price and resulting opportunity cost and extraction rate are plotted in Figure 12. Figure 12 shows that for this particular example, extraction rate increases over time, starting at the lowest level and ending at its highest level, even with price declining from one year to the next. Opportunity cost declines more rapidly than does the price, beginning at $8.75/unit and ending in year 21 at $0. The rapid decline of the opportunity cost is the result of the large partial derivative of cost with respect to stock, even with low extraction rates. For this example, had prices been constant at P and had the time horizon been sufficiently far distant, then extraction rate would have decreased over time,

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converging to zero as opportunity cost increased towards P . For the time horizon far in the future, 4, converges to P , while as time approaches the horizon, the opportunity cost converges to zero. Hence we see that it is quite possible for price movements and extraction rate movements to be inversely related when the system approaches a time horizon: declining prices may well be linked to increasing outputs, a situation which makes empirical research very difficult. 2.3.6.4. The role of price Assume that in the first case price was always P and in the second it was P', where P' > P . Let SP = P' - P. We now examine the comparative dynamics of the optimal extraction path. First consider impacts on the steady state. We can totally differentiate eqs (24) and (32) in order to determine impacts on the steady-state stock and opportunity cost. The extraction rate is zero in steady state so that extraction rate is not treated as a variable in differentiating eqs (24) and (32). We examine infinitesimal changes in P in order to determine the impacts on steady-state stock and opportunity costs. For discrete changes, impacts can be integrated and properties of the infinitesimal change will be preserved. Totally differentiating eqs (24) and (32) gives:

Combining these equations gives the impacts on steady-state stock and opportunity cost:

The numerators of the right-hand side expressions are both positive and the first term in the denominators is also positive. We expect no learning by doing in steady state and therefore the second term is also positive. Thus we can determine the signs of the changes and can bound the magnitude of the change in opportunity cost. These equations show that the steady-state opportunity cost must be an increasing function of price 23. This increase must be less than the price change. The steadystate stock 3 must be smaller in the higher-price case and a greater total amount of the resource must be extracted before steady state is reached. Note that the steady-state stock and opportunity cost are independent of L. Both the numerators and the denominators will tend to be proportional to the length of the time period.

23


Locus

F

$'$

S

Fig. 13. Phase diagram with increase in price.

These changes can also be examined through analysis of the changes in the phase diagram. Equation (24) implies that the S-constant locus would be shifted upward by the amount of the price increase. The form of eq. (32) would be unchanged: for any fixed value of stock and extraction rate, steady-state opportunity cost would be unchanged between the two cases. Differentiating eqs. (24) and (32) shows that the @-constantlocus must rise by an amount smaller than SP as long as marginal cost is a decreasing function of remaining stock, a condition we expect at steady state. The changes in opportunity cost and in steady-state stock are those indicated in the equations above. These shifts are shown in Figure 13. We now examine the impacts of higher prices on the convergent trajectory. For those stock levels at which marginal cost is a decreasing function of remaining stock, higher price leads to a higher opportunity cost. However for levels at which marginal cost is an increasing function of remaining stock, we cannot assure that opportunity cost will decline with increases in price24. However, as long as the "dominance of extraction rate on marginal cost" assumption holds, the change in opportunity cost must always be smaller than SP. These variations in the opportunity cost imply that the optimal extraction for any given stock along the convergent trajectory is higher, the higher is the price of the extracted commodity. These results can be established by examining infinitesimally small changes. Assume the converse: that for some S (at time t - 1) the convergent trajectory is Equation (29) suggests this counter-intuitive result for stock levels from which a 2 c / a ~ a E > 0. Higher prices lead to more extraction in early years when a2c/a~ BE > 0 and less extraction in later years when a2C/8SaE < 0. Thus aC/aS increases in both early and later years. Thus the discounted present value of - aC/aS must decrease as a result of the price increase. Note that if a2clas aE < 0 for all years, then aClaS would decrease in early years and increase in later years. In that case the discounted present value of - aC/aS could be expected to increase as a result of the price increase. 24

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shifted upwards so that S4,-, 2 SP. Totally differentiating eq. (25) with respect to 4, and E,, for S fixed, gives:

We can similarly differentiate eq. (24) to obtain an expression for 6Et:

These two equations can be combined to eliminate SE,:

(64, - SP) ( 1 + a2CiaSaE) a2ClaE2

= (64,-1 - SP) (1

+ p) + p6P

By eq. (36), if 64,-1 >, SP, then 64, > SP since the "dominance of extraction rate on marginal cost" assumption (eq. 12) implies that the factor multiplying 64, - SP must be positive. In addition, since 64, > SP, stock must decline less (SS, > 0). Along the original convergent trajectory, stock is declining and opportunity cost is increasing. Therefore SSt > 0 and S4t > 6P implies that the new convergent trajectory would be shifted up beyond the initial trajectory by an amount greater than SP at stock equal to St. For the next period the same logic can be repeated. Hence if the new convergent trajectory is shifted above the initial one by an amount greater than 6P at any stock level, then it must be shifted up by an amount greater than SP for all lower stock levels. However, in the steady state, the change in opportunity cost must be smaller than SP, a contradiction. Thus the trajectory cannot be shifted by greater than 6P at any stock level. Assume now that S4,-1 < 0 at some stock level. We can rearrange terms in eq. (36):

6 L (I

a2ciasa ~ =),4 a2ciaE2

a2ciasa~ SP.

( I-'

+

P)

+

a2ClaE2

Equation (37) shows that if S$,-I < 0 and a2ClaSaE < 0, then 64, < 0, under the "dominance of extraction rate on marginal cost" assumption. In addition, since 64, < 0 and 6P > 0, stock must decline more (SS, < 0). Along the original convergent trajectory, stock was declining and opportunity cost was increasing. Therefore SSt < 0 and 64t < 0 implies that the new convergent trajectory would be shifted down below the initial trajectory at stock equal to St. For the next period < 0. Hence if the new convergent the same logic can be repeated if a 2 C / a ~ a E trajectory is below the initial trajectory at any stock level, then it must be shifted below for all lower stock levels, under the assumption that a2ClaS aE < 0 for all


809

lower stock levels. But since the convergent trajectory must shift upward at the steady state, it can not be so shifted at any such stock level unless a2ClaSaE > 0 for some lower stock level 2 5 . In summary, the net result of a constant increase in price for all time is an increase in the extraction rate from any stock level, an increase in the total quantity extracted, and an increase in the steady-state opportunity cost. Opportunity cost increases at all levels along the new convergent trajectory unless marginal cost is an increasing function of remaining stock over some range of stock. 2.3.6.5. The role ofprice expectations As we did for resources without stock effects, we here again examine the case in which the prices do not change currently but in which beliefs about future prices do change. Again we assume that after some future time T, in the new situation all prices will be higher than they were in the old situation. We identify three cases: Low-Price Case: P, = P for all t , High-Price Case: P, = P' > P for all t, P for t < T, Changing-Price Case: Pi = P' > P for t 3 T. Both the low- and the high-price case satisfy the time-invariance assumption, and the changing-price case maintains the time-invariance assumption after time T. The high- and low-price cases will provide upper and lower bounds for the opportunity cost (as a function of remaining stock) for the changing-price case. We will show that at times before T, the changing-price case will exhibit lower extraction rates than will either of the other cases. Here again, expectations of changing prices will influence current behavior. Figure 14 displays the phase diagram. In the low-price case, steady state would be $, 3 and the convergent trajectory is the lower of the three in Figure 14. In the high-price case and in the changing-price case steady state is 8 , s ' . Before time T the changing-price case convergent trajectory is always strictly above the low-price case convergent trajectory and is never as much as 6P below the convergent trajectory in the high-price case. This conclusion will be established in subsequent paragraphs. From time T onwards, the convergent trajectories in the high-price case and the changing-price case are identical since all conditions are identical after time r.

{

We could reasonably assume that if marginal cost is decreasing in S for one stock level it is decreasing in S for all lower levels. Convexity implies that if aClaS is negative for some level, it must be negative for all lower levels if E is held constant at those levels. However, that does not strictly imply that if marginal cost is decreasing in S for one stock level it is decreasing in S for all lower levels. Thus the awkward statement in the text.

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Fig. 14. Optimal trajectories for high-price, low-price and changing-price cases.

Equation (24) and the lower bounds on the opportunity cost imply that for times before r, extraction will be lower in the changing-price case than in either of the other cases. Price in the changing-price case is the same as in the lowerprice case but the opportunity cost is strictly higher. Price in the high-price case is SP larger than in the changing-price case but the opportunity cost is increased by less than 6P; hence extraction rate is higher in the high-price case. The net result is that extraction is reduced in anticipation of the higher prices to come. Stock declines less rapidly in the changing-price case than in either of the other two. Equation (36) or (37) provides the basis for showing that the convergent trajectory for the changing-price case can never be below that for the low-price case. For times before r, eq. (36) or (37) show the evolution of S$[, where S$[ is based on the variation from the low-price to the changing-price case, recognizing that the variation in price before T between these two cases is zero. These equations become

Under the "dominance of extraction rate on marginal cost" assumption (12), the factor in parentheses on the left-hand side of the equation is positive, as is ( 1 p). Thus the sign of is the same as that of S$t-l: if S$,-, < 0, then S$[ 6 0. But < 0 implies that SE, 2 0, so that SSt < 0. Along the original convergent trajectory, stock was declining and opportunity cost was increasing. Therefore SS, 0 and 6qht < 0 imply that the changing-price case convergent trajectory could not be above the low-price trajectory at stock St either. The logic can be repeated for all lower stocks on the convergent trajectory until time T.At time 7 opportunity cost could not lie above the low-price convergent trajectory and therefore must lie below the high-price convergent trajectory. But at time r the convergent trajectory

+

SP. This implies that SE, < 0 and SS, > 0. The combination of 64, > SP and SS, > 0 implies that at St the high-price convergent trajectory will also exceed the changing-price convergent trajectory by more than SP. The logic applies for all future times and corresponding stock levels. But we know that at time r the convergent trajectory of the changing-price case must be identical to the convergent trajectory for the highprice case, a contradiction. Hence the opportunity cost on the convergent trajectory for the high-price case can never exceed the equivalent opportunity cost for the changing-price case by 6P or more. The results are similar to those obtained for models without stock effects. For times before r , the change in expectations leads to an increase in opportunity cost but impacts no other elements of eq. (24). Thus for these early times, optimal extraction for the given level of stock must decline as a result of the changed expectations about future prices. The effect would be very small for times long before the anticipated price increase, since the opportunity cost would be raised only slightly. However, as the date of price increase becomes imminent, the effect would get larger and extraction rates would be significantly reduced. 2.3.6.6. The role of the price trajectory

This sectior, relaxes the time-invariance assumption, allowing prices and costs to vary over time, and expands the questions addressed in the previous two sections. We assume an increase in price both now and in the future and examine the impact of such changes on extraction from a given stock. We will focus attention only on those price changes whose present value remains constant or declines over time: SP, (1 + p) 6Pt_,. This restriction is in contrast to the previous analysis in which the expectation of a very rapid price increase motivated extraction reductions in anticipation of the increase. Under these fairly general conditions, the optimizing trajectory for the high-price case will lead to greater extraction from a given stock than would occur with the lower-price case. These results will not necessarily hold if the present value of price rises over time. Equations (24) and (25) can be differentiated totally to give the relationships between changes in the variables. Differentiating eqs. (24) and (25) plus the

0 then SSt > 0 and 64, - SP, > 0. These inequalities imply that if at any time in the high-price situation ( 1 ) stock is increased or unchanged and (2) the increase in opportunity cost exceeds the price increase, then stock would always afterward be increased and the change in opportunity cost would always exceed the price change. At the initial time, So is


813

unchanged by definition. Therefore by eq. (24), both (641 - SPI) and SSI must be positive or both must be negative. Therefore if 641 > & P I then , SSI > O,S$, > SP,, and &St> 0 for all subsequent time. But if at the time horizon (no matter how far distant) stock and opportunity cost were both to increase as a result of the price increase, eq. (26) could not hold: both opportunity cost and stock would be positive. This contradiction shows that Sq51 < GP1.Furthermore, if the deposit were not ultimately to be fully depleted, then the final opportunity cost would be zero: it cannot increase, as would be required if 64, = &PI. Therefore 641 is strictly smaller than &PIand the initial extraction rate must be higher in the higher-price casez6. As a result of the price increase, from any stock level, the firm would extract at a higher rate and would, over time, have smaller stocks. Smaller stocks would reduce optimal extraction rate from that which would be optimal had past prices been lower and had more stock been left for future use. Higher prices would therefore move extraction toward the present from the future and would increase the total amount of the resource ultimately extracted. 2.3.6.7. The role of the interest rate

Under the time-invariance assumption, the model implies that the higher the interest rate, the more rapid the extraction from a given stock, again under the assumption that interest rates have no impact on extraction costs. A demonstration follows. It must be remembered, however, that interest rate increases may also increase marginal extraction costs and that such cost increases can imply that the higher the interest rate, the less rapid the extraction from a given stock. Equation (34) remains unchanged by the interest rate difference; only eq. (35) is altered. This variation shifts the 4-constant trajectory downward in the highinterest rate case and therefore leads to lower steady-state opportunity cost and lower steady-state stock (unless the steady-state opportunity cost is zero and then there is no change in these steady-state variables). These differences are illustrated in the phase diagram of Figure 15. Mathematically, we can examine changes in the steady state by totally differentiating eqs. (34) and (35) to give impacts on steady-state stock and opportunity cost:

Alternatively, in an infinite-time problem which converged to a steady state, the increase in the steady-state opportunity cost must be smaller than the increase in the price in the steady state as shown in the body of the chapter. But this would be impossible if the initial opportunity cost increase equalled or exceeded the initial price increase.

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Fig. 15. Impacts of interest rates on the optimal trajectory.

We turn now to the examination of the convergent trajectory, as illustrated in Figure 15, and show that the convergent trajectory with high interest rates is always lower than the trajectory with low interest rates. The basic idea is that by eq. (25), for a given stock and opportunity cost, the opportunity cost will grow less rapidly with low interest rates than with higher interest rates. Growing less rapidly, but ending at a higher level, implies that the opportunity cost must always be higher in the low-interest rate case. Equations (24) and (25) plus the depletability constraint of problem (8) can be differentiated totally and combined to give the relationships between changes in the variables from the initial situation. We use the same procedure as in the previous section to show:

Each of the factors multiplying Sdt, 64,-1 and SS,-I must be positive. If is positive (which will always be the case absent learning by doing) the factor multiplying Sp is also strictly positive. This leads to the condition For

2 0 , if 6St-1 2 0 and then 6St > 0 and 64, > 0. $,-I

6q5-1 2 0


815

These inequalities imply that if at any time in the high-interest rate situation both stock and opportunity cost are increased or unchanged, then stock and opportunity cost would always afterward be increased. So is unchanged by definition. Therefore by eq. (24), both 641 and SSI must be positive or both must be negative. Therefore if 64, > 0, then SS1 > 0, and hence 64, > 0, and SS, > 0 for all subsequent time. But if at the final time (no matter how far distant) both stock and opportunity cost were to be increased as a result of the price increase, then eq. (26) could not hold: both opportunity cost and stock would be positive. This contradiction shows that S41 is strictly negative and the initial extraction rate must be higher in the higher-interest rate casez7. The net result of the interest rate increase then is that from any stock level, the firm would extract that stock at a higher rate and would, as time goes on, be left with smaller stocks. Over time, these smaller stocks would reduce the optimal extraction rate from that which would be optimal had the interest been lower and had more stock been left for future use. Higher interest rates would therefore move extraction toward the present from the future and would increase the total amount of the resource ultimately extracted. This result is similar to that obtained in the absence of stock effects.

2.3.6.8. The role of externalities As discussed above, some environmental or national security externalities associated with depletable resource extraction or use imply costs which depend upon the rate of depletable resource extraction. Since externalities imply a divergence between the price and the social value of the output, then the results derived in previous sections for price changes can be used directly to analyze such externalities. Other externalities, however, may be related to the stock of the resource extracted to date. Subsidence of land, the amount of carbon dioxide accumulation in the atmosphere, and some local environmental impacts are more related to the total quantity of the resource extracted to date. Here we assume there are some environmental damages whose costs increase with the amount of the resource extracted (and hence decrease with the amount of the resource remaining). We will adopt the assumption of time invariance in order to illustrate the results but the general conclusions can be obtained for a more general case. This formulation implies that aC/aS is more negative when the externalities are internalized. Such impacts can be analyzed by use of eqs (24) and (25), in which the Alternatively, in an infinite-time problem which converged to a steady state, the increase in the steady-state opportunity cost must be negative, as shown in the body of the chapter. But this would be impossible if the increase in initial opportunity cost were non-negative.

27

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J.L. Sweeney

only change is that for a given value of 4 and S, the right-hand side of eq. (25) is reduced when externalities are incorporated. Figure 15can be used to illustrate this situation as well as that of changed interest rates, modifying the "Low r" label to "Internalize externalities" and the "High r" label to "Ignore externalities". The $-constant locus is increased when the stockrelated externality is internalized and therefore in steady state the opportunity cost and the final stock are both increased. Less of the resource is extracted cumulatively over time. The convergent trajectory is higher for all stock levels when externalities are internalized, as illustrated in Figure 15. This result can be established by assuming the opposite, that for some stock at some time the opportunity cost is less when externalities are incorporated. Then the opportunity cost will always be less, contradicting the conclusion that in steady state the opportunity cost will be increased. The formal mathematical equations would be analogous to eqs. (40) and (41), except that the externality (the change in aC/aS) would appear in eq. (40) in place of Sp. Higher opportunity costs imply lower extraction rates for a given stock level. The net result of internalizing stock-related externalities is a reduction in the depletable resource extraction rate and a decrease in the amount ultimately extracted. This result is different from that obtained for flow-related externalities. When the externality depends on extraction rate rather than on stock, then the direction of bias depends on whether the present value of the marginal external cost grows or declines. If flow-related externalities are small now but are expected to be large at a later time, then an incorporation of external costs into decisionmaking would lead to more extraction in early years, avoiding those times in which the marginal externality cost were large. However, for stock-related externalities this is not true. Internalization of any stock related externalities (for which marginal external costs are positive) will result in less rapid extraction of the depletable resource with smaller quantities ultimately extracted. We turn now from analysis of individual deposits to analysis of depletable resources in a market environment.

3. Extraction with prices determined endogenously

The theory presented so far is directed toward the profit-maximizing extraction trajectories of a single resource or a group of resources operating in a competitive market. In particular, each decisionmaker correctly believes that his or her actions alone have no effect on the overall market price. In the theory presented in the previous sections we did not address the issue of the price determination and in particular, the impact of resource extraction patterns on the prevailing prices.


817

In this section, we address joint determination of prices and quantities in markets. We first address purely competitive markets and then turn to monopolistic markets. More complex market structures are not addressed here but are examined in the chapters by Karp and Newbery (19) and Teece et al. (24) in this Handbook.

3.1. Competitive equilibrium

The concept of competitive equilibrium for depletable resource markets is fundamentally identical to the competitive equilibrium concept for conventional commodities. Each firm and consumer is so small that its input and output decisions can have no significant impact on the prices prevailing in the market. Market clearing occurs when the quantity supplied equals the quantity demanded in each market. In addition, however, markets are explicitly linked over time in that firms can substitute extraction among time periods. It is not meaningful to address a static concept of competitive equilibrium which fails to recognize the essential intertemporal linkage through depletable resource supply. Thus competitive equilibrium for a depletable resource requires market clearing in each time period. Definition: Competitive equilibrium. Competitive equilibrium is said to occur if each agent is so small as to have no individual impact on prevailing prices and if for each time period the quantity of the commodity extracted by all firms together is equal to the quantity of the commodity demanded. We define Ef as the quantity of the commodity extracted by the ith firm at time t. Then the market supply at time t, Q,, is equal to the summation of extraction quantities over all firms:

This market supply will be a function of all current and future commodity prices, current stocks remaining in each resource deposit, cost functions for each deposit, and the interest rate. The impacts of these factors on the market supply function derives directly from the impacts discussed above for individual deposits. The market demand for the commodity will be represented by a conventional static demand function. Although demand can be analyzed more fully, as shown in the chapters by Jorgenson and Wilcoxen (27) and Slade et al. (20) in this Handbook, we will adopt this fairly simple static formulation in the remainder of this chapter. We will denote QD(pt,t) as the demand function at time t. We will assume that Q ~ ( P , ,t) is a continuous decreasing function of price.

J.L. Sweeney

818

Competitive equilibrium is characterized by a sequence of prices over all time such that supply equals demand at each t: Qt

=

C El = Q ~ ( P , ,t) for all t. I

In most of our analysis it will be more convenient to use the inverse demand function P(Ql, t) to determine market clearing price as a function of the market quantity supplied:

The inverse demand function is defined so that QD(P(Ql, t), t) = Qt for all values of Q,. If market demand is finite for Pt = 0, the inverse demand function is defined to be zero for all market quantities greater than or equal to the market demand at zero price 28. In competitive equilibrium, then, eqs. (15) and (16) or (24)-(26) must hold for each firm, and eqs. (42) and (44) must link the firms to one another through a market. Depletability of the resource immediately implies that in a competitive equilibrium there is an upper limit on the cumulative quantity of the resource demanded over all time. Summing eq. (43) over time gives:

The right-hand side of eq. (45), S A , is the initial aggregate resource base. Depletability of the resource implies that the cumulative demand can be no larger than the initial aggregate resource base. For T arbitrarily large, the cumulative demand remains bounded above by the natural endowment of the resource. At some time as the resource is depleted, prices must increase enough to drive demand to zero or demand functions must shift so as to reduce or eliminate demand without large price increases. For an infinite time horizon, price must ultimately increase enough for demand to converge to zero. There may exist some price which reduces demand to zero. In that case, there will always exist some price trajectory for which inequality (45) holds. We will refer to the price which just reduces demand to zero as the "choke price", and denote it by PF. Note that the choke price may itself be a function of time. This clarification of the concept will be necessary for establishing the existence of a competitive equilibrium.

28


819

The existence of a choke price can be related either to the demand function for the extracted commodity or to the supply function for a perfect substitute. On the demand side of the market, consumers may be willing to forgo all use of a particular commodity or class of commodities if price rises enough. Dasgupta discusses such possibilities in ch. 23 of this Handbook. Commodities can be described as "essential" or "non-essential", depending upon whether demand can be driven to zero at finite prices. If a commodity is "non-essential", it will have a finite choke price. O n the supply side, there may be technologies which allow large or unlimited quantities of a perfect or virtually perfect substitute to be produced at some price. Such "backstop technologies", as they have been dubbed by Nordhaus (1973),can assure the existence of a choke price, with choke price equal to the average or marginal cost of the backstop technology. Even essential commodities may have a choke price if a backstop technology exists. If no choke price exists, inequality (45) could still be satisfied, even for arbitrarily long time horizons, as long as demand converges towards zero for sufficiently high prices. For this chapter, however, we will assume that a choke price always exists, since such an assumption allows us to avoid mathematical difficulties. We will not differentiate between the two reasons for the existence of a choke price, but will simply assume that the commodity is non-essential. Assumption:Non-essential,static, continuous demand. Market demand in each time will be a continuous function of price at that time and will be independent of price at other times. A finite choke price will exist at each time.

3.1.1. Existence of competitive equilibrium The first question is whether a competitive equilibrium exists at all. Under our assumptions that cost functions are convex and that a choke price exists, we can establish existence of a competitive equilibrium. We start with markets for which all cost functions are strictly convex. With strict convexity, each price trajectory leads to a unique optimal extraction path for each deposit. This extraction path is a continuous function of the price trajectory. For this situation we can use the Brouwer fixed-point theorem to establish the existence of a competitive equilibrium. A fixed point of a function f is a point x such that x = f(x). The simplest fixed point theorem, due to Brouwer, is applicable to functions which map an m dimensional real number, denoted by x , back to m-dimensional real numbers. In particular, if X is a subset of the space of m-dimensional real numbers, Rm,the

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Brouwer fixed point theorem provides conditions under which one can assure that a fixed point exists for a function which maps X into itself 29. Brouwer Fixed Point Theorem. If X is a compact convex subset of Rm and f is a continuous function mapping X into X, then there exists a jixed point of$

To establish existence of a competitive equilibrium, we will define f to be a mapping from market quantity trajectories back to market quantity trajectories. A market quantity trajectory is an m-dimensional vector, with m corresponding to the number of time periods before the time horizon. Let X be the set of market quantity trajectories such that 0 < Q, 6 SA for each t , limiting the possible market clearing quantity trajectories to a set for which market quantity in any time period is no greater than the aggregate total resource base SA. Then X is a compact convex subset of Rm.For every market quantity trajectory inX, the inverse demand functions, P,(Q,, t), as defined in eq. (44), map that quantity trajectory to a unique trajectory of prices. For every price trajectory, there is a unique optimal extraction trajectory for each deposit (under the strict convexity assumption). Those individual extraction trajectories define a trajectory of market supply, Qt, as indicated by eq. (42), thus completing the mapping. The physical constraints facing each firm assure that the trajectory of market supply is a member of set X. The demand function is a continuous downward-sloping curve, and thus the inverse demand function is a continuous function; the mapping from the market quantity trajectory to the price trajectory is a continuous function. Strict convexity of cost functions implies that the mapping from the price trajectory back to the market supply trajectory is also a continuous function. Thus the mapping from the market quantity trajectory to the price trajectory back to a market quantity trajectory is a continuous mapping from set X into set X. All of the premises of the Brouwer fixed point theorem are met. Thus its conclusion holds: there exists a fixed point of the mapping we have constructed. That fixed point is a market demand quantity trajectory which leads to a market price trajectory, which in turn leads back to the same market quantity trajectory. Alternatively, it can be envisioned as a price trajectory which leads to a market supply and a market demand trajectory which are identical to one another. A competitive equilibrium exists. The role of the choke price should be noted in particular. With finite choke prices, it is possible to define a price trajectory for any market quantity trajectory inX, since for each possible market supply trajectory, the inverse demand functions imply that 0 < P, < P: for each t. If choke prices do not exist, then price

A discussion of these fixed-point concepts as well as the basic mathematical concepts embedded in the fixed-point theorems appears in chapter 1 by Green and Heller in the Handbook of Mathematical Economics.

29


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trajectories may not exist for some market quantity trajectories in X and thus the mapping needed for the Brouwer fixed point theorem cannot be defined. To illustrate possible non-existence of a competitive equilibrium, assume that the commodity were essential and that market demand always exceeded the quantity QMfor all finite prices until the time horizon of T. Then cumulative market , no competitive demand must exceed Q Mfor~ all finite prices. If SA < Q ~ T then equilibrium will exist. Prices would be driven to infinity and markets would still not clear. We now turn to markets for which cost functions for some deposits are weakly, but not strictly, convex. For example, Hotelling costs are in this class. In this situation market supply for a given price trajectory is not unique. Rather a range of extraction rates may be consistent with profit maximizing for each firm. Thus we can define only a correspondence - a set-valued mapping - from the price trajectory to the market supply trajectory. For our analysis we will follow the same approach as above, using inverse demand functions to provide a mapping from the same set X of possible market quantity trajectories. Optimizing choices of firms will define a correspondence back to a set of market quantity trajectories. The existence of a fixed point will be established. The fixed point will describe a trajectory of market clearing prices and resulting trajectory of market demands. This demand trajectory will equal one of the (possibly many) optimal supply trajectories for the market clearing price trajectory. The Kakutani fixed point theorem provides the necessary mathematical tool to establish the existence of a competitive equilibrium under the weak convexity assumption 30: Kakutani Fixed Point Theorem. Let X be a compact convex subset of Rm,and let y be a closed correspondencefrom Xinto subsets ofX. If y(x) is a convex set for everyx E X , then there is a $?xed point.

To establish existence of a competitive equilibrium, again let X be the set of market quantity trajectories such that 0 < Q, < SA for each t. X is a compact convex subset of Rm. For every market quantity trajectory in X , the inverse demand functions P,(Q,,t), as defined in eq. (44), map to a unique trajectory of prices. Optimizing responses of firms to the price trajectory complete the mapping back to market quantities. The physical constraints facing the firm assure that all trajectories of market supply belong to set X. This statement is quoted directly from Green and Heller (chapter 1of the Handbook ofMathematical Economics, p. 51). A correspondence y is closed if and only if its graph is a closed set. The Green and Heller chapter also provides a discussion of upper hemicontinuity of a correspondence. Essentially, a correspondence y(a) is upper hemicontinuous if it does not blow up discontinuously in any small neighborhood of any point a.

30

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The set of optimal extraction trajectories for each deposit must be convex. To see this, consider a convex combination of two optimal trajectories, with the first trajectory given a weight of P and the second given a weight of 1 - P, where 0 < ,O < 1. The convex combination would remain feasible since it would have no more cumulative extraction than would the maximum of the two optimal trajectories. The present value of the revenue from the convex combination would be a weighted average of the present values of the two revenues, with weights corresponding to P and 1- P. The present value of the costs would be no greater than the weighted average of the two optimal present values of costs (with weights of p and 1- p), under the assumption that the cost function is convex. Therefore the present value of profit from the convex combination could be no smaller than the weighted average of present values of profits for the two optimal trajectories. But if the two trajectories are optimal, they must give the same present value of profit and no feasible trajectory could give strictly greater present value of profits. Thus the convex combination must give identical present value of profits as either of these two optimal trajectories: the set of individual optimal trajectories is convex. The market demand is a summation of individual demands and thus the set of market supply trajectories is the set summation of optimal supply trajectories from individual firms. Because the set summation of convex sets is itself a convex set, the set of market supply quantity trajectories must be convex for every price trajectory and thus for every initial market demand quantity trajectory. We need only to show that the correspondence so constructed is closed. However, every upper hemi-continuous mapping must be closed, so we need only show that the mapping is upper hemi-continuous. Finally, to establish the upper hemicontinuity of the correspondence we must invoke the theorem of the maximum 31 Theorem of the Maximum. Let f(x, a) be the objective function of the constrained maximizationproblem: Maximize f(x, a) such that x is in G(a).Assume thatf(x, a) is a continuous function with a compact range and that the constraint set G(a) is a nonempty, compact-valued continuous correspondence of a. Then x(a) is an upperhemicontinuous correspondence.

For our problem, the constraint set for each firm is fixed, nonempty, and compact. The objective function is continuous both in prices and in extraction trajectories. The market demand function is a continuous downward-sloping curve, and thus the inverse demand function is a continuous function of market demand. Therefore the objective function is continuous in the market quantity trajectory as well. For each firm, the feasible set of extraction quantities is a compact set. Thus the set of optimal extraction trajectories must be a compact set for any given price trajectory. The set of market supply trajectories is the set summation of individual firm extraction See, for example, Varian (1992) for more discussion. The statement given here is a restatement of the theorem as cited by Varian.

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trajectories. Compactness of the individual sets implies compactness of the set summation. Hence the conditions of the theory of the maximum are met and thus the correspondence we have defined is upper hemicontinuous and hence closed. All premises of the Kakutani fixed point theorem are met. Thus its conclusion holds: there exists a fixed point of the mapping we have constructed. Thus a competitive equilibrium exists even with weak convexity of the cost functions. Given the existence of an equilibrium, we can now turn to characteristics of the price and quantity trajectories in competitive equilibrium. The nature of these trajectories will depend on several factors: The direction and rate of change of the demand function over time; The rate of technological change in resource extraction; and The nature of the cost function. These relationships will be examined in what follows. We start with the classical Hotelling cost assumption, progress through non-Hotelling models without stock effects and end with models which include stock effects. 3.1.2. Hotelling cost models For this section we assume that the Hotelling cost assumption is satisfied. There may be many deposits, each characterized by different costs and initial stocks. Competitive equilibrium price and quantity trajectories can be solved comparatively simply under Hotelling assumptions. By eq. (21), extraction can be positive for resource deposit i only during that time interval in which price is growing along a Hotelling path: pt = ci + X~ ert. (46) Here c' represents the marginal cost for resource i, and Xi the present value opportunity cost associated with resource stock i. The opportunity cost Xi is equal to the maximum (over time) of the present value of PI - c'. Whenever price is below ci + ~ ' e " ,there would be no extraction from the ith deposit. If A' > 0, then deposit i must ultimately be totally depleted. We can explore properties of competitive equilibrium, assuming that all firms satisfy the Hotelling cost assumption. We will assume that any time horizon is far enough in the future that extraction ceases because of resource depletion, not because of a time horizon. We start first with the simplest case: Hotelling cost models with no technological progress. The demand function, however, will be allowed to depend on time. Once results are presented, we will examine the differences in results if there is technological progress. 3.1.2.1. Hotelling cost models with no technological change

We assume that there is no technical progress so that extraction costs for any given deposit are independent of time. Demand functions may be time varying.

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Several results will emerge from the analysis. (1) Whenever demand is positive, price will always be growing and present value of price always declining. (2) If the demand function is time invariant or shrinking over time, then market supply and demand will decline over time. (3) If several resource deposits have different costs, then resources will be extracted strictly in order of increasing cost, except that at the transition time between two deposits both could be extracted simultaneously. (4) Higher cost resources will have lower opportunity costs. (5) Each resource with an extraction cost below the maximum market price will ultimately be totally depleted. (6) Once started, extraction from a deposit will not stop until it is totally depleted, unless there is sufficient stock of the resource for it to be a "backstop technology". We will now demonstrate these propositions. Whenever demand is positive, price will always be growing and present value of price always declining. By eq. (46), for extraction to occur from deposit i, price must be changing along the following path where A' is strictly positive for any resource which will ultimately be totally depleted:

Along this path, price is growing but the present value of price, Pte-", is declining. If price were declining or growing so rapidly that P,e-" were increasing, the equation above could not hold for any deposit and market supply would equal zero. That would not be a competitive equilibrium if there were positive demand. If the demand function is time invariant or shrinking over time, then market supply and demand will decline over time because price must always be rising. However, if the demand function is increasing rapidly enough, then market clearing quantities can grow over time. For example, if, for some time, the inverse demand function increases at the interest rate, so that P(Qt, t) = P(Q,)ert for a time interval, then Pt ecrt declining implies that market clearing supply and demand must be growing. The order of competitive extraction will be strictly from low to high cost. To demonstrate, assume the converse, that deposit i is more costly than deposit j: c' > c', but that some quantity of resource i is extracted before some quantity of depositj is extracted: Ef > 0 and E; > 0 for two times t and T , with T > t . By eq. (46) both of the following inequalities must hold:

The inequalities can be rewritten as follows:

By these inequalities, X J - Xi > 0, and thus these inequalities also imply that e" 2 err, a contradiction, because r > t and r is positive. It is thus established that


825

in a competitive equilibrium with time-invariant Hotelling costs, deposits must be extracted strictly in order of cost, with low-cost deposits used up before higher-cost deposits are initiated. At the moment of transition between two deposits, both would typically be extracted s i m ~ l t a n e o u s l y Therefore ~~. at such times of transition, eq. (46) must hold for both resources. If T is the transition time from the jth to the ith deposit, then:

Equation (47) shows that higher-cost deposits will have lower opportunity costs. In the Hotelling case competitive equilibrium, price exceeds the unit cost of the deposit being extracted by an amount equal to the opportunity cost of that resource. Opportunity cost increases at the rate of interest. When the next resource is being extracted, its opportunity cost becomes the relevant one for determining price and the price increases based on growth of that lower opportunity cost. Ultimately, all deposits will be fully depleted if their costs are strictly below the maximum value that the market price reaches over time, P M .If a deposit were not fully extracted, then its opportunity cost would be zero. But if firm i's opportunity cost were zero and p M > ci, it would extract its entire stock. p M must be at least as high as the maximum value of the choke price at the time of final shutdown or afterwards. Otherwise there would be a positive demand for the resource. Therefore, all deposits whose costs are below any value of the choke price at or after final shutdown will ultimately be fully depleted. Since (1) resources will be extracted strictly in order of increasing cost, and (2) a resource will ultimately be fully depleted if price ever exceeds its cost, then once started, extraction from a deposit will not stop until it is totally depleted. The exception is if the resource is the last being extracted, market price at maximum just equals its cost, and its stock is sufficiently large to satisfy all demand for all time that choke price remains above its extraction cost. If this condition holds, then the resource satisfies all characteristics of a "backstop technology". Market quantity can either increase or decrease over time, depending upon changes in the demand function. For demand functions that do not grow rapidly, market clearing quantities will decline over time. However, for rapidly growing demand functions, quantities can grow. Based on these characteristics, in what follows we develop equations to allow explicit calculation of market clearing prices and quantities for resources with Hotelling costs. The statement assumes that the firms producing resources of a given cost d o not have exactly enough stock left during the last period of production from that resource grade to meet total market demand precisely. If they did, then there would be a small range of possible price variation at that time. The shorter the time intervals in the model, the smaller the range of possible variation. In the limit of a continuous-time model, there would be no possibilities for price variation at the time of transition.

32

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J.L. Sweeney

At the time of transition from the jth to the ith deposit, all deposits with cost lower than cj must be depleted, while at the end of the preceding time some of the jth deposit will remain. Cumulative demand to time T must be at least as great as the total initial stock of resources having cost j or smaller, but cumulative demand up to time T - 1must be smaller than the total initial stock of resources having cost smaller than or equal to cJ:

At the final time, the right-hand inequality of (48) may be an inequality or a strict equality, depending upon whether the maximum price ever obtained is equal to or greater than the unit cost of the most expensive resource extracted:

Here PM denotes the maximum value reached by PI over all time. The competitive equilibrium price path can be determined uniquely by eqs. (46)(49). If P I is known, eq. (46) determines price until the lowest-cost deposit is totally depleted and determines opportunity cost for that deposit. Once the deposit is depleted, eq. (47) determines opportunity cost for the next-lowest-cost deposit. Inequality (48) determines the transition timing. Equation (46) determines price until the next transition, and so on. The final time of positive extraction is determined as the last time before price equals or exceeds the choke price (unless extraction occurs up to a final time horizon). Finally, eq. (49) must also hold in equilibrium. Unless choke price is declining over time, p M would typically equal choke price at final shutdown of extraction. With a discrete set of extraction costs (as might be typical in a quantitative model), the right-hand side of eq. (49) is a step function, with cumulative extraction increasing in steps as PM increases. The right-hand side will depend on initial price P I , to the extent that P I influences time of final shutdown and choke price depends on final shutdown time. The left-hand side of this equation represents cumulative demand until final shutdown and is a decreasing, continuous function of P I . If P I is too high, cumulative demand is reduced, and resources for whichci < PMwill remain after all extraction ceases. If P I is too low, the cumulative demand will exceed the total stock of resources with costs no greater than PM. Neither case would be a competitive equilibrium. A unique P I exists which allows eq. (49) to be satisfied.


Fig. 16. Determination of the initial price: Hotelling costs.

Determination of P I through eq. (49) is diagrammed in Figure 16 for a time invariant demand function. Cumulative demand is a decreasing function of P I . With time-invariant demand, cumulative demand is zero for P I = P M because p M just equals the choke price. Cumulative supply is an increasing step function of pM.This diagram illustrates choke price determining which resources will be depleted and thus determining the cumulative supply. Cumulative supply determines cumulative demand, which in turn determines P I .

3.1.2.2. Hotelling cost models with technologicalprogress With technological progress in resource extraction, costs decline over time. In this case each of the equations (46)-(49) must continue to hold, but with each ci declining over time. Resources may not be extracted strictly in order of increasing costs. If the low costs decline rapidly enough relative to the high-cost resources, then competitive firms could extract low-cost resources after higher-cost deposits. In addition, equilibrium prices need not necessarily grow. By eq. (46), if cishrinks more than A' ert grows,,then price will decline over time. For example, assume that each cost function decreases at the same exponential rate. In that case, low-cost resources will still be extracted before high-cost resources. Higher-cost resources will still have lower opportunity costs. Right after transition from a lower-cost to a higher-cost resource the price growth rate must decline and could become negative. While that resource is being extracted, the absolute growth of the opportunity cost increases and the absolute decline of unit cost will become smaller. Thus price could again begin growing after some time. The process could then repeat as progressively poorer grades of resources are extracted. With technological progress, equilibrium price may either increase or decrease over time and could alternate between periods of price growth and periods of price decline. Market clearing quantities could similarly alternate between growth and decline.

J.L. Sweeney

.I1.3. Non-Hotelling models without stock effects We now turn to more complex models in which marginal extraction costs from individual deposits are increasing functions of extraction rate, but remain independent of remaining stock. In competitive equilibrium of such a model, the quantity supplied for each resource as a function of the price trajectory is determined by eqs. (15) and (16). Market demand as a function of price is determined by the demand function and eq. (43) links the market together, equating market supply to market demand. Characteristics of the equilibrium will depend upon properties of the cost functions and of the demand function. We will first explore models in which all cost functions are time invariant but in which the demand function may vary over time. We will then relax the assumption of time-invariant demand functions and admit technical progress. We assume now that there is no technical progress so that extraction costs for any given deposit are independent of time. Several results will emerge from the analysis. (1) If the inverse demand function is time invariant or growing, equilibrium price will always be growing. If the present value of the inverse demand function is never growing, then the present value of equilibrium price will always be declining. (2) If the inverse demand function is time invariant or declining over time, then market supply and demand will decline over time. If the present value of the inverse demand function is growing, then market supply and demand will increase over time. (3) If several deposits have different costs but identical initial stocks, these deposits will generally be extracted in order of increasing cost, but typically there will be deposits of several different costs being extracted simultaneously. (4) Higher-cost deposits will have lower opportunity costs for initial stock fixed and larger deposits will have lower opportunity costs for cost functions fixed. (5) Each resource will ultimately be totally depleted if the market price remains above its minimum marginal extraction cost for long enough. These propositions are far more limited than those obtained for Hotelling cost functions. Thus insights from Hotelling models cannot necessarily be generalized to non-Hotelling models. We will demonstrate these propositions in turn. The time pattern of increases or decrease in the market clearing price trajectories and quantity trajectories will depend upon the rate at which the inverse demand function shifts. We will identify three ranges: (a) P(Qt,t) declining over time, (b) P(Qt,t) increasing over time but P(Q,,t)e-" decreasing over time, and (c) P(Qt,t)ePrt increasing over time. These three ranges lead to the two sets of propositions above about price changes and quantity changes. In the middle range we can place upper and lower bounds on price changes but no bounds on quantity changes. In the upper range we can put lower bounds on price and quantity changes while in the lower range we can put upper bounds on both rates of change.

Ch. 17: Economic Theory of Depletable Resources - Infroducfion

829

Table 2 Time patterns of market clearing price and quantity trajectories for three ranges of change of the inverse demand function Rate of change: Inverse demand function Declining Rate of change: Market clearing prices

Present value declining

Rate of change: Market clearing quantities

Declining

Growing, Present Present value growing value declining Increasing, Present value declining Indeterminate

Increasing

Growing

If the inverse demand function is time invariant or growing, equilibrium price will always be growing. By eq. (15), if the equilibrium price were constant or declining, extraction rate from each firm would decline over time and the market supply would decline. Declining supply (and hence demand) would imply increasing prices, a contradiction. If the present value of the inverse demand function is never growing, then the present value of equilibrium price will always be declining. By eq. (15), if Pte-" were constant or increasing from one time period to the next, extraction would be increasing for each deposit and thus market supply would be growing over time. Growing market supply (and hence market demand) implies that Pte-" would be declining over time, a contradiction. If the inverse demand function is time invariant or declining over time, then market supply and demand will decline over time. If quantities were increasing or constant, then prices would be declining or constant. But by eq. (15), declining or constant prices imply declining extraction rates from all deposits and hence declining market supply, a contradiction. If the present value of the inverse demand function grows, then market supply and demand will increase over time. If quantities were decreasing, the present value of price would be increasing. But by eq. (15), increasing present value of prices implies increasing extraction rates from all deposits and hence increasing market supply, a contradiction. In summary, unless demand functions are shrinking over time, prices must rise until the choke price is reached. The rate of price growth will depend upon movements of the demand function, characteristics of individual cost functions, the interest rate, and the sizes of the various deposits. The overall characteristics for the three ranges of inverse demand function change are displayed in Table 2. Assume that there were two deposits in a market and that one had a lower marginal cost than the other for each rate of extraction. The first will be referred to as the "low-cost" deposit and the second as the "high-cost" deposit. We assume that

830

J.L. Sweeney

they are both ultimately totally extracted. In market clearing, if both initial stocks are the same size, then the high-cost deposit will have a lower opportunity cost than will the low-cost deposit. (If they were ultimately not totally depleted, then they would have zero opportunity costs.) To see this, assume that the opportunity cost of the low-cost deposit were at least as low as that of the high-cost deposit. Then by eq. (15), the low-cost deposit would have a higher extraction rate at all times33.But because both have the same initial stock, this would be impossible. If two deposits have the same marginal cost function, but different initial stocks, the larger deposit will have a lower opportunity cost than the smaller. If the reverse were true, then by eq. (15), the smaller deposit would have higher extraction over all time, which again would be physically impossible, unless the deposits were ultimately not totally depleted. Deposits will generally be extracted in order of increasing cost, but typically there will be deposits of several different costs being extracted simultaneously,even though they may each have different cost functions. This pattern corresponds far more closely to that found in reality than does the pattern forced by Hotelling cost functions, in that many different resource grades could be extracted simultaneously under this model. More precisely, two propositions can be established to formalize the sense in which deposits are generally extracted in order of increasing cost. Extraction from the lower-cost deposit must either be initiated first, terminated first, or both. When the lower-cost deposit reaches its peak extraction rate, the extraction rate of the higher-cost deposit will still be increasing. Let i represent the high-cost deposit and j the low-cost deposit. Then X j > Xi. Assume that extraction from deposit i is positive and extraction from depositj is still zero at time 7. Then, because both deposits face the same price, eq. (15) implies:

where both marginal costs are evaluated at zero extraction rate. Because XI > A', the growth over time of the right-hand side of the above inequality is greater than that of the left-hand side. Thus the inequality must remain valid for all future time. Consider that time at which the extraction rate of deposit j (the low-cost deposit) just declines to zero. Then this inequality implies that the extraction rate of the high-cost resource must still be positive, in fact, must be higher than it was when extraction was first initiated for the low-cost resource. Hence if the high-cost extraction is initiated before the low-cost extraction, then extraction must stop for the low-cost resource first. We can now demonstrate that when the lower-cost deposit reaches its peak extraction rate, the extraction rate of the higher-cost deposit will still be increasing. 33

It should be remembered that both resources face the same price.

Ch. 17: Economic Theoly of Depletable Resources - Introduction

831

If both are being extracted simultaneously, then the following equation must hold, where the marginal costs are now evaluated at the positive extraction rates:

When the extraction rate from deposit j just reaches its maximum, extraction rate remains constant from that period to the next. Thus the marginal extraction cost of resource j just remains constant. However the opportunity costs continue to grow, with XJ ert increasing by more than does Xi err (since X i > Xi). Thus the marginal extraction cost of resource i must continue to increase from one time period to the next for the equation above to hold. Therefore the ith extraction rate must still be increasing; the extraction rate from the ith resource will not yet be at its peak 34. For models assuming Hotelling costs, we concluded that each deposit will ultimately be totally depleted if the market price ever gets above its marginal extraction cost. That conclusion is not valid for non-Hotelling models. We can only conclude that each resource will ultimately be totally depleted if the market price remains above its minimum marginal extraction cost for long enough. If it were not totally depleted, then the opportunity cost would be zero and extraction rate would be positive as long as market price exceeded the minimum marginal extraction cost. With enough time the deposit would be totally depleted. Once technical progress is introduced, fewer results can be established. In particular, if extraction costs decline over time, then prices tend to increase less rapidly or may decrease even though they would have increased absent technical progress. In Table 2, all results predicting declines in price or present value of price or those predicting growth in quantities can still be established. Those predicting increases in price or present value of price or those predicting declines in quantities cannot. Other results must be weakened or eliminated as well. Since models with Hotelling costs are extreme limiting cases of this class of models, the wide range of possibilities for Hotelling solutions implies an even wider range for these models. Additional characteristics of the competitive equilibrium, either with or without technical progress, are dependent upon the specific demand function and cost functions. Typically numerical simulation is required to solve such models. The equations presented within this chapter provide a complete basis for such numerical simulations, once market demand functions, costs functions, and initial stocks are specified. This discussion assumes that time intervals are so small that at the maximum extraction rate there is virtually no change in extraction rate from one time to the next. For larger time intervals, the more precise statement would be: if the low-cost deposit increases in extraction rate from one time period to the next, then the higher-cost deposit must also increase in extraction rates between these two time periods.

34

J. L. Sweeney

3.1.4. Models with stock effects A more complex case is one in which marginal extraction cost from any particular deposit is an increasing function of the extraction rate and a decreasing function of the remaining stock. In competitive equilibrium of such a model, the quantity supplied for each resource as a function of the price trajectory is determined by eqs. (24)-(26). Market demand as a function of price is determined by the demand function, and eq. (43) links the market together, equating market supply to market demand. We assume now that there is no technical progress so that extraction costs for any given deposit are independent of time, although dependent on remaining stock. Unless otherwise indicated, we will assume that the time horizon is so far in the future that its existence has no significant impacts on the extraction patterns. In addition, we will assume that total cost and marginal cost are decreasing functions of the amount of the stock remaining. A few results will emerge from the analysis: If the inverse demand function is time invariant or growing, equilibrium price will always be growing except when market supply and demand are zero 35. A corollary follows: If the inverse demand function is time invariant, market supply and demand will decline over time. Under the further assumption that - aC/aS is convex in E, if the inverse demand function is time invariant or declining over time, market supply and demand will decline over time. Note that these propositions are far more limited than those obtained for models without stock effects. Thus some of the conclusions based upon models without stock effects cannot be generalized to models with stock effects. We will demonstrate the propositions in turn. If the inverse demand function is time invariant or growing, equilibrium price will always be growing (except when market supply and demand are zero) if the time horizon is so far in the future that its existence has no significant impacts on the extraction patterns. There exists some time r after w h i ~ h 3equilibrium ~ price will not be lower than PT, since the system must at some time reach a choke price, which is itself constant or growing. Equations (24)-(26) imply that if some 7 exists after which prices will not be lower than P,, then P,-, < P,. To demonstrate, assume that P,-1 2 P,. As a consequence, market supply and demand must be non-decreasing from time r - 1 to r and thus so must be output from some deposit, say deposit i. By eq. (24), Here it is important that we assumed that the time horizon is so far in the future that its existence has no significant impacts on the extraction patterns. As the system approaches a time horizon, we have seen that extraction can rise over time with constant prices. For the competitive equilibrium, that implies that prices can be falling as the horizon is approached. 36 Price could decline as the time horizon is approached. However that time is assumed to be so far in the future as to be irrelevant for the current choices. 35

Ch. 17: Econoiivic Theory of Depletable Resources - Introduction

833

non-decreasing output with non-increasing price occurs only if 8, < &T-l. Hence @, must be below the &constant locus. Because future price will never be lower than P,, the &constant locus will not decline from its position at time T ; thus 8, will always stay below the $-constant locus and can never converge to a steady state. Rather opportunity cost must forever decrease and must become and stay negative, violating co~ndition(26). This contradiction implies that P,-I < P,. Hence it follows that price will never again be lower than P,-,. The same logic then shows that price will never again be lower than P r 4 , and so on. Thus price must always be rising if rnarket supply and demand are positive. From this conclusion it follows directly that if the inverse demand function is time invariant then market supply and demand will decline over time, since in this situation prices will always be increasing whenever demand is positive. Under the further assumption that - aC/aS is convex in E , if the inverse demand function is time invariant or declining over time, market supply and demand will decline over time. If market supply and demand were increasing or constant from time 7 - 1 to 7 then PTU1 2 P, and E',-, 6 E', for at least one deposit i . But we have shown in a previous section of this chapter that under these assumptions, whenever price is declining, extraction must also be declining for each individual deposit. This contradicts the supposition that market supply and demand were increasing or constant. The results change dramatically if time were approaching a final horizon. Then it would be possible for the inverse demand function to either shrink or grow over time, yet have competitive equilibrium prices decline and output increase over time. We have seen from the example illustrated in Figure 12 that for an individual deposit, it is possible for both price to decline and output to increase over time as the final horizon is reached. If all deposits were siinilar to that individual deposit, then this woluld be true for the overall market supply. One could easily construct an inverse demand function which was either growing or shrinking and which gave the quantity path of Figure 12 when the price path of Figure 12 occurred. 3.1.5. Models with new discoveries

In the work presented so far, locations of all resource deposits are known at the beginning of' time and firms can extract from these deposits at any time. However, one important feature of most depletable resource systems is the process of discovery of new deposits. Discovery implies that these deposits were not available for extraction in the time prior to discovery, in contrast to the assumption made so far. The assumption of exogenous discovery can be readily incorporated into the theory, althclugh endogenous discovery requires a careful discussion of uncertainty and information, a discussion beyond the scope of this chapter. Assume that the deposits will be discovered at various dates, denoted by T',. Then for each deposit we need only add the additional constraint that Ef = 0 for

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J.L. Sweeney

t < T',. If that constraint is added, the optimal extraction trajectory for each firm follows the same optimality conditions for all time after discovery. Under this model, discovery of additional deposits has no effect on optimal trajectories of previously discovered deposits, except to the extent such discoveries change current prices or expectations of future prices. And if all participants in the market have rational expectations about future discoveries, the actual event of a new discovery need have no significant impact on any prices and thus need have no effect on optimal extraction of any other deposits3'. Competitive equilibrium still would be characterized by supply and demand equality for all times. The properties of this competitive equilibrium can differ as a result of the addition of new resource deposits over time. Late discovery implies that more of the resource stock remains at any given time than would have been the case had the deposit been discovered earlier. Thus early year prices would be increased and extraction rates decreased and later year prices would be decreased and extraction rates increased if such discovery constraints were incorporated into the model. Therefore, even without technical progress, market clearing prices need not rise over time, except in Hotelling models. Prices could fall over a long period of time if new deposits were constantly being discovered. All deposits, once discovered, would be extracted at high rates initially and their extraction rates would decline over time. However, if sufficient numbers of new deposits were being discovered, this process could dominate the decline from existing deposits so that supply would be increasing over time, satisfying a growing demand. Empirically, these observations are important, in that we have observed depletable resource prices declining over significant periods of USA and world history as new deposits become available. This price decline does not suggest the invalidity of depletable resource theory, since once new discoveries are incorporated into the competitive models, we can generate patterns of declining prices along with decreasing extraction from existing deposits and growing total market quantities. But such incorporation of new discoveries does make empirical research in depletable resource theory even more challenging. We turn now from competitive market models to examine an alternative market structure.

3.2. Depletable resource monopoly In the analysis so far, we have maintained the assumption that all firms and consumers are price takers in markets for commodities extracted from Note that depletable resource models based upon an aggregate cost function for all existing resources, rather than the disaggregated concept used here, could well lead implicitly to predictions of changes in the extraction from existing resources, based upon the discovery of new deposits.

"

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835

depletable resource stocks. However, as discussed more fully in the chapters by Teece et al. (24) and Karp and Newbely (19), many commodities extracted from natural resources are sold in non-perfectly competitive markets. The diamond cartel, the Organization of Petroleum Exporting Countries (OPEC), and the copper cartel are examples of organizations that have market power to influence prices at which their outputs are sold. In this section we examine models which assume the opposite extreme from perfectly coimpetitive markets, models of markets dominated by a single extractor of the depletable resource. Such monopolies, taking into account the impact of their output choices on market clearing prices, can generally be expected to operate differently firom perfectly competitive firms. More complex structures are covered in the two chapters of this Handbook cited above. We will maintain the monopoly assumption throughout this section, unless otherwise indicated. Assumption: Monopoly. A single firm controls all deposits of the depletable resource. That firm chooses extraction patterns so as to maximize the discounted present valu'e of its profit. There are many consumers of the commodity, all of which are price takers.

We will assume that a monopoly faces the same conditions as do competitive firms, except that it owns all of deposits, incurs all costs, and collects all revenues from extraction of the resource. The monopoly controls N resource deposits, numbered from 1 to N. As in a competitive model, if markets clear, price is determined by the inverse demand function from eq. (44). Revenue obtained from selling Ef units from resource deposit i depends upon the commodity price, which in turn depends on the total quantity sold from all deposits. Total monopoly revenue will be denoted as R,(E:, E:, . . . ,E f ) :

Optimization of each deposit must account for the impact of extraction from that individual deposit on prices facing all extraction. The cost facing the monopolist is the sum of costs over all resource deposits. Underlying cost functions could be as simple as Hotelling cost functions or could be more connplicated, with each marginal cost depending on the extraction rate and remaining stock in that deposit. We will go directly to the more general cost functions, recognizing that the simpler models are all special cases of the more general cost functions.

J.L. Sweeney

The problem facing the monopoly is then:

Max II =

[R~(E:,E:, . . . , i

EY) - c;(E~, S:-I)]

e+"'

t=l

Under: s ~ = s ~ - , - E ; ,

Ef>O,

(51)

$20.

3.2.1. Necessary conditions for optimality

This monopoly optimization can be solved using the same methods applied above. The Lagrangian can be written as

-

'1

[sf- S:-, + Ef] 4: e-") + pi S',

.

First-order necessary conditions require that at the optimal point, the Lagrangian must be a stationary point with respect to each Sf and Ef. Differentiating C with respect to each variable and combining equations yields

4:

= @f-, er

act +as:-1

for t < T,

Equation (50) can be differentiated to relate marginal revenue to market clearing price:

where R', is marginal revenue at time t , Qt is the market quantity of the resource, and &,(Qt)is the elasticity of demand, defined to be a positive number. Rlt is a function of Qt and depends on the shape of the inverse demand function.


3.2.2. Characterizing monopoly vs. competitive equilibrium solutions The conditions for monopoly optimality are very similar to the conditions describing the competitive equilibrium. Equations (52)-(55) are identical to eqs. (24)-(26) plus (42) and (44), which define optimal paths for competitive deposits, with one crucial exception. In eq. (52) marginal revenue appears in place of the price. Marginal revenue is itself simply price scaled down by a factor dependent on elasticity of demand. In a competitive industry each deposit is small enough that its extraction will not influence price significantly from the perspective of the individual deposit owner or manager. The same must be true if these deposits are organized monopolistically. Each deposit manager faces a price and a marginal revenue which he or she cannot influence significantly from the perspective of the individual deposit manager. But insignificant impacts at the deposit level can be important when applied to the entire enterprise. Therefore, the manager in a monopolistic industry must look to marginal revenue; while the owner or manager in a competitive industry must look to price. In both markets, optimality conditions for individual resource deposits can be solved separately, using but one variable to link the various commodity m~arginalrevenue for a monopoly and price for a competive firm. All differences in market clearing trajectories stem from the difference between marginal revenue and price. Equation (:55)shows that for any given demand function there is a mapping that relates price to marginal revenue. For "well-behaved" demand functions marginal revenue is a c no no tonically increasing function of price. In what follows we assume that monoto.nic relationship to hold. In addition, if a choke price exists, then at that choke price marginal revenue and price are equal, although for all other prices marginal revenue is strictly smaller than price. The monotonic relationship implies that once characteristics of the marginal revenue trajectory are determined, these characteristics can be translated to the price trajectory. In previous sections, we have analyzed characteristics of the price trajectory for a competitive equilibrium. For a monopoly, each of these characteristics become precisely the equivalent characteristics of the optimal marginal revenue trajectory. For given demand functions, the marginal revenue trajectory can be translated directly into a price trajectory. Thus the analysis of a competitive industry can be translated cc~mpletelyto analysis of monopoly solutions. We now turn to several examples of that principle.

This fact is perhaps important for decentralization of decisionmaking within a monopoly or a cartel. The central controller needs only to communicate one variable to managers of the deposits, the derivative Q,aPr/aQr,or equivalently, P I / E,. The central controller must motivate or cause the manager of each deposit to maximize its own profit, with relevant price adjusted downward by PI/ E,.

38

J. L. Sweeney

3.2.2.1. Hotelling cost models with no technology changes We again assume that the Hotelling cost assumption is satisfied. Deposits are characterized by different costs and initial stocks; extraction costs are independent of time. Any time horizon is far enough in the future that extraction ceases due to resource depletion and not to a time horizon. Inverse demand functions may be increasing, decreasing, or constant. Several results can be translated immediately from the competitive equilibrium analysis: (1) Whenever demand is positive, marginal revenue will always be growing and present value of marginal revenue always declining. (2) If the marginal revenue function is time invariant or shrinking over time, then market supply and demand will decline over time. (3) If several resource deposits have different costs, then resources will be extracted strictly in order of increasing cost, except that at the transition point between two deposits both could be extracted simultaneously. (4) Higher-cost resources will have lower opportunity costs. (5) Each resource with an extraction cost below the maximum marginal revenue will ultimately be totally depleted. (6) Once started, extraction from a deposit will not stop until it is totally depleted, unless there is sufficient stock of the resource for it to be a "backstop technology". We need not demonstrate these propositions because they are established in exactly the same manner as the parallel propositions for a competitive equilibrium. Characteristics of the optimal price trajectory can be ascertained from the marginal revenue trajectory for particular demand functions. As examples, we examine two demand functions: the constant-elasticity and the linear functions. 3.2.2.2. Hotelling cost models: constant-elasticity demand functions The constant-elasticity demand function has the form

QP = APFE

with

E

> 1,

(56)

whereA and E are positive constants. Elasticity of demand must exceed unity or the monopoly could obtain unlimited profit by selling a vanishingly small total output and no optimal would exist. Note that for the constant elasticity demand function no choke price exists. While the ith resource is being extracted the first-order necessary conditions for the monopoly solution become

Ch. 17: Economic Theory of Depletable Resources - In troduction

839

This equation can be rearranged to give the price equation applicable while the ith resource is being extracted:

Equation (57) can be compared with eq. (46) which shows the competitive price trajectory. The cost term on the right-hand side of eq. (57) is multiplied by a factor greater than unity: E/(E- 1). The second term is simply a new opportunity cost which increases at the interest rate, just like the second term on the right-hand side of eq. (46). The optimal price and quantity trajectories for a monopoly facing a constant elasticity denland function would be identical to equilibrium trajectories in an equivalent competitive market with all extraction costs scaled up by a factor of &I(&- 1). Equation (.57) can be used to illustrate the case, discussed by Stiglitz (1976), in which a monopoly extraction path is identical to that of an equivalent competitive industry. Stiglitz assumed a constant elasticity demand function with E > 1 and c' = 0 for all deposits. For such a monopoly, eq. (57) becomes

where ki is a positive constant selected so that cumulative demand equals the initial stock. For a competitive industry, eq. (46) becomes

where A' is a positive constant selected so that cumulative demand just equals initial stock. The two price trajectories must be identical. They both rise at the interest rate and they both begin at a level which just causes the resource to be totally depleted over all time. This specia.1 case, although not representative of many depletable resources, illustrates an important point. If there are sufficient incentives to assure ultimate total depletion of resources, a monopolist cannot manipulate market prices by altering ultimate cumulative extraction. The only option is to shift the time pattern of the given total extracted quantity. The monopolist can increase its profit only if there are intertemporal differences in the discounted present value of the 'wedge' between price: and marginal revenue. This 'wedge' will be formalized as a 'market imperfection Function' and discussed more fully in a later section of this chapter. In the constant-elasticity case, the 'wedge' between price and marginal revenue is equal to PtI&.With zero extraction cost, both price and marginal revenue rise

840

J.L. Sweeney

at the interest rate, as does this 'wedge'. Thus the present value of this 'wedge' is independent of time. There are no intertemporal differences to motivate the monopolist and thus the monopolist chooses an extraction path identical to that of a competitive industry. For positive extraction costs eq. (57) implies that the initial monopoly price will exceed the competitive equilibrium price. Monopoly price will rise less rapidly than the competitive price so that in later years the monopoly would have a larger stock remaining and would charge a price lower than would occur were the market perfectly competitive. If the initial monopoly price did not exceed the competitive equilibrium price, by eq. (57), the initial Xi in the competitive equilibrium would - I)] for the monopoly and the monopoly price would grow be larger than Xi[&/(& more slowly than the competitive equilibrium price. If the monopoly price starts lower and grows slower, it would always be below the competitive price and more of the resource would be extracted. However, in the competitve industry all would be extracted, so extracting more would be infeasible. This contradiction implies that the initial monopoly price will exceed the initial competitive equilibrium price. In this case, the monopoly would shift extraction from the present to the future, charging higher than competitive prices at early times and lower prices at later times. 3.2.2.3. Hotelling cost models: linear demand finctions The linear inverse demand function has the form

where B is a positive constant and PC is the choke price. Calculating marginal revenue gives the necessary condition for the price path while resource deposit i is being extracted:

Equation (60) can be compared with eqs. (46) and (57). In a monopoly with a linear cost function, the cost term on the right of eq. (60) is the average of actual cost and choke price. Since the only deposits which are extracted are those for which unit cost is smaller than the choke price, this average is larger than the actual unit cost. The second term is simply a new opportunity cost which increases at the interest rate. The optimal price and quantity trajectories for a monopoly facing a linear demand function are identical to the equilibrium trajectories in a competitive market with all extraction costs increased to the average of actual cost and choke price.


84 1

A similar analysis to that above shows that this monopoly will initially charge a price higher than the competitive equilibrium price and will thereby extract the resource more slowly than would be the case in competitive equilibrium. Prices will rise less rapidly for the monopoly. If the time horizon is long enough, extraction will cease when the choke price is reached. The monopoly facing a linear demand function will reach this choke price strictly later than would the competitive industry" and will extract the resource over a longer period. 3.2.2.4. Non-Hotelling models without stock effects

Here again, we can use all of the results obtained for competitive markets, translating price to marginal revenue. Several conclusions follow for models in which all cost functions are time invariant but in which the demand function may vary over time: (1) If the inverse demand function, and hence the marginal revenue function, is time invariant or growing, marginal revenue will always be growing. If the present value of the marginal revenue function is never growing, then the present value of marginal revenue will always be declining. (2) If the marginal revenue function is time invariant or declining over time, then market supply and demand will decline over time. If the present value of the marginal revenue function is growing, then market supply and demand will increase over time. (3) If several deposits have different costs but identical initial stocks, these deposits will generally be extracted in order of increasing cost, but typically there will be deposits of several different costs being extracted simultaneously. (4) Higher-cost deposits will have lower opportunity costs for initial stock fixed and larger deposits will have lower opportunity costs for cost functions fixed, unless they are ultimately not totally depleted. (5) Each resource will ultimately be totally depleted if market price remains above its minimum marginal extraction cost for long enough. 3.2.2.5. Non-1Liotelling models with stock effects

We again assume that extraction costs for any given deposit are independent of time and that the time horizon is so far in the future that its existence has no significant impacts on the extraction patterns. Total cost and marginal cost are assumed to be decreasing functions of the amount of the stock remaining. A few resul!ts will emerge immediately based on the parallel of the monopoly solution to the competitive equilibrium: If the marginal revenue function is time invariant or growing, marginal revenue will always be growing except when market This proposition can be provedby assuming the converse and examining the difference in opportunity costs backward, starting from the time which the choke price is reached.

39

J.L. Sweeney

842

supply and demand are zero40. Thus, if the marginal revenue function is time invariant, the monopoly supply and demand will decline over time. Under the assumption that - aC/aS is convex in E, if the marginal revenue function is time invariant or declining over time, monopoly supply and demand quantity will decline over time as well. 3.3. Comparative dynamics and intertemporal bias We saw above that the monopoly optimum and the competitive equilibrium solution were described by the same equations, with but one difference. In a competitive industry each deposit owner faces price derived from an inverse demand function, while in a monopolistic industry each deposit manager faces marginal revenue derived from a marginal revenue function. These differ by a timevarying 'wedge' equal to Q, aPt/aQt. We will refer to this 'wedge' as a 'market imperfection function' and denote it by g(Q,,t). Thus the market imperfection function for the monopoly problem is just: d Q t , t) = Qt-

apt aQt

< 0.

The market imperfection function depends on market conditions and may well vary in its magnitude and sign over time, but is the same for all deposits participating in the market. Here we analyze how properties of the market imperfection function translate to changes in extraction and price trajectories. Market imperfection functions are applicable to additional situations. Any postulated alteration in the demand function can be referred to as a 'market imperfection function'. For example, an excise tax on resource extraction in competitive markets reduces the inverse demand function by the amount of the tax. Regulations on use of the extracted commodity, failure to internalize externalities common to all the firms, expectations of the development of a backstop technology, or exogenous shifts in the extraction of a close substitute product: all could shift the inverse demand function. The shift may well vary over time but it is the same for all deposits. If the inverse demand function shifts from Pt(Qt) to P1,(Qt), the market imperfection function will equal the difference between these inverse demand functions:

Here it is important that we assumed that the time horizon is so far in the future that its existence has no significant impacts on the extraction patterns. As the system approaches a time horizon, we have seen that extraction can rise over time with constant prices. For the competitive equilibrium, that implies that prices can be falling as the horizon is approached.

40

Ch. 17: Econorn8;c Theory of Depletable Resources - Introduction

843

The market iimperfection function allows analysis of market quantity trajectories as if the inverse demand function shifts in a competitive market. Whenever there are no stock effects, properties of the market imperfection function -whether its sign is positive or negative and whether its present value grows or shrinks - are sufficient for determining whether the resource will be extracted more rapidly or more slowly as a result of the change. With market imperfection functions, the new market solution becomes

If g(Qt,t) is, identically zero, then eqs. (64)-(67) represent the unchanged competitive equilibrium. Analysis of changing conditions reduces to analysis of changing solutions to eqs.(64)-(67) as the function g(Qf,t) changes. In conducting our analysis we assume that there are no stock effects and that Pt(Qt) + g(Qf, t) is a decreasing function of Q,. We can then formally define the market imperfection function: Definition: Market irnpet$ectionfunction. If one market situation can be represented by eqs. (64)-.(67) with g(Qf, t) = 0 and another by the same equations but with g(Qf,t) f 0, then g(Qt, t) is referred to as a market imperfection function.

3.3.1. The impact of market impact functions

In important special cases we can analyze impacts of market imperfection functions on extraction trajectories. For situations in which all deposits will ultimately be fully depleted, if present value of the market imperfection function either (1)decreases below its initial level for all future time, (2) increases above its initial level for all future time, or (3) equals its initial level for all time, we can determine the direction of changes in the first period market rate of extraction, or more generally, in the extraction rate standardized for remaining resource stocks. If the initial extraction rate is increased, stock will decline more rapidly and at some later time less of the resource will be extracted. Therefore the absolute change in extraction

J.L. Sweeney

844

Table 3 Impacts of market imperfection function on initial extraction rates: positive values of market imperfection function Present value of market imperfection function over time

A x e d deposits ultimately fully depleted?

Yes

No

AQI > 0 AQo = 0 AQl< 0

AQI> 0 AQI > 0 Indeterminate

will be predicted only for the initial time4'. The dimtion of change will depend upon whether the market imperfection function is positive or negative. If some resource deposits are not ultimately fully depleted, then results will be available for constant or declining present value of the market imperfection function but not for increasing present value. For positive values of the market imperfection function, Table 3 summarizes impacts on the initial rate of extraction. For negative values, impacts on extraction would be opposite those indicated here. Proof of this result appears in the Appendix. Table 3 indicates that if the present value of the market imperfection function is positive initially and decreases below its initial level f o r all future time, then the initial extraction rate will increase as a result of the changed conditions, independently of whether all deposits are ultimately fully depleted. Results will be reversed for a negative market imperfection function. If the present value of the market imperfection function remains constant over time, then the entire extraction trajectory will be unchanged if all deposits are ultimately totally depleted but the initial extraction rate will increase if some deposits are not ultimately totally depleted. Finally, if the market imperfection function is positive and its present value decreases below its initial level for all future time, then the initial extraction rate would be decreased if all resources would ultimately be fully depleted but its sign would be indeterminate if some deposits wouM not ultimately be fully depleted. 3.3.2. Application: Intertemporal bias under monopoly The theory of market imperfection functions allows a generalization of the results obtained previously for intertemporal bias of monopolies. We previously have More precisely, the prediction is only for the first period when the remaining stock varies with the market imperfection function. However, as will be seen, when the discounted present value of the market imperfection function remains constant over time and the entire resource will be fully depleted, there is no initial impact on extraction. Thus the stock will be unchanged and there will never be an impact on extraction rates.

41

Ch. I7: Economic Theory of Depletable Resources - Introduction

845

shown that a monopoly (absent technical progress) facing either a linear or a constant-elasticity demand function would reduce supply and raise price relative to performance of a competitive industry with the same remaining stocks. These resu1l.s can be generalized using the theory of market imperfection functions. The market imperfection function for a monopoly is g(Q,, t) = Qt aP,laQ, < 0. For the constant-elasticity demand function in eq. (56), g(Q,, t) = -PtI&. If the present vallue of price were rationally expected to decline, present value of the market irn~perfectionfunction would always be smaller than its initial value. By Table 3, such a monopoly would extract its resources less rapidly than would a competitive industry. Similarly, if price were rationally expected to grow at the interest rate so that expected value of price were expected to remain constant, present value of the market imperfection function would remain constant over time. By Table 3, if all deposits would ultimately be fully depleted, such a monopoly would extract its resources at exactly the same rate as would a competitive industry. In a competitive market with Hotelling costs, present value of price will decline unless extraction is costless or extraction costs are expected to increase rapidly enough. Absent these two circumstances, the monopoly would always extract less rapidly than vuould a competitive industry. Similarly, for a non-Hotelling costs without stock ~effects,present value of price must decline unless the present-value inverse demand function were increasing or cost functions were increasing rapidly enough. Absent these circumstances, the monopoly facing a constant-elasticity demand function would extract more slowly and charge higher prices than would a competitive industry. For competitive markets with linear demand functions, the market imperfection function equals the difference between current price and the choke price: g(Q,, t ) = Pt(Qt) - pC, by eq. (59). The market imperfection function is negative and its magnitude is increasing with market quantity. Therefore, for time-invariant demand functions, unless Q, is increasing rapidly, the present value of the market imperfection function must be declining in absolute value. By Table 3, a monopoly would extract more slowly than would a competitive industry and would charge higher prices. I[f present value of the inverse demand function is growing over time, present value of the market imperfection function would be declining in absolute value whenever market quantity is stationary or declining. Again, the monopoly would reduce extraction rates and charge higher prices than would a competitive industry. In summary, monopolies typically can be expected to extract less rapidly and to charge higher prices, relative to stocks, than a competitive industry, although this need not be the case if demand functions are growing rapidly enough. Nor need it be the case for all shapes of demand functions. Market imperfection functions can be used in many cases to derive theoretical conditions which determine monopoly directions of intertemporal bias.

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3.3.3. Application: Expected future demand function changes Here we use the theory of market imperfection functions to examine market implicationsof a change in regulatory or economic conditions rationally expected to decrease demand functions in the future but to have no effect on current demand functions. For example, in the mid-1970s, USA efficiency standards were set for future vintages of automobiles. Those standards were expected to reduce demand functions for petroleum starting five to ten years after their passage but to have no effect on demand functions before that time. Under these assumptions the market imperfection function was zero during the mid-1970s. The expected future demand reduction implied that g(Ql, t ) < 0 for all t > T , where T is the date at which the standards would first become effective. Table 3 suggests that if ultimate full depletion were expected, the market response would be an initial increase in extraction and a reduction in initial price. Anticipation of future demand function changes would lead to market responses before the exogenous changes in fact occurred. After T , extraction could be increased or decreased, depending on the particular form of the shift in demand function. However, at some future times, extraction would be reduced compensating for the initial increase. However, if ultimate full depletion were not to be expected, the immediate changes could not be predicted directly from Table 3. Furthermore, Table 3 has not been proved to apply to situations in which stock effects are important.

4. In conclusion

This chapter has presented a deterministic theory of depletable resource economics, both for individual deposits and for market equilibrium including extraction from a group of deposits. For both situations we have examined a sequence of models, beginning from the most common Hotelling models, progressing through non-Hotelling models without stock effects, and finally ending with non-Hotelling models with stock effects. As we have gone through the sequence, results became scarcer and scarcer. Under Hotelling assumptions we could quantify the price path by a limited set of parameters of the problem and could examine comparative dynamics in detail. With non-Hotelling costs absent stock effects, we could characterize directions of price and/or quantity changes in the overall market and could derive general theorems describing the comparative dynamics. But once stock effects were introduced, even the direction of the impact of changing conditions on price and quantity could not be established in general. The problem became even more complex when the normal process of new deposit discovery was added to the models and results were still fewer.


847

Since results from the simpler models may not remain valid for more complex models, without further work we cannot be confident that insights from the simpler models will remain valid for the more complex. Serious empirical work, such as that discussed by Epple and Londregan in this volume (ch. 22), is necessary to specify appropriate cost functions, demand conditions, and market structures. More sophisticated theoretical models are needed to address the many phenomena ignored by the models discussed in this chapter. While much work has been completed and some of that work is described in subsequent chapters of this Handbook, much needed work remains. Our hope is that this Handbook will help to motivate renewed theoretical and empirical attention to issues of depletable resource economics. 5. Appendix: p~rool's

5.1. Marginal cost for a discrete time cost finction (eq. 10) As Et varies, iinstantaneous extraction rates, E(Y), must vary so that their sum remains equal to E,. Their variation leads to the change in cost:

We can change the order of integration for the second term under the integral above and switch the designation of the differentials dy and dB to rewrite the above equation as

Combining the: terms under one integral gives

) The derivative aCt/aE,would seem to depend on the resulting changes in ~ ( yand the impacts of' those changes on cost. However, because the cost function is the ) result of a minimization problem, it is not necessary to know how each ~ ( ychanges in response to changes in E,. First-order conditions for optimality within the time interval can be expressed as follows, where 9 is a constant, independent of time within the interval:

J.L. Sweeney

Inserting this relationship into the equation above gives:

where the functions on the right-hand side of the equation are all evaluated at y = t. Equation (10) is derived.

5.2. Intertemporal bias result In establishing the results of Table 3, we begin with an analysis of how the opportunity costs change in response to the change ing(Qt, t). The basic result can be stated as

Lemma 1. The maximum and minimum values (over time) of the market imperfection function place limits on changes in present value opport~initycost for the ith deposit: T

If maxg(Qt , t ) > 0 or

E': = So, then AXi

< max [g(Q,, t) e-"1

.

t =O

T

If ming(Qt , t )

< 0 or

E; = So, then AX' 2 min [g(Q,, t) e-"1 , t =O

where ~f and E' f represent extraction absent and with the market impe~ection function, respectively. The maxima and minima are defined over the time that deposit i is being extracted. If g(Q,, t) e-" reaches its maximum (or minimum) value at only one time, then AXi < max [g(Q,, t) e-"1 (or AXi > min [ g ( ~ ,t) , e-"1). Assume the converse of the first part of Lemma 1: for that deposit with the largest value of AX] (here denoted as deposit i), that either AXi > maxg(Q,, t) e-" or that AXi = maxg(Q,, t) ecrt > g(Qr, r ) ecrr for all other r # t and for which E'f > 0. If maxg(Qt, t) > 0 then AXi > 0 and Xi > 0: the deposit will ultimately be totally depleted. If maxg(Q,, t) 6 0, then by the premise of the Lemma, deposit i will be totally depleted. In either case, for deposit i, AE',2 0 at some time 7. Then at r , for all j: 0 A [P, g(Qr, 7) - Xi err] < A [ P + ~g(Qr , 7) - X j e rT ] .

1, then AQ, > 0; if g(Q,, t) eCr('-') = g(Q1, 1) for all t , then AQ, = 0; if g(Qt, t ) e-'('-') > g(Q1, 1) for all t > 1, then AQI < 0. Ifg(Q1, 1) > 0 (andsome deposits would not ultimately be fully depleted in the original situation, then if g(Qt, t)e-'(t-') < g(Q1, 1) for all t > 1, then AQ, > 0; if g-(Q,, t) e-'('-') = g(Ql, 1) for all t, then AQl 2 0. If g(Q1, 1) < 0, all the inequalities above are reversed. Assume thatg(Q1, 1) > 0. Assume first thatg(Q,, t ) ec'" = g(Ql, 1) for all t and that all deposit:^ ultimately are fully depleted in the original case. By Lemma 1, max [g(Ql.,t) e-l"]

< AX' < max [g(Qt, t) ePrt] for all i.

Thus max [g(Q,, t) e-"1 = AX' = max [ g ( ~ ,t) , e-'"1 = g(Q,, t) e-" for all t. Then for all i and all t: A {P,

+ g,(Q,, t) - A' e'")

=MI.

Therefore if AP,> 0, then AE; > 0, AQ, > 0, and AP, < 0, a contradiction. A similar contradiction is reached if it is postulated that MI < 0. Therefore AP, = 0, AEf = 0, and AQ, = 0 for all i and all t if all deposits would be fully depleted. If some deposits would not be fully depleted, then Axi

< mas [ g ( ~ tt)e-rt] ,

= g(Q1, 1).

Therefore AQ11 2 0 in this situation. Assume next that g(Q,, t) e-" < g(Ql, 1) for all t > 1. Then by Lemma 1, Axi

< g(Ql, 1) for all i,

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J.L. Sweeney

independent of whether all deposits would be fully depleted. Assume the converse of the theorem, that AQ1 < 0. Then AP1 2 0. These results imply that

+

A [PI g(Ql, 1) - A'] > 0 for all i, thus that A,!?,> 0 for all i, and that AQl > 0, a contradiction. Thus AQl > 0. Assume finally that g(Qt, t ) e-" > g(Ql, 1 ) for all t > 1. Then by Lemma 1, Axi > g(Ql, 1) for all i if all deposits would be fully depleted. Assume the converse, that AQ, 2 0. Then aP16 0. These results imply that

A [PI + g(Ql, 1 ) - A'] < 0 for all i and thus that AE; < 0 for all i, and that AQ1 < 0, a contradiction. Thus AQ1 < 0 if all deposits would be fully depleted in the initial case. A similar demonstration can be used when g(Ql, 1) < 0. References Arrow, Kenneth J., and Michael D. Intriligator, 1981, Handbook of Mathematical Economics (NorthHolland, Amsterdam). Barnett, H., and C. Morse, 1963, Scarcity and Growth: The Economics of Natural Resource Availability (Johns Hopkins Press, Baltimore, MD). Berg, Claude, 1964, Topological Spaces (The Macmillan Company, New York). Brennan, M., and E.S. Schwartz, 1985, "Evaluating Natural Resource Investments", Journal of Business 58 no. 2, 135-157. Burness, H.S., 1976, "On the Taxation of Nonreplenishable Natural Resources", Journal of Environmental Economics and Management 3,289-31 1. Burness, H.S., 1978, "Price Uncertainty and the Exhaustive Firm", Journal of Environmental Economics and Management 5,128-149. Cairns, R.D., 1990, "Geological Influences, Metal Prices and Rationality", Resources and Energy 12, 143-171. Caputo, M.R., 1990, "A Qualitative Characterization of the Competitive Nonrenewable Resource Extracting Firm", Journal of Environmental Economics and Management 18,206-226. Caputo, M.R., 1990, "New Qualitative Properties in the Competitive Nonrenewable Resource Extracting Model of the Firm", International Economic Review 31,829-839. Cremer, J., and M. Weitzman, 1976, "OPEC and the Monopoly Price of World Oil", European Economic Review 8,155-164. Cummings, R.G., and O.R. Burt, 1969, "Communications: The Economics of Production from Natural Resources: Note", The American Economic Review (December) 985-990. Dasgupta, PS., and G . Heal, 1974, "Optimal Depletion of Exhaustible Resources", Review of Economic Studies, Symposium, pp. 3-28.


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Dasgupta, P.S., ancl G. Heal, 1979, Economic Theory and Exhaustible Resources (Cambridge University Press, Cambridge). Dasgupta, P.S., R.J. Gilbert and J.E. Stiglitz, 1982, "Invention and Innovation Under Alternative Market Structures: The Case of Natural Resources", Review of Economic Studies 49,567-582. Del Sol Guzman, Patricio, 1987, Dominant Firm and Competitive Fringe Interaction in Exhaustible Resource Markets, Ph.D. Dissertation (Department of Engineering-Economic Systems, Stanford University, Stanlord, CA, July). Devarajan, S., and A.C. Fisher, 1981, "Hotelling's Economics of Exhaustible Resources: Fifty Years Later", The Joursval of Economic Literature 19 no. 1,65-73. Devarajan, S., and .A.C. Fisher, 1982, "Exploration and Scarcity", Journal of Political Economy 90,12791290. Drury, R.C., 1982, "Exploitation of Many Deposits of an Exhaustible Resource: Comment", Economem'ca 50 no. 3,769-774. Energy Modeling E:orum, 1982, World Oil (The Energy Modeling Forum, Stanford University, Stanford, CA). Eswaran, M., and T. Lewis, 1985, "Exhaustible Resources and Alternative Equilibrium Concepts", Canadian Journa'l of Economics 18 no. 3,459-473. Eswaran, M., T.R. ]Lewis and T. Heaps, 1983, "On the Nonexistence of Market Equilibria in Exhaustible Resources Markets with Decreasing Costs", Journal of Political Economy 91,145-167. Farzin, Y . Hossein, 1984, "The Effect of the Discount Rate on Depletion of Exhaustible Resources", Journal of Politic,alEconomy 92 no. 5,841-851. Fisher, A.C., 1981, Resource and Environmental Economics (Cambridge University Press, Cambridge). Gamponia, V, and R. Mendelsohn, 1985, "The Taxation of Exhaustible Resources", The Quarterly Journal of Economics (February) 165-181. Garg, Prem C., 1974, Optimal Economic Growth with Exhaustible Resources Ph.D. Dissertation (Department of Engineering-Economic Systems, Stanford University, Stanford, CA, May). Garg, PC., and J.1L. Sweeney, 1978, "Optimal Growth with Depletable Resources", Resources and Energy 1,43-56. Green, J., and W.1: Heller, 1981, "Mathematical Analysis and Convexity with Applications to Economics", in: K.J. Arrow and M.D. Intriligator (eds.), Handbook of Mathematical Economics (NorthHolland, Amsterdam). Gilbert, R.J., 1978, "Dominant Firm Pricing Policy in a Market for an Exhaustible Resource", Bell Journal of Economics (Autumn) 385-395. Gilbert, R.J., and S.M. Goldman, 1978, "Potential Competition and the Monopoly Price of an Exhaustible Resource", Journal of Economic Theory 17,319-331. Gray, Lewis C., 1914, "Rent Under the Assumption of Exhaustibility", QuarterlyJournal ofEconomics 28 (May) 466-489. Hartwick, J.M., 19'77, "Interregional Equity and the Investing of Rents from Exhaustible Resources", American Economic Review 67 no. 5 (December) 972-974. Hartwick, John M., 1978, "Exploitation of Many Deposits of an Exhaustible Resource", Econometr i c ~46,201-217. Hartwick, John M., 1989, Non-Renewable Resources, Extraction Programs, and Markets (Hanvood Academic Publishers, Chur, Switzerland). Heal, G., 1976, "The Relationship between Price and Extraction Cost for a Resource with a Backstop Technology", Th8eBell Journal of Economics 7 no. 2,371-378. Hendricks, K., anti D. Kovenock, 1989, "Asymmetric Information: Information Externalities, and Efficiency: The Case of Oil Exploration", Rand Journal 20 no. 2, 164-182. Herfindahl, Orris C., 1967, "Depletion and Economic Theory", in: Mason Gaffney (ed.), Extractive Resources and Taxation (University of Wisconsin Press, Madison, WI).

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Hoel, M., 1978, "Resource Extraction, Substitute Production, and Monopoly", Journal of Economic Theory 19,28-37. Hotelling, H., 1931, "The Economics of Exhaustible Resources", Journal ofPolitical Economy 39 (April) 137-175. Jacobsen, Lawrence R., 1987, Optimal Investment and Extraction Rates for a Depletable Resource Ph.D. Dissertation (Department of Economics, Stanford University, Stanford, CA, May). Kamien, M.I., and N.L. Schwartz, 1977, "Disaggregated Intertemporal Models with an Exhaustible Resource and Technical Advance", Journal of Environmental Economics and Management 4,271-288. Kemp, Murray C., and Ngo Van Long, 1980, "On Two Folk Theorems Concerning the Extraction of Exhaustible Resources", Econometrica 48,663-673. Kerry Smith, V, 1981, "The Empirical Relevance of Hotelling's Model for Natural Resources", Resources and Energy 3, 105-1 17. Koopmans, T.C., 1973, Some Observations on Optimal Economic Growth and Exhaustible Resources, Cowles Foundation Paper No. 396 (Yale University Press, New Haven, CT). Kuhn, H.W., and A.W. Tucker, 1951, "Nonlinear Programming", in: J. Neyman (ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, CA). Kuller, R.G., and R.G. Cummings, 1974, "An Economic Model of Production and Investment for Petroleum Reservoirs", The American Economic Review 64 no. 1,66-79. Lewis, T.R., 1976, "Monopoly Exploitation of an Exhaustible Resource", Journal of Environmental Economics and Management 3,198-201. Lewis, T.R., 1977, "Attitudes Towards Risk and the Optimal Exploitation of an Exhaustible Resource", Journal of Environmental Economics and Management 4,111-1 19. Lewis, T.R., 1979, "The Exhaustion and Depletion of Natural Resources, " Econometrica 47 no. 6,15691571. Lewis, T.R., 1982, "Sufficient Conditions for Extracting Least Cost Resource First", Econometrica 50, 1081-1083. Lewis, T.R., and R. Schmalensee, 1983, "On Oligopolistic Markets for Nonrenewable Natural Resources", The Bell Journal of Economics 14 no. 1,263-271. Lewis, T.R., S.A. Matthews and H.S. Burness, 1979, "Monopoly and the Rate of Extraction of Exhaustible Resources: Comment", American Economic Review 69 (March) 227-230. Lind, Robert C., 1986, Discountingfor Time and Risk in Energy Policy (Johns Hopkins University Press, Baltimore, MD). Livernois, John R., 1987, "Empirical Evidence on the Characteristics of Extractive Technologies: The Case of Oil", Journal of Environmental Economics and Management 14 no. 1,72-86. Livernois, John R., and Russell S. Uhler, 1987, "Extraction Costs and the Economics of Nonrenewable Resources", The Journal of Political Economy 95 no. 1, 195-203. Loury, G.C., 1978, "The Optimal Exploitation of an Unknown Reserve", Review of Economic Studies 45, 621-636. Lozada, Gabriel Alfredo, 1987, Equilibrium in Exhaustible Resource Industries, Ph.D. Dissertation (Department of Economics, Stanford University, Stanford, CA, May). Marks, Robert E., 1978, Non-Renewable Resources and Disequilibrium Macrodynamics, Ph.D. Dissertation (Department of Engineering-Economic Systems, Stanford University, Stanford, CA, February). Marshalla, Robert A,, 1978, An Analysis of Cartelized Market Structures for Non-Renewable Resources, Ph.D. Dissertation (Department of Engineering-Economic Systems, Stanford University, Stanford, CA, August). Modian, E.M., and J.F. Shapiro, 1980, "A Dynamic Optimization Model of Depletable Resources", Bell Journal of Economics 11,212-236.


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Newberry, D., 1980, "Oil Prices, Cartels, and the Problem of Dynamic Inconsistency", Economic Journal 91 (September) 617-646. Nordhaus, William D., 1973, "The Allocation of Energy Resources", Brookings Papers on Economic Activity 3, 529-570. Nordhaus, W.D., 1974, "Resources as a Constraint on Growth, "American Economic Review 64 no. 2 (May) 22-26. Olsen, Trond E., 1986, Strategic Development of a Backstop Technology, Ph.D. Dissertation (Department of Engineering-Economic Systems, Stanford University, Stanford, CA, July). Patrick, Robert H., and Janie M. Chermak, 1992, The Economics of Technology Research and Development: Recovery of Natural Gas from Tight Sands, Report No. GRI-9210267 (Gas Research Institute, Washington, DC); National Technical Information Services. Pindyck, R.S., 19'77, "Gains to Producers from the Cartelization of Exhaustible Resources", Review of Economics and Statistics 60 no. 2 (March) 238-251. Pindyck, R.S., 19'78, "The Optimal Exploration and Production of Nonrenewable Resources", Journal of Political Economy 86 no. 5 (October) 841-861. Powell, Stephen G., 1983, The Pansition to Nondepletable Energy, Ph.D. Dissertation (Department of Engineering-Economic Systems, Stanford University, Stanford, CA, June). Reinganum, J.F., and N.L. Stockey, 1985, "Oligopoly Extraction of a Common Property Natural Resource: The: Importance of the Period of Commitment in Dynamic Games", International Economic Revicw 26 no. 1,161-173. Salant, S., 1976, "Exhaustible Resources and Industrial Structure: A Nash-Cournot Approach to the World Oil Market", Journal of Political Economy 84 no. 5, 1079-1093. Schultze, W.D., 1974, "The Optimal Use of Non-Renewable Resources: The Theory of Extraction", Journal of Envi,ronmentalEconomics and Management 1,53-73. Scott, A., 1967, "The Theory of the Mine Under Conditions of Certainty", in: Mason Gaffney (ed.), Extractive Resources and Tawation (University of Wisconsin Press, Madison, WI). Slade, Margaret E., 1982, "Trends in Natural Resource Commodity Prices: An Analysis of the Time Domain", Journal of Environmental Economics and Management 9, 122-137. Slade, Margaret E., 1988, "Grade Selection Under Uncertainty: Least Cost Resource and Other Anomalies", Journal of Environmental Economics and Management 15, 189-205. Smith, VL., 19613, "Economics of Production from Natural Resources", The American Economic Review (June) 409-43 1. Soladay, John J., 1979, "Monopoly and Crude Oil Extraction", American Economic Review 69 (March) 234-239. Solow, Robert Mi., 1974, "The Economics of Resources or the Resources of Economics", American Economic Revicw, Papers and Proceedings, Richard T. Ely Lecture. Solow, Robert M., 1974, "Interregional Equity and Exhaustible Resources", Review of Economic Studies, Symposium, pp. 29-45. Solow, R.M., and EY. Wan, 1976, "Extraction Costs in the Theory of Exhaustible Resources", Bell Journal of Ecorromics 7,359-370. Stiglitz, J.E., 1974.,"Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths", Review of Economic Studies, Symposium, pp. 123-137. Stiglitz, J.E., 1976, "Monopoly and the Rate of Extraction of Exhaustible Resources", American Economic Review 66 (September) 655-661. Stiglitz, J.E., and P. Dasgupta, 1982, "Market Structure and Resource Depletion: A Contribution to the Theory of Intertemporal Monopolistic Competition", Journal of Economic Theory 28,128-164. Sweeney, J.L., 1977, "Economics of Depletable Resources: Market Forces and Intertemporal Bias", Review of Economic Studies 44 (February) 125-141.

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Tullock, Gordon, 1979, "Monopoly and the Rate of Extraction of Exhaustible Resources: Note", American Economic Review 69 (March) 231-233. Varian, Hal R., 1992, MicroeconomicAnalysis, 3rd Ed. (W.W. Norton & Company, New York). Weinstein, M.C.,and R.J. Zeckhauser, 1975, "The Optimum Consumption of Depletable Natural Resources", Quarterly Journal of Economics 89 (August) 371-392.

Chapter 18

THE OPTIMAL USE OF EXHAUSTIBLE RESOURCES GEOFFREY M. HEAL* Columbia University,Business School, Uris Hall, New b r k , NY 10027, USA

1. Introduction

The aim of this chapter is to review issues connected with the analysis of 'optimal natural resource use'. The focus will be on certain key analytical issues which lie at the heart of any analysis of optimal resource use, with indications of the application of these to a range of different problem specifications. It is appropriate to start with definitions to delimit the areas of concern. The first distinction is between exhaustible resources and renewable resources. An exhaustible resource is one of which there is only a finite amount on earth and which has no natural regeneration process. A renewable resource is one whose stock is replenished by a natural regeneration process. Forests and fisheries are obvious examples. There is a hybrid category which consists of exhaustible resources for which there is a backstop technology, i.e. a technology which can provide substitutes for the resource once it is fully depleted, and can provide these substitutes on a very large scale indeed. Nuclear power could be regarded as a backstop for fossil fuels in many of their applications. Extraction from very low-grade high-cost ores could become a backstop fc~rmany metals. Nordhaus (1979) reviews the concept of backstop in the context of the allocation of energy resources. Obviously, it is not an implication of exhaustibility that the size of the stock of a resource is known. All that is assumed known, is that the stock is finite. The allocation of inputs to discovering more about the size of the stock of an exhaustible resource is an interesting economic process giving rise to an extensive literature on exploration [see for example Pindyck (1978)l. The concern here is solely with exhaustible resources with or without backstop technologies. The analysis covers cases where the stocks are known or unknown, and where the availability of a future backstop technology is either known with certainty or is the outcome of a stochastic process subject to influence by economic * I am grateful to Graciela Chichilnisky, Partha Dasgupta and Jim Sweeney for very valuable advice and comments. 'They are of course not implicated in any remaining errors. Handbook of Natural Resource and Enevgy Economics, vol. Ill, edited by A. K Kneese and J.L. Sweeney O 1993 Elsevier .Science Publishers B. K All rights reserved

85 6

G.M. Heal

policies. Many of the key analytical issues have relevance to renewable resources, but the literature on that topic is sufficiently extensive and specialized that it merits separate treatment. Certain questions arise naturally. A classic question concerns the optimal rate of depletion of an exhaustible resource. How fast should this be depleted? How do we strike the correct balance between present and future use? What do we know about scarcity rents in connection with optimal depletion? All of these issues were first addressed by Hotelling (1931). A related question concerns the optimal allocation of resources to exploration forfirther resource deposits in cases where the total stock of an exhaustible resource is unknown. Closely connected is the issue of how to allocate resources to research and development intended to produce a substitute for an exhaustible resource. How much, for example, do we allocate to the development of synfuels as replacements for conventional crude oil? Another related question is: "How will the shadow price of the resource move over time along an optimal use path? Will it rise, and if so at what rate and from what level?" An understanding of these issues is important if we are to be able to compare actual consumption rates for exhaustible resources with theoretical optima. Data on price movements are often more visible and more accurate than those on consumption levels, so that an understanding of the movement of shadow prices along optimal use paths can enable us to compare actual and optimal paths in price space rather than in quantity space. These issues all hinge around striking a correct intergenerational balance: the more of an exhaustible resource is used now, the less is left for future users. The more effort is allocated to exploration or research and development, the more there is a chance of reducing the conflict between present and future use by supplementing future stocks. In determining the intertemporal balance, the key parameters within the generally used Utilitarian framework are the discount rate and the elasticity of the marginal utility of consumption with respect to the level of consumption. There is considerable confusion about the role of the discount rate. Discounting is held to be necessary for optimal depletion problems to be soluble, and yet also to be ethically indefensible. Indeed it is a practice widely criticized for this reason by non-economists working in the area of resource use. A main thrust in the review of optimal intertemporal use which follows will be to elucidate the role and implications of discounting, as this seems to be one of the most basic and yet most confused and controversial topics. There is a different, atemporal, aspect of resource use which has received attention and has proven intriguing. This concerns the general equilibrium impact of the development and sale of extractive resources on the economy as a whole. This has sometimes been said to have adverse consequences for income distribution and for long-run economic growth in developing countries: in industrial countries it has been linked to the 'Dutch disease' and deindustrialization. Given the general perception of resource endowments as enriching, these associations are puzzling

Ch. 18: Optimal Use of Exhaustible Resources

857

and give rise to an interesting and analytically rich set of issues. There is a literature on multi-sectlor general equilibrium models of resource-producing economies which study th~einteractions between a capital-intensive resource-producing sector and the rest of the economy. They show how under certain conditions these can lead to counterintu~itiveeffects. This literature gives rise to a comparative static concept of optimal resource use, in contrast to the intertemporal concept of optimality on which I shall fbcus here. Aspects of this literature have been reviewed by Corden (1981), Chichi~lnisky(1985) and Chichilnisky and Heal (1991). In summary: the aim is to review key aspects of the analytical framework appropriate for discussing optimal resource use, and then to give pointers about how and where these issues are developed further in the literature. Economists have always been concerned with resource use, though the precise focus of their interest has varied. Classical economists saw natural resources as determinants of national wealth and of economic growth rates, and saw differences in resource en~dowmentsas explanations of interregional income differentials. They were thus focussing on the general equilibrium aspects of resource use. Depletion and its management were first analyzed by L.C. Gray (1914) and, In a still classiic piece, by H. Hotelling (1931). The boom in resource economics in the 1970s and 1980s developed the depletion theme further. The macro- and general-equili'brium aspects of resource use developed separately, and were poorly integrated with the resource depletion literature. Recently interest in resource use has been stimulated by the connection between resource use and environmental issues [see for example Dasgupta (1982b)l. Resource use generates waste and pollution. One of the most complex interactions here is between the use of fossil fuels and the emission of carbon dioxide with its potential greenhouse effect. The depletion of one of the few really exhaustible resources (fo:ssil fuels) has a potentially major environmental impact. The economic issu~:s raised by this interaction have been reviewed by Nordhaus (1982), Heal (1984,1990). Even if some of the more apocalyptic visions of the greenhouse effect turn out to be invalid, a strong connection remains between fossil fuel depletion ancl more mundane forms of environmental pollution (acid rain, photochemical smog, etc.). Hotelling's 1931 article is still interesting and insightful. I cannot resist quoting its opening sentence: Contempllation of the world's disappearing supplies of minerals, forests, and other exhaustible assets has led to demands for regulation of their exploitation. The feeling that these products are now too cheap for the good of future generations, that they are being selfi~shlyexploited at too rapid a rate, and that in consequence of their excessive cheapness they are being produced and consumed wastefully has given rise to the Hotelling (1931) conservation movement.

G.M. Heal

858

Much of the 1970s literature on conservation and depletion would have given him a sense of dkjh vu. Hotelling's paper contains a fully rigorous analysis of the pure depletion problem analyzed in Section 2.1 below, and constitutes one of the earliest applications of dynamic optimization in economics. In addition to the treatment of the pure depletion case, Hotelling offers interesting formulations of various cases of imperfect competition, noting features that were only rediscovered many years into the 1970s literature on market structure and depletion. 2. Characterizing optimal depletion 2.1. Pure depletion In formulating an optimal depletion policy, one is deciding how best to spread the consumption of a fixed stock of a resource over time. In its simplest form this problem can be posed as follows:

l=o t=T

Maximize

~ ( c tePb' ) dt (1)

t=T

subject to St = So -

L o

ctdt, S, = -ct,

$20

'dt E[O,T],

where So is the initial stock of an exhaustible resource, assumed to be known with certainty, c, is the rate of consumption of that resource at date t, St is the total stock remaining at date t, T (which may be finite or infinite) is the time horizon of the problem, U(c,) is the instantaneous utility of consumption of the resource, and S > 0 is a discount rate. We shall denote by U1(c) the first derivative of U(c,) with respect to c,, and assume that U(c,) is strictly concave, and in addition that lim U1(ct) = +a.

c, -0

It is convenient to define the elasticity of the marginal utility of consumption as:

In problem (1) the aim is to spread the consumption of an exhaustible resource over an interval of time so as to maximize the integral of discounted utility: there is an integral constraint on total consumption over the period because of the exhaustibility of the resource, and this is represented by the conditions that the remaining stock must always be non-negative and that the rate of change of this stock equals the rate of consumption.


859

Intuitively, it is clear what the solution to problem ( 1 ) must be. Consumption levels must be chosen so that the present value of the marginal utility of consumption is the same in all periods, as the possibility of storing the resource means that consumption can be shifted costlessly between periods. This intuition is developed in the article by Hotelling (1931) and also very lucidly by Solow (1974). In fact this very simple and intuitive observation is the key to understanding many of the characterizations of optimal depletion policies. To solve problem ( 1 )formally we construct the Hamiltonian

where p, is a costate variable which can be interpreted as the shadow price of the resource constraint at date t. Necessary conditions for a solution to problem ( 1 ) can be obtained from eq. (2) as pr = 6pt and U 1 ( c t )= p,. From these it follows that

so that: Along a consumption path which satisfies the necessay conditions for optimal depletion, the rate at which consumption falls over time is equal to the ratio of the discount rate and the elasticity of marginal utility of consumption. Hence the earlier observations about the importance of these two parameters. The greater the rate of discount, the greater the rate at which consumption declines over time. A decrease in the elasticity of marginal utility also increases the rate at which consumption falls over time. Section 6 below gives graphical and intuitive explanations of the roles of the discount rate and the elasticity of the marginal utility of consumption. By specifying a particular functional form, these equations can be made to yield information not only about the rate of change of consumption but also about the initial level of consumption. Assume that the elasticity of marginal utility of consumption is constant: then

so that for an infinite time horizon

G.M. Heal

Fig. 1. A utility function having average and marginal utility equal at c*

Obviously, higher initial stocks imply higher initial consumption levels and so higher consumption levels at all dates. And a higher discount rate implies higher initial consumption levels in addition to a faster rate of decline [from eq. (3)]. A smaller elasticity of marginal utility also boosts initial consumption. The necessary conditions for optimality enable us to characterize the movement of shadow prices along an optimal resource use path. The movement of the shadow price will satisfy

This equation is now generally known as the 'Hotelling Rule' after its discoverer, and has an obvious intuitive rationale: the present discounted value of the resource will be the same at all dates, reflecting the need to equate the marginal contributions to the sum of discounted utilities at all dates. Clearly, the discount factor plays a key role in determining shadow price movements. An important fact is that in a competitive economy with a complete set of futures markets (or, equivalently, perfect foresight about future spot prices), the price path of an exhaustible resource will satisfy the 'Hotelling Rule'. This is an illustration of the First Theorem of Welfare Economics: a competitive Arrow-Debreu economy leads to an allocation that is Pareto Efficient. The 'Hotelling Rule' is necessary not only for optimality as defined by problem (1) but also for Pareto efficiency [see, for example, Solow (1974) and Dasgupta and Heal (1979)l. There are a number of papers which extend the analysis of this section to cases where the total amount of the resource So is uncertain. These include Kemp (1976), Loury (1978), Gilbert (1979) and Heal (1979). This formulation of the problem introduces an important analytical extension, which arises from the fact that optimal policies now involve a positive probability of exhausting the

Ch. 18: Opfimal Use of Exhaustible Resources

861

stock of the resource in finite time. They therefore have to satisfy an interesting terminal or right-hand end point condition first introduced in a deterministic model by Koopmans (1973,1974). The deterministic version of this condition requires the equality of the average and marginal utilities of consumption, i.e.

The marginal utility U1(eT)is of course the cost of reducing current consumption by one unit: the average utility U(cT)/eT is the benefit from using the unit so saved to prolong consumption at the current rate, in which case the prolongation is for a period of l/cT and the utility from this extension is U(cT)/cT.This condition is best illustrated by the non-concave utility function in Figure 1, for which U(0) = 0 and for which average and marginal utility are equal at c * . This function reflects the fact that there is a certain minimum level of consumption below which no utility is generated, i.e., there is a minimum 'threshold' level of consumption. Note that the equality of average and marginal utility can never hold for an isoelastic utility function such as the function U(ct) = loge,. Formally, consider problem (1) with the utility function given in Figure 1. The solution involves following eq. (3) until a date T at which condition (6) holds, and then setting ct = 0 for t > T. Obviously, it does not make sense for consumption to decline gradually to zero given that the marginal utility of consumption reaches zero at a positive consumption level. The models with an uncertain resource stock referred to above have optimal paths with this characteristic. In their simplest form, they can be stated as follows. Let the initial stock So be a random variable with marginal density function w(So). Let Z, be cumulative consumption up to date 7.The marginal density function describing the likelihood of exhaustion at date is w(Z,), which is the probability of exhaustion at date r on the consumption path of which Z, is the integral. The expected utility on any consumption path is therefore

and optimality requires that we maximize expression (7) subject to the obvious constraint that

Application of the techniques used above leads to the following as a necessary condition for optimality:

G.M. Heal

862

Jp

where p(Z,) = w(Z,)l w(Z) dZ, the probability of exhaustion at time t conditional on the resource stock remaining at time t. Clearly condition (9) is an extension of condition (3) with the addition of a term which is zero if the conditional probability of exhaustion is zero, i.e., if there is no uncertainty about the stock. The presence of uncertainty introduces a term in the difference between the marginal and average utility levels multiplied by the probability of exhaustion at current depletion levels, and this number is the expected cost of advancing the exhaustion date by a small increase in current consumption. Mathematically, the term [p(Z,)(Uf(ct) - U ( ~ t ) l ~ t ) ] l U ' (acts ~ r ) just like an addition to the discount rate, an issue to which we shall return later. 2.2. Depletion and capital accumulation

Qualitatively similar results hold for more complex models involving the use of the exhaustible resource as an input to the production of a good which is then consumed, so that the resource is an input to production rather than a consumption good. Typically in such models there are two inputs to production, the resource and capital. The output which is produced from these may either be consumed or invested in augmenting the capital stock. A widely-used model of this sort is as follows. Kt is the capital stock at time t , and the production function is Y = F(K,, R,), where Y is the output of a good which may be either consumed or invested in increasing K t . Production occurs under conditions of constant returns to scale, so that the production function is linear homogeneous. The economy's basic equation of evolution is therefore

and the overall optimal depletion problem can be posed as: Maximize subject to eq. (lo)

and 03

S,=So-~=oR,dt,

sf=-R,,

c,,Kt, R,,S, 3 0 and KO> 0 is given. Necessary conditions for a solution are again obtained by forming a Hamiltonian:

H = eP6' U(ct) + e - 6 t p , ( - ~ t ) + e-*' q,(F(K,, R,) which yields as necessary conditions

- c,),


863

After extensive manipulation, these equations yield two relatively simple and intuitive statements. Lettingx = K/R and f (x) = F(K/R, I), and recalling that the elasticity of substitution between capital and resources can be represented as

we have as necessary conditions for optimality

Once again the discount rate and the elasticity of marginal utility play a crucial role in determining the rate of change of consumption, although in this case consumption no longer refers to the rate of consumption of the exhaustible resource: it refers rather to the consumption of the output good produced from the resource. The rate at which the level of resource input is changed, is given by condition (15.2) and is captured most neatly in terms of an expression for the rate of change of the capital-resource ratio, or the rate at which reproducible capital is substituted for the non-reproducible resource. It is also again the case that the movement of shadow prices along an optimal resource-use path is determined by the discount rate. Equation (13.3) of the necessary conditions gives the movement of this shadow price, and eq. (13.2) shows that at each date the shadow price of the resource will equal the value of its marginal product, where valuation is in terms of current marginal utility. Equation (13.3) is of course identical to eq. (5) giving price movements in the pure depletion case with no production, so that in this sense the introduction of production changes nothing with respect to resource price movements. However, the use of the exhaustible resource as an input to production does make possible another interpretation, which is the following. Define y = plq, so that y is the price of the resource divided by that of the produced good, i.e. it is the price of the resource in terms of output. (A shadow price is of course a price in terms of units of the maximand, which in this case is discounted utility.) A little manipulation now confirms that

so that the rate of increase of the resource price in terms of output is the marginal productivity of capital. This will vary along an optimal path as the capital resource ratio changes according to condition (15.2). The rate of change of the price in terms of discounted utility is the utility discount rate, which is of course constant.

864

G.M. Heal

A more detailed analysis of this case can be found the literature [Dasgupta and Heal (1974), Koopmans (1973, 1974), and Stiglitz (1974)l. It can be regarded as a cross between the pure depletion case reviewed in the previous section and first analyzed by Hotelling, and the pure optimal accumulation problem first studied by Ramsey (1928). Dasgupta and Heal extend the model to allow for the possible occurrence of a technological breakthrough which leads to the introduction of a backstop technology.

2.3. Depletion, capital accumulation and technical progress through R&D

The basic model of production and depletion, just summarized, has been developed in many ways. One is to introduce the possibility of allocating resources to research and development activities at a rate r,. This expenditure affects the probability of finding a replacement for the extractive resource. In this case we introduce a date T > 0 at which the resource constraint no longer binds, because an abundant substitute has become available. T is a random variable, and its density function depends upon expenditure on research and development. This dependence is via the stock of knowledge V,, which depends on cumulative past R&D activities through the equation

where h(0) = 0 and h(r) is strictly concave. More R&D expenditure at a given date increases the probability of a technological breakthrough, but at a diminishing rate. The density function describing the likelihood of T assuming a particular value is a function of the stock of knowledge:

With this formulation, the probability that T is between tl and t2 is:

and if V t , = V t , so that r, = 0, t E (tl, t2), then the associated probability is zero. For a small interval of time At starting at tl the probability of a substitute for the resource being developed is

865


which depends both on the stock of knowledge reached by the start of the period and on the level of R&D expenditure during the period. This, and the no researchno substitute feature noted above, seem to be very desirable features of any model in this area. Following a widely used technique, we now define a function W(K,, St) as follows: W

W(Kt, St) =

ax

~ ( c ,e-6(t-T) ) dt,

where the maximization is subject to whatever constraints are operative in the period from T on. The function W(K,,St) is assumed to be real-valued and differentiable. It is essentially a state valuation function, showing the maximum welfare that could be derived over the entire future if the technical change under consideration occurred at date T and the stocks then remaining were K, and St. The overall problem of optimal depletion and R&D can now be posed in the following terms: Maximize E

{iT

~ ( c . ) e - *dt~ + W(KT, sT)e-"

subject to K, = F(K,, R,) S, = -Rt,

-

lim St 2 0,

t-W

(20.1)

ct - r,,

V, = h(rt).

(20.2, 20.3)

Here E is the expectations operator, and initial values of K , S and V are given. This rather complex problem, and others similar to it, have been studied in detail by Dasgupta, Heal and Majumdar (1976) and Dasgupta, Heal and Pand (1980). Under certain simplifying assumptions, the conditions necessary for a solution can be derived as:

and

where

866

G.M. Heal

For present purposes the important point here is that the rate of change of consumption is given by an expression vely similar to that in the previous simpler cases: it again depends on the discount rate and the elasticity of the marginal utility of consumption. It has been shown by Dasgupta and Heal (1974) and Dasgupta, Heal and Majumdar (1976) that in fact the term cp(V)h(r)/q can be interpreted as an addition to the discount rate arising from uncertainty about future resource constraints, so that the general features of the results from the simple case survive well in more complex models. This is exactly analogous to the observation at the end of Section 2.1, where it was also noted that the introduction of uncertainty introduces into the optimality conditions a term which behaves mathematically exactly like the discount rate. The discount rate and the elasticity of the marginal utility of consumption continue to play a central role. In this case, the shadow price of the resource can be shown to follow the equation

Once again the discount rate is prominent in determining the rate of change of price, although now it is modified by a term reflecting the probability of the resource becoming inexhaustible as a result of technical change. The model summarized in this section is set out in detail in the articles by Dasgupta, Heal and Pand (1980) and Dasgupta, Heal and Majumdar (1976). A closely related model has been studied by Davidson (1978). Kamien and Schwartz (1978) examined optimal depletion policies in the context of technical change which occurs continuously and gradually, rather than in a single discrete event, as assumed in this section. Pindyck (1978) considered a problem related to that of investment in R&D, which is investment in exploration aimed at discovering additional deposits of the resource.

2.4. Depletion with a backstop In the previous section we considered the case of a resource which might be made inexhaustible by technical progress. Now we turn to the case of an exhaustible .resource for which there is a backstop technology. In this case we know for certain that there is a substitute for the resource. A simple model to describe this case is as follows. z ( t ) will represent the total cumulative resource extraction up to date t : z ( t ) = J,' t , d ~We . now assume that extraction of the resource is costly, and that the cost is a function of cumulative extraction to date. This captures the idea that high-grade resource deposits are used up first, and that cumulative extraction therefore leads to higher and higher


costs. So extraction cost per unit at date t is given by ag g(z) with - = g' > 0 for 0

az

< z < 2,

and by ,B > 0 for z 2 2 , g(2) = P. This formulation reflects the idea that extraction costs rise with cumulative extraction up to a level of cumulative extraction equal to 2, at which point conventional deposits are exhausted and a backstop technology takes over. This technology supplies limitless amounts of the resource, or a perfect substitute for it, at a constant cost per unit of p. The problem of optimal resource use is now a modification of the problem studied in Section 2.2, with eq. (10) now replaced by the statement that

Solving this modified problem leads to an equation for the time path of consumption identical to eq. (15.1) of Section 2.2. Equation (15.2) of Section 2.2 is modified to become

The substantial changes come in the equation determining price movements. Using the notation of Section 2.2 so that q, is the shadow price of the produced good, we define q, F R = A, SO that A, is the shadow value of the marginal product of the resource, or its shadow price in terms of discounted utility. Letting A, g(zt) = E l , the extraction cost per unit of resource in terms of the output good, the movement of this shadow price now satisfies

Two points need to be noted about this. One is, of course, that the discount rate is still important. The other is that this equation has a simple intuitive interpretation. The shadow marginal value product, or shadow price, of the resource changes at a rate which equals the discount rate times the proportion of this price equal to pure scarcity rent (the difference between price and marginal extraction cost), plus the rate of change of output price times the proportion of the price made up of extraction costs. In other words, price changes at a rate equal to a weighted average of the discount rate and the rate of change of output prices, with the weights being the proportions that royalties and costs contribute to price. As in previous sections, we can find a slightly different interpretation if instead of the shadow price in terms of discounted utility we study the ratio of the shadow

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price of the resource and that of the produced good, y = Xlq. Here y is the price of the resource in terms of the output good. A little manipulation establishes that

so that the price of the resource in terms of output changes at a rate equal to the marginal productivity of capital (cf. eq. (16), Section 2.2) multiplied by the fraction of the shadow price that is pure scarcity rent. The model of this section draws heavily on Heal (1976), Clark (1978), Hanson (1979, 1980) and Oren and Powell (1985). In particular, Hanson (1980) gives a detailed characterization of the time path of prices and of scarcity rents, and Oren and Powell (1985) give a relatively simple general derivation of the main results.

3. Perspectives on discounting

We have seen that the discount rate occupies a central role in the determination of the quantitative and qualitative characteristics of optimal resource depletion policies and the associated price and rent paths. Discounting - using a positive discount rate - is however a very controversial practice. It is widely regarded by non-economists as an unreasonable embodiment of shortsightedness, and even within the economics profession strong positions have been taken. Two very famous statements are Frank Ramsey's (1928) pronouncement that discounting "is ethically indefensible and arises merely porn the weakness of the imagination," and Roy Harrod's (1948) comment that discounting is "apolite expressionforrapacity and the conquest of reason by passion". These positions are understandable: many studies [e.g., Smith (1980), D7Argeet al. (1982)], have noted that discounting benefits as much as 50 or 70 years ahead can render them insignificant relative to present costs and benefits. There are of course alternatives to the present discounted value of benefits as welfare criteria. The Rawlsian criterion, which in the intertemporal context implies selecting the path that gives the highest level of consumption sustainable indefinitely, has received considerable attention [see Solow (1974) for a detailed application of this technique in the context of exhaustible resources, and Dasgupta and Heal (1979) for a general review and comparison of alternatives]. Although alternative intertemporal welfare criteria have been proposed, none have ever been operationalized: no literature exists on how to implement project evaluations on the basis of alternative welfare criteria. This suggests that these alternatives have won little acceptance, and that welfare criteria based on present values of benefits are invariably those on which decisions in this area will be based - if they are

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based on anything so coherent as a welfare criterion. Given such pointedly stated positions against discounting, it is important to understand why the practice of discounting has survived and indeed blossomed in economics. In fact there are two points which must be made here. One is that there are very compelling logical reasons for discounting. The other is that there is confusion in the minds of many commentators - possibly including those cited above - about exactly what we are doing when we discount. The statement that future benefits must be given less weight than present, does not imply that future consumption should be given less weight than present consumption. There is avery important distinction between the utility rate of discount and the consumption rate of discount. The utilitarian theory of intertemporal welfare economics only implies that the former must be positive. The theory is quite consistent with the consumption rate of discount being negative (i.e., with future consumption being given more weight than present). In the following sections this point will be developed in some detail, and conditions derived under which future consumption should be given at least as great a weight as present consumption, even though future utilities are discounted. The logical reason for discounting is that certain very basic problems in the area of optimal depletion cannot be well posed unless we choose a positive rate of discount. In this section I will illustrate the difficulty that arises without discounting. In the next section, I show how discounting resolves this difficulty, and that this is almost the only way of doing so. The subsequent section will make a distinction between utility discounting and consumption discounting, arguing that the fundamental logic of depletion problems requires utility discounting, but that this does not imply consumption discounting, which is almost certainly the practice to which the statements by Ramsey and Harrod quoted above were meant to apply. To understand the logical point, return to problem (1) above: Maximize

[=T

( i ( c t ) eC6' dt

subject to St = So -

ctdt,

st = -ct,

St 2 0 Vt E [O,T].

Let T be finite, and the discount rate be zero. Then it is clear from condition (3),

that an optimal policy involves a constant consumption level, say c ~and , clearly this constant level must be SOIT.Now consider the behavior of this solution as the time horizon T increases to m. Then c~ goes to zero, and the infinite-horizon limit of the optimal consumption levels for finite horizons is zero. Obviously zero consumption is not an optimal policy over an infinite horizon (or any other) so that

G.M. Heal

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we have to enquire whether there are other ways of locating an optimum for the infinite-horizon case. There are none: eq. ( 3 )makes it clear that when the discount rate is zero, a necessary condition for optimality is that the level of consumption is constant over time, and of course the only constant consumption level which is consistent with the constraints on resource use, is zero. So we really have no sensible solution to the optimal depletion problem when the time horizon is infinite and the discount rate is zero. This paradoxical observation is known as the 'cakeeating problem'. The point was first noted by Gale (1967) [see also Heal (1973)l. Hotelling (1931) made an insightful aside when he remarked that Problems of exhaustible resources are peculiarly liable to become entangled with the Hotelling (1931)p. 139 infinite.

4. Existence of optimal policies I indicated in the last section that a very straightforward pure depletion problem might be insoluble without a positive discount rate. I next indicate the role played by a discount rate in ensuring the existence of an optimal depletion policy. I shall show that discounting is very close to being necessary for the existence of solutions to infinite-horizon optimal depletion policies. The infinite-horizon case has importance in real-world terms for two reasons. One is that the choice of any finite horizon T involves the designation of a date beyond which the benefits of resource use are no longer to be counted. An optimal depletion policy with respect to a welfare criterion defined only on the first T periods will certainly exhaust the entire resource stock by the end of period T. Few people aresufficiently certain of their apocalyptic vision to make this choice of T with confidence, and the accepted convention has been to avoid the problem and make the choice of T infinite. There is also a general unease about taking seriously finite-horizon solutions whose limit with the time horizon is obviously not optimal. Consider an economy with a fixed stock of So units of an exhaustible resource. At each point in time the economy Gonsumes this resource, using it at a rate of c, at time t. At all times, c, 3 0, and the exhaustibility implies that Cr dt So. Let E = {c,,t = 0 to co, c, continuous in t} and define F = {E : c, 3 0 Vt & Som ct dt 6 S o ) . Then F is the set of feasible consumption sequences. The total benefit associated with a consumption sequence c is u ( c ~dt, ) assuming for the moment thatt this is defined. The problem of then selecting an optimal resource use profile can thembe formalized as

Sr

0. If the value function is differentiable, X(t) gives the value to the buyer of a marginal increase inp(t) 12. If cl(S) # 0, we can interpret the co-state variable X as the buyer's shadow value of price. Given a value ofp(t), the buyer at t faces a standard control problem which induces avalue function defined over S andp 13. If cl(S) # 0 it can be shown that the seller's price is strictly greater than extraction costs at every point along the openloop trajectory (except at the last instant, T, when this is finite). Therefore, for all prices along the open-loop equilibrium (for t < T) a small positive or negative change in the current price leads to a small change in the buyer's welfareI4. His value function is continuous in price. If U ( q ) and c(S) are smooth and have the right curvature properties, the buyer's value function is also differentiable in price. [See Benveniste and Scheinkman (1979) and Seierstadt and Sydsaeter (1987) for a discussion of differentiability of the value function Is.] The boundary condition X(0) = 0 and eq. (3.3~)imply that X(t) is positive for t < 0. In the situation where X(t) can be interpreted as the buyer's shadow value of the price, this implies that if the buyer at time t were able to renege on the open-loop path announced at time zero, he would alter the program in a way which increases the price received by the seller. This observation should not be surprising in light of the two previous remarks that the open-loop extraction path is more conservative than the efficient path, and that the open-loop path need not exhaust the resource (i.e., cumulative extraction may be less than under the efficient regime). If we think of the buyer choosing a tariff rather than a consumption profile, we can interpret the l 2 This interpretation is not valid if extraction costs are constant since in that case the value function is not differentiable in price at p = c. A small increase in the current price lowers the monopsonist's pay-off by a small amount, since this transfers rent to the seller without altering the extraction path. However, an arbitrarily small decrease i n p below c causes the buyer's pay-off to fall to zero, since the resource owner will not sell at a price below extraction costs. (Sop c must be the optimal price path for the buyer.) Since the value function is not continuous i n p at p = c, it is clearly not differentiable; in this case X cannot be interpreted as a shadow value. In fact, when cr(S) 0 we can think of the monopsonist choosing a constant price rather than a function of time; the state variable p is replaced by a constant. This approach has the advantage of not causing confusion over the interpretation of the co-state variable A, but it impedes a unified treatment of the problem. l3 If the buyer at t regardedp(t) and eq. (3.2) as given, he would have no incentive to depart from the open-loop trajectory. The problem of DI arises precisely because he does not takep(t) as given, unless he is in some way committed to continuing on the open-loop path announced at t = 0. l 4 This is the condition that fails when cl(S) = 0. l5 One way to think about the different cases cr(S) = 0 and cl(S) # 0 is to note that in the former the open-loop equilibrium price path is on the boundary of the set of feasible price paths (those which induce positive extraction), whereas in the latter case the open-loop equilibrium is in the interior of that set.

=

Ch. 19: Intertemporal Consistency Issues in Depletable Resources

897

open-loop path as a threat. The buyer threatens to use a high tariff in the future in order to obtain the resource for a low price in the current period. The buyer would prefer not having to carry out the threat: he would like to defect to a program with a lower tariff and a higher price trajectory for the seller. It is clear that the open-loop policy is not perfect (since it is not even timeconsistent) whenever c'(S) # 0. The open-loop tariff is not perfect even ifcl(S) 0, but a perfect equilibrium can sustain the same result. From eq. (3.3), the openloop unit tariff rises at the rate of interest when ct(S) 0. Suppose that over some interval the importer deviates from the open-loop tariff, so that at the end of that interval there is either more or less remaining stock than would have been the case along the open-loop trajectory. If the importer were then allowed to resolve his problem, he would not want to return to the open-loop policy, which, we emphasize, gives the tariff as a function of time and the initial condition at t = 0. The reason is that that policy would not result in the optimal profile of consumption, given that the state is off the equilibrium path. [To see this, notice that the time profile of the co-state variable p(t) implied by the original open-loop policy does not solve the importer's problem at t given an off-the-equilibrium value of S(t); recall that p gives the value of the open-loop unit tariff.] Thus, the open-loop policy is not perfect even if ct(S) 0. However, the openloop path can be sustained as a (Markov) perfect equilibrium. In order to do this we can write the open-loop policy in 'feedback form'. By this we mean that we solve for the open-loop tariff, p, as a function of the state, S. In principle this is easy to do. We have already discussed how to obtain a differential equation for consumption in the open-loop equilibrium. We can solve this to obtain the future trajectory of S as a function of time in the future and an arbitrary value of the state at time t, S(t). By substituting this function into the integral form of eq. (3.3b) we obtain p(t) as a function only of S(t). This gives the open-loop tariff as a function of the stock: it gives the 'feedback form of the open-loop policy'. This equilibrium is perfect. If the importer were to deviate over some interval, causing the stock to be off the equilibrium path, and if the importer were then given the option of resolving the problem, taking as given the level of the stock, he would want to use the open-loop trajectory that is optimal from the given stock level. That is, he would want to use the feedback form of the open-loop policy. The following example may help to clarify this concept. Suppose that demand is llp for p < p and zero for p > p. (The buyer has access to a backstop technology, and has a unit elastic demand.) Suppose c = 0, and let the tariff r(t) = where T is such that the oil is just exhausted by that date. The equation for the stock remaining at date t is

-

-

-

L. K a p and D.M. Newbery

898

so the feedback form of the open-loop tariff can be written as

Any deviation or exogenous shock (an unexpected discovery) which changes S(t) can be promptly corrected and the tariff remains optimal given remaining stocks.

3.2. Monopsonist with fnnge buyers The situation where a monopsonist attempts to capture rents when resource owners are competitive and there are fringe (non-strategic) buyers was studied by Newbery (1976), Maskin and Newbery (1978,1990) and Kemp and Long (1981). These papers assume that extraction costs are constant. We s2w in the previous subsection that this assumption in a pure monopsony model leads to a very simple equilibrium. The introduction of competing buyers leads to the same sorts of complications as do stock-dependent extraction costs. We begin by showing how the formal model of the previous section is altered by including competing buyers when their aggregate demand is given by the stationary functiony(p); we maintain the assumption that cl(S) 0. The producer's problem is unaltered. The stock dynamics facing the dominant importer are now given by s = - [q + y(p)], where q now represents imports by the dominant buyer and q + y gives aggregate consumption. The buyer's Hamiltonian is altered by including the term - py(p). The necessary conditions (3.3a,b) must still hold, except that cl(S) 0 by assumption. The additional term pyl(p) must be included in eq. (3.3~); however, the rate of change of the unit tariff, p, is independent of X in this case. The necessary conditions therefore imply that the dominant buyer's unit tariff increases at the rate of interest: a constant present-value tariff is optimal. This was also true for the pure monopsonist, as noted in the previous subsection. To understand this result, imagine that at time zero oil importers bid for oil fields and then extract them as they wish. The dominant importer will bid for fewer than his domestic consumers collectively would bid for, because this enables him to drive down the price of the fields. Once the oil field is purchased, it pays the importer to extract it efficiently, which requires that the rent rise at the rate of interest; the price facing consumers is the extraction cost plus this rent. This result is duplicated by a tariff if the price paid by consumers is the same in both cases. This requires that the time path of rent for the imported oil (received by the oil producers) plus the import tariff should be the same as the time path of rent for the purchased and domestically exploited oil field. Only if the tariff rises at the rate of interest will this condition hold. In general, the open-loop tariff is DI if there are competing buyers, even if extraction costs are constant. The clearest example of this occurs where both

-

-


899

the dominant importer and the fringe have the same choke price (the price at which demand falls to zero), p. At a finite time T the world price rises to p, so there is some interval of time before T when the world price is strictly less than p but the price in the dominant country is no less than p. That is, there is an interval of time when the dominant importer has ceased importing even though world price is less than its choke price. During that interval the dominant country would certainly want to renege from its open-loop tariff, which is therefore DI. Newbery (1976) demonstrated that if both the dominant importer and the fringe had the same constant elasticity demand functions (in which there is no choke price), and extraction costs were zero, the open-loop policy is time-consistent. We consider a slightly more general version of this result in the next subsection. As in the case without a fringe, the open-loop tariff is a threat: the importer is able to import at a low price in the current period by threatening a high tariff, and a resulting low world price, in the future. Distinguishing open-loop policies on the basis of whether they constitute threats or promises is sometimes useful. Arguably, it is harder to precommit to threats than to promises, since in the former case both the threatener and the threatened would like to permit a defection at a later time; with promises, it is in the interest of one of the parties to make sure that the open-loop plan is followed. The open-loop tariff is the unique optimal program from the standpoint of the dominant importer at the initial time, and it is (typically) not time-consistent. Therefore, it is generically true that requiring the importer to use a perfect strategy would reduce the discounted stream of his pay-off (below the level obtained in the open-loop equilibrium). Maskin and Newbery (1978, 1990) demonstrate a stronger result; they show that in a perfect equilibrium the dominant importer's total discounted pay-off may be lower than the level he would have achieved had he been able to commit to a zero tariff in every period, i.e. behave competitively. Such a commitment is not feasible in a perfect equilibrium. This result implies that market power may be disadvantageous '6. It is easiest to obtain a perfect equilibrium in a discrete time setting. We first consider the case were there are two periods, and then discuss how the problem generalizes to an arbitrary number of periods 17. A two-period model means that the resource is worthless after the end of the second period; one justification for such an assumption is the anticipated introduction of a substitute which is cheaper to produce than the extraction costs. The solution method uses dynamic programming. In the second period the dominant importer is faced with a standard optimal tariff problem. The dominant importer chooses the optimal point to l6 There is a growing body of literature that recognizes that increased market power, or, in an international policy framework, increased cooperation, does not necessarily improve welfare. " If there are a finite number of periods the perfect equilibrium obtained using the dynamic programming approach is often unique. The types of punishment strategies discussed in Section 2 cannot be used to support other outcomes, since the punishments always 'unravel'.

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L. Karp and D.M. Newbery

consume on the excess supply curve which, for prices greater than the extraction cost, is given by S2 -y2@). Here S2 is the remaining supply at the beginning of period 2, and the subscript on the fringe's demand function indicates that it may be non-stationary. The solution to this problem induces an equi!ibrium price function, p2(S2). Competitive producers have rational expectations and therefore understand that price in the second period will be given by this function, even though they do not behave strategically. If the resource is extracted in both periods, competitive arbitrage requires thatp, = ,D [P2(S2)- C] + C,where ,D is the discount factor. Rational expectations and competitive arbitrage may make it very costly, and perhaps impossible, for the dominant importer to influence the time path of extraction; this is the reason why market power may be disadvantageous. An extreme example illustrates this. Suppose that y2@) is arbitrarily close to zero and yl@) is large; that is, the fringe nearly disappears in the second period but has high demand in the first period. In this case the dominant importer can and will essentially expropriate whatever of the resource remains in the second period. Competitive arbitrage then implies that virtually all of the resource is extracted in the first period: producers have no incentive to delay extraction when they know that they will obtain a very low price in the second period. If the dominant importer's utility of consumption is low in the first period, relative to his utility in the second period, his total discounted utility under the perfect equilibrium is lower than under the equilibrium in which he behaves competitively (uses no tariffs). (To verify this, think of the limiting case where he has no utility of consumption in the first period and high utility in the second period -the opposite of the fringe's situation.) This argument does not rely on there being only two, or even a finite number of periods. Consider a continuous-time infinite-horizon model in which the fringe's choke price is finite but its demand is very elastic below this price. In this case (under a perfect equilibrium) price never rises above the fringe's choke price, and exhaustion occurs relatively quickly (due to the assumption of elastic fringe demand). Suppose also that the dominant importer's demand is positive at the fringe's choke price and is very inelastic at all prices. With this pair of demand functions, the dominant importer's total utility is likely to be lower in a perfect equilibrium than in the perfectly competitive regime. As in the two-period example, the reason for this result is that in the perfect equilibrium the dominant importer consumes much less than he would have under perfect competition. In a perfect equilibrium the possibility of disadvantageous monopsony power arises because of the competing importers: the dominant importer is not a pure monopsonist. In the absence of a fringe, monopsony power cannot be disadvantageous. This is easy to see in the two-period model. In the last period the monopsonist has a static problem, so market power can not be disadvantageous. For any stock level the monopsonist will charge a tariff, resulting in a lower price than would his competitive counterpart. In the second to the last period the monopsonist


901

could charge a zero tariff; if he were to do so the level of sales would be greater than under the competitive regime, due to the arbitrage equation and sellers' rational anticipation of a tariff in the second period. By charging a positive tariff in the penultimate period the monopsonist can induce the same level of sales as occur in the competitive regime. That is, it is feasible for the monopsonist to duplicate the competitive extraction path but pay lower prices in both periods: so market power cannot be disadvantageous. This argument can be extended to an arbitrary number of periods. Maskin and Newbery (1990) show that forward trading or storage can prevent disadvantageous outcomes. Futures markets allow the dominant importer to sell oil forward at an agreed price, which means that he will make losses on these futures sales if the second-period price is driven down, thereby effectively committing himself to the open-loop equilibrium. In the case of storage, negative stocks are infeasible, but the only case in which market power is disadvantageous is when the importer's future demands are relatively high - and if he stores oil he can meet this demand from his own stocks. Of course, futures markets typically have a limited future coverage, and storage is expensive relative to leaving oil in the ground, so that these options may not alleviate the problem of disadvantageous market power in practice. In summary, both the requirement of perfection and the presence of competing buyers are necessary for market power to be disadvantageous. The dominant agent's power is 'incomplete' or 'imperfect' in two senses: he cannot control the behavior of other buyers (since he is not a pure monopsonist), and he cannot make credible promises about his own behavior in the future (since he is restricted to using perfect strategies). The removal of either of these 'imperfections' is sufficient to ensure that market power is advantageous.

3.3. Oligopsonistic buyers We saw in the previous subsections that the problem of dynamic inconsistency arises in the cases where a single buyer faces competitive sellers with stock-dependent costs, or a dominant buyer faces a fringe of competitive buyers. The situation where more than one strategic buyer uses open-loop tariffs presents a minor variation of the latter case. Since each buyer takes the tariff trajectories of his rivals as exogenous functions of time, he behaves as if he were facing competition represented by a nonstationary rest-of-world demand, y(p,t). The fact that the form of the non-stationarity is caused by strategic behavior is of no concern to any individual buyer. Therefore the results of the previous subsection are not altered: the open-loop unit tariff rises at the rate of interest, and in most cases is timeinconsistent.

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Bergstrom (1982) points out that if extraction is costless and importers impose a constant ad valorem tax on consumption, the entire incidence of the tax falls on producers. This result holds because of two equilibrium conditions which must hold for any consumption tax. First, the intertemporal arbitrage condition requires that the producers' rent, which equals price (since extraction is costless) must rise at the rate of interest. The price at time t is thereforepo ert, wherepo is the producers' initial price. The (constant) ad valorem tariff can affect the price trajectory only by affecting the initial price. The second equilibrium condition is that cumulative consumption equals the initial stock level; this is the 'exhaustion condition'. Now compare two regimes with arbitrary but different (constant) ad valorem tariffs. Due to the arbitrage condition and the assumption of zero extraction costs, the ratio of producer prices in the two regimes is a constant (given by the ratio of the initial prices). We now use the exhaustion condition to show that the consumer prices in the two regimes are the same. By the previous remark, the ratio of consumer prices is a constant, given by the product of the ratio of the initial producer price and the ratio of 1 plus the tariff. This means that the two consumer price trajectories are either identical or one lies strictly above the other. In the latter case, the exhaustion condition cannot be satisfied in both regimes. Therefore it must be the case that the trajectories of consumer price are the same for both regimes: the tariffs affect producer prices but leave consumer prices unchanged. The entire incidence of the tax falls on producers when extraction costs are zero 18. Bergstrom studies a one-shot non-cooperative game amongst importers in which they each optimally choose a constant ad valorem tariff, and each takes the tariffs of other importers as given 19. By the previous argument, producers bear the entire incidence of the tax (for zero extraction costs). He points out that in general a constant tariff is not an optimal response, except for the special circumstance where all importers have constant elasticity of demand. In that case, the open-loop Nash equilibrium does involve a constant ad valorem tariff. Karp and Newbery (1992) show that if the importers in the non-cooperative game are identical and if extraction costs are a constant, c, then the open-loop Nash equilibrium to the game in which importers choose unit tariffs is time-consistent if and only if demand in country i is qi@) = a'k(ai - c)-€, where a' is the domestic, I s If extraction costs are constant but positive, a constant ad valorem tax does alter the price trajectory that consumers face, so consumers bear some of the tax burden. In this case a constant tax based on the difference between the producer price and cost shifts the entire burden to the producer and is equivalent to a rent tax. l 9 When there is a dominant agent using an open-loop policy, we can think of him as choosing either a consumption trajectory or a tariff trajectory to support that consumption trajectory. In the noncooperative game each agent takes his rivals' tariffs as given. The individual is indifferent between using price and quantity controls; but it does matter what each agent takes as given. That is, importer i's optimization problem differs depending on whether he takes as given his rivals' import trajectories or their tariff trajectories, and in the latter case it matters whether he takes as given unit or ad valorem tariffs.


903

tariff-ridden price. If the scaling parameter a' is country-specific, this form is sufficient for the open-loop Nash equilibrium to be time-consistent. The condition for consistency is stronger, when there is more than one buyer, than in the pure monopsony case. In the latter case constant costs are necessary and sufficient, whereas the former requires constant costs, a particular demand function, and a particular relation between the parameters of the demand function and cost. The conditions given above for time consistency of the open-loop Nash equilibrium hold if importers choose unit tariffs. If, however, importers choose ad valorem tariffs and the demand functions are as shown, the additional restriction that c = 0 is required for the open-loop equilibrium to be time-consistent. In general the open-loop Nash equilibria differ depending on whether unit or ad valorem tariffs are used; constant elasticity of demand and zero extraction costs provide an exception. Static games also predict that Nash equilibria differ depending on whether agents use ad valorem or unit tariffs, so it is not surprising that the same result carries over to dynamic games. Recall that for any level of constant extraction cost the open-loop unit tariff rises at the rate of interest. Therefore the ad valorem equivalent is a constant if and only if world price also rises at the rate of interest, which requires that extraction costs be zero20. In the case where the pure monopsonist confronts competitive producers with constant extraction costs, we saw that although the open-loop tariff is not perfect, the same result could be sustained as a perfect equilibrium using the feedback form of the open-loop tariff. In general, this procedure does not work if there is more than one strategic agent. Consider the case of constant extraction costs and the demand function ql(p) = a'k(al - c)-€ so that the open-loop unit tariff is time-consistent. In principle it is straightforward to find the feedback form of this function; that is, to write i's (open-loop) equilibrium unit tariff as a function of the current stock. If, however, j takes the function rather than the tariff level as given, his decision problem is altered; he then know that he will be able to affect the trajectory of i's future tariffs by deviating from his own open-loop tariff level, and thus altering the rate of extraction. This result holds even if c = 0. If, however, c = 0 and the importers (with constant elasticity of demand) choose ad valorem tariffs, then the open-loop tariff can be sustained using the feedback form of the open-loop policy. The reason here is that the (open-loop) equilibrium involves a constant ad valorem tariff, so the feedback form is simply the trivial function: the equilibrium tariff is independent of the stock2'. Therefore importers have no incentive to deviate from their equilibrium tariff in the hope of inducing their rivals to deviate. It is likely that this restriction could be relaxed by, for example, making the ad valorem tax depend profit (rent) rather than price. The proof of independence follows from the fact that the constant ad valorem tariff is time-consistent in this case. The range of possible stock levels is from zero to the initial stock. By the fact of consistency, the constant tariff chosen at the initial time represents an equilibrium at all initial times, and therefore from all initial stocks.

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From these remarks it should be clear that open-loop strategies are unlikely to result in a perfect equilibrium. It is worth considering how to construct such an equilibrium. For reasons discussed above, we restrict attention to Markov equilibria. For discrete-time models with general functions, dynamic programming can be used; this approach becomes unwieldy if there are more than two periods. The infinite-horizon continuous-time model is often easier to work with. Markov equilibria in these models involve decision rules for agents; these give the current control (e.g. tariff) as a function of the current stock level. In a stationary model it is reasonable to look for stationary decision rules. These decision rules and the optimizing but non-strategic behavior of producers induce a function which gives the current price as a function of the current stock level. Although the price function is endogenous to the game, each importer (even where there is a single importer) takes it as given. This price function is a sufficient statistic for any single player. He does not have to know his rivals' decision rules; he is able to predict how he himself will behave in the future, but is unable to commit himself to future actions which will be suboptimal given the stock level at the time the actions occur. (Importers are unable to make binding commitments.) The problem then is to find a price function such that when all importers take this function as given, their optimal decision rules and producers' behavior induce that price function. It is easy to solve this equilibrium in the case where all agents have linear demand functions with the same choke price, p, and the cost of extracting at rate Q is (ko - klS)Q, provided that p < ko. A linear price function and linear decision rules provide a stationary equilibrium for this model. The importance of the last inequality is that it insures that the non-negativity constraint on the stock is satisfied. If that inequality is not satisfied, there is no linear equilibrium. The problem with linear demand and constant extraction costs is consequently more difficult. An analytic characterization of the equilibrium for that case has not been obtained. Karp and Newbery (1991) show that it is given by the solution to a system of ordinary differential equations; this can be solved numerically, and their solutions are discussed in the reference. There are several features of the Markov equilibrium that are apparent from its definition, and other features which can be determined from numerical solutions to particular problems. Since the equilibrium price must be increasing over time and the stock level must be decreasing over time, given any initial stock level greater than zero, it must be the case that the equilibrium price function decreases in the stock level. Since each importer takes the current stock and the price function as given, he takes as given the current price. The incentive to use the tariff remains, however. Current tariffs affect the rate of extraction and thus the evolution of the stock, and thereby affect future prices and future tariff revenues. Numerical solutions provide further insights into the perfect tariff. For the case of n identical importers with linear demand, and constant cost of extraction, the perfect (unit) tariff is non-monotonic in the stock, as Figure 1 shows. [This figure,


3.5

,

Tariff levels

0.125

I

0.5

2

8

32

128

Stock (log scale) - Perfect

Nash

- Reneged

Fig. 1. Tariff levels as stock varies.

taken from Karp and Newbery (1991), gives the tariff levels when the terminal pricep = 10 and c = 1. The figure shows two other trajectories, labelled 'Nash' and 'reneged'. These are described below.] For low levels of stock, the equilibrium tariff is increasing in the stock. For large stock levels the tariff is decreasing. Since there is an inverse relation between the remaining stock and calendar time, this means that for large initial stock levels the tariff initially increases and later decreases over time. In the Markov equilibrium (as in the open-loop equilibrium) player i's unit tariff equals i's shadow value of the stock. The previous remarks imply that i's value function is concave in stock at large stock levels and convex at low stock levels. To understand why, consider the limiting cases as the stock approaches either infinity or zero. In the former case, the fact that i's value function is bounded above (because of discounting) and non-decreasing in stock, implies that it must be concave (under the maintained hypothesis that it is differentiable). The value function is also bounded below by zero, and is equal to zero when the stock is exhausted). Moreover, the shadow value of the stock (for player i) approaches zero as the stock approaches zero: as the importers compete for an arbitrarily small remaining stock they drive the price to their choke price. These remarks imply that the value function must be convex near the origin. The economic interpretation is as follows. When the stock is arbitrarily large the situation of the buyers approximates that of importers of an ordinary good that

L. Karp and D.M. Newbeiy Reneged tarhent

Nash tartrent

8 25

0.125

0.5

8

2

32

128

Stock (log scale)

-

Narh 2

-

- Reneged 2

Nash 4 Reneged 4

Nash 8

- - Reneged 8

Rauo to perfect tarifflrent, r = 5%

Fig. 2. Tarifflrent as n varies.

can be produced at constant costs. In this case the excess supply curve facing any importer is perfectly elastic, and it is optimal to impose a zero tariff. As the stock becomes very small competition amongst the importers for the remaining supply intensifies, as suggested above. This is because the supply (a flow) must approach zero as the stock approaches zero (as can be shown using a proof by contradiction), so the excess supply facing any importer is again infinitely elastic and a zero tariff is optimal. For intermediate stock levels a positive tariff is optimal; hence the nonmonotonicity. Karp and Newbery (1989) compare the perfect equilibrium to a 'reneged or naive open-loop equilibrium'. In the latter, at each moment importers choose a trajectory of open-loop tariffs. However, only the tariff in the first period (instant) is used. The importers are able to continually revise their policies. This is an implausible description of a market (why would anyone continue to believe the announcements?) but it is useful as a benchmark. The reneged open-loop tariff lies above, but has the same shape as, and appears to provide a good approximation to the perfect tariff, as Figures 1 and 2 show. The approximation improves with the number of importers, n, and is very close for three or more. The reneged open-loop tariff is useful because its simplicity makes it easy to compute even for asymmetric games - thus Karp and Newbery (1989) compute it for the case of the single dominant importer. To the extent that it approximates the perfect equilibrium

Ch. 19: Intertemporal ConsistencyIssues in Depletable Resources

907

it is an appealing alternative to a difficult computational problem. Figure 1 also illustrates that the naive open-loop tariff tends to be more 'pro-competitive' than the Markov tariff. When agents use Markov strategies they have an incentive to 'preempt' their rivals by using a relatively low tariff in order to consume more of the stock, and thus influencing rivals' future tariffs. This preemptive incentive is absent with open-loop strategiesz2. We conclude this section with an alternative description of buyer and seller interaction. The model discussed above assumes that at each moment (i.e., each period) importers choose their tariffs knowing how sellers will arbitrage supply intertemporally. Importers thus make their decisions before sellers in each period while sellers have rational point expectations of how importers will behave in the future. In this case, importers view aggregate supply at each moment as perfectly elastic. An alternative is to assume that buyers and sellers make their decisions simultaneously within a period, in which case the outcome is the same if sellers move first. Each agent's decision is conditioned on the current level of the stock. As above, importers are strategic and sellers are price takers with rational expectations. If importers take sellers' decision rules as given, and take the current stock level as given, then at each instant they take the current aggregate flow of supply as fixed. In contrast to the previous model, importers here act as if current aggregate supply is completely inelastic; they play a succession of static tariff setting games. In this case the equilibrium tariff for country i is

where ri is the tariff imposed by country i and is demand by country j. When the demand schedule is linear, so that demand by i is qi = cui,O(p - p - T'), and cui is the market share of country i when the aggregate (untaxed) demand schedule is Q = p ( p -p), then the formula for the tariff is

The resulting equilibrium, referred to simply as 'Nash', is graphed in Figures 1 and 223. The papers by Fershtman and Kamien (1987), Reynolds (1987), Kaep and Perloff (1988) and Van der Ploeg (1987) provide other examples where Markov strategies are more pro-competitive than open-loop strategies. Fudenberg and Tirole (1986), discuss situations where Markov strategies are either more or less pro-competitive than open-loop strategies. 23 This terminology is not entirely satisfactory, since both tariffs are Nash and both are perfect. In Karp and Newbery (1991) we use the inelegant but more accurate terminology PIMF and PEMF - 'perfect, importers move first' and 'perfect, exporters move first'. The former is shortened to 'perfect' and the latter to 'Nash', purely because perfect sounds as though it involves a more complex determination, and Nash sounds as though it is simpler, both of which are the case here. 22

908

L. Karp and D.M. Newbe~y

4. Strategic sellers, competitive buyers We have seen in the previous section that if buyers are strategic, and sellers both competitive and able to arbitrage instantaneously prices by switching their sales between different time periods, then open-loop import tariff plans are DI, except for special cases. There are a number of papers characterizing the intertemporal equilibrium of an exhaustible resource where there is market power on the sellers' ~ i d e 2in~ contrast , to the rather small number which look at the buyers' or importers' side. The consensus is that the open-loop Nash-Cournot equilibrium in which the sellers each take the extraction profile of the other sellers as given, is timeconsistent. The obvious question to ask is "wherein lies the difference in the two kinds of problems which explains the difference in the dynamic consistency of the open-loop equilibria?" Agents that wield market power do so subject to the constraints imposed by optimizing behavior of non-strategic agents. For exhaustible resource problems it is standard to model competitive sellers as solving dynamic problems, while competitive buyers typically solve a sequence of static problems - given the current price of the exhaustible resource, how much should the country buy? There are exceptions - if buyers are selecting durable goods or investment goods, then they must decide on the time path of investment or purchase by solving an intertemporal problem, and it is notable that the open-loop solution to such problems [for example, the durable good monopolist described by Bulow (1982), Coase 1972, Kahn (1987)l frequently exhibit DI. It is also the case as argued in the previous section that one can restore the symmetry between the two types of problem by modelling the sellers as Nash suppliers choosing a time profile of extraction plans. Once the link between different time periods has been severed on the supply side of the market, the open-loop Nash equilibrium is again dynamically consistent. It is perhaps natural to model oligopolistic supply models as open-loop Nash equilibria, but this is only one of the possible market structures. Pure monopoly on the supply side is a straightforward generalization of the classic Hotelling (1931) problem, except that marginal revenue instead of price is arbitraged. [Stiglitz (1976), Sweeney (1977), Hoe1 (1978), Dasgupta and Heal (1979)l. Given the absence of any other strategic agents making dynamic decisions, there is no problem of DI. The other main type of market structure which has a natural appeal for modelling the oil market is that of a dominant producer (or cartel, such as OPEC) facing a competitive fringe of suppliers (the non-OPEC oil producers). The natural equilibrium concept is that of von Stackelberg (1952), in which the cartel takes the supply behavior of the fringe as given, and optimizes against this. See, for example Bergstrom et al. (1981), Gilbert and Goldman (1978), Gilbert (1978), Lewis et al. (1979), Loury (1986), Newbery (1981), Pindyck (1978), Salant (1976), Ulph and Folie (1980), Ulph and Ulph (1989).

24


909

Several papers [Gilbert (1978), Ulph and Folie (1980,1981), Newbery (1981,1984), Ulph (1982), Ulph and Ulph (1989), Groot, Withagen and de Zeeuw (1989)l explore this equilibrium concept and show that the 'Binding Contract' or openloop Stackelberg equilibrium, in which the cartel announces that it will follow its best open-loop plan, is potentially DI. What is interesting about these results is that the open-loop Stackelberg equilibrium is not necessarily DI, in contrast to the case of a dominant buyer, where, except for a knife-edge case, the open-loop equilibrium is always DI. The reason is that although there is a jump state in these problems, in which the costate variable can be freely chosen to be zero at time zero, it may be that the costate then remains at this zero value - that is, there is nothing in the problem to change its value. In practice, the papers cited have not used this diagnostic technique to identify cases of DI - instead they have checked the open-loop Stackelberg equilibrium directly to see whether the cartel would have an incentive to deviate subsequently. This raises the question of whether the time-consistent open-loop Stackelberg equilibrium is perfect. The answer, as before, is no, for if the fringe deviates or sells a non-optimal amount, then fringe stocks will differ from that expected. If all agents were to recompute their optimal open-loop strategies from the present stocks, the paths would not coincide with those previously computed, and in that sense the cartel's open-loop plans are not perfect. However, if the cartel's original openloop extraction plans are transformed into a function of remaining stocks instead of time, then there would be no need to recompute a new plan, and the original strategy would be Markov perfect. This was described in the previous section as the 'feedback form of the open-loop policy'. With that modification, if the openloop Stackelberg equilibrium is time-consistent, it can be supported as a Markov perfect equilibrium, since it reflects all the available market power (at least, in the Markov setting in which the fringe have perfect foresight). For the simple market structure of a single dominant producer one does not have to worry about the vexing problems of oligopoly (which, of course, are not peculiar to dynamic games). The next section surveys this literature. 4.1. Dominant seller facing competitive fnnge: Open-loop equilibria

There are two different solution techniques and two alternative ways of modelling fringe supply. The standard approach is to model the problem as a singleagent intertemporal maximization problem using Pontryagin's Maximum Principle, where the behavior of the fringe producers is taken as a constraint on the actions of the cartel, and is described by an arbitrage equation. The problem with this approach is that it is often opaque and inaccessible to all but the most mathematically literate. Because the emphasis is on the formalism of problem, early practitioners were slow to identify issues of DI. The alternative, advocated by

L. Kavp and D.M. Newbery

910

Newbery (1981), is to develop an intuitive, quasi-graphical approach which makes the analysis accessible to mathematically unsophisticated economists, drawing on principles with which they are familiar. Given the emphasis on visualizing the result and understanding the interaction of objectives and constraints over time, it is easier to see whether the proposed equilibrium is dynamically consistent. There are limitations - it is necessary to simplify the problem (constant unit extraction costs, static demand), though the same is typically true for deriving analytically tractable solutions using P~ntryagin'~. There is a more serious problem with both techniques, and that lies in piecing together the successive phases. With intertemporal control problems such as these, there are a sequence of constraints, not all of which will bind at each moment. Successive phases are distinguished by the set of binding constraints, and much of the skill in deriving the full solution lies in determining the correct sequence and in piecing together the successive phases. Provided the co-state variables are continuous across the boundaries of successive phases it is relatively simple to piece together the solution path, and, acting on this assumption, earlier papers have proposed solutions to this problem. However, Groot, Withagen and de Zeeuw (1989) have pointed out that this assumption of continuity of the co-state variables is unwarranted, and argued that as a result, the equilibrium price path may also be discontinuous. Their approach also illustrates the second of the two alternative methods of modelling fringe supply. The standard method is to describe the outcome of competitive arbitrage in terms of a competitive price path which constrains the sales of the cartel. The other method, which is equivalent, but suggests a different set of control variables, is to take fringe supply as a function of the price and cartel supply (essentially computing the residual demand facing the fringe). Groot, Withagen and de Zeeuw (1989) adopt this approach which enables them to model the cartel's problem as one in which the choice variables are production levels. The cartel's maximization problem is 03

ax

[P - cC- xC(t)- xf(t)] xC(t)e+"' dt,

subject to

Ulph and Folie (1981) assume time-invariant linear demand and constant unit extraction costs, and follow a more informal analytical approach to piecing together the phases without recourse to the Maximum Principle.

25


Price

Demand

Fig. 3. Marginal revenue with limit price.

dXf(t) = 0, dt xC(t)+xf(t) + cf + Xf(t)e" - p 2 0 xf 0

comp.,

where xC is cartel extraction, xf is total fringe extraction (all members being identical), ci is unit extraction cost (i = c, f), the demand schedule is linear: p = p - Q (Q being total demand), Xf is the co-state variable for the typical fringe producer's stock depletion decision, and Si is remaining stock. The control variables are xC(t) and x f ( t ) , and the state variables are SC,Sf, and Xf. For this problem the constraint qualification (required for the normal application of the Maximum Principle) does not hold at some points, and the authors rely on an alternative set of necessary conditions, due to Neustadt (1976), and set out in Seierstadt and Sydsaeter (1987). These alternative conditions do not require the co-state variables to be continuous, and in this problem they can indeed be discontinuous. With this qualification in mind, we can still approach the derivation of the solution geometrically, using the principles enunciated by Newbery (1981). These require a number of simplifying assumptions. The first is that the maximum feasible sales price exceeds the unit extraction costs from all stocks or fields (and this can be taken as the defining characteristic for inclusion of a field among the set of economically viable resources). Next, extraction costs are stock-independent

L. Karp and D.M. Newbeiy Price

Demand

12

-1

2

Time to go

Fig. 4. Dynamically consistent open-loop equilibrium.

by field, and finally, that demand is ~tati0nar-y'~.The first principle, already mentioned, is the Hotelling arbitrage principle, which requires the equality of the present value of the marginal rent at each moment of positive production. For a competitive producer, the marginal rent is equal to the rent, or the price less the marginal cost, but for an agent with market power it is equal to the marginal revenue less the marginal cost. The second principle is that the price path can be computed as a function of 'time to go' (to exhaustion), working back from the terminal price, which is the maximum feasible sales price for the resource (equal to p, the choke price, above). Over the period to this terminal date all stocks of oil must be exhausted (if they are competitively supplied), or the stocks of oil that the cartel finds it advantageous to sell must be exhausted. This principle can be described as the exhaustion principle. Finally, the ability of the fringe to arbitrage prices presents the cartel with a truncated or kinked instantaneous net demand schedule, as shown in Figure 3. The cartel can sell an amount up to q{p(t)) at a price infinitesimally belowp(t), and its marginal revenue will there be equal to the sales price as it faces a perfectly elastic net demand. If it wishes to sell more thanq{p(t)), then it faces the original demand schedule with the old marginal revenue lying below it. The marginal revenue will thus be discontinuous at point B, dropping from B to A. This shows that the cartel This assumption of stationarity can be relaxed, but then the location of the terminal date will require iterative calculations.

26

Ch. 19: Intertemporal Consistency Issues in Depletable Resources Price

!

Time to go to exhaustion

Fig. 5. Dominant producer price path

will be willing to sell at p(t) or at point B if the opportunity cost of the oil (i.e. its present discounted value if sold at some other date) lies between A and B. Figure 4 shows the application of these principles when the fringe extraction cost is substantially above the cartel's unit cost. The location of the various points is found as follows. The point E is fixed by the choke price, p, and the competitive price path EDC is found by the arbitrage principle. At a date z years before exhaustion, the price is

where p,C is the competitive price at time-to-go z. The length of E D is such that cumulative demand is equal to fringe stocks. At point D the cartel's marginal rent must be equal to the competitive price less cartel cost (since the fringe imposes a limit price as in Figure 3). Along AD the marginal rent rises at the rate of interest, and this locates the monopoly price path CB. For the linear demand schedule is given by

where p m ( t )is the monopoly price and m(t) is marginal revenue at time t . The starting date, initial price, and time taken before the exhaustion of all oil is determined by the requirement that along the cartel's extraction path BCD, cartel

914

L. Katp and D.M. Newbery

oil is exhausted at the moment the price reaches DZ7.The open-loop equilibrium is dynamically consistent, for the same solution would be derived starting from any point during the cartel's extraction phase BCD. The fact that the fringe does not deplete any of its oil until all the cartel oil is exhausted means that the constraints facing the cartel do not change over time and cannot be affected by the cartel's actions, so the conditions under which DI is a problem never materialize. One other simple case occurs when the cartel's extraction costs are, implausibly, above that of the fringe: cc > cf. This implies that the fringe extracts before the cartel starts to produce, as in Figure 5. The monopoly price path ABM is located by the marginal revenue path ADF, and BCDE is a competitive price trajectory, located so that the cartel exhausts along CBA and the fringe exhausts along EDC. The exact location of point B is found by balancing two offsetting tendencies. Along BC the cartel is constrained by the limit price of the fringe for the following reason. Although the fringe does not plan to sell after C, if the cartel announced in advance that it planned to sell at any higher price than those along the continuation of the competitive price path beyond DC, then the fringe would not choose to sell along ED, and the proposed solution would not be an equilibrium. Consequently, the cartel cannot announce sales on a price trajectory higher than CB, but, other things being equal, it is willing to supply provided the market price lies between the unconstrained monopoly price and the marginal revenue trajectory (which gives the value of delaying extraction until some point on the unconstrained trajectory BA). However, other things are not equal, as the length of the constrained extraction phase, BC, is a choice variable. The longer is the constrained phase, the lower is the price at C, and the faster is the cartel oil and the fringe oil extracted. This advances the date at which oil is first sold by the cartel (at C) (and is therefore desirable), but lowers its price (which is undeciralde). Balancing these two factors determines the location of point C. This open-loop equilibrium is clearly DI, for once the fringe has extracted all its oil at C, the cartel is free to raise the price to the unconstrained monopoly level along ABM. Knowing this, the fringe would retain some oil to benefit from the capital gain as the price is raised from C to some point on BM. If the cartel is unable to make binding commitments, the fringe will not cease extracting until the price has reached the unconstrained monopoly price trajectory. One solution that is dynamically consistent is the open-loop Nash-Cournot equilibrium, in which the cartel takes the fringe's extraction trajectory at the initial date as given (and similarly each fringe member chooses its extraction plan given that of all other agents; as argued above, in the limit as each fringe member is a vanishingly small fraction of the total fringe, they behave competitively, but

*'

The sequencing of the cartel and fringe extraction phases is determined by the relative steepness of the price paths at their point of intersection C . The cartel price path is steeper, encouraging the fringe to delay extraction until after the cartel is exhausted.


Price

Time to go

Fig. 6. Dynamically inconsistent open-loop equilibrium.

aggregate fringe supply is still given at each date). The equilibrium is shown in Figure 5 as ABMNFG. Along G F the fringe is the sole seller, along MBA the cartel is sole seller, and along FNM both sell, with the fringe share gradually moving from 100% at F to 0% at M. The point F is found from the intersection of the marginal revenue trajectory ADF with the competitive price trajectory MNFG. The sales level of the cartel is given byxm = O, - m)lb, where b is the slope coefficient of the linear inverse demand schedule. Again, the location of this trajectory is determined by working back from the terminal price, and its location is independent of the fringe stocks28.The Nash-Cournot equilibrium is one in which everyone takes the others' extraction rates as given, so there are no jump states and the equilibrium is dynamically consistent. All these equilibria have continuous price paths. In the first case, the cartel cannot sell at a price above the competitive price path, for the fringe would then flood the market. He will either sell at the unconstrained monopoly price or at the highest price limited by the fringe - and so the price path will be continuous at points such as C and D. This is not the case if the fringe has higher extraction costs than the cartel, but not so much higher that the fringe extracts in the final phase. The location of M and MF depends only on total cartel stocks, though if the fringe does not have enough stocks to supply along the whole of FM, then that part of the path will be truncated, and extraction will start somewhere along FM.

916

L. Karp and D.M. Newbe~y

Figure 6 shows a possible sequence in which the cartel sells in the final phase along an unconstrained monopoly price trajectory AB, and is constrained by the competitive price trajectory BCD in the early phase. Given that the cartel is constrained by the competitive price path, it would prefer to sell earlier rather than later on that path, i.e. along DC, as its costs are lower than those of the fringe (and hence its present discounted rent is falling with the passage of time along DCB). Again, there is a problem of deciding the location of the point B, but once that is done, the length of BC is such as to exhaust the fringe, and the initial price and time until exhaustion is such as to exhaust the cartel along DC and BA taken together. Now consider raising the competitive price path an infinitesimal amount to FGH. The rate of supply will be lower at each point (i.e. at each point equally distant from the date of exhaustion) as the price is higher, and so the period of sales along the competitive path will be slightly extended, as shown. This will be a small-order effect. The price at which the cartel sells along HG will be higher, which will be more profitable. Finally, the downward jump in the price at date F creates no problems, as the fringe plans to exhaust over GF, and will not find it attractive to delay until after F and face a capital loss. As BA is the unconstrained monopoly price path, the cartel will not wish to sell at the higher price F, and so this is a satisfactory equilibrium for the cartel. The argument is that it would be desirable to raise the competitive price path, starting from a continuous price path such as DCBA, as this has a first-order positive effect on cartel profits during HG, and only a small effect in delaying the date of the monopoly sales along BA. As the competitive price path is raised further, this delay becomes increasingly costly, until at some point the balance of initial advantage is offset by the extra delay of subsequent profits. Groot, Withagen and de Zeeuw (1990) give the formal derivation using the Maximum Principle, and show how to locate the various phases and the initial price. An alternative approach is to see the problem as a choice of two variables: the level of the competitive price at the moment of fringe exhaustion and the date at which the final cartel phase begins, at B. Further examples of discontinuous price paths are given by Groot, Withagen and de Zeeuw (1992) and are discussed by Newbery (1992b). It may not be so obvious that this open-loop equilibrium is DI, but the location of the competitive phase FG depends on balancing the advantages of higher cartel prices along G H with deferred profits along BA. With the passage of time, the cartel would like to change the location of this competitive segment, and to raise and defer it, to further raise the current cartel price. This problem would arise even if there were no discontinuity in the price path at F, and the discontinuity itself creates no problems of DI, at least on the assumption that consumers are passive and only concerned with the current price. In a world in which consumers held precautionary stocks, a prediction that the price would move sharply down in the near future would be accompanied by a fall in stockholding, though once consumer stocks had fallen to zero, nothing further could be done to undermine


917

the equilibrium. As for the cartel, B is the unconstrained profit maximizing price, and F, being above B, is therefore not an attractive alternative. If the fringe stocks are relatively small, then the competitive price path during which the fringe sells may be above the unconstrained monopoly price at a points such as G where the fringe begins to sell. The competitive price path may still intersect the monopoly path, and the sequence would then be: a first phase in which the cartel is constrained by this competitive phase, a second phase in which the competitive price exceeds the monopoly price and the cartel is unconstrained, a jump up in price to the competitive level when the fringe begins to sell, followed by a jump down at a point such as F to B, and the final unconstrained cartel phase. Discontinuities can only occur between the monopoly phase and the competitive phase in which the fringe is selling, and only when the competitive price is above the monopoly price. Of course, if consumers can store oil and have rational expectations, then upward jumps in the price cannot occur - consumers would buy in anticipation, and then consume from stock until the point at which the cost of purchasing and holding the stock (price plus the accumulated interest) were equal to the market price. Newbery (1981) has pointed out that other cases of DI may arise if the cartel delays extraction not because fringe costs are relatively low compared to cartel costs, but because the cartel discounts future oil rents at a lower discount rate than the fringe. This is quite likely because issues of sovereignty which are the source of the inability to enforce international oil supply contracts will also lead to a fragmented capital market. Capital surplus oil exporters, whose marginal product of investment is below that in oil-importing countries, but who have nationalized the overseas concessions of the oil-importing countries during the OPEC crisis, will be understandably wary of locating immobile capital hostages within those oilimporting countries, for fear they be expropriated in due course, if not explicitly, then by taxation. Lower OPEC interest rates will encourage the cartel to delay, inducing fringe producers to extract first. As a result, OPEC will be left with relatively greater market power in the future - and, indeed, this seems to be the current pattern, with the high-cost fringe producers like the UK, Norway and the US extracting as rapidly as possible, despite low Reserve/Production ratios, and the low-cost Gulf States extracting at far less than capacity, while their ReserveIProduction ratios remain high. It would therefore be rational to expect OPEC's market power to increase over time unless non-OPEC discoveries proceed more rapidly, or alternative sources of fuel become available. 4.2. Peqfect Stackelberg equilibria

If the open-loop Stackelberg equilibrium is dynamically consistent, then it can be supported as a perfect equilibrium, by constructing the feedback form of the open-

918


loop strategy, as explained in Section 3.1. This involves solving for time or time to go as a function of fringe and cartel stocks, and then replacing time by this function of stocks in the expression for the cartel's extraction plan - making the cartel's decisions depend on current stocks. Provided there are no errors or disturbances to stocks, the feedback solution will appear identical to the open-loop solution. If the open-loop Stackelberg equilibrium is DI, then the perfect equilibrium will differ from the open-loop equilibrium, and it will not be possible to derive it from the open-loop solution. Newbe~y(1980, 1992a) presents a model in which the openloop Stackelberg equilibrium is DI, and derives an analytical expression for the perfect equilibrium. The model is set up in discrete time, and there is a date T after which oil is valueless. Demand in each period is given by the same unit elastic demand schedule, truncated above by a 'backstop' price, p, sufficiently high not to affect the open-loop or competitive equilibria. Extraction costs of fringe producers are zero and those of the cartel are constant at c. The model thus captures the idea that the cartel will have a comparative advantage in delaying sales. The (truncated) unit elastic demand means that the cartel's price would be set at the backstop price in the absence of the fringe, dramatically illustrating its potential market power. The open-loop or binding-contract equilibrium is easy to characterize, for the cartel will be constrained by the competitive price path over the whole T periods, and the competitive price is given by

where ,B < 1 is the discount factor, or 1/(1 + r ) , if r is the rate of interest. The cartel will not plan to sell more than Sc < Sb, and if the fringe stock is SL, then the initial price is given by

which comes from the fact that demand in any period is llp(t). The fringe sells first, the cartel sells last, and the cartel chooses SCto determine a profit-maximizing initial price. Clearly, this equilibrium is DI. The cartel will wait until the fringe has exhausted, and then raise its price top for the remaining time periods. The perfect equilibrium is found recursively. Let n denote the number of time periods remaining before oil becomes valueless (n = 0, 1, . . . , T.) Let the terminal price be p, so that pn = ,Pp is the price n periods before the terminal date. Let supply by the fringe beyn, supply by the cartel bex,, and remaining stocks be Y,, X,, all in period n. In the final period, or period 0, the cartel choosesxo to maximize:


subject to demand equals supply:

The solution is

The cartel's credible supply is a function of the state of the system, and can be written as

Fringe supply in the final period is particularly simple: Yo = Y O ( ~yo) O , = yo.

(4.11)

In the penultimate period the cartel announces X I , and the fringe chooses yl, and hence yo = Y1 -yl, knowing that the cartel will sell an amount xo = $o(Xo,Y1 -yl), and hence knowing what the price will be in the final period. Define the critical credible stock as the maximum amount that will be sold by the cartel in future periods, then, provided at any date the current cartel stock exceeds this critical level, the future sales of the cartel will be solely determined by fringe stocks. In that case

The cartel choosesxl to maximize the two period discounted profits, where prices in each period are ultimately a function of Y given, and X I ,a choice variable. The resulting solution gives a value for x l , xo, and hence the critical credible stock in period 1,XT(Y I), a function of fringe stock. This technique works recursively, and analytical recursive relations can be found for the sales of the fringe in each period, the price, and hence the sales of the cartel. Cartel sales will be positive, working back from the terminal date, until the critical credible stock in period n first exceeds the initial cartel stock. If this does not happen before reaching the initial date, the cartel will sell in every period, not just the final n periods. Newbery (1980,1992a) gives the recursive formulas and solves these numerically for a range of values of the cartel extraction cost, c. It is easy to derive the open-loop Nash-Cournot equilibrium (OLNCE), and the competitive equilibrium (CE), and to compare the cartel's profits in each of these equilibria,


Profits

Cartel costs

Fig. 7. Cartel profits.

and in the open-loop Stackelberg (OLSE) and feedback Stackelberg (FBSE) or perfect equilibria. The comparisons are given in Figure 7 29. It is clear that the OLSE must yield the highest level of cartel profits, as any of the other equilibria were feasible OLSE but were not chosen. None of the other equilibria can be ordered, and examples of each ordering are visible in Figure 7. In particular, as with the perfect import tariff of Maskin and Newbery (1976, 1990), the agent with market power may be disadvantaged by his market power in the absence of the ability to commit, relative to the competitive equilibrium in which he exercises no market power at all. Given the difficulty of computing the perfect equilibrium it is worth asking whether there are any plausible candidates which can be computed and are not too different from the perfect equilibrium. Karp and Newbery (1989) show that the reneged or naive open-loop Nash equilibrium3O is a reasonable approximation to the perfect Nash equilibrium in a dynamic game of symmetric importers each with market power facing a competitive supply, as illustrated above in Figures 1 and 2. The parameters are: discount rate = 5%; T = 30; Fringe stock = 30; cartel stock = 10. This is found by solving for the optimal open-loop decision at date t as a function of the remaining stock at that date, and then characterizing the decisions of the agent as functions of his remaining stock. There is of course an implausibility inherent in computing the current open-loop decision on the assumption that the whole time path of future decisions will be adhered to, when at each successive moment they will in fact be recomputed. But the concept is useful only in so far as it approximates the perfect equilibrium, not as a plausible equilibrium concept in its own right.

29

30


921

Would the same approach work in the current problem, bearing in mind that there is an essential difference between an oligopolistic equilibrium, and a dominant agent or Stackelberg equilibrium? It is, however, clear that the reneged open-loop Stackelberg equilibrium is not a candidate in the above example, for until the fringe exhausts its stocks, the cartel makes no sales. It is true that the total amount that the cartel plans to sell in the future (i.e. the critical credible stock in the language above) depends on the amount of fringe stock remaining, but if the fringe continues to believe that the cartel is committed to its original plan, the fringe will observe nothing to persuade it that the plan has changed, until it finally exhausts and the cartel reneges. A more promising alternative is the feedback Nash-Cournot equilibrium. This is computed in the same way as the perfect equilibrium, working back from the terminal period, but differs in that in each period the cartel and the fringe each choose their supplies without observing the plans of the other. In the Stackelberg equilibrium the fringe decides its output in each period after observing the cartel's supply decision, and the cartel takes this response into account in choosing its supply. The two equilibria coincide in the final period, since at that date the fringe must sell all its remaining oil. Newbery (1992a) shows that in the above model, if the cartel has enough oil, then the feedback Nash-Cournot equilibrium coincides with the open-loop Nash-Cournot equilibrium. (In Figure 7 this holds for c 3 0.6.) The reason is that if the cartel would not wish to sell all its oil, then cartel sales in later periods will not affect sales decisions in earlier periods, since they do not affect the effective availability of oil then - a situation corresponding to the open-loop Nash-Cournot equilibrium with excess oil. The two equilibria differ in that the cartel appears to sell more oil in the feedback Nash-Cournot equilibrium than in the feedback Stackelberg equilibrium (when oil is in excess supply, i.e. when c 3 0.6), and earns higher profits. Whether this is a general result is not clear, but it could result from the inability of the fringe to condition their decisions on the cartel's output in the feedback Nash-Cournot case, allowing the cartel to sell more oil in the current period than might otherwise be prudent. For lower cartel costs, and lower cartel oil stocks, when oil has a scarcity value in the open-loop Nash-Cournot equilibrium, the feedback NashCournot equilibrium will differ from the open-loop Nash-Cournot equilibrium, and the latter may yield lower profits than the feedback Stackelberg equilibrium. One tentative conclusion is that the feedback form of the open-loop Nash-Cournot equilibrium, though in general not perfect, may be a defensible approximation, increasingly so if there are several suppliers with market power.

922


4.3. Endogenous market structure Ulph and Ulph (1989) studied a two-period model in which there are two identical large suppliers competing with a fringe of competitive producers. They assume zero extraction costs and different discount rates for the fringe and dominant suppliers. They study the consequences of two different kinds of commitment. The dominant agents may be able to commit to cooperate and behave as a cartel in both periods. Each agent (acting separately or collusively, depending on the market structure) may also be able to sign binding long-term supply contracts with its customers, thus committing itself to the open-loop Stackelberg equilibrium. Whether either form of commitment is feasible will depend on the institutional structure - longterm contracts may not be enforceable across national boundaries, and collusive behavior may be illegal, or unsustainable for other reasons. There are thus four possible market configurations: (i) Collusion and long-term contracts. (ii) Collusion without long-term contracts. (iii) Non-cooperative production with long-term supply contracts. (iv) No collusion and no long-term contracts. The first case is the best for the dominant suppliers. In (ii) and (iv) the perfect equilibrium differs from the open-loop equilibrium. The interesting finding is that case (iv) may yield higher profits than case (ii), suggesting that it is not in the interest of the large producers to collude if they are unable to bind themselves to the open-loop supply plan. If the large suppliers cannot collude, they will be too competitive in the first period. If the large suppliers discount the future more heavily than the fringe, they will also wish to sell more in the first period, and so their inability to make either commitment reinforces each other, and their joint absence is doubly harmful. If the large suppliers discount the future less heavily than the fringe, then the two forms of precommitment pull in opposite directions, and it will not be clear which is stronger, and either one by itself may be worse than when both are absent. If suppliers cannot precommit their supply plans, and if the open-loop equilibrium is time-inconsistent, then cartels may be less likely to form than if precommitment were possible.

5. The period of commitment If there is a single dominant agent, it is obvious that that agent prefers the open-loop equilibrium to the Markov equilibrium, unless the two result in the same outcome. The open-loop equilibrium allows the dominant agent to make a commitment for the entire horizon of the problem, so the outcome in the Markov equilibrium is feasible. If there are two or more strategic players, the open-loop and Markov equilibria are (again) typically not equal. However, it is no longer unambiguous


923

which equilibrium gives the dominant agents higher pay-offs. Nevertheless, there are several known cases where symmetric agents do better under the open-loop equilibrium. The reason, as discussed in a previous section, is that with Markov equilibria agents have incentives to alter their rivals' behavior, and this tends to cause them to behave more competitively - i.e., to move further away from a cooperative solution; with open-loop strategies there is no such incentive. Whether there are one or many strategic players, the open-loop equilibrium corresponds to an infinite period of commitment, and the Markov equilibrium corresponds to a finite period of commitment. We denote the period of commitment by E which can take any non-negative value. We can view the value of E as exogenous, and ask how the equilibrium depends on that value. There are two ways to model this issue. The first method begins by fixing the times at which agents' controls can be changed. For example, it may be possible to have a tariff that changes every day or every year. We often want to know what happens as the period of commitment becomes arbitrarily small. This suggests that it is convenient to assume that decisions are made in continuous time, e.g., the tariff can be adjusted continuously. In this case, altering E changes only the period of commitment. Letting E equal infinity (or whatever the horizon of the problem is) reproduces the continuous time open-loop equilibrium. Letting E approach zero reproduces the continuous-time Markov equilibrium. Obviously, it makes no sense to have a period of commitment shorter than the period between the moments in time when controls can be changed. That is, if it is possible to change the tariff at most once a year, the period of commitment cannot be shorter than a year, and this may provide a natural restriction. Alternatively, if futures contracts can be enforced, and if contracts extend for one year forward, then again the period of commitment may have a natural length. A second alternative is to identify E with the amount of time during which the control must be constant. The disadvantage of this approach is that with it, changing E involves not only a change in the period of commitment, but also a change in the degree of flexibility that the agents possess. If, however, one is primarily interested in the limiting behavior as E approaches zero, this disadvantage is not likely to be serious. The reason is that the continuous time trajectory can be approximated to any degree of accuracy by choosing the length of the intervals between changes in the control to be sufficiently small. This means that the loss resulting from being required to choose a constant control over a period of length E, rather than being allowed to choose a path over that period, is of a smaller order of magnitude than E. (This assumes that the path that would have been chosen is continuous over that interval, so that any two points on that path are close - an assumption that holds for most economic models.) The advantage of the second method, relative to the first, is that it provides a simple way of motivating the continuous-time Markov equilibrium. We can do this by setting up a discrete-time dynamic programming equation which is standard

924

L. Karp and D.M. Newbeiy

except for the dependence of the value function(s) and the decision rule(s) on E. A first-order Taylor expansion around E = 0 yields the dynamic programming equation for the continuous-time Markov equilibrium". Reinganum and Stokey (1985) illustrate the first approach. They model the problem of duopolists who extract a resource in the absence of property rights. Demand has constant elasticity and extraction costs are zero. In the open-loop equilibrium ( E = co)the duopolists choose a trajectory of extraction and receive positive profits. As E approaches zero, the duopolists extract essentially the entire stock in the first instant. This drives price arbitrarily close to zero, so profits are negligible. The inability to precommit means that the duopoly equilibrium reproduces the open-access competitive equilibrium (in the limit as E approaches zero). For intermediate values of E , the equilibrium lies between the two extremes. The intuition is as follows. When E -+ co each duopolist takes the other's extraction trajectory as given, and consequently takes its total extraction as given. It therefore takes the stock available to itself as given, and chooses the profitmaximizing sales strategy. Such a strategy clearly does not entail instantaneous exhaustion. If E is finite, each duopolist takes its rival's current actions and future decision rules as given. These rules imply that equilibrium sales by one's competitor is a decreasing function of the stock available. This gives each duopolist two reasons to increase its own current extraction: (i) by doing so it increases the aggregate amount that it will sell over the remaining program, and (ii) it causes the residual demand that it will face in the future to shift out. Neither of these incentives are present under open-loop strategies. As E becomes arbitrarily small the incentives become overwhelming. This result is in the same spirit as the Coase Conjecture, which maintains that as the period of commitment of a durable goods monopolist (who produces under constant costs with no capacity constraint) approaches zero, the monopolist looses all market power and behaves competitively. We know that in a Markov equilibrium for the durable goods monopolist, eliminating either the assumption of constant cost or the assumption of no capacity constraint is enough to overturn the Coase Conjecture. The analogous result holds in Reinganum and Stokey's model: either convex extraction costs or an upper limit on the rate of extraction implies that exhaustion does not occur instantaneously, and also implies that the duopoly equilibrium does not approach the competitive equilibrium as the period of commitment approaches zero. The validity of this expansion requires that the value functions and future decision rules be analytic in E. This implies that the equilibrium is a continuous function of E near E = 0. Since E = 0 is of interest for its role as a limiting case, rather than its empirical plausibility, it seems reasonable to require continuity, as a defining characteristic. If the equilibrium was not continuous at E = 0, that limiting case would not be of interest, since it would convey no information about equilibria for small positive values of E .

31


925

Karp and Newbery (1991) illustrate the second approach. This paper, described above, considers the continuous-time perfect equilibrium in which strategic buyers choose state contingent consumption rules or, equivalently, tariff rules that support that level of consumption. The tariff trajectory in the continuous-time Markov equilibrium (infinitesimal period of commitment) lies below the tariff trajectory in the open-loop equilibrium (infinite period of commitment). Here too, shrinking the period of commitment causes the strategic agents' behavior to move toward competitive behavior - a zero tariff. However, the Markov equilibrium does not converge to the competitive equilibrium, as was the case in Reinganum and Stokey's model. (Recall that in that case convergence to competitive behavior occurs because of restrictive assumptions of their model, and is not robust.) If there is a single strategic agent, the Markov equilibrium pay-off to that agent is monotonic in the period of commitment; decreasing the period of commitment reduces the feasible set of options and therefore cannot increase the agent's payoff. One would expect the same result to hold in a game with more than a single strategic agent. Indeed, this is true in Reinganum and Stokey's model, but it has not been shown more generally. It is worth emphasizing that this result is due to the assumption that agents are restricted to Markov strategies. Consider the case of a single strategic agent. The smaller is the period of commitment, the worse is the outcome for that agent in a Markov equilibrium. However, in non-Markov games, bad outcomes are useful because they provide 'threats' that can support good outcomes. This is easiest to see in the durable goods monopolist model with constant production costs and no capacity constraints. The following argument is taken from Ausubel and Deneckere (1989). If the period of commitment is infinite, the monopolist can achieve the first best outcome. If the period of commitment is infinitesimal, the monopolist achieves zero profits in the Markov equilibrium. In this case it is very important for the monopolist to preserve its reputation that it will not use a Markov strategy. The threat of losing its reputation enables it to obtain a pay-off arbitrarily close to the infinite-commitment pay-off. Therefore, if the period of commitment is either zero or infinite, the monopolist's pay-off can be essentially the same 32.Since the set of perfect equilibria is not independent of E , it follows that there is some value of E between zero and infinity which minimizes the supremum of the set of perfect equilibria33.

The expression 'can be' is used advisedly, since there are many other perfect equilibria with very different characteristics. 33 More concisely, let E ( E )be the set of equilibrium payoffs for the monopolist, given E , and let e ( ~be ) the supremum of E ( E ) .Then there is an E* that minimizes e ( ~ ) . 32

926

L. Karp and D.M. Newbey

6. Conclusions

Problems of dynamic inconsistency are likely to arise when the constraints of an agent's intertemporal optimization problem involve forward-looking behavior by other, nonstrategic agents. The current actions of those agents depend on what they expect to happen in the future. This gives the dominant agent an incentive to make promises or threats that yield benefits in early periods, but impose costs in later periods. Over time, the future costs outweigh the future benefits of maintaining the original program, and the dominant agent would like to change his mind. The same type of situation arises if there is more than one dominant agent, i.e. if the optimization problem is replaced by a non-cooperative game. Modelling rational behavior in depletable resource markets requires dynamic models. Sellers base current sales on expectations of future prices as well as the current price. Whether dominant buyers attempt to extract rent from competitive sellers, or dominant sellers attempt to manipulate fringe sellers, the problem of dynamic inconsistency is likely to arise. If dominant agents in resource markets are unable to make binding commitments, a dynamically inconsistent equilibrium is implausible. It makes little sense to think of non-strategic agents as being sufficiently rational to solve their intertemporal optimization problems, but being sufficiently naive to believe promises or threats which will not be carried out. Binding commitments typically require an institutional structure, such as an international judicial system, which does not exist or is very weak. Dynamically inconsistent equilibria are therefore poor candidates for studying imperfectly competitive markets. Such equilibria do, however, have their uses. They are obtained as solutions to standard control problems or non-cooperative games with open-loop strategies, and therefore can be studied using the Maximum Principle. The advantage of this is that it is often quite easy to detect special cases where DI does not arise. In these situations dominant agents are permitted to make promises or threats but no enforcement mechanism is required, since the original plans continue to be optimal at subsequent stages. We discussed such special cases in contexts where either buyers or sellers are dominant. Even where the open-loop equilibria are dynamically inconsistent, they sometimes provide a useful benchmark against which to compare other equilibria. We emphasized the distinction between an equilibrium which is simply timeconsistent, and one which is perfect. The former type can be obtained by solving a standard control problem or non-cooperative game with open-loop strategies, provided that there are no jump states. The resulting equilibrium is not perfect. If there is a single strategic agent, the same realization can often be supported as a perfect equilibrium if the open-loop strategy is replaced by the feedback form of that strategy. This approach does not work if there is more than one strategic agent; that is, the feedback form of open-loop strategies does not constitute a

Ch. 19: Intertemporal Consistency Issues in Depletable Reso~lrces

927

perfect equilibrium in a non-cooperative game. We have illustrated the approach in situations where there is a single dominant agent, on either side of the market. We discussed the fact that there generically exist a multiplicity of perfect equilibria. The intuition provided by the Folk Theorems of infinitely repeated noncooperative games carries over in a straightforward manner to dynamicldifferential games (even if the game is degenerate, in the sense that there is only one strategic agent). There is an emerging literature which suggests that not all of those perfect equilibria are reasonable, since they may fail to be 're-negotiation proof'; the putatively credible punishment strategies that support a particular realization may not be credible after all. If this new literature succeeds in calling into question some of the strong conclusions of the Folk Theorems, we can expect a corresponding tendency in the theory of dynamic games. We may decide that not all of the perfect equilibria to such games are plausible, despite their perfection. These comments are speculative, since the issues they raise have not been resolved. We chose instead to concentrate on a particular type of perfect equilibrium, in which agents' actions and expectations are conditioned on the current value of the state variable. The state could be defined so generally as to make this restriction empty, and to avoid this we require the state to consist only of variables that have intrinsic economic meaning. The result is a Markov equilibrium. For depletable resource models, the (only) obvious candidate for the state is the remaining stock of the resource (or the vector of stocks held by the various resource owners). The resulting equilibrium can then be obtained using dynamic programming. We illustrated this technique with a two-period model and an infinite-horizon continuous-time model, and showed that market power can be disadvantageous. The models also indicate why equilibrium decision rules need not be monotonic functions of the state, and they suggest alternative ways of approximating perfect equilibria, for instance as the continuously reneged open-loop equilibrium for the case of the optimal import tariff. The multiplicity of perfect equilibria emphasizes the extent to which the analysis of a market structure depends on the assumptions of the model. Although this dependence is true of modeling in general, it has special force when an attempt is made to model imperfectly competitive dynamic markets. In these cases there is no widely accepted definition that is likely to lead to a unique equilibrium. We have defended the Markov assumption on the grounds of plausibility. However, one can think of markets that appear to provide counter-examples. Major diamond producers have apparently operated a cartel which relies in large part on the type of reputational considerations that are excluded by the Markov assumption. Even the requirement of perfection is not beyond criticism. We discussed a time-consistent but not perfect equilibrium in which only buyers exercise market power. This was obtained by beginning with a game in which buyers and sellers choose open-loop strategies, and letting each seller become individually insignificant. Whether such an equilibrium is more or less plausible than the

928


Markov equilibrium depends on the degree of sophistication of agents, the cost of processing information, and the ease with which plans can be altered. The answer to these types of questions must necessarily be found in the facts of the case rather than theory. The problem of dynamic inconsistency is fundamental to the study of imperfectly competitive resource markets, and especially to problems of resource taxation. It is fundamental to a number of other problems in economics, and the insights gained from a careful modelling of solution concepts in the depletable resource case may throw light on these other areas of enquiry, and conversely. Resource economists have been slow to take account of this (and the earlier volumes in this series have no entry on the subject). Practical men have long been sensitive to the problem of credibility and commitment. Companies deciding on large irrecoverable investments in foreign countries have long had to decide whether the announced tax policies of that country were likely to remain in force, or be changed opportunistically, and have made their forecasts taking into account what, ex post, it would be in the interest of the host country to do. The problem of the 'obsolescing bargain' which arises because the balance of advantage shifts from the investor to the host country after the investment has been made, has vexed multinational companies for years. [See the interesting papers in the book edited by Pearce, Siebert and Walter (1984).] Oil companies contemplating exploration have had to take a view of the likely rate of future oil taxation, and have generally been rather cautious as a result. More naive economists in international organizations have often criticized them for a bias against investment in developing countries, failing to appreciate the nature of the problems they face, though the UK oil tax regime may have the record for the frequency with which it has been adjusted to extract rent. We do not wish to imply that it is a simple matter to characterize perfect equilibria - the fact that we still lack a satisfactory theory of oligopoly shows how difficult the task is. Many of the most difficult problems in understanding resource markets arise because these markets are oligopolistic. So far, most of the theoretical progress has been in models which greatly simplify the market structure, and abstract from issues of learning, asymmetric information, and straightforward uncertainty and ignorance. Nevertheless, we have made considerable progress in understanding at least some of the simpler forms of market structure, and taking due account of problems of dynamic inconsistency. References Ausubel, L.M., and R.J. Deneckere, 1989, "Reputation in Bargaining and Durable Goods Monopoly", Econornetrica 57 no. 3,511-532. Benveniste, L.M., and J.A. Scheinkman, 1979, "On the Differentiability of the Value Function in Dynamic Models of Economics", Econornetrica 47,727-732.


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Bergstrom, Theodore C., 1981,"On Capturing Oil Rents with National Excise Tax", American Economic Review 71, 194-201. Bergstrom, Theodore C., John G. Cross and Richard C. Porter, 1981, "Efficiency Inducing Taxation for a Monopolistically Supplied Depletable Resource", Journal of Public Economics 15,23-32. BP Statistical Review of World Energy, 1987, (British Petroleum Co. plc, London). Bulow, J., 1982, "Durable Goods Monopolists", Jo~rrnalof Political Economy 90,314-332. Chari, VV., Patrick J. Kehoe and Edward C. Prescott, 1989, "Time Consistency and Policy", Staff Report 115 (Federal Reserve Board of Minneapolis Research Dept.). Coase, R., 1972, "Durability and Monopoly", Jo~rrnalofLawand Economics 15, 143-149. Dasgupta, P.S., and G.M. Heal, 1979, Economic Theory and Exhaustible Resources (Cambridge University Press, Cambridge). Fershtman, Chaim, and Morton R. Kamien, 1987, "Dynamic Duopolistic Competition with Sticky Prices", Econometrica 55, 1151-1 164. Fudenberg, Drew, and Eric Maskin, 1986, "The FolkTheorem in Repeated Games with Discounting or Incomplete Information", Econometrica 54,533-554. Fudenberg, Drew, and Jean Tirole, 1986, Dynamic Models of Oligopoly, Arndamentals of Pure and Applied Economics, Vol. 3 (Hanvood Academic Publishers, London). Gilbert, Richard J., 1978, "Dominant Firm Pricing Policy in a Market for an Exhaustible Resource", Bell Joirinal of Economics 9,385-395. Gilbert, Richard J., and Steven N. Goldman, 1978, "Potential Competition and the Monopoly Price of an Exhaustible Resource", Journal of Economic Theory 17,319-331. Groot, Fons, Cees Withagen and Aart de Zeeuw, 1990, "The Binding Contracts Stackelberg Equilibrium in the Cartel-Versus-Fringe Model Reconsidered, Center Discussion Paper 8924 (Tilburg University, the Netherlands). Groot, Fons, Cees Withagen and Aart de Zeeuw, 1992, "Note on the Open-Loop von Stackelberg Equilibrium in the Cartel Versus Fringe Model", The Economic Journal 102, 1478-1484. Gul, F., H. Sonnenschein and R. Wilson, 1986, "Foundations of Dynamic Monopoly and the Coase Conjecture", Journal of Economic Theory 39,155-190. Haurie, Alain, and Matti Pohjola, 1987, "Efficient Equilibria in a Differential Game of Capitalism", Journal of Economic Dynamics and Control 11,65-78. Heal, G., 1976, "The Relationship between Price and Extraction Cost for a Resource with a Backstop Technology", Bell Journal of Economics, 7 no. 2,371-378. Hillier, Brian, and James M. Malcomson, 1984, "Dynamic Inconsistency, Rational Expectations and Optimal Government Policies", Econometrica 52, 1437-1453. Hoel, M., 1978, "Resource Extraction, Substitute Production, and Monopoly", Journal of Economic Theory 19,28-37. Hotelling, H., 1931, "The Economics of Exhaustible Resources", Journal of Political Economy 39, 137175. Kahn, C., 1986, "The Durable Goods Monopolist and Consistency with Increasing Costs", Econometr i c ~54,274-294. Karp, Larry, 1984, "Optimality and Consistency in a Differential Game with Nonrenewable Resources", Journal of Economic Dynamics and Control 8,73-98. Karp, Larry, and David M. Newbery, 1989, "Optimal Tariffs on Exhaustible Resources", mimeograph (Department of Applied Economics, Cambridge, England). Forthcoming as:. Karp, Larry, and David M. Newbery, 1991, "Optimal Tariffs on Exhaustible Resources", Journal of International Economics 30,285-299. Karp, Larry, and David M. Newbery, 1992, "Dynamically Consistent Oil Import Tariffs", Canadian Journal of Economics 25,l-21.

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Karp, Larry, and Jeffrey Perloff, 1988, "Open Loop and Feedback Models of Dynamic Oligopoly", mimeograph (University of California, Berkeley, CA). Kemp, Murray C., and Ngo V. Long, 1980, "Optimal Tariffs and Exhaustible Resources", in: M.C. Kemp and N.V. Long (eds.), Exhaustible Resources, Optimality and Trade (North-Holland, Amsterdam) Essay 18. Kydland, Finn, and Edward Prescott, 1977, "Rules Rather than Discretion: the Inconsistency of Optimal Plans", Journal of Political Economy 85,473-491. Lewis, Tracy R., Stephen A. Mathews and H. Stuart Burness, 1979, "Monopoly and the Rate of Extraction of Exhaustible Resources: Note", American Economic Review 69,227-230. Loury, Glenn, 1986, "A Theory of 'Oil'igopoly: Cournot Equilibrium in Exhaustible Resource Markets with Fixed Supplies", International Economic Review 27,285-301. Maskin, Eric, and David M. Newbery, 1978, "Rational Expectations with Market Power: The Paradoxof the Disadvantageous Monopolist", Watwick Economic Discussion Paper and Massachusetts Institute of Economics Discussion Paper (Cambridge, MA). Maskin, Eric, and David M. Newbery, 1990, "Disadvantageous Oil Tariffs and Dynamic Consistency", American Economic Review 80 no. 1,143-156. Neustadt, L.W., 1976, Optimization. A Theory of Necessary Conditions (Princeton University Press, Princeton, NJ). Newbery, David M., 1976, "A Paradox in Tax Theory: Optimal Tariffs on Exhaustible Resources", SEER Technical Paper (Stanford Economics Department, Stanford, CA). Newbery, David M., 1980, "Credible Oil Supply Contracts ", Economic Theory Discussion Paper 34 (Department of Applied Economics, Cambridge, England). Published as. Newbery, David M., 1981, "Oil Prices, Cartels, and the Problem of Dynamic Inconsistency", The Economic Journal 91,617-646. Newbery, David M., 1984, "The Economics of Oil", in: R. van der Ploeg (ed.), Mathematical Methods in Economics (Wiley, New York) ch. 20, pp. 519-568. Newbery, David M., 1992a, "Credible Oil Supply Contracts", in: P. Dasgupta, D. Gale, 0 . Hart and E. Maskin (eds.), Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn (MIT Press, Cambridge, MA) pp. 340-369. Newbery, David M., 1992b, "The Open-Loop von Stackelberg Equilibrium in the Cartel Versus Fringe Model: A Reply", The Economic Journal 102,1485-1488. Papavassilopoulos, George, and J.B. Cruz Jr, 1980, "Sufficient Conditions for Stackelberg and Nash Strategies with Memory", Journal of Optimization Theory and Applications 31,253-260. Pearce, David, Horst Siebert and Ingo Walter, 1984, Risk and the Political Economy of Resource Development (MacMillan Press, London). Pindyck, Robert S., 1978, "Gains to Producers from the Cartelization of Exhaustible Resources", Review of Economics and Statistics 60, 238-251. Reinganum, Jennifer F., and Nancy L. Stokey, 1985, "Oligopoly Extraction of a Common Property Natural Resource: the Importance of the Period of Commitment in Dynamic Games", International Economic Review 26,161-173. Reynolds, Stanley S., 1987, "Capacity Investment, Preemption and Commitment in an Infinite Horizon Model", International Economic Review 28,69-88. Salant, Stephen W., 1976, "Exhaustible Resources and Industrial Structure: a Nash-Cournot Approach to the World Oil Market", Journal of Political Economy 84,1079-1094. Seierstadt, A,, and K. Sydsaeter, 1987, Optimal Control Theory with Economic Applications (NorthHolland, Amsterdam). Simaan, M., and J.B. Cruz, 1973, "Additional Aspects of the Stackelberg Strategy in Non-zero Sum Games", Journal of Optimization Theory and Applications 11,613-626. Solow, R.M., and F.Y. Wan, 1976, "Extraction Costs in the Theory of Exhaustible Resources", Bell Journal of Economics 7 no. 2,539-570.


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Stiglitz, J.E., 1976, "Monopoly and the Rate of Exhaustible Resources",AmericnnEconomic Review 66, 655-661. Stokey, Nancy, 1981, "Rational Expectations and Durable Goods Pricing",BellJoumal ofEconomics 12, 112-128.


PART 2

ANALYTICAL TOOLS


Chapter 20

BUYING ENERGY AND NONFUEL MINERALS: Final, Derived, and Speculative Demand* MARGARET E. SLADE Department of Economics, The University of British Columbia, Vancouvel;Canada BC V6T IZ1 CHARLES D. KOLSTAD The University of Illinois at Urbana-Champaign, Institute for Environmental Studies, 1101 West Peabody, Room 352, Urbana, IL 61801, USA ROBERT J. WEINER Department of Economics, Brandeis University,415 South Street, Waltham, MA 02254, USA

1. Introduction

It might be appropriate to begin a chapter on the demand for mineral commodities with the question - why is there a need for a special chapter on mineral demand? Is there anything unique about the consumption of minerals or are minerals just another factor of production? ' Nonrenewable or mineral resources are unique because, unlike labor and man-made capital whose supply is potentially unlimited, minerals occur in the Earth's crust in finite stocks. Minerals are therefore the principal potential limit to economic growth. For centuries people have been concerned about resource scarcity and the adequacy of our mineral endowment. And, even though the finite nature of mineral resources is a supply consideration, it is not possible to discuss scarcity or adequacy without giving equal importance to demand. If no one wants a mineral commodity, or if that commodity has a perfect substitute that is completely reproducible, the mineral should not be considered scarce or in short * We would like to thank Morris Adelman, Charles Blackorby, Christopher Gilbert, Mel Fuss, Robert

Halvorsen, Jong-kun Lee, Gordon Phillips, James Sweeney, and Campbell Watkins for thoughtful comments on an earlier draft. We use the term mineral to denote a naturally occurring substance extracted from the earth for man's use. For example, crude petroleum, coal, and metal ores are minerals. Mineral commodities also include processed minerals such as refined petroleum and metals.

'

Handbook of Natural Resource and Energy Economics, vol. 111, edited by A. K Kneese and J.L. Sweeney O 1993 Elsevier Science Publishers B. K All rights reserved

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supply. Economists therefore consider both supply and demand in evaluating the implications of the finite nature of mineral resources for economic well-being. Over the centuries, economists and political philosophers have paid special attention to the nonrenewable resources. Some have been pessimistic about man's ability to overcome constraints imposed by finite resource stocks while others have taken more optimistic positions. Because the debates that occur today deal with issues that have been discussed for centuries, this chapter begins with a brief summary of the historic treatment of the demand for and supply of nonrenewable resources.

1.1. Classicalperiod

The early nineteenth-century classical economists such as Malthus, Ricardo, and Mill were very concerned with natural resources or 'land'. To them, 'land' was principally agricultural land, but they recognized that mines were also fixed factors (limited in supply), subject to diminishing returns (of differential quality and extraction cost), and capable of earning economic rents (prices in excess of their supply price). In addition, Mill recognized that the situation in mining is worse than that in agriculture because extraction is a one-way process. A mineral once extracted cannot be extracted again. On the demand side, classical economists were principally concerned with population growth. They recognized that, in the absence of constraints, a population grows geometrically. (People produce people and therefore the rate of growth of a population is proportional to the population itself.) Malthus saw limited natural resources as the principal constraint to economic growth; in Malthus' view, population would increase until driven to the subsistence level by a shortage of agricultural production. Mill, however, was more optimistic about man's foresight and voluntary restraint. He believed that In proportion as mankind rise above the condition of the beast, population is restrained by the fear of want rather than by want itself.

Implicit in the classical economists' view of demand is the idea that the size of the population and per capita income determine consumption. Price is not well integrated into their analysis.

1.2. Neoclassical period

It was the neoclassical economists of the late nineteenth century, such as Walras and Marshall, who developed the concept of a demand schedule -an entire pricequantity relationship. On the consumer side, the utility function and the principle

Ch. 20: Buying Energy and Nonfuel Minerals

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of diminishing marginal utility determined the downward-sloping demand curve. And on the producer side, the production function and the principle of diminishing marginal productivity played the equivalent role. Natural resources, however, were not of particular concern to the neoclassical economists. Land was one of several factors of production, all of which were subject to diminishing returns and all of which could earn rent, at least in the short run. The neoclassical economists, while providing us with the tools with which to estimate the demand for mineral resources, were partially responsible for the decline in interest in limited natural resources as constraints on growth.

1.3. Laissez-faire and conservation During the three decades that followed the Civil War, the United States was characterized by rapid industrial expansion and unhampered growth of bigbusiness corporations. And the industrial capitalist became the regnant figure in American life. The businessman felt a need for a philosophy to explain and justify his preeminent position. He found what he sought in the precepts of Herbert Spencer's social Darwinism (survival of the fittest) and of laissez-faire economics. The free market was extolled as a purveyor of social optimality and the state pursued a hands-off economic policy. The use of the nation's natural resources was determined by market forces (which actually meant big business) and the unregulated outcome was thought to be the best possible. Unfortunately, the actual outcome of unfettered exploitation of natural resources is difficult to consider socially optimal. For example, the history of exploitation of copper in Butte, Montana, in the late nineteenth century reads more like a story of cowboys and Indians (with wars in the mine shafts, bribes in the State legislature, and unhealthy working conditions) than one of market-induced perfection. It eventually became obvious that some form of control was needed. At the turn of the century, a political movement based on conservation and progressive political reform developed in the USA as a reaction to the idea of a self-regulated-market economy. Land was considered to be a national heritage, not just a factor of production. Consumption of natural resources could be either prudent or wasteful and inefficient, and the laissez-faire philosophy was criticized as inevitably leading to the latter alternative. An attempt was made to inventory the Nation's stocks of natural resources, and much land was taken out of the private domain.

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1.4. Recent events

In the 1950s, high prices and commodity shortages associated with the aftermath of World War I1 and the Korean War led once more to concern over our use of natural resources. However, it was not until the 1970s that resource shortages became a primary focus of attention. The Arab-oil embargo, OPEC-price increases, and the commodity boom of 1973-1974 caused natural-resource considerations to become headline items. The majority of the articles discussed in this chapter stem directly or indirectly from the concern created at that time. The decade of the 1970s experienced an explosion in the publication of energy and nonfuel-mineral-demand studies. Today's economists line up on both sides of the resources-as-constraints-ongrowth issue. Contemporary neoclassical economists such as Solow (1974) and Stiglitz (1979) emphasize that technical progress and substitution diminish resource scarcity whereas contemporary Malthusians such as Georgescu-Roegen (1976) and Daly (1977) stress physical laws that constrain progress and substitutability. In contrast to the 1970s, the 1980s were plagued by falling energy prices and depressed metal markets. As a consequence, countries like Mexico that based spending plans on forecasts of increasing energy revenues experienced severe financial problems. Oil companies had to close refineries and to cancel plans for the development of alternative energy sources. And financial institutions that made large loans to producing countries and companies were on the verge of bankruptcy. In academic and government circles, interest in energy-demand studies diminished, perhaps for the wrong reasons. A soft market is partially due to underestimation of long-run demand and supply elasticities for energy. It should therefore be obvious that rational planning for resource-based economies (both producing and consuming) requires accurate projections and an improved understanding of the dynamics of supply and demand. 1.5. Organization of the chapter

This chapter summarizes and synthesizes previous studies of energy and nonfuelmineral demand. It also attempts to point to areas that have received inadequate attention and where, as a consequence, our understanding is poorest. Any summary of such a vast body of literature must inevitably be inadequate. However, it is hoped that the chapter will stimulate thinking about demand studies, that it will not summarize an area that is closed, but that it will encourage researchers who plan to branch off in new and innovative directions. The organization of the chapter is as follows. Sections 2 4 consider demand from a conventional point of view. In Section 2, the theory of consumer and derived demand is laid out. This section forms the theoretical background for the rest of


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the chapter. Section 3 describes and contrasts various types of demand models, whereas Section 4 discusses important issues that all types of demand models might confront. These include substitution possibilities, technical change, and adjustment to changed market conditions. Section 5, in contrast, looks at consumption from an unconventional point of view. We emphasize the producer who is not a user, and deal with issues that are not traditionally considered to be "demand". The speculator neither produces nor consumes. Nevertheless, for many commodities such as silver and gold, purchases . by merchants, traders, and arbitrageurs far outstrip 'legitimate' trade. Moreover, the introduction of new commodity markets, new contracts on existing markets, and new financial instruments such as commodity options, has stimulated interest in the subject of demand by nonusers. As a consequence, we consider natural-resourcecommodity exchanges, both old and new, and discuss the implications of hedging and speculative demand for market performance. Finally, Section 6 summarizes and concludes.

2. Theoretical background Energy is used by both consumers, who purchase gasoline or fuels for home heating, and producers, who purchase fuel for a variety of uses, including boilers and blast furnaces. In contrast, very few nonfuel minerals are used directly by the final consumer. Whether the commodity is iron, phosphate, or sand and gravel, it is usually combined with other inputs to produce another intermediate input or a final product. Theories of derived demand are therefore relevant to both energy and nonfuel-mineral modeling whereas theories of consumer demand are most applicable to energy modeling. This section summarizes theories of derived and consumer demand. Rather than looking at specific models, it lays the groundwork for a broad class of modeling efforts. Concepts are explained and notation is introduced that are used throughout the rest of the chapter. The point of the discussion is to specify demand equations that are consistent with economic theory. For example, a firm's demand for inputs should be consistent with profit-maximizing or cost-minimizing behavior. To achieve this consistency, demand equations must satisfy certain restrictions. The presentation is necessarily sketchy and incomplete. The reader who would like a more detailed analysis is referred to Jorgenson (1986) for derived demand and Deaton (1986) for consumer demand.

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2.1. Derived demand The basic construct that underlies the theory of derived demand is the neoclassicalproduction function, which shows how given inputs can be combined to produce the maximum level of output. LetxT = (xI,x2,. . . , xN) be a vector of N inputs used in the production of a single output, q. The production function, which describes the technology available to the firm, is written as

Each input has a price or rental rate that is parametric to the firm. The vector of factor prices is denoted bypT = (pl,p2, . . . ,pN). Finally, output price is denoted by V and is also parametric. Given any set of input and output prices, the firm's profit-maximization problem is max {V f (x) - p T ~ ) . X

(2)

The first-order conditions for the maximization of eq. (2) (which tell the firm to choose xi such that its price is equal to the value of its marginal product) can be solved for the optimal level of each factor, xi*. If the production function is concave, the first-order (necessary) conditions are sufficient to ensure that the objective function (2) is maximized. In fact, most recent mineral-demand studies do not rely directly on the production function. More powerful and simpler techniques are based on duality theory. Factor demands and all of the technological information contained in the production function can be obtained by various methods, all of which are equivalent and consistent with optimizing behavior 2. A frequently used alternative to the production function is the cost function, which shows the minimum cost of producing a given level of output. If TC is total cost, the cost function is defined by TC = C(p,q) := min {pTx: f (x) b q ) . I f f is continuous from above, then C is continuous in p and continuous from below in q, non-negative, nondecreasing in p , increasing in q, and positively linearly homogeneous and concave i n p for fixed q. Conversely, if C satisfies these conditions, there exists a production function f dual to C . Equivalence is used here to mean that two formulations lead to the same factor demands and the same technological information such as substitution elasticities. It does not mean that the parameters off can be retrieved from the parameters of the cost or profit functions.


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From a practical point of view, the cost function has several advantages over the production function. First, with the minimization (3), unlike the maximization (2), output is exogenous. Formulation (3) thus assumes only cost minimization, which is weaker than profit maximization. A cost-function approach is therefore more suitable to modeling the demand for factors by a regulated firm such as an electric utility. By far the most important advantage of the cost function, however, relates to the use of Shephard's (1953) lemma to obtain factor demands. Shephard's lemma states that the optimal demand for the ith factor,^:, is given by

Obtaining factor demands from eq. (4) is in general much simpler than solving the profit-maximization problem (2). If an arbitrary system of demand equations of the form (4) is homogeneous of degree zero in prices and if the matrix of partial derivatives (aXilapj) is symmetric and negative semidefinite, the system is consistent with cost-minimizing behavior for some technology. That is, these properties form a complete list of the restrictions on demand functions imposed by economic theory. An alternative equivalent formulation is the variable or restricted-cost function. Suppose that some subset of inputs xv is variable whereas the remaining inputs xf are fixed, at least in the short run. The restricted-cost function shows the minimum variable cost that the firm can obtain, given variable-input pricespv and the levels of the fixed factors xf:

Shephard's lemma can be used again to obtain optimal-variable-factor demandsxv and shadow pricespf for the fixed factors,

For an arbitrary system of demand equations of the form (6) and (7) to be consistent with cost-minimizing behavior, it must satisfy restrictions that are similar to those placed on eq. (4). Long-run costs are related to short-run-variable costs through eq. (7). For example, if capital k is fixed, and the left-hand side of eq. (7) is equal to the marketrental price of capital, pk, then eq. (7) implicitly defines the equilibrium quantity

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of the quasi-futed factor, k*. More generally, variable costs and long-run total costs are related through

where xf* is defined by

There are many possible extensions to the production and cost functions described here. For example, when output is chosen optimally, a profit function is appropriate. In this case, output price V appears in the function instead of output quantity q. Finally, all of these functions can be generalized to handle multiple outputs. 2.2. Consumer demand

The basic construct that underlies the theory of consumer demand is the neoclassical-utility function. A utility function, u = U(x), is a way of representing an individual's preferences over a vector of N commodities x in such a way that if a vector x is at least as desirable as another vector x' then U(x) 2 U(xl). If a preference ordering is complete, reflexive, transitive, monotonic, and continuous, it is always possible to represent it by a continuous utility function. Given income Y and commodity pricesp, the individual is assumed to purchase a commodity vector that maximizes utility subject to the budget constraint. The problem is thus to max {U(x): pTx < Y) . The set of first-order conditions for the maximization (10) can be used to solve for the consumer's optimal commodity demands, X ( p , Y). If the utility function is quasiconcave, the first-order (necessary) conditions are also sufficient for a maximum. Just as the production function is now rarely used in derived-demand studies, the utility function is rarely used directly in consumer-demand studies. Two equivalent formulations that are often more convenient are the indirect-utility function and the expenditure function. The indirect-utility function expresses utility as a function of prices and income,

u = g(p, Y ) := max {U(x): pTx < Y ) .


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Roy's (1942) theorem can be used to obtain the Marshallian (uncompensated or income constant) commodity demands xi" from the indirect utility function,

Finally, the expenditure function e(p, u) shows the minimum expenditure required to reach a specified level of satisfaction u, given commodity prices, e(p, u) := min { p T ~U(X) :

U)

.

(13)

X

Shephard's lemma can be used to obtain the Hicksian (compensated or utility constant) commodity demands x: from the expenditure function:

Given an arbitrary system of demand equations of the form (14), a complete set of restrictions for the system to be consistent with utility-maximizing behavior is that X: be homogeneous of degree zero in prices and that the matrix of partial derivatives (ax:/ Bpi) be symmetric and negative semidefinite. Both eq. (11) and eq. (13) involve the unobservable quantity u. In practice, the system of demand equations (12) is estimated. Equation (14) is obtained from eq. (12) using the relationship x"

W P , u) = X r (p, e(p, u)). api

=

If the system of equations (14) satisfies the restrictions necessary for utility maximization, it can be integrated to obtain eq. (13), and eq. (12) can be integrated to obtain eq. (11). Thus in theory, one can move freely between compensated and uncompensated demand. This is important since one usually estimates uncompensated demand but must do welfare analysis using compensated demand. Unfortunately, as Hausman (1981) and Vartia (1983) have shown, in practice it is nontrivial to move between the two demand systems. Starting with an Marshalliandemand system (12), one must first integrate the system of equations to obtain the indirect utility function u = g(p, Y). This is no small task. Second, this utility function must be inverted to obtain Y = e(p, u), an expenditure function. Finally, this expenditure function must be differentiated with respect to price to obtain the compensated-demand system (14).

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2.3. Aggregation and separability All models are attempts to condense real-world complexities into a set of simple relationships that can easily be analyzed, and the process of condensation necessarily involves the use of simplifying assumptions. One class of simplifying assumptions enables the modeler to treat broad groups of commodities as if they were a single commodity, a large number of technologies as if it were a single technology, and a diverse set of agents as if they were a single agent. In other words, it is frequently assumed that groups can be aggregated in a meaningful way. This section discusses conditions that must hold if aggregation is to be valid (if it is to be consistent with economic theory). Restrictions that systems of demand equations must satisfy if they are to be consistent with optimizing behavior were discussed in Sections 2.1 and 2.2. Here, restrictions that technologies and preferences must satisfy for consistent aggregation are identified. Problems of aggregation across goods (inputs and outputs) and across consumers (firms and households) are briefly touched upon. The subject is very large and cannot be covered in detail here. The interested reader is referred to Blackorby, Primont and Russell (1978), Fisher (1965), and the Gorman references cited below for much more complete and rigorous treatment. 2.3.1. Aggregation of inputs and outputs

In the discussion of production and utility, it was assumed that there were N distinct inputs purchased by a single firm or N distinct commodities purchased by a single individual. No mention was made of the size of N. In practice, N may be extremely large. To make the problem of specifying and estimating production (utility) functions and demand equations tractable, it is almost always necessary to aggregate inputs and outputs. For example, if the plant is a steel mill, it might use many sorts of fuels and materials and many classes of workers and capital equipment to produce various steel alloys of different strength and hardness. It is convenient to say that the plant produces 'steel' with 'capital', 'labor', 'energy', and 'materials' (a KLEM production technology). It is also convenient to discuss the 'prices7 of these aggregate inputs and outputs. The question is - what assumptions make these simplifications possible? Let us focus on energy for a moment. Aggregate energy is not bought and sold in a market and does not have a price. In spite of this fact, people routinely estimate the demand for aggregate energy. To do this, aggregate-energy price and quantity indices must be constructed. Moreover, the method chosen for aggregation purposes has important implications for the results obtained. Suppose that there are n types of energy xT = (xl,xz, . . . ,x,) with prices PT = (p1,p2, . . . ,p,). A quantity aggregator is a function X = w(x,p) and a price


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aggregator is another function P = p(x,p). It is desirable that P and X satisfy the condition

If condition (16) is satisfied, a price aggregator implicitly defines a quantity aggregator and vice versa. A common practice is to construct a price (quantity) aggregate or index as a weighted average of individual prices (quantities), where the weights are constant. If such a price index is constructed, the implication is that quantities are used in fixed proportions so that the implicit-quantity aggregator is Leontief 3 . And if such a quantity aggregate is constructed, the implication is that quantities are perfect substitutes so that prices move in a way that keeps their ratios constant (Hick's aggregation) 4. The popularity of these indices lies in their ease of construction. Unfortunately, perfect price or quantity proportionality is rare, and therefore the implicit assumptions under which these indices are constructed are usually violated. A special case of the fixed-weighted quantity aggregate is to choose a single characteristic (Btu value, for example) and form a quantity aggregate in terms of this characteristic (lo6Btu). As before, this practice implicitly assumes that all energy sources are perfect substitutes. In addition, for most inputs it is not clear what characteristic to choose. For example, there is no single important characteristic shared by all materials. One possible solution is to pick a vector of important characteristics (strength, weight, conductivity, resistance to corrosion, etc.) and estimate 'hedonic' price equations for materials, as suggested by Lau (1982). When people's willingness to pay for characteristics is known, the appropriate price for a group of commodities can be estimated from the characteristics of the group. There is a strong connection between aggregators or index numbers and production technologies. For example, if aggregate energy is 'produced' from individual energy types in such a way that the unit-cost function is quadratic in the logarithms of energy prices (a translog unit-cost function) then a Tornqvist (1936) index is an exact aggregator that is consistent with optimizing behavior on the part of producers [Diewert (1976)l. The choice of aggregation procedure is thus equivalent to the choice of production technology. An important property of the aggregators P and X defined above is that they are functions solely ofp andx. In other words, aggregate-energy price and quantity depend only on individual energy prices and quantities but not on the capital stock or on the price or quantity of any other input. This can be seen by considering the relationship between indices and production functions discussed later. With a Leontief production function, the cost function (price index) is linear. Straight-line isoquants imply perfect substitutability.

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A necessary and sufficient condition for the existence of meaningful price and quantity aggregators for a subset of inputs (commodities) x is that the production (utility) function be homothetically separable in x and other inputs. A production function

is separable in the inputsxl,xz, . . . , x,, if it can be written as

A function is homothetic if it is expressible as a monotonically increasing transformation of a linearly homogeneous function (that is, if input proportions are independent of the level of output). For homothetic separability, the aggregator function X must be homothetic. Homothetic separability is a fairly strong assumption. One implication is that if purchases of X increase, purchases of each xi, i = 1, . . . , n, increase by a common factor A. Another implication is that the elasticity of substitution between x, and x,, i,j 6 n, is independent of the level of any xk, k > n. In other words, the way in which one energy type is substituted for another is independent of the capital stock or the level of any other input. We know that this is an unreasonable assumption because, for example, the capital stock (type of boiler in a plant) influences whether the plant manager purchases gas, coal, or residual-fuel oil. Nevertheless, it is a convenient fiction that usually must be maintained if demand studies are to be possible. When homothetic separability is assumed, estimation can proceed by stages. For the case of the steel mill, aggregate input and output price and quantity indices can be constructed by some familiar procedure (a Divisia index, perhaps). These aggregates can then be used in estimating the cost function and derived-demand equations, which now involve only four inputs. The process of separating the estimation into stages results in estimations that are manageable at each stage. 2.3.2. Aggregation across households and firms

The theory of consumer demand applies to individuals or households. Individuals or households have preferences and make optimal-spending decisions. It is rare, however, that studies of consumer demand for energy are based on household data5. More often, the data used are aggregate cross-section (by state, for example) or time series. The question is then - is it possible to treat the residents of a region as if the group had a utility function and made optimizing decisions? The existence of consumer-expenditure surveys makes the use of household data possible, but it is still the exception not the rule.


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Unfortunately, the conditions under which this is possible are very restrictive. Gorman (1953,1961) derived the basic results for this problem. Consider avector of commoditiesx with pricesp and M individuals with incomesyT = (yl,y2,. . . ,yM). The problem is to construct an aggregate-demand function, Hj(p,Y), for commodity j such that

where Y = C yi is aggregate income and xj = h j ( ~ , ~ is' ) the ith individual's demand for the jth commodity. Gorman showed that this is possible if and only if xj can be written as

and

The implications of eqs. (20) and (21) are very strong. For example, aggregate consumption of Xi depends on aggregate income Y but not on the distribution of income across consumers. This restriction is possible only if when a dollar is taken away from one consumer and given to another, the second consumer spends the dollar in exactly the same way as the first would have done. Another implication of eq. (20) is that all consumers have Engel curves that are identical up to an additive term aj(p). If aggregate demand is zero when aggregate expenditure is zero, then all aj(p) = 0 and all individuals have identical homothetic preferences. Identical preferences, however, are inconsistent with well-established regularities in consumer behavior, such as the finding that expenditure patterns depend on the demographic characteristics of households. In fact, these results are so restrictive that it is hard to imagine empirical work on aggregate demand proceeding. There must be ways of getting around the problem. Several have been suggested. For example, Berndt, Darrough and Diewert (1977) assume that each consumer has identical nonhomothetic preferences of the form

An Engel curve is a demand curve drawn in commodity space, letting income vary but holding prices fixed.

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and that income is distributed among consumers according to the density function 9 ( y ) . Under these assumptions, the relationship analogous to eq. (21) is

Aggregation here depends on the distribution of income and requires preferences to be identical but not homothetic. Lau (1977) proposed the notion of exact aggregation, which introduces household characteristics into consumer demand. Let ci be a vector of characteristics or attributes for the ith household. Examples might be age of head, region of residence, or number of family members. And suppose that the ith household's consumption of Xi, xj,depends on the household's characteristics,

Lau showed that it is possible to aggregate across consumers if and only if

With this formulation, preferences are not identical and Engel curves depend on household characteristics. Perhaps even more important for mineral-demand studies is the issue of aggregation across firms or plants with diverse technologies. Almost all nonfuel minerals and a substantial proportion of the fuels are intermediate inputs. Consumers are thus firms, not households. In the earlier discussion, consumption of energy and materials by a steel mill was considered. The consumption of a single plant or mill is however not usually of interest. Instead we are more apt to be interested in the demand for energy or materials by the entire steel industry. The steel industry is not a plant, it may not have a well-defined cost function or a manager who makes optimizing decisions. The steel industry consists of numerous firms that own plants covering a broad range of technologies and have managers with different goals. Yet it is routine to apply the theory of production and cost to obtain derived demands for an industry. The question is then -what assumptions make this simplification possible? If all factors are variable and firms are price takers in input and output markets, there are no restrictions for aggregation across firms. If output is exogenous however, as is especially common in regulated industries or industries that operate under long-term contracts, then the conditions for consistent aggregation


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across firms are very similar to the conditions for consistent aggregation across households. Assume that M firms in an industry purchase vectors of variable inputs x at parametric prices p. Each firm produces an exogenous output qi. Under these assumptions, consistent aggregation across firms is possible if and only if inputdemand functions can be written as

and

where Q = C qi is aggregate industry output and xf:is the ith firm's demand for the jth input. Equations (26) and (27) imply that firms have straight-line parallel expansion paths (factor demand as a function of output) and that marginal costs are constant and equal across firms. Lau's exact aggregation can be generalized to handle this situation in an obvious fashion (so that individual and aggregate demands depend on vectors of firm or plant characteristics). Complications also arise if some of the factors are fixed. Suppose that a competitive industry produces an output Q that sells for a price V. Firms in the industry purchase vectors of variable inputs x at parametric pricesp. Finally, firms use a fixed factor k (capital). Gorman (1968) showed that under these conditions, consistent aggregation is possible if and only if

and

where @' is a function that transforms ki into efficiency units, and K = C @'(ki) is the aggregate-capital stock. Equations (28) and (29) imply that the shadow price of capital is the same in all industries. There are many other generalizations of Gorman's basic results. Unlike the conditions for aggregation across inputs and outputs and the separability conditions necessary for the construction of indices, which are frequently discussed in the empirical-demand literature, the conditions for consistent aggregation across consumers (firms or households) are routinely ignored without apology '.

' There are exceptions such as Muellbauer (1975) and Jorgenson, Lau and Stoker (1982).

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Numerous empirical studies have demonstrated that the requirements for consistent input aggregation are rarely found in practice and that aggregation at any level is likely to be improper in a theoretical sense8. If requirements for consistenttechnology aggregation were tested, it is likely that they would also be violated. The question then becomes -what sort of errors are committed if we aggregate when it is inappropriate? The issue of technology aggregation is especially important because it affects the interpretation of the neoclassical-production function as an approximation to a set of interrelated-engineering activities. When technology aggregation takes place, even the aggregation of simple subprocesses, there is no guarantee that the engineering character of the subprocess will be reflected in the aggregate. In an empirical study of resource substitution under input and technology aggregation, Kopp and Smith (1981) conclude that aggregation of progressively more diverse inputs leads to a diminution of the statistical significance of the estimated elasticities but not usually to a reversal of their signs. The loss of statistical significance can be interpreted as a decrease in the power of the neoclassicaleconometric model to approximate the underlying engineering features. More seriously, they find that aggregation across technologies may lead to the inability of the neoclassical-econometric model to discriminate between relationships of substitutability and complementarity, which is intuitively plausible because inputs can be substitutes in one technology and complements in another. In view of these results, it seems desirable that demand studies be undertaken at a fairly disaggregate level. This concludes our discussion of the theory of consumer and derived demand. In subsequent sections, the concepts and notation developed here are applied in the analysis of specific models and modeling techniques.

3. Qpes of econometric demand models

A very large number of energy and nonfuel-mineral-demand models have been constructed and estimated, and it would be impossible to survey the entire field9. This section simply describes some of the features of typical econometric-demand models and points to examples that we feel are representative. Not all models are econometric in nature. Nevertheless, as this is the largest class, we choose to emphasize this technique lo. These tests have principally been parametric. It is unlikely that non-parametric tests [Varian (1982) for example] would reject as frequently. See Bohi (1981) or Kolstad (1987) for detailed reviews of specific energy-demand models. l o Another approach that is frequently employed by mineral-industry analysts is known as intensity of use (IU) analysis. IU analysis consists of extrapolating historic trends in certain ratios to predict future


3.1. Estimation Econometric models are constructed from economic data with the aid of the techniques of statistical inference. These models are usually based on economic theories that assume optimizing behavior on the part of economic agents. The principal data used in the construction of econometric models are observations on prices and quantities. These data can be time series or crosssection or some combination of the two (panel data). The data show the actual purchases of firms or households at some level of aggregation. Consumers purchase different quantities of goods (commodities for direct consumption or to be used in the production of other goods) at different sets of relative prices and income or output. The equations that are estimated from the data are usually derived from firstorder conditions from an optimization problem (utility or profit maximization, for example). The data on behavior (purchases of goods) is thus used to infer the underlying structure of technology or tastes. Once the underlying structure is known, the model can be used to predict the quantity of a particular commodity that will be consumed at any set of relative prices and income or output. In other words, the entire schedule is inferred from a discrete set of observations on agent behavior. There are two basic approaches to estimating models of energy and nonfuelmineral demand. One approach views the commodity of interest in isolation from other commodities. For instance, if one is interested in natural-gas demand then an equation will be developed for gas consumed as a function of gas price and other appropriate variables. The second approach to estimation is to view the firm or household's consumption choice as a whole, whereby the household or firm is choosing many commodities and trading consumption of one against another based on prices. The result is a more complete set of demand equations (equations for more than just the commodity of interest). We discuss each of these approaches in turn. 3.2. Single-commodity models

Single-commodity models of nonfuel-mineral demand tend to be market models whereas single-fuel-demand models tend to emphasize demand in isolation from other market phenomena. mineral use. For example, to project aluminum consumption, one would look at trends in the aluminum intensity of important end-use markets such as beverage containers (i.e., tons of aluminum/tons of beverage containers) and trends in the importance of these markets in GNF?Most economists would not call this a 'demand' projection since price is not integrated into the analysis. Instead, it is an attempt to construct the expansion path. Discussions of this method can be found in Humphreys (1987), Tilton (1990), and Considine (1991).

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The treatment of demand in nonfuel-mineral-markets is often ad hoc; that is, it is not based on a specific model of optimizing behavior. Instead, demand is postulated to be a function of own price, the prices of substitutes and complements, and the level of economic activity. The functional form of the demand equation is often chosen to provide a good statistical fit. Many of the early nonfuel-mineral models were constructed by Charles River Associates for the US General Services Administration (GSA). These models were designed to facilitate analysis of the effects of purchases for and sales from the GSA strategic stockpile. An example of such a model is Charles River Associates (1971) aluminum model. Demands for almost all major commodities however were modeled in this effort. The construction of nonfuel-mineral-market models grew steadily, and many books and articles dealing with particular minerals were published. Perhaps the most studied commodity is copper; examples include work by Fisher, Cootner and Baily (1972), Banks (1974), Mikesell (1979), and Taylor (1979). Cobalt was studied by Burrows (l971), tin by Desai (1966), tungsten by Burrows (1971) and Tan (1977), and zinc by Gupta (1981). This is of course only a partial list and neglects many interesting mineral-market models. Most early models of energy demand were for single fuels, with electricity being the most popular". Typical exogenous variables were own price, income, and sometimes weather. The Houthakker et al. (1974) study of residential demand for electricity and gasoline is one of the latest to ignore the prices of competing fuels. This might be justified for gasoline but certainly is not for electricity, where substitution plays a significant role in determining consumption. Prices of competing-energy forms are included in some single-equation models of energy demand. In fact one of the earliest studies, by Houthakker (1951) of residentialelectricity demand in the UK, included the price of gas as an exogenous variable. And Fisher and Kaysen (1962) indirectly treat the price of substitutes through their appliance-choice equation. Including the price of substitute fuels in single-equation models, however, is only one step towards recognizing that the consumption decision, whether for a household or an industry, is a decision about a bundle of goods. Just as prices of substitute fuels are important, characteristics of factor markets other than energy also play a part in determining energy demand. This fact is generally not reflected in the single-equation models. Models of demand for single fuels tend to be more diverse than models of single nonfuel minerals and therefore more difficult to summarize. Fortunately, books have been devoted to the subject [Halvorsen (1978) and Bohi (1981) for example]. No attempt is made here to survey the entire literature. Instead a pioneering study Early models of the demand for electricity include Houthakker (1951), Fisher and Kaysen (1962), Baxter and Rees (1968) and Griffin (1974). These and other studies are summarized by Taylor (1975). "


953

reported in Balestra and Nerlove (1966) and Balestra (1967) is briefly summarized and related to later models. Balestra and Nerlove studied the demand for natural gas in the residential and commercial sectors of the United States, using pooled annual time-series (19501962) and cross-section (state) data. They distinguish between the short and the long run. Short-run demand is determined by the rate of utilization of a fixed stock of gas-burning appliances. In contrast, in the long run consumers are free to replace their appliance stocks, so that changes in the composition of the stock affect demand 12. The Balestra-Nerlove study emphasizes the new market for gas (the incremental demand due to changes in the stock of appliances). Relative prices of different fuels play a major role at the planning stage but, once an appliance is installed, little or no substitution among fuels is possible. Other modelers of the demand for natural gas have modified the BalestraNerlove model while maintaining its basic structure. These include MacAvoy and Pindyck (1973) and Berndt and Watkins (1977). Some models of the demand for gasoline also use the basic Balestra-Nerlove structure. Long-run decisions in this case determine the size and energy efficiency of the stock of gasoline-using vehicles, whereas short-run decisions determine the intensity of use of the existing stock. Cato, Rodekohr and Sweeney (1976), Pindyck (1979b), Wheaton (1982), and Berkowitz et al. (1990) model the two choices explicitly whereas Houthakker, Verlager and Sheehan (1974) and Berzeg (1982) use distributed lags to collapse the two stages. In addition, some models of residential-energy demand take this approach, separating the choice of appliance from fuel use '3.

3.3. Multicommodity models

It may seem obvious that demand for one type of energy (e.g. electricity) is intimately related to demand for other types of energy and other commodities such as capital and labor. For example, as relative prices vary, energy services are traded for the services of capital and labor. Furthermore, the consumer looks at the relative merits of different energy forms in providing those energy services. Nevertheless, this notion of substitution among fuels and other factors was lateblooming. It was not until the mid-1970s that models began to appear that explicitly treat the simultaneous determination of demand for more than one form of energy or for energy and non-energy factors. This issue is covered in greater detail in the section on dynamics. See Fisher and Kaysen (1982), Acton et al. (1978), Archibald and Gillingham (1981), Parti and Parti (1980), and Roth (1981). l2 l3

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Multicommodity-demand models for nonfuel minerals have been constructed by Moroney and Trapani (1981), Hazilla and Kopp (1982a), and Slade (1984). The vast majority of multicommodity models however deal with energy. Because the modeling techniques used are independent of the commodities modeled, only energy models are discussed here. Multi-commodity energy-demand models can be classified into models of interfuel substitution and models of the substitution of energy and non-energy inputs. The two sets of models however share a common structure that is discussed first. Most energy-demand models start with a flexible-functional form that approximates either indirect utility, g(p,Y), or cost, C(p,q) 1 4 . While the transcendental logarithmic (translog) form, introduced by Heady and Dillon (1961) and later by Christensen et al. (1971), was one of the first and perhaps remains the most popular in empirical work, many other forms have been used, including the generalized Leontief [Diewert (1971)], generalized Box-Cox [Berndt and Khaled (1979)], and flexible Fourier [Gallant (1981)l. Diewert and Wales (1987) survey the properties of a number of these forms. Because the approach to estimation is in fact quite similar among the different functional forms, for expository purposes we focus on the translog here. Furthermore, we discuss a model of the firm although a very similar development applies to the household. Assume that a vector of inputs x sold at market prices p is used to produce a commodity q. Furthermore, assume constant returns to scale and the absence of technical change (these can be included but only complicate the presentation). Then total cost TC can be expressed as In TC = lnC(p,q) = a 0

+ Inq +

ai

Inpi +

i

1

xx i

-

i

y,- lnpi Inpi. (30)

Shephard's lemma is used to obtain optimal-factor-cost shares, ST,

C

a C pi alnC ST := pix* = - = -= ai + yv Inpi. C api C alnpi i Symmetry and linear homogeneity in prices impose the following parameter restrictions:

y,- = yji for all i,j,

ai I

= 1,

C yij = 0 for all i. i

A flexible-functional form provides a local second-order approximation to an arbitrary twicedifferentiable function. l4


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Concavity of the cost function should be tested. When concavity is rejected, there are a number of methods that allow one to impose it a priori [see Diewert and Wales (1987)l. Factor shares (31) can be jointly estimated by themselves or with the cost function (30) to obtain an approximation to the underlying production technology. The estimated parameters can then be used to obtain (output-constant) optimalfactor demands, xi*,

Elasticities of substitution, which measure the percentage change in an optimal factor ratio xrl xi* due to a percentage change in the factor-price ratio pjlpi, can also be calculated. Allen-Uzawa-partial elasticities of substitution between factors are given by

which, with a translog-cost function, becomes ai,

=

ri,

+ Sr S,? ,

sts;

i f j ,

oii=

ni + ST)^ - ST (St l2

Constant-output cross-price elasticities of demand

EV

are then

The vast majority of energy-demand studies use the Allen-Uzawa elasticity as a measure of substitutability. Nevertheless, there are other measures. In the case of two factors, all elasticities of substitution are the same. With more than two factors, however, we must be careful to specify what is held constant when partial derivatives are taken. For example, the Morishima elasticity of substitution [Morishima (1967), Blackorby and Russell (1989)l is calculated as

In the next section we will see that the choice of measure of substitutability matters, both quantitatively and qualitatively. Variants of the above procedure have been used to model interfuel and energynon-energy substitution. With interfuel substitution, x is a vector of energy types

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(oil, natural gas, coal, etc.) and p is a vector of energy prices 15. And with energynon-energy substitution,^ is often a vector of four aggregate inputs - capital, labor, energy, and intermediate materials - a n d p is a vector of aggregate-input pricesI6. Some studies look at both interfuel and energy-non-energy substitution. These are two-stage models 17. In the first stage, a total-energy measure (a homotheticenergy-aggregator function) and an aggregate-energy-price index (often a translog function of the individual energy prices) are computed. The first stage provides an estimate of the structure of substitution among energy types and gives rise to individual-energy-demand equations. Homothetic separability is then invoked so that the estimated aggregate-energy price can be used as an instrumental variable in the second stage of the estimation. This stage provides an estimate of the structure of substitution among energy and other inputs and gives rise to an aggregateenergy-demand equation.

4. Issues treated by demand models

In this section, broad issues such as substitution and technical change are considered. Some effort has been made to discuss how several different techniques might handle each issue. Because econometric techniques have been used with such great frequency, however, they again dominate the discussion.

4.1. Capital-energy substitutability

The issue of substitution lies at the very heart of all demand studies. In fact, when studying output-constant-derived demand (as with the popular cost-function approach) or compensated-consumer demand, demand and substitution are one and the same. If changes in output (utility) have been ruled out, changes in factor use (commodity purchases) are the only possible response to changes in relative prices. In some sense, therefore, this entire chapter is about substitution. In this section, however, we focus on a narrow aspect of substitution that has received l5 Interfuel-substitution studies include Hudson and Jorgenson (1974), Fuss (1977), Halvorsen (1977), Joskow and Mishkin (1977), Pindyck (1979), Denny, Fuss and Waverman (1981), Jorgenson and Fraumeni (1981), and Hazilla and Kopp (1982b). l 6 Examples of energy-non-energy substitution models include Hudson and Jorgenson (1974), Berndt and Wood (1975), Griffin and Gregory (1976), Fuss (1977), Mork (1978), Berndt and Khaled (1979), Halvorsen and Ford (1979), Magnus (1979), Uri (1979), Pindyck (1979), Berndt and Morrison (1979), Field and Grebenstein (1980), Jorgenson and Fraumeni (1981), Hazilla and Kopp (1982b), McRae and Webster (1982), Harper and Field (1983), Berndt and Hesse (1986), Kolstad et al. (1986), and Lee (1990). The two-stage models are those that are listed in both of the previous footnotes.

''


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much attention in the last two decades - the relationship between energy and capital in aggregate manufacturing. The energy-price increases of the middle 1970s fuelled much of the interest in energy-demand studies. In particular, one question occupied the attention of many energy modelers - the relationship between energy price and the growth of the capital stock. If energy and capital are close substitutes, then when energy prices increase, man-made capital will be substituted for scarce energy and the economy will adjust without severe dislocations. If on the other hand energy and capital are complements, increased energy prices will be accompanied by a decline in growth and per-capita income. The nature of the energy-capital relationship (positive or negative crossprice elasticity of demand or elasticity of substitution) was sought by many. Unfortunately, the experts did not agree. For example, Berndt and Wood (1975) and Magnus (1979) found significant energy-capital complementarity whereas Griffin and Gregory (1976) and Pindyck (1979a) found significant substitutability 18. Many explanations for the disagreement have been proposed. Griffin and Gregory (1976) and Griffin (1981) note that their own study as well as Pindyck's used pooled time-series cross-section data by country, whereas Berndt and Wood and Magnus used time-series data for a single country. They claim that, because regional energy-price differences persist over long periods of time, cross-section studies pick up long-run substitution possibilities that cannot be observed in timeseries studies. Griffin and Gregory postulate that substitution possibilities are small in the short run but much larger when firms are free to install new technologies. It is likely that time-series cross-section differences partly explain the differences in estimated elasticities. However, cross-section estimates are long-run estimates only if all countries are simultaneously in long-run equilibrium (a very remote possibility). In addition, when dynamic adjustment is introduced into a time-series model (see Section 4.4), results are still mixed. For example, Denny, Fuss and Waverman (1981) find long-run capital-energy complementarity for fourteen out of eighteen two-digit manufacturing industries in the United States and for six out of eighteen Canadian manufacturing industries. The long-runlshort-run distinction thus cannot completely account for substitutability/complementary differences. Another explanation for the different findings is proposed by Berndt and Wood (1979) who note that their study used four factors - capital K, labor L, energy E, and intermediate materials M -whereas Griffin and Gregory and Pindyck assume that K, L, and E are homothetically separable from M and that M can thus be ignored in the estimation of substitution possibilities among K, L and E. Suppose that a group of inputs x is homothetically separable from the other inputs used in the production of an output q. Let X(x) be the aggregator Many others studied this relationship. However, the discussion is not enhanced by enlarging the number of studies (many of which found an insignificant relationship).

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subfunction. Berndt and Wood define the gross-price elasticity, E;, as the proportional change inxi due to a proportional change inp, (wherep, is the price of somex,) when the output of the subfunctionX(x) is held constant. In contrast, they , be the comparable elasticity when output q is define the net-price elasticity, ~ i , to held constant. They show that

It is thus possible for two inputs to be gross substitutes but net complements. Berndt and Wood hypothesize that the gross-net distinction can account for the difference in elasticity estimates. The gross-net distinction might account for some of the difference in estimates, but it is unlikely that it accounts for all of it. As Griffin (1981) points out, the elasticity of substitution between materials M and nonmaterials X(x) would have to be 3.7 to reconcile the discrepancy between the Berndt-Wood and GriffinGregory findings. Most studies of substitution between materials and nonmaterials find an elasticity of substitution that is well below unity, implying that such a large value is highly unlikely. A third explanation is proposed by Field and Grebenstein (1980) who note that the treatment of capital is not the same in all studies. Griffin and Gregory and Pindyck use the traditional value-added approach to estimating the cost of capital. Their capital is thus a residual that includes working capital and land. In contrast, Berndt and Wood and Magnus use a service-price approach due to Christensen and Jorgenson (1969). Their capital stock includes physical capital but excludes working capital and land. Field and Grebenstein disaggregate the capital stock into physical and working capital and find that physical capital and energy are predominantly complements whereas working capital and energy are predominantly substitutes. They go on to attribute some of the difference in estimated elasticities to a difference in the treatment of the capital stock. What Field and Grebenstein do not emphasize is that their results cast doubt on the very existence of a capital aggregate and thus on the meaningfulness of the entire question 19. The question of the existence of a homothetically separable capital aggregate must be answered before elasticities of substitution between this aggregate and other inputs can be calculated. Additional doubt is cast on the existence of a capital aggregate by Hazilla and Kopp (1982) who maintain the service-price approach and disaggregate physical capital into structures and equipment. They find that in several sectors one physicalcapital component is a substitute for energy whereas the other component is a l9 If a group of inputs (e.g. capital-stock components) is homothetically separable from other inputs, then the elasticities of substitution between two components of the subgroup and another input must be of the same sign.


959

complement. Their findings indicate that even physical capital is not a meaningful aggregate. Another problem with computing elasticities of substitution between factors at the level of aggregate manufacturing was emphasized in Section 2. When aggregating across such diverse technologies, some of which exhibit capital-energy complementarity and others substitutability, it is unlikely that a single robust capital-energy relationship can be determined for the aggregate. The problems of technology aggregation may be at least as great as those of input aggregation. The problems with technology aggregation point to the desirability of estimating elasticities at a much more disaggregate level. This approach has been taken by many, including Halvorsen and Ford (1979), Field and Grebenstein (1980), Denny, Fuss and Waverman (1981), Jorgenson and Fraumeni (1981), and Hazilla and Kopp (1982b). Judging from the results of these studies (substitutability in some sectors and complementarity in others), it seems unlikely that a single well-defined answer to the aggregate energy-capital relationship exists. To summarize, the estimated elasticities do not provide us with a consensus concerning the implications of capital-energy substitutability for sustained growth. We saw that different data sets yield different estimates of the sign and magnitude of the crucial measure - the capital-energy elasticity of substitution. Moreover, different ways of calculating this elasticity yield different answers, even when the same data set is used. For example, Morishima K-E elasticities calculated from the Berndt-Wood (1975) data are positive whereas Allen-Uzawa elasticities are negative [see Slade (1987a)l. Finally, even if we knew the value of this elasticity evaluated at today's factor shares, it would tell us little about substitution possibilities when mineral use is small (when we are running out of natural resources). Any information gleaned from current estimates is therefore apt to be misleading when extrapolated to unobserved regions of the technology set.

4.2. Technical change Technical change, unlike substitution, involves changes in the set of production possibilities available to society, generally due to invention, innovation or various types of learning20. Such changes might mean that a larger output can be produced with the same inputs or it might involve changes in factor proportions at constant relative-factor prices (changes in the shapes of isoquants). Occasionally, technical change is the most important factor determining the demand for a commodity. For example, the price of ferroalloys constitutes only Technical change is associated with derived demand. However, similar techniques can be used to model changes in tastes on the consumer side.

20

M.E. Slade et al.

960

a small fraction of the cost of final products. The demand for ferroalloys is therefore often more sensitive to new uses of steel that require special properties (hardenability or noncorrosiveness) than to changes in relative-ferroalloy prices 2 1 . In theory, it is straightforward to distinguish between substitution (movement along an isoquant) and technical change (shifts in isoquants). In practice, however, the distinction becomes blurred. For example, a new technology might only be adopted when factor prices change in such a way as to make it economical. In our discussion, we consider technical change to be a one-way movement whereas substitution can go in either direction depending on relative prices. Changes in technology, like substitution, can be both marginal and radical. Marginal changes involve the continual improvement in the efficiency with which products are produced and materials are used over time. In contrast, radical change refers to a fundamentally new way of doing things. Econometric models tend to be quite good at explaining demand when economic variables such as prices and income play a major role and where technical change is marginal. Because this progress proceeds in a steady fashion, it is easy to incorporate by introducing a trend variable into the production or cost function. Unfortunately, whereas models of this sort are useful for measuring the rate of technical change in the past, they are not good at explaining the engineering or micro basis of this change. Technical change can be incorporated into the production function by including a vector of 'knowledge' variables. In practice, it is often difficult to identify and measure knowledge and we are forced to make do with time as proxy for accumulated knowledge2*. Our exposition adopts this simpler convention; the production function is modified so that output q is produced by a vector of inputsx in a way that changes over time,

If marginal rates of substitution between inputs are independent of technical change, technical progress is said to be Hicks neutral 23. This is equivalent to saying that the inputs form a separable group so that the production function can be written as

-

In this case, the intensity-of-use method that is described in footnote 10 is very useful. 22 There are more flexible approaches to modeling technical change. For example, Baltagi and Griffin (1988) propose a general index with time-specific dummies and Slade (1989a) proposes one that is based on the Kalman filter. 23 Other types of neutrality (Harrod, Solow, Leontief) correspond to cases where technical change affects capital, labor or other inputs in a differential fashion [see Berndt and Wood (1982) for a summary]. Various forms of factor biases are discussed by Stevenson (1980). 21

Ch. 20: Buying Energy and Nonfiel Minerals

961

If in addition production is homothetic, the production function takes the form

All of these restrictions can be tested. By definition, neutral technical change leaves certain relationships unchanged. These relationships can therefore be estimated without making any assumptions about the time path of technical change. In particular, factor demand, price elasticities of demand, and elasticities of substitution are not affected by Hicksneutral technical change. This assumption is often adopted for convenience and without testing. Another popular restriction on technical change is factor augmentation. Factor augmentation occurs when there exist indices ai(t), i = 1, . . . , N, representing the efficiency of factor i relative to some base, such that the production function has the representation

When eq. (42) holds,i;, := ai(t)x;, is the ith input measured in efficiency units. Another significant distinction is whether technical change augments the flow of new investment in quasi-fixed factors or the stock of quasi-fixed factors (such as capital). Solow (1957) and his student Intriligator (1965) led the debate on this issue. Lee (1990) has recently revisited the question, focusing on the embodiment of technical change as an explanation for international differences in energy demand and productivity growth. Many empirical-demand studies test the restrictions imposed by various assumptions about technical change. Most of these studies use cost functions, for reasons stated earlier. Suppose that the technology represented by eq. (39) (the technology with no restriction on the form of technical change), is approximated by a translog-cost function 24,

Factor shares are then

i 24

The assumption of constant returns to scale is maintained. Scale economies are discussed shortly.

M.E. Slade et al.

Furthermore, the rate of cost diminution is given by

With constant returns to scale, this dual rate of cost diminution is equal to the primal rate of multifactor-productivity growth, a lnqlat, which is the difference between the rate of change in output and the rate of change of an index of inputs. Different restrictions on the form of technical change can be tested. For example, the coefficients pi, i = 1, . . . , N , measure the biases in technical change (the rate of change of factor shares at constant relative factor prices). Following Sato (1965), technical change is i-using, neutral or saving according to whether Pi is positive, zero or negative. Technical change is Hicks neutral if Pi = 0, with i = 1, . . . , N . Parameter restrictions for factor-augmenting technical change for the special case where

can be found in Wills (1979). This case corresponds to the situation where the 'quality' of an input grows exponentially. Wills tests for Hicks-neutral and factor-augmenting technical change in the primary-metals industries. Moroney and Trapani (1981) examine biases in several natural-resource-intensive industries, Stevenson (1980) investigates electric-utility generation, and Jorgenson and Fraumeni (1981) assess thirty-six industrial sectors. The overwhelming evidence is that Hicks-neutral technical change must be rejected. The evidence with respect to other sorts of restrictions such as factor augmentation is mixed. The implication of these findings is that factor demands and elasticities of substitution obtained under the assumption of Hicks neutrality are biased. For example, Wills (1979) finds that elasticity estimates from the unrestricted specification are generally smaller in magnitude than those from the neutral specification. This is to be expected because some of what is classified as substitution response under one specification is reclassified as technical change under the other. Most studies of technical progress maintain the assumption of constant returns to scale. In general it is difficult if not impossible to separate the effects of economies of scale from technical change. To distinguish these effects in practice requires considerable structure to be imposed on the estimating procedure 25. Distinguishing among the effects of technical progress, exploitation of economies of scale, and cheaper mineral-resource inputs as causes of economic growth is 25

This problem is discussed by Diamond and McFadden (1965).


963

however an important issue. Berndt and Khaled (1979) formulate and estimate a model of producer behavior for aggregate USA manufacturing that simultaneously identifies substitution elasticities, scale economies, and the rate of bias of technical change. However, the same caveats about aggregation across inputs and technologies apply to this study as to the capital-energy-substitution studies26. 4.3. Scale effects

When constant returns to scale prevails, the cost function can be written as where c(p) is the unit-cost function. With this restriction, a single isoquant contains all information about factor demands and substitution possibilities. Demands for any other output levelq' are obtained by multiplying demands at q byq'lq. Constant returns to scale is therefore a very restrictive assumption. Scale effects can occur at the plant level for various reasons including indivisibilities and shared equipment. Scale effects can occur at the industry level if externalities related to industry output are present or if entry and exit are not free and firm production functions are not linearly homogeneous. A technology is homothetic if the production and cost functions can be written as 4 = f (x) = F(h(x)),

(48)

(49) TC = C(p,q) = ~ - ' ( q ) c ( p ) , where h(x) is linearly homogeneous and F ( . ) is monotonic and increasing. Technology is homogeneous of degree X if ~ - ' ( q )= q'lX.

(50)

In either case (homogeneity or homotheticity) substitution possibilities are independent of the level of output. When technology is not homothetic, factor proportions as well as factor levels vary with the level of output. The translog approximation to the cost function for a nonhomothetic technology can be written as

Atkinson and Halvorsen (1976) examine the demand for fossil fuels by the electric utilities. They find an absence of strong scale economies and little technical change in this industry.

26

M.E. Slade et al.

Factor shares become Sf = ai +

C 7~lnpj + 6i lnq. I

Parameter restrictions for homotheticity are 6; = 0, i = 1, . . . , N. For homogeneity (of degree 1/60) the additional restriction that SN+1 = 0 is required. Economies of scale are usually defined as the relative increase in output from a proportional increase in all inputs. It is often more appropriate, however, to define scale economies as the relationship between total cost and output along the expansion path (where input prices are constant and costs are minimized for every level of output). The latter definition is adopted here. In this case, a measure of scale economies, SE, is unity minus the elasticity of total cost with respect to output,

Christensen and Green (1976) estimate economies of scale for US firms producing electric power. They use cross-section data for 1955 and 1970, thus abstracting from changes in technology. They find that in 1955 there were significant economies of scale available to nearly all firms. By 1970, however, the bulk of firms was operating in the essentially flat area of their average-cost curves. Much of the data used in estimating economies of scale involves the investorowned electric utilities, firms that are rate-of-return regulated. A rate-of-return regulated firm does not minimize cost [see Averch and Johnson (1962)l and, as a consequence, many duality relationships break down. This fact is often ignored in the econometric analysis. An exception is Atkinson and Halvorsen (1984) who show how to replace market prices with shadow prices that can be estimated from market data. When these shadow prices are substituted into eq. (53), an unbiased estimate of SE is obtained. Engineering methods, which can also be used to estimate economies of scale at the plant level, often focus on the physical relationships that underlie these economies. For example, the quantity of petroleum that a pipeline can ship is proportional to the area of the cross-section of the pipeline. The quantity of materials required to construct the pipeline is however proportional to the circumference of this circle. As the pipeline industry expands, therefore, the demand for pipeline materials will increase less than proportionally.

4.4. Dynamics

While energy may be a variable factor of production, its use is intimately tied to the character of the energy-using capital of a firm or household. As Fisher and


965

Kaysen (1962) noted in their seminal study of electricity demand in the USA, in both households and industry the use of electricity is complementary to the use of a stock of electricity-using equipment. It is intuitively clear that the more electricityusing appliances we have, the more electricity we will use. The importance of this is that whereas energy may be a variable factor of production, energy-using capital is fixed in the short run. Thus, adjustment of energy use in response to an energy-price shock will be complete only after the capital stock has had a chance to re-equilibrate. In fact, this description of demand is not at all unique to energy. For any variable factor of production, as long as there is some substitutability or complementarity between it and a quasi-fixed factor, the effect of a price change on demand for that factor will take time to work out. The importance of dynamics has been recognized for a long time. However, methods for dealing with dynamics have matured markedly in recent years. Early models are characterized by a good deal of intuitive appeal but no foundation in the theory of the firm or the household, where profit or utility maximization dictates the form of the demand function. Following the terminology of Berndt et al. (1981), early models are termed 'ad hoc' because of their lack of foundation in theoryz7.Progress in treating dynamics within demand models has been made by successively introducing more and more economic theory into the specification of demand equations. 4.4.1. Ad hoc models

Two of the most common ad hoc models are the stock and flow-adjustment models of demand 28. Both are based on a partial-adjustment framework where there is a distinction between the desired level of a variablexr and the actual valuex,. In each time period, x, partially adjusts to the desired value according to

The flow-adjustment model involves a partial adjustment of the commodity of concern. Letx, be demand for energy at time t , and let 2, be a vector of exogenous variables affecting demand. Then eq. (54) becomes x, = X(x: -xtPl)

+ x,-,

and x: = g(z,).

(55)

These equations reduce to

*'

Although it is convenient to call such models 'early', in fact their use is quite common in recent energy-demand studies [e.g. Cato (1981)l. 28 The terminology varies. Sometimes a flow-adjustment model is referred to as a stock-adjustment or simply partial-adjustment model.

M. E. SIade et al.

966

which involves a lagged-dependent variable on the right-hand side plus the exogenous variables and the speed-of-adjustment parameter, A. A basic criticism of flow-adjustment models is that they do not recognize the extent of disequilibrium in other factor markets. Although disequilibrium in the capital market is the rationale for using flow-adjustment, the process of capital adjustment is not considered. This problem is remedied to a certain extent in the stock-adjustment models, which we now consider. Stock-adjustment models are similar to flow-adjustment models in that they involve a distinction between a current stock and a desired stock. The difference is that the focus is on adjustments in the capital stock, which in turn affect energy use. In effect, the energy-consumption decision is divided into two parts: the decision of how to utilize a given capital stock, and the decision of how to change that stock. These are short- and long-run decisions. The stock-utilization decision can be written as

where kt is the capital stock and zt is a vector of exogenous variables. It is quite common to write eq. (57) in terms of a capital-utilization rate,

where the utilization rate may be a constant [e.g., Balestra and Nerlove (1966)l or may vary [e.g., Taylor et al. (1982)l. Recently, a whole literature on estimating models of the form (58) has arisen. Such models, which are termed conditional-energy-demand models [see Lawrence and Parti (1984)], are concerned with the utilization of very specific types of capital (e.g. dishwashers) and are usually estimated using detailed household-level data. Whether eq. (57) or eq. (58) is estimated, one obtains a short-run-demand function describing energy consumed as a function of the capital stock. The second part of the stock-adjustment model specifies how the capital stock adjusts through time. A popular specification for stock adjustments is the partial-adjustment framework, kt -kt_, = A(kf - kt-,),

(59)

k; = g(zt).

(60)

Equation (57) or (58) in conjunction with eqs. (59) and (60) constitute a dynamic model of energy demand based on stock adjustment. There are many variants of this model. Balestra and Nerlove (1966) combine the equations, eliminating any need for capital-stock information. In contrast, a number of authors [e.g., Fisher and Kaysen (1962), Taylor et al. (1982)l use time-series data on capital


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stocks to estimate eqs (58)-(60) separately. Other specifications for stock change are possible. For instance, Hausman (1979) uses a hazard-rate model, where zt determines a probability that a particular household will acquire a particular energy-using appliance at time t. The basic criticism of all these models, however, is that the dynamics is not based on theory. The speed of adjustment of a factor is assumed to be related solely to the difference between desired and current use. Furthermore, most models of the sort described in this section are structured in such a way that the relationship between short- and long-run elasticities is restricted a priori [see Berndt et al. (1981)l. This is, of course, undesirable.

4.4.2. Long-run costs fvom short-run costs Although the so-called 'ad hoc' models of the last subsection have been very popular, their basic fault is the lack of economic theory in the adjustment process. One way around this problem is to estimate a series of short-run-cost functions for different levels of the quasi-fixed input, capital. As is well known, the long-run cost function with capital as a variable input can then be generated as the lower envelope of the short-run-cost functions. More precisely, recall the restricted or variable-cost function (5), which is reproduced here as

Viewed as a functioniof q;withrpv and xf fixed, this function is simply the familiar short-run cost function (excluding fixed costs). Long-run costs are minimized overxf when condition (9) holds. This is the well-known condition that in long-run equilibrium, the marginal saving in variable cost from the utilization of an extra unit of a quasi-fixed factor must equal the market price of that factor. Equation (9) can be solved for xf* and the result substituted into eq. (8) to obtain the long-run function C(p,q). Short-run demand functions for the variable inputs are given by eq. (6) and long-run demands are given by eq. (4), both by Shephard's lemma. Thus, both long- and short-run demand can be derived by estimating the shortrun cost function (5). This approach has not been as widely used as the partialadjustment approach, although it became fairly popular in the 1980s. Outside the energy area, Brown and Christensen (1981) developed such a model for US agriculture. And, in the context of energy, Mork (1978) applied the model to aggregate-energy demand in the USA, Berndt and Hesse (1986) examined OECD data, and Morrison (1988) considered international data. The advantage of this approach is that both long- and short-run demand can be estimated without specifying the dynamic-adjustment process. Furthermore, the method contains no ad hoc elcment (other than choosing which factors are variable

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and which are quasi-fixed). A disadvantage is that no information is available about the transition path from the short to the long run. A further problem is that equation (9) may not have a solution. It is difficult to estimate a cost function subject to the restriction that its gradient be nonpositive. A possible remedy suggested by Berndt and Hesse (1986) is to assume that production is characterized by constant returns. Under this assumption, the difference between the value of output and variable cost is the return to the fixed factor. These returns are the product of the quantity of the fixed factor and its shadow price. 4.4.3. Adjustment costs

Perhaps the most advanced treatment of the dynamics of energy demand involves the recognition that it is costly to adjust levels of quasi-fixed factors and that the more rapid the adjustment process, the more costly it becomes. The adjustment-cost model of investment, which seems to have been originally suggested by Eisner and Strotz (1963), was developed by Lucas (1967), Treadway (1974) and others. However, it took some years for the approach to make its way into energy-demand analysis. Berndt et al. (1977) were the first to apply this model to energy consumption. Although several other applications now exist [Berndt et al. (1980)), Berndt et al. (1981), Denny et al. (1981), Pindyck and Rotemberg (1983a,b), Lee (1990)], it remains a fertile ground for research. The basic idea is as follows. The reason why a firm does not adjust its capital stock (or other quasi-fixed factors) instantaneously in response to changing market conditions is that it is costly to do so (over and above the standard acquisition cost of capital). For example, rapid shifts in the capital stock may require some redundancy with the existing stock, a premium may have to be paid for rapid delivery, or production may be disrupted for capital installation. Moreover, there are a variety of reasons why the cost of adjusting the capital stock is a function of the rate of change of that stock. Thus, in an intertemporal sense, production costs depend on the rate of change of the quasi-fixed factors as well as the use of both variable and quasi-fixed factors. In choosing an investment strategy, the firm seeks to minimize the net-present value of costs of particular production and investment paths, where costs include adjustment costs. We first consider a simple, discrete-time adjustment-cost We then extend this model to include multiple factors of production and show how adjustment-cost models relate to the earlier partial-adjustment models. Let a firm produce a single output q using a single variable input x and a single quasi-fixed input k 30. If the price of x is p, then the firm's restricted-cost function is k,q).

e(p,

29 30

This model is similar to the one developed by Pindyck and Rotemberg (1983a). The notation is simplified here withx, k,p, and r replacingxv,xf,pVandpf.


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The firm must decide how much to invest in the quasi-fixed factor. This decision is made by minimizing the net-present value of costs, including an adjustment cost A(I,) associated with gross investment I, = kt - (1 - 6) kt, where S is the depreciation rate. The overall cost function C* depends on the future path of prices { p,) and {r,) and output {q,), where r, is the rental price of kt. If p is the discount rate, the firm faces the problem

The solution to this problem is C*({p,) , {r,) , {q,)) First-order conditions for the minimization of eq. (61) are

Equation (62) has the following interpretation. At an optimum level of k,, using one more unit of kt will result in a decrease in variable cost that is exactly offset by an equivalent increase in capital-acquisition and adjustment costs. From Shephard's lemma, it also follows that

The model that is estimated consists of equations ( 5 ) , (62) and (63). It should be pointed out that at any point in time the firm is only deciding how much to invest at that time, even though deciding how much to invest now requires that an investment path for all future time be forecast. Thus the maximization (61) must be solved for every t . Estimation of this model, which requires time-series data, is not straightforward. Expectations of future output and prices are required, and there are a number of models of expectation formation including rational expectations [Pindyck and Rotemberg (1983a,b)] and the model of Epstein and Denny (1983). It is straightforward to generalize this problem to include multiple factors of production. In this case,x,,p,, kt and r, are vectors. Ifp,, r,, andq, are constant over time, there will be a steady-state level of k,, which we denote k*. When in addition, and A are quadratic functions of kt and I,, it can be shown that the solution to the minimization (61) can be written as

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where M ( p ) is a matrix that is a function only of the discount rate [Epstein and Denny (1983)l. More generally, Lucas (1967) shows that, for any cost function, eq. (64) represents a solution to a linear approximation to the first-order conditions of the minimization (61). In this more general case, however, M becomes a function of k* as well as of p. Note the similarity between eq. (64) and the partial-adjustment model (59). If M were a constant matrix, then eq. (64) would resemble the multivariate partial-adjustment model proposed by Nadiri and Rosen (1969). However, Berndt et al. (1981) argue that there are some fundamental differences between the multivariate partial-adjustment model and eq. (64). Probably the most significant differences are that M ( p ) in eq. (64) is a function of the discount rate, not a constant, and that economic theory imposes certain restrictions on the elements of M ( p ) . 4.4.4. Expectations

Purchases of many commodities are made on the basis of expected prices. This is most apt to be the case when the commodity is durable. For example, the choice between a gas or an electric home heater is usually influenced by expected relative-fuel prices. Demand modelers must therefore have ways of modeling expectations. Moreover, when considering any of the dynamic-factor-demand models reviewed in the previous section, it is necessary to specify some sort of expectation mechanism. There is a wide variety of possible ad hoc mechanisms for forming price expectations. The simplest is that firms have static expectations, in other words, they expect today's price to persist forever. This assumption is made by Berndt et al. (1977). Another frequently employed hypothesis is that consumers expect current trends to persist. They therefore extrapolate from historic to future prices. Formally, ifp&is the price expected in period t , then

where, when the forecast is formed, w;is the weight given to the price observed i periods ago. Equation (65) contains an infinite number of unconstrained weights. It is common practice to constrain the weights to conform to a particular pattern. For example, Baxter and Rees (1968) and Uri (1980) assume that the weights decay geometrically [a Koyck (1954) distributed lag], Griffin (1974) assumes that they lie along a polynomial of specified degree [an Almon (1965) distributed lag], and

Ch. 20: Buying Energy and Nonfiiel Minerals

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Slade (1984) uses a Bayesian technique due to Shiller (1973) to impose smoothness on the weights. The geometric-price lag has much in common with the partial-adjustment model for quasi-fixed factors. Here it takes the form of the adaptive-expectations model of Cagan (1956),

where current information on price,pt, is used to update expected pricesp;. Equation (66) can of course be rewritten with expected price equal to a geometrically decaying weighted average of past observed prices. The conventional partial-adjustment model can be viewed as incorporating some sort of adaptive-price expectations. Adjustments in factor usage are not instantaneous due to a variety of factors, including a non-instantaneous adjustment in price expectations following a price change. There are other ad hoc specifications. For example, Epstein and Denny (1983) assume that prices follow a first-order differential equation, dpldt = a + pp,. As with the treatment of dynamics, however, the trend in representing expectations is away from ad hoc specifications of the expectation process towards the development of models based more on economic theory. In the area of expectations, this has led to the rational-expectations hypothesis. In the seminal article on rational expectations, Muth (1961) suggested "that expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory". Thus it is appropriate to specify a mechanism for expectation formation that is consistent with the model of market operation within which the expectations are embedded. For instance, consider a model for a commodity whose supply cannot be adjusted within the current period,

Dr= St.

(69)

The quantity demanded (67) is a function of price and income. The quantity supplied (68), however, is a function of expected future price and a disturbance term (eg. strikes or embargoes); producers must make production plans based on their price forecasts. Finally, eq. (69) is an equilibrium condition. An ad hoc method would specify some functional form forp;, substitute it into equation (68), and estimate the model. However, our objective is to introduce rational expectations. There are two ways to embody the rational-expectations hypothesis in our model [see Sheffrin (1983)j.

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First, we can use the fact that p: is an unbiased estimator of p,, given the information available at t - 1. Thus the identity Pr = P&+ ' I t

(70)

can be used in eq. (68) where v, is a disturbance term with a conditional expectation of zero. This is the approach taken by Pindyck and Rotemberg (1983a) in their study of energy demand under rational expectations. The second approach, which generally yields more efficient estimates of the coefficients, is to extract the functional form for p," that is implicit in the model. Solving for p, yields

Taking conditional expectations of both sides of this equation and solving forp,", we obtain

where we assume that the disturbance E has mean of zero and y&is the conditional expectation of the exogenous variable y,. The second method clarifies the distinction between expectations concerning endogenous and exogenous variables. Our model describes the evolution of p, and thus lends structure to expectations about p,, namely eq. (72). However, eq. (67) has nothing to say about the future value of y,. Predicting exogenous variables is generally relegated to purely statistical means. A popular procedure is to assume that exogenous variables follow some stochastic process. Another is to assume that y," is an unbiased predictor of yt based on the information available at time t - 1. Under this assumption, the realized value y, plus an error term can be substituted fory," in eq. (72). The end result is that eq. (72) with the appropriate specification of y& is substituted back into eq. (68), thereby eliminating p,". The revised model, which is usually nonlinear in the structural parameters, is then estimated. Few full-blown rational-expectations models of the second type have been estimated for mineral demand. For an approximation to this model, see Morrison (1986). 4.5. Disequilibrium and rationing Disequilibrium can occur in mineral markets for several reasons. For example, producers may not be using the optimal input mix or markets may not clear.


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The first reason was discussed in Section 4.4, where it was noted that adjustment costs can account for short-run disequilibrium (or temporary equilibrium) in factor markets. The second reason is discussed here. In many commodity models, markets are assumed to clear; the output of any industry is entirely accounted for by purchases by other industries or by final consumers. However, many real-world markets do not clear - inventories build up or are depleted. A significant fraction of unplanned inventory movement results from random errors in forecasting supply and demand. Single-commodity-market studies usually model this movement by including an equation for changes in inventories, which are often calculated as a residual. Disequilibrium is however not always due to random forecasting errors. Sometimes it is a conscious policy. In many metal markets, particularly those that are fairly concentrated, rationing is a common phenomenon. That is, producers choose to ration customers on a non-price basis rather than allow price to rise to market-clearing levels. Rationing is sometimes explained as an attempt to prevent the long-run substitution away from a commodity that might be triggered by a very high price for that commodity [see McNicol (1975) and, for a game-theoretic treatment of this issue, see Slade (1991a)j. Markets that have a history of rationing include copper, aluminum, and molybdenum 31. When rationing occurs, consumers are unable to obtain metals at their marketclearing prices. This fact is usually ignored by demand modelers. If equilibrium is wrongfully assumed, estimated coefficients are biased toward zero. MacKinnon and Olewiler (1980), in an empirical study of the US copper market, use a simple modification of the Tobit model to show that the magnitudes of estimated price elasticities of demand are significantly different when rationing is considered from those obtained when it is ignored32. Another sort of disequilibrium results from legal restrictions on input use or output production. Such restrictions are common when the input generates an externality or when the output is a pollutant. Engineering-process models deal with quantity constraints in a very straightforward way. Kopp and Smith (1980) incorporate various sorts of quantity restrictions into an engineering-process model and then generate pseudo data from the model. The pseudo data is in turn used to estimate a translog-cost function. They find that discharge constraints affect the ability of the econometric model to estimate substitution possibilities in a way that is statistically significant. Rationing is common in energy markets in periods of price controls. However, these periods are easy to identify and energy demand is usually estimated with data from periods when controls were not in place. 32 For a criticism of this model, see Ghosh et al. (1987) and for a different rationing model, see Fuss (1980). 31

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In markets where rationing is prevalent, disequilibrium models provide better estimates of substitution possibilities than do equilibrium models. Disequilibrium modeling would therefore seem to be a fruitful area for further research. It has, however, received little attention.

4.6. Discrete choice

Most demand studies are based on the assumption that consumers can purchase continuously varying quantities of commodities. This is certainly the case when buying gasoline, for example. A consumer can purchase any quantity up to the amount that fills her tank. A large class of purchases, however, is inherently discrete. This class includes automobiles, home-heating systems, air conditioners, and many other consumer durables. With this class of good, the minimum purchase is substantial and consumers rarely buy more than one item at a time. Discretechoice estimation techniques [e.g. McFadden (1974)l are therefore suitable to estimating demand for these energy-using commodities. It is common to model energy demand in two phases - changes in the stock of energy-using durables and the utilization rate of an existing stock. Discretechoice techniques are usually applied at the first stage. When a consumer decides to purchase a new durable, she often faces a discrete set of options. Each alternative is characterized by a set of attributes or characteristics. The alternative chosen depends on the characteristics of the alternative, the consumer's tastes, and her income. Discrete-choice techniques can be used to model both consumer and derived demand. Consumer-durable studies include Baughman and Joskow (1975), who consider appliance choice, and Wheaton (1982) and Berkowitz et al. (1990), who model the choice of automobile. Hausman (1979) incorporates a discount rate into his study of appliance choice and models the trade-off between capital and operating costs. Because the consumer's choice depends on her private discount rate, with Hausman's model it is possible to solve for the discount rate implied by consumer behavior. Information on revealed discount rates can then be used to determine if markets are operating efficiently. For example, if consumers have high private discount rates, as Hausman finds, government policy that encourages the purchase of more energy-efficient durables might be advantageous. Discrete-choice techniques can also be used to model derived demand. For example, Joskow and Mishkin (1977) study the choice of fuel by electric utilities and Joskow and Baughman (1976) model fuel choice in the residential, commercial, and industrial sectors of the US economy. Discrete-choice models incorporate the preferences of individuals and should therefore be estimated using data on the actual choices of households or firms.


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Many discrete-choice studies, however, rely on aggregate data 33. Hartman (1982) develops an estimation technique for incorporating aggregate data into individualchoice models and demonstrates that the uncorrected use of such data results in inconsistent coefficient estimates34. 4.7. Durability and secondary markets A mineral commodity is recyclable if its valuable properties remain intact after use. It is nonrecyclable if they are dissipated. Desirable properties of metals such as strength, conductivity, and noncorrosiveness persist in discarded metal products. In contrast, fuels are valued for their heat content, which is dissipated in combustion. The demand for nonprecious metals such as copper and aluminum is predominantly a flow relationship (because these metals must be substantially transformed from their scrap condition to yield useful services). In contrast, the demand for precious metals such as gold is predominantly a stock relationship. It must thus be modeled as the demand for an asset. These two possibilities are discussed in turn.

4.7.1. Flow demand with secondary markets

Primary and secondary metals are usually such close substitutes that their consumption must be studied simultaneously. The demand for most primary metals therefore cannot be modeled in isolation from the demand for secondary (recycled) metals 35. The supply of secondary metal and the demand for primary metal are interrelated in several important ways. For example, metal consumption is an important determinant of the supply of recyclable metal (the stocks of scrap available for reclamation) 36.This relationship is however very complex. Each type of metal product has a different average lifetime and each average lifetime can be affected by metal price. Not only does metal consumption partially determine secondary supply, but the supply of recycled metal is an important factor in determining the quantity of primary metal consumed. When cheap sources of scrap are plentiful, less virgin metal is used. A final complication in modeling metal demand occurs because primary and secondary metals can be either perfect of imperfect substitutes. For example, Baughman and Joskow (1975), Joskow and Baughman (1976), and Wheaton (1982). Hartman assumes identical linear utility functions for each consumer and therefore avoids the aggregation problems discussed in Section 2.3. The problems that he discusses are statistical. 35 A secondary metal is one that has been processed and is distinguished from unprocessed scrap. 36 This discussion pertains to 'old' scrap - metal from discarded products - and not to 'new' scrap that results from the production process itself. New scrap is not an addition to supply. 33

34

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All metal modelers must deal with the relationship between metal consumption and scrap supply. Fisher, Cootner and Baily (1972) make the simplifying assumption that metal is available for secondary consumption immediately after it is first consumed. This seems, however, unrealistic. The complex lagged relationship between metal consumption and scrap supply is modeled by Slade (1980) who also considers the efficiency of scrap recovery as a function of primary price. Radetzki and Van Duyne (1985) explore changes in scrap's share of consumption when the longevity of products and the rate of growth of demand are allowed to vary. They model primary and secondary metals as imperfect substitutes and thus focus on changes in relative prices. 4.7.2. Demand for a secondary stock

The demand for most precious metals is primarily the demand for the stock of metal in circulation rather than for flows of production. Price is therefore set so that speculators are just willing to hold the existing stock. Purchasers, in making their consumption decisions, must perform intertemporal calculations. Suppose that St is the stock of metal in circulation at time t and that v(S) is the marginal value of the services from the stock. Price is then set as

where p is the discount rate. Because consumers are making intertemporal decisions, expectations play an important role in determining the demand for a stock. Consumers care about future price changes and about the size of the stock in the future (which is partly determined by future metal production). This means that the relevant price for demand studies is the expected value of eq. (73). Future expectations of v(S), however, are not easily specified. All of these considerations imply that the demand for precious metals is very difficult to model.

4.8. Imperfect competition The assumption that consumers (households and firms) are price takers in the markets in which they purchase goods is very common in demand analysis. The assumption that firms' output markets are competitive is also made, but with less regularity. Unfortunately, the markets in which mineral commodities are bought and sold are rarely perfectly competitive. These markets can be characterized by few sellers. For example, a single firm, AMAX, dominated the molybdenum market for many


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years. Markets can also be characterized by few buyers. For example, a large proportion of metallic sodium went into the production of lead-based antiknocks, and there were few firms in the antiknock industry. The industry may also be subject to regulation, which can distort factor choice. When competition is imperfect, competitive-market models are inadequate. Market power in the output market is irrelevant for the cost-function approach to derived demand. With this approach, output is exogenous and the demand equations that are estimated are compensated (output-constant). It is often desirable, however, to obtain demand projections for the case where output is endogenous. If the industry is a monopoly, endogenous-output choice can be obtained from a well-defined profit-maximization calculation. Unfortunately, perfect monopoly is as rare as perfect competition. When market structure is intermediate, it is usually necessary to resort to a game-theoretic solution to output determination. For example, it can be assumed that each firm is a Nash player in output or in price. A statistical procedure for testing for noncompetitive behavior in output markets is outlined by Applebaum (1979). He applies his approach to the US crudepetroleum and natural-gas industries and finds that the degree of monopoly power is significant. Applebaum uses aggregate data and can therefore not identify the demand facing each oligopolist. Slade (l986,1987b), in contrast, uses retail-gasoline data at the service-station level to estimate demand equations facing imperfectly competitive firms. When imperfect competition occurs in input markets, the situation is more complex. If some xi is not competitively supplied, pTx, the objective function for the firm's cost-minimization problem is nonlinear. When this occurs, the duality between production and cost functions breaks down 37. Diewert (1982) suggests a procedure for dealing with the monopsony problem. For any fixed expenditure, letx' be the vector of inputs that maximizes output,f (x). The objective function (the firm's 'budget constraint') can then be linearized by taking a first-order Taylor-series expansion about x = x'. In this way, the cost function can be traced out. It is possible to modify Applebaum's (1979) procedure so that price-taking behavior in factor markets can be tested. Another important question concerns regulated firms. Beginning with the seminal paper of Averch and Johnson (1962), there has been a large literature on factor-choice bias induced by regulation. While the empirical evidence of this bias is less than complete, a number of papers have analyzed how the standard model of the firm must be adapted for estimating the structure of production for regulated firms [see Fare and Logan (1983) and Atkinson and Halvorsen (1984)l. More recently, Wolak (1990) has examined how asymmetric information between the

" The separating-hyperplane theorem cannot be used.

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regulator and regulated must be taken into account when estimating the technology set. There is a strong tendency to overemphasize competitive models and their empirical applications in all areas of economics, not just mineral-demand studies. These models, however, are often adopted for convenience and do not always provide a satisfactory approximation to reality. The modeling of imperfect competition in demand studies, both theoretical and empirical, is therefore an area that deserves future attention.

4.9. Time-of day, seasonal, and block pricing

The energy crisis of the 1970s gave the issues of forecasting and controlling time-ofday and seasonal electricity use a new importance. The power that is generated to meet peak demand comes mainly from burning oil and gas in combustion turbines. This technology has a high energy-capital ratio. In addition, it relies on fuels that were in temporary short supply (gas) or that are imported into the USA (oil). In contrast, base-load power is frequently generated by more capital-intensive nuclear and coal steam-electric technologies. For these technologies, average costs increase substantially if they are used for cycling or peaking. The twin goals of energy conservation and energy self-sufficiency therefore put a premium on controlling time-of-day and seasonal fluctuations in demand. Three issues in formulating and estimating models of electricity demand are discussed in turn - demand by time of day, load forecasting, and block-rate structures. 4.9.1. Demand by time of day

Like the demand for natural gas and gasoline, residential demand for electricity can be separated into two stages; in the short run, the rate of utilization of a fixed stock of electricity-using appliances determines consumption, whereas in the long run, the characteristics of the stock of appliances (energy efficiency, type of fuel used, etc.) can be changed. Many electricity-demand studies model these two stages. A common way to do this is to estimate short-run demand by time of day for individual households from time-series data. This stage determines the time-ofday-load pattern. Next, the way in which household characteristics and differences in appliance ownership affect time-of-day demands is investigated. The second estimation uses cross-section data on household-demographic characteristics, appliance stocks, and dwelling size to explain differences in the first-stage parameter estimates.


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Formally, let xj be the jth household's demand for electricity and let y be a vector of short-run causal variables that capture the general shape of and shortrun variations in the time-of-day-load pattern. Then

is the first-stage estimation. Let zj be a set of long-run causal variables that vary among households but are assumed constant for the duration of the experiment. Differences in individual-household time-series regression coefficients are then explained by

Variants of this approach are used by Granger, Engle, Ramanathan and Andersen (1979), Hendricks, Koenker and Poirier (1979), and Ramanathan and Mitchem (1982). Another approach is taken by Atkinson (1979) and Lawrence and Braithwait (1979), who use the neoclassical paradigm of utility maximization subject to a budget constraint to estimate a complete system of demand equations for a homothetically separable subset of commodities. The commodities in this case are electricity consumption during the various periods of the day that correspond to different rate structures. The separability of electricity expenditures allows for a two-stage budgeting process. Optimal expenditure on electricity is determined in one stage and its distribution by time of day in the other. Lawrence and Braithwait use the linear expenditure system (LES) [Stone (1954)], where the committed quantities of the LES are parametrized as linear functions of household characteristics and appliance stocks. And Atkinson approximates preferences with a translog indirect-utility function. Caves and Christensen (1980) point out that elasticities obtained in the above fashion are calculated with total expenditure on electricity held constant, and are thus gross elasticities. They endogenize total electricity expenditures and find peak and off-peak consumption to be gross substitutes but net complements. Caves and Christensen thus emphasize the need to evaluate time-of-day pricing experiments in a more comprehensive framework. Special statistical problems in using data from time-of-day pricing experiments are discussed by Aigner and Hausman (1980) and Hill, Ott, Taylor and Walker (1983). To encourage participation in time-of-day pricing schemes, households were guaranteed that they would never pay more for electricity than under the prevailing rate structure. Aigner and Hausman consider the bias in estimated coefficients due to the truncated nature of the sample (where the truncation point varies by household and over time). And Hill, Ott, Taylor and Walker consider the effect that incentive payments given to participants have on coefficient estimates.

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4.9.2. Load forecasting and seasonal demand

Load forecasting is an important part of system planning for any electric utility. Annual peak load determines plans for capacity expansions whereas monthly, weekly, or daily forecasts determine the mix between base and peak-load generating capacity. Various methods have been used to project peak loads. Spann and Beauvais (1979) take a structural econometric approach to load forecasting. They explain monthly peak demand as a function of such variables as electricity price, prices of competing fuels, measures of economic activity, and temperature. In contrast, Parzen and Pagano (1979) take a pure time-series approach. They construct a filter that identifies periodicity in the data and improves forecasts from fitted time-series models. Their model however has no causal structure linking consumption to prices or other economic variables. Uri (1979) creates a hybrid time-series/econometric model in order to assess the comparative advantages of the two techniques. He relates the estimated parameters from his time-series model to structural variables. His findings point towards the usefulness of the hybrid model compared to either pure approach and compared to the hybrid alternative of first estimating an econometric (structural) model and then fitting its residuals with a time-series model. When considering the adoption of either seasonal or time-of-day rate structures, it is important to assess the welfare gains or losses due to the adoption. Lillard and Acton (1981) estimate a random-coefficients model of seasonal demand, which they use to evaluate the welfare gains of seasonal pricing. Whether they choose an (uncompensated) measure consisting of the sum of producer and consumer surplus or an exact measure based on compensating variations, they find the welfare gains to be quite small. This contrasts with the findings of Acton and Mitchell (1980) who use similar techniques and estimate much larger welfare gains from the adoption of time-of-day pricing. 4.9.3. Block rates

Pricing practiced by regulated monopolists in the USA generally discriminates among consumers through the vehicle of nonlinear prices. Traditionally, this took the form of rates that declined in blocks. More recently, however, some utilities have introduced increasing-block rates. Our discussion focuses on the decliningblock system. The modifications for increasing rates, however, are straight forward. Under a declining-block system, the price schedule is downward sloping with each additional unit purchased costing less than the previous unit, although in practice prices do not decline continuously but in steps. Thus the first xl units purchased may cost pl each, the next x2 units cost p2 each, and so forth, with p, >p2 >p3, etc. The difficulty arises in determining the price to


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which consumers are reacting. Suppose consumers are consuming y3 < x3 units in the third 'block'. Their marginal cost is p3 yet their average cost is ( p l x l + ~ 2 x 2+ p3y3)l(x1+ x2 + y3) > p 3 Unfortunately, price data are generally constructed as revenue divided by sales - average price. Yet consumers are likely responding to marginal price". The declining-block structure of prices causes problems in formulating and estimating demand models. For example, when marginal prices decline by discrete amounts, the consumer's budget constraint is kinked and the set of feasible purchases is nonconvex. Because an indifference curve can have one point of tangency with the section of the budget constraint that corresponds to one set of relative prices and another tangency with another section of the budget constraint that has a different slope, demand curves may not be single-valued. In addition, demand curves can be discontinuous, with jumps at the points where the consumer's equilibrium switches from one section of the budget constraint to another. A number of approaches have been taken to dealing with average-price data [Taylor (1975),Taylor et al. (1982)l. As Taylor et al. point out, there are two basic approaches. One is to construct marginal price data. The other is to use a twoequation system, supplementing a demand equation with an equation dealing with average price. A common approach to constructing marginal-price data for the US electricityutility industry is to utilize the US Department of Energy publication Typical Electric Bills, which indicates typical total costs for monthly consumption of 100, 250,500, 750 and 1000 k w h for each state. While this is clearly a step in the right direction, the data reflect one sample from what may be a variety of rate schedules within a state. Also, the levels of consumption reported may not be the same as the break-points on the actual rate schedules. Taylor et al. (1982) compare Typical Electric Bills data with actual data on rates and find fair agreement, although the match is poor for some states. Taylor et al. also develop several other procedures for obtaining marginal-price data. One is to build up a state aggregate-rate schedule from individual schedules and then approximate the aggregate schedule by either a linear function or a double-logarithmic function. This approach appears to be successful, although data-intensive. Alternatively, a linear approximation to each rate schedule can be made before aggregating to the state level. A second approach involves specifying demand as a function of marginal price and then specifying a price equation so that the demand equation can be identified. Halvorsen (1978), for example, uses a price equation that gives average costs of producing electricity as a function of quantity.

38

For a counter view on this, see Stern (1984).

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4.10. Uncertainty

Mineral markets are characterized by a high degree of uncertainty. There is uncertainty on the supply side of the market because mineral exploration is risky and the results of investment in exploratory activity are difficult to predict. In addition, strikes or producer-country embargoes can cause unforeseen supply disruptions. Price behavior is an additional source of uncertainty. The prices of mineral commodities are on the average more volatile than are the prices of other commodities. If consumers are risk averse, they will be concerned with variations in prices as well as with their average level and, all else being equal, will prefer commodities whose prices fluctuate less. Demand-side uncertainties occur because it is difficult to predict the long-run response to changed market conditions such as higher prices, and because forecasts of technical change are subject to large errors in both timing and extent. For example, the widespread use of fiber optics has had an important impact on copper consumption, and both timing and extent of the adoption of this technology were very uncertain ex ante. It is useful to look at uncertainty from the point of view of both consumer and producer. Each is concerned about future prices. In addition, the consumer tries to assess the future availability of the commodities that she purchases. Supply disruptions and price shocks are the principal sources of uncertainty for demanders of mineral commodities. Cutbacks may have many causes including mining strikes, political problems in producer countries, and deliberate reductions in offerings by producer cartels. The producer, in contrast, concerns himself with new uses for his product and with the possibility that substitutes will reduce future sales. He attempts to deal with uncertainty by forecasting long-run forces that might shift the demand for his product and by hedging against that uncertainty. Price uncertainty was covered in Section 4.4, where expectation formation was discussed. When price is a random variable that must be forecast, the techniques described in that section can be used to project future prices from currently available information. Typically, demand models are based on the assumption that a consumer can obtain commodities at a constant price or according to an upward-sloping-supply schedule. Supply disruptions however imply that commodities can be unavailable at any price. Consumers may therefore wish to form stockpiles as insurance against shortages of critical materials. There is a large literature on stockpiling, much of it dealing with commodityprice stabilization. Books have been devoted to the subject [see, for example, Adams and Klein (1978) and Ghosh et al. (1987)l. However, this literature principally addresses policies that can be undertaken by governments or by


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organizations of producers and consumers. Less has been written about optimal demands when a firm faces uncertain future supplies. The modeling of derived demand when supply disruptions are likely is therefore an area where research might fruitfully be directed 39. Faced with uncertainty, whether about future supplies or of some other nature, the firm purchases commodities for insurance purposes as well as for consumption. The notion of purchase for insurance (hedging) brings us to the last major section of the chapter.

5. Demand by hedgers and speculators 5.1. Background

The earlier sections of this chapter deal with demand by firms and households who consume energy and nonfuel-mineral commodities. Not all buyers, however, are consumers. When a forward or a futures markets is created, two new sets of purchasers are introduced - hedgers and speculators. A hedger is a buyer or a seller who establishes the opposite position on a futures market from that held and priced in the physical commodity. Without hedging, the physical position would be at risk to price fluctuations. Hedging is therefore undertaken by producers and consumers for insurance purposes. A speculator, in contrast, neither mines, refines, nor processes a mineral commodity. The speculator enters the market in order to realize a profit on price movements. Speculators either do not take delivery of physical commodities or hold inventories only for speculative purposes. This does not mean, however, that the speculator is a parasite. The speculator provides the market with the risk money that it needs to operate. Forward and futures markets for natural-resource commodities have existed for centuries. Nevertheless, their role has grown in importance in the last decade. This period has witnessed the introduction of new commodity markets, new contracts on existing markets, and new financial instruments such as commodity options. We devote the final section of our chapter to an analysis of the workings of forwards and futures markets for natural-resource commodities. This analysis includes a brief history of energy and nonfuel-mineral exchanges and a discussion of the effects of hedging and speculative demand on the behavior of markets. Before turning to the history of commodity markets, it should be mentioned that the ultimate buyers and sellers on these markets are producing or consuming There is however, a moderately large literature on factor choice for a firm facing uncertain prices for its inputs. In effect, the firm develops a portfolio of suppliers in order to hedge the risk [Wolak and Kolstad (1991)l.

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firms. Nevertheless, these firms often act through intermediaries, their brokers. In addition, merchants and traders enter the market for speculative reasons. Having devoted considerable attention to models of demand by consumers, we use this section to investigate the role of merchants and traders. Readers uninterested in institutional detail can skip directly to subsection 5.4 without loss of continuity.

5.2. The purchase and sale of energy commodities This subsection reviews current and historic trends in energy-product marketing, focusing on crude oil as a case study. Crude oil is the largest energy market in value terms, and is the one responsible for the recrudescence of interest in, and research on, natural-resource economics in the last two decades. According to the prevailing wisdom, energy markets have become freer and freer over time, and the addition to the market of derivative financial products (futures, forwards, and options) is a new development in the energy sector. An earlier era of market dominance has been forgotten.

5.2.1. Origins of the petroleum market Energy commodities were traded on informal open markets at least as far back as the beginning of the industrial revolution in late seventeenth-century England. Coal was the primary commercial fuel, and the London Coal Exchange was the center of the coal trade. The exchange was formally constituted in 1769 and survived until the nationalization of the British coal industry in the 1940s40. Organized exchanges for trading crude-oil spot and futures contracts sprang up in western Pennsylvania not long after the first commercial discoveries around 1860. The development of oil pipelines in the mid-1860s allowed standardized delivery terms. Informal forward transactions led rapidly to trading on centralized exchanges, with formalized membership and self-regulation similar to those of today. Unlike today's exchanges, however, government regulation was entirely absent. In the late nineteenth century, the United States was the world's primary crudeoil producer and possessed at least ten exchanges on which crude was traded. Evidence on foreign exchanges is more scattered, but there are references to one in Ontario, as well as several in Europe 41. The oil exchanges were not merely places where merchants congregated and made deals for the physical commodity, as was the case with the London Coal Details on the London Coal Exchange can be found in Reed (1972). Hausman (1980) develops a model of the coal trade during the industrial revolution. 41 The chief primary sources for the nineteenth-century oil market are Petroleum Age and Derrick's Handbook of Petroleum. 40


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Exchange, but rather financial markets in the modern sense. The trade press of the day refers to margins, clearing houses, options trading, brokerage fees, selfregulation by the exchanges, interexchange arbitrage (via telegraph), and attempts to standardize rules across exchanges. Then, as now, it was not the physical commodity itself that was traded, but instead 'pipeline certificates', which could be used to obtain the commodity if delivery was desired. The exchanges flourished from the early 1870s until refining was monopolized by the Standard Oil Trust in the mid-1890s. Spot and futures markets dried up and knowledge of these exchanges was lost to economists until quite recently 42. They were replaced, in part by vertical integration and in part by 'posted prices'. These prices represented what Standard was willing to pay producers in each field. The posted-price system survived essentially unchanged into the 1970s.

5.2.2. Era of vertical integration For the next three-quarters of a century, there was little in the way of open markets for crude oil. The industry consisted of large, vertically integrated companies, many of them the legacy of the breakup of the Standard Oil Trust by the US government on antitrust grounds in 1911. Posted prices were used for purchasing crude oil in the field from independent producers. Virtually the entire international petroleum trade was conducted through the channels of the 'majors' or 'seven sisters' vertically integrated firms that functioned as a tightly knit oligopsony in relations with crude-oil-exporting countries, and a tightly knit oligopoly in selling refined products 43. The majors' control over the international market eroded gradually during the 1950s and 1960s. In the late 1960s and early 1970s, many oil-exporting countries began to nationalize their oil concessions, which had been owned by the majors. The state-owned companies, however, had little expertise in petroleum trade, and sold their 'participation crude' (nationalization was partial) to the ex-concessionaires, who were obliged to 'buy back' the oil they had produced in order to maintain their equity positions. This change in ownership served to redistribute rents, but had little effect on market structure. For example, the US Federal Trade Commission's (1920) discussion of "commodities subject to future trading": "It is said there was at one time a futures market in petroleum in Oil City, PA." (p. 26). These futures markets were not forgotten by business historians, but neither were they a subject of much interest. Giddens (1938) is the only secondary source that provides more than a cursory mention of the oil exchanges. A description and economic analysis of crude-oil trading in the nineteenth century can be found in Weiner (1990b). 43 This period has been written about extensively, and nothing further will be said here [see especially Adelman (1972)l. 42

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5.2.3. From vertical integration to long-tern contracts and spot markets After the 1973-1974 oil embargo and supply disruption, the majors and other refiners sought to secure supplies through long-term (typically five-year) contracts with state-owned exporting companies. These contracts were for fixed prices and volumes (sometimes with small quantity tolerances), with the understanding that the contract price would be adjusted periodically. A very thin crude-oil-spot market developed, accounting for perhaps one or two percent of total trade. The oil-supply shock associated with the Iranian Revolution of 1978-1979 advanced the disintegration of vertically integrated petroleum trade. In 1973, the majors alone handled roughly three-quarters of the crude oil moving in international trade (excluding the Eastern-bloc and intra-OECD trade, where the institutions are quite different). By 1978, this figure had fallen to about half, and by 1979 to about 40 percent. Some reduction came from within the majors' distribution system, but the main structural change was the end of the role of integrated companies as resellers to third parties. Third-party sales were replaced by direct contracts between exporters and a variety of smaller purchasers and by spot-market sales. When contracts signed in the mid-1970s came up for renewal, buyers were reluctant to enter into further long-term agreements for several reasons. First, the value of supply security was questionable, given the frequency of contract abrogation as the price of a barrel of crude skyrocketed from about $12 to over $40 by 1980. Second, the non-price provisions of these contracts had become increasingly onerous. For example, many contracts included destination restrictions that limited the resale of contract purchases and often prohibited them altogether unless the exporter's permission was obtained. Expansion of spot trade paralleled the decline of term contracts.

5.2.4. Re-emergence of forward, futures, and options trading The expansion of the crude-oil spot market in the late 1970s and early 1980s led rapidly to informal forward trading, and then to formal exchanges, much as it had in the late 1860s and early 1870s. In March 1983, the New York Mercantile Exchange (NYMEX) and the Chicago Board of Trade (CBOT) introduced futures contracts in West Texas Intermediate (WTI), a type of crude for which forward trading had developed. The CBOT's contract failed soon afterward for lack of liquidity, but the NYMEX's contract has been tremendously successful, and WTI crude is now one of the world's largest futures markets in terms of trading volume. The other major market that developed out of spot trading in the early 1980s was for forward delivery of Brent Blend crude oil, which is produced in the


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North Sea44.In the absence of a centralized exchange or clearing house, all Brent forward trading is bilateral, with transactions consummated via telephone and telex. Entering into an agreement therefore requires the ability to take or make delivery should that be necessary. Despite these characteristics typical of informal forward markets, the Brent market is primarily one of financial transactions - a feature usually associated with futures trading. Contracts are standardized, as in a futures market, with all contract terms, save price, pre-established. In the absence of a clearing house, trading is not anonymous, so it is necessary to keep track of the parties that have made commitments for future purchase and delivery. These are referred to as 'daisy chains'. A chain of bilateral deals is, by its very nature, vulnerable to default. If any of an average of ten links per chain breaks, then the companies farther down the chain will likely be obliged to default on their delivery obligations as well. The Brent market experienced widespread default when crude-oil spot prices plunged from roughly $30 to $10 per barrel in a short period of time in early 1986. Buyers who had entered into forward contracts at high prices refused to take delivery in the face of losses of $10 million per cargo. The market recovered from the default episode and has survived with its daisy-chain microstructure unaltered, and still flourishes, despite the successful introduction of a standard futures contract in Brent by the International Petroleum Exchange (IPE) in London in July 198845. The increased volatility of oil prices since the mid-1980s has resulted in a search for additional ways to cope with risk. Following on the success of its petroleumfutures contracts as instruments for hedging and speculation, the NYMEX introduced options trading. Options on crude-oil-futures contracts started trading in November 1986, and have been extremely s u c c e ~ s f u lMoreover, ~~. the demand for hedging longer-term risk has recently led to expansion of crude-oil futures contract trading on the NYMEX to 36 months ahead, maturities that are longer than those typical for commodities traded on futures exchanges. 5.2.5. Natural gas and coal Natural gas and coal, the two major fuels after oil, are characterized by transactionspecific investment, which tends to lock in buyers and sellers. In the case of natural gas, this investment takes the form of the well and gathering lines that transport The market developed in part in response to tax incentives in the United Kingdom. Detailed descriptions of its origins and institutions can be found in Bacon (1986), Mabro et al. (1986), and Sas (1987a,b). 45 Description and economic analysis of the default and its effects in this market can be found in Dominguez et a1 (1989) and Weiner (1990a). 46 Options on futures differ from options on physicals in that exercising the option implies taking delivery of a futures contract, rather than the underlying commodity itself. Brent fonvard contracts actually contain an embedded option [see Phillips and Weiner (1990a)l.

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the gas through the field to the pipeline. Transactions with alternative buyers or sellers are often costly, even prohibitive. In contrast, oil tankers and refineries are less tied to specific trading partners, and buyers and sellers are not locked in. In the presence of specific capital, spot markets tend to work poorly and are often replaced by long-term contracts and vertical integration. Natural gas, however, was heavily regulated in the USA from 1938 until the late 1980s, with effective price ceilings in place since 1960. The regulations contained disincentives for vertical integration 47; thus natural gas was sold primarily through long-term contracts that locked in the producer and purchasing pipeline 48. Like crude oil, natural-gas futures followed development of a spot market, starting with partial deregulation in the mid-1980s. Futures trading of natural gas on the NYMEX began in April 1990. Coal is a much less homogeneous fuel than oil or natural gas. It will be necessary to overcome delivery problems associated with great heterogeneity in quality along several dimensions if a coal-futures market is ever to be developed. There have long been spot markets for various types of coal, which is sold primarily through longterm contracts. The largest coal-consuming sector is electric-power generation, and backward integration by electric utilities is common. The specific capital in this case is the generation plants, which are configured to burn given types of

5.3. The purchase and sale of metals In sharp contrast to energy markets, well-developed commodity exchanges have played a continuous and active role in metal markets for nearly one hundred and fifty years. Nevertheless, the influence of metal exchanges has increased sharply in the last decade. This section deals with buying and selling nonferrous metals (aluminum, copper, lead, silver, tin and zinc, for example). Iron and steel, which constitute the largest market in value terms, are not sold on commodity exchanges. Iron ore is a largevolume, relatively low-value commodity. A combination of low value per ton and product heterogeneity mean that an iron-ore contract is unlikely to be introduced on an exchange in the near future. This market thus resembles the market for coal. Steel specifications also vary substantially by use. It is perhaps for this reason that steel is sold at prices set by the major firms in the industry. Nonferrous metals, in contrast, have traditionally been sold under two pricing systems: prices set by the major firms in the industry and prices set in commodity -

See Hubbard and Weiner (1991) for details. Analyses of natural-gas contracting can be found in Masten and Crocker (1985) and Hubbard and Weiner (1986) for the regulated era, Mulherin (1986) and Hubbard and Weiner (1991) for the unregulated era. 49 Analysis of vertical relationships in the coal industry can be found in Joskow (1985, 1987). 47

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exchanges. All buyers of metals sold under a producer-pricing system are users. Metals sold on exchanges, in contrast, are also purchased by hedgers and speculators. For this reason, we concentrate here on the workings of exchanges.

5.3.1. The emergence of metal exchanges50 Many commodity exchanges exist throughout the world. However, by far the most important for metal pricing, both currently and in the past, is the London Metal Exchange (LME). Commodity markets in London began developing into their present form in the middle of the nineteenth century. Four nineteenthcentury developments were fundamental in the evolution of a modern market: the introduction of a standard contract, the change from forward dealing for delivery to hedging, the growth of speculation, and technological developments that enabled rapid transmission of information. By the 1870s London had a vigorous and well established market, and in 1876 the London Metal Exchange company was formed. It was at this time that the custom of dealing in a 'Ring' developed. It became the custom for some member to draw a large chalk circle on the floor and to call "ring, ring". Members then stood in their recognized places and cried their bids and offers across the floor. Superficially, little has changed since the formation of the LME. The chalk line on the floor has been replaced by a set of curved benches that are divided into seats allocated to the thirty-six firms authorized to deal. Members of the Exchange, however, continue to transact business by means of open outcry across the floor. In addition, Ring dealing in each commodity is still limited to two five-minute intervals in the morning and two in the afternoon5[.

5.3.2. Parallel developments in North America Pricing in North America developed along very different lines, where a producerpricing system dominated. Producer prices, which were set by the major firms in the primary industry, represented a common set of price quotations for delivery. They were based to a large extent on production cost and were moderately stable. In the late 1970s and early 1980s, radical changes occurred in North-American metal markets. This period saw the virtual demise of the producer price of copper when the major firms adopted an exchange-based pricing system. In addition, aluminum and nickel contracts were introduced on the LME. The weakening of the producer-pricing system was due to a combination of factors including a Much of the information in this section comes from Prain (1975), Rudolf Wolff & Co. (1987), and Slade (1988). Trade also takes place outside the Ring and is then known as 'kerb' trading.

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decline in horizontal concentration and vertical integration and an increase in both international integration and government participation. 5.3.3. Today's exchanges The LME underwent fundamental structural changes in 1987, innovations that stemmed from the Financial Services Act of 1986. The most fundamental change mandated by the Act was a switch from a principals' market (a market where members act as principals for the transactions that they conclude across the Ring and with their clients) to a clearing-house system. A clearing house is an independent body that clears and guarantees business transacted between member brokers and insures contractual performance in the market regardless of any member's failure. A consequence of the new clearing-house system was the introduction of margins. The LME system of margins is unusual, however, in that it applies only to the net position of brokers. The appearance of traded options on the official market also coincided with the advent of the clearing house. An option gives the buyer the right, but not the obligation, to buy or sell (or both) an agreed quantity of metal for delivery at a fixed price in the future. Options offer greater flexibility in hedging operations. The LME is not without competitors. Principal among these is the Commodity Exchange of New York (Comex), which opened in 1933. Current Comex contracts include copper, silver, gold, and aluminum (although the aluminum contract has not achieved any practical success). 5.3.4. Recent crises

Two crises have challenged the very existence of the LME and other metal exchanges. The first was the silver-price manipulation that occurred in the 19791980 period, and the second was the financial crisis in the tin market that caused the suspension of the LME tin contract 5 2 . The silver manipulation is associated principally with the name of Nelson Bunker Hunt. This attempt to corner the silver market eventually failed. Nevertheless, in the space of a year, silver prices rose from under $6 to over $40 per troy ounce, only to come tumbling back down again. During the crisis, all formal silver markets were under considerable stress. Comex, however, was the most threatened. Its continuous-settlement system facilitates pyramiding and allows more scope for speculative purchases 53. AS the For more details on the tin crisis, see Anderson and Gilbert (1988). Unlike Cornex, the LME has a system of settlement on due date. This means that funds cannot be withdrawn during the life of a trade.

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price advanced, initial purchases engendered cash-margin credits, which were used to buy still more silver. When the crash came, therefore, speculators on Comex lost heavily. Even in normal periods, the volume of silver trading on Comex can be more than fifty times annual mine production. It is thus clear that only a small fraction of silver trading is for insurance purposes and even less is for ultimate delivery. The tin crisis of 1985-1986 had a much more profound impact on the LME (Comex does not deal in tin). The affair involved traders around the world, but the Exchange bore the brunt of what was at one point a f900m default. Prior to the crisis, the tin market was dominated by one large client, the International Tin Council (ITC) -which included both producers and consumers. The ITC was charged with the task of stabilizing tin prices through purchases for and sales from a stockpile. Funds for this project came partially from member contributions, but the bulk of the assets were financed through large borrowings. On October 24, 1985, the ITC ran out of money. Within minutes of receiving the news, LME transactions in tin were suspended. Trading companies worried that if the crisis brought bankruptcies to ring-dealing members with tin-council contracts, the entire exchange would collapse. Due to the complex financial transactions among brokers, a single bankruptcy could threaten all members of the Exchange. The principals' market with no formal insurance, was therefore under considerable stress. It was not until the summer of 1989 that LME tin trading resumed. These crises serve to illustrate both the strengths and weaknesses of an exchangepricing system. Fortunately, even though these markets were severely tested, with the exception of the suspension of tin trading, they continued to operate under very stressful circumstances.

5.4. Hedging and speculative demand Having concluded an analysis of trading institutions, we now turn to formal models of speculative demand, empirical tests of these models, and the implications of speculative demand,for both market efficiency and price stability. 5.4.1. Formal models 54 Suppose that a firm in a competitive industry must make plans for output q to be produced in the next period. The future spot price, pS, is a random variable whose realization is as yet unknown. The firm can supply (demand) F futures contracts at a parametric price pf. When F is positive (negative), the firm is short 54

The model laid out in this section follows Danthine (1978).

M.E. Slade et al.

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(long) on the futures market. Finally, the firm uses a vector of inputs x sold at parametric prices v to produce the commodity q. This relationship is summarized by the production function, q = f (x). The firm's problem is to

where V is the risk-averse manager's Von Neuman-Morgenstern utility function, and the expectation in eq. (76) is taken with respect to the conditional distribution of the spot price, given the futures price. First-order conditions for this maximization can be solved for the optimal supply of futures contracts 5 5 ,

Equation (77) is the basic hedging relationship. The status of pf in eq. (77) is ambiguous because it both affects the firm's profit and (potentially) modifies the distribution of the spot price. In addition to producers, the market contains speculators. The speculator decides how many futures contracts, @, to buy on the basis of the expected difference between the spot and futures prices, pS-pf. Each speculator, who has private information y concerning the realization of a random variable that affects the spot price, maximizes expected capital gains. The speculator's problem is thus to

where U is the speculator's utility function, and the expectation in eq. (78) is taken with respect to the conditional distribution of pS, given the futures price and the speculator's private information. First-order conditions for the maximization (78) can be solved to yield the speculator's demand for futures contracts, @* = b(pf, y).

(79)

Equilibrium in the futures market occurs when the market clears. In other words, when

55

If the production function is concave, necessary conditions are also sufficient.


where the first sum is taken over firms and the second over speculators.

Speculators buy (sell) until no further capital gains are possible. It follows from eq. (78) that market equilibrium, with a large number of speculators and in the absence of transactions costs and basis risk 56,occurs when

wherepf,,, is the futures price at date t for delivery at date t+k, the subscript on the expectation operator E denotes the period in which expectations are formed, p;+, is the spot price at date t+k, and R, is the information available at date t. Equation (81) is known as the efficient-market hypothesis (EMH). Tests of the EMH differ according to the contents of fl,. For example, Fama (1976) considers (i) weak-form tests, in which 0, is restricted to historical spot and forward prices, (ii) semi-strong tests, in which R, consists of all publicly available information, and (iii) strong-form tests, in which 0, also includes inside information. For practical reasons, most empirical tests of the EMH have been confined to forms (i) and (ii). One particularly simple (and therefore popular) form of the EMH is

where E is a white-noise error term known as an innovation or a forecast error associated with news arriving tomorrow (the subscript for contract maturity is suppressed here for simplicity of presentation). Prices (or any other time series) that behave in this way are known as martingales5'. A defining property of a martingale is that the optimal forecast of any future value of the variable is today's value. In principle, empirical tests of eq. (82) entail running the regression

and testing whether a = 0 and b = 1. In practice, this regression suffers from several problems. First, in small samples, when b equals unity (when markets are efficient) the OLS estimator of b is biased and will typically be well below unity; this is known as the Basis risk usually occurs when a commodity is needed in one location but delivery occurs in another. The efficient-market hypothesis can also fail to hold when speculators are few or when some agents have market power. If in addition the variance of the forecast error is constant over time, prices are said to follow a random walk. For further discussion and examples of tests of informational efficiency, see Hodrick and Srivastava (1987).

56

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"unit-root" problem. One remedy is to use the "t-statistic" whose distribution was tabulated by Dickey and Fuller (1979) by Monte Carlo methods. Second, the ordinary-least-squares-regression assumption that the errors u, have constant variance is unlikely to be satisfied here. For example, futures and forward prices are for contracts with varying lengths to maturity. As the 'roll date' (the date on which the near contract stops trading, the second-month contract becomes the near contract, etc.) approaches, the contract length grows shorter. In addition, commodity markets have been characterized by periods of great price volatility and periods of relative tranquility over the period since futures contracts started trading. The variance of the forecast error is almost certainly greater for the former. A possible remedy for this problem is to fit an ARCH model [Engle (1982)l to the error term. The ARCH model corrects for conditional heteroscedasticity that takes an autoregressive form. The efficiency of metal markets has been examined by Goss (1981, 1983), Gilbert (1986, 1987), and Jones and Uri (1990) among others. The results of these tests are in general negative, at least for some metals. Moreover, markets that are less speculative (lead and zinc, for example) appear to be less efficient. Nevertheless, even gold and silver, the most speculative commodities, exhibit evidence of informational inefficiency [Chan and Mountain (1988)]. Occasional extended periods of price increases followed by rapid collapses, as illustrated by the silver-market 'bubble', are a symptom of this inefficiency. It is also interesting that both Goss (1983) and Gilbert (1986) find strongest evidence of inefficiency in the tin market, the market where manipulation was most obvious. Because the current era of open markets for crude oil is relatively new, and data from the past era are not easily available, results from tests of this type for oil markets should be regarded as preliminary. Dominguez et al. (1989) examine the NYMEX futures contracts and Brent forward contracts in crude oil and find them to be relatively efficient, a somewhat surprising result considering that analogous tests on other commodities, notably foreign exchange, have found evidence of inefficiency [see Hodrick and Srivastava (1987)l. In contrast, tests performed on the Rotterdam spot market for petroleum products have rejected the efficiency hypothesis. Using a nonparametric runs test, Gjolberg (1985) found that an increase in the spot price of gasoil on a given day was more likely to be followed by another increase than by a decrease the following day, which indicates that the current price does not reflect all available information. This inefficiency finding is supported by Bird (1987), who used parametric-filter tests to demonstrate that small price changes tend to be followed by further movements in the same direction, whereas large price changes tend to be followed by movements in the opposite direction. Bird attributes this finding to insufficient speculation, resulting in unexploited arbitrage opportunities. A finding that spot markets are in general less efficient than futures markets would not be very surprising because speculation on spot markets is much more


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costly (i.e., it involves the ability to take delivery of and to store the physical commodity). A striking finding is that the Brent market did not become less efficient during the period of default in early 1986, even though the market almost collapsed when trading volume roughly halved. Moreover, the WTI futures contract, which did not experience analogous problems, functioned smoothly through this price plunge. The difference between the 1990 crisis, when the price of a barrel of crude oil climbed by more than 100% in a few months, and the previous run-up of 19781980 is that then, the spot market was small and forward and futures markets nonexistent. Today, all of these markets are large and, according to the efficiency tests, reasonably liquid. These markets functioned smoothly in the Persian-Gulf crisis, although price volatility was enormous with changes of several dollars per barrel in a day not uncommon.

5.4.3. Volatility Naive economic models predict that speculative demand should stabilize commodity prices. For example, if speculators buy when the price is low and sell when it is high, speculative activity will tend to have a stabilizing effect. Nevertheless, many resource-market participants believe that opening futures markets tends to be destabilizing. Moreover, in the last decade, economists have developed models that demonstrate that speculation need not be unprofitable to raise market v ~ l a t i l i t y ~ ~ . For example, if speculators buy when the chance of price appreciation is high and sell when it is low, it is entirely possible for speculation to destabilize prices. The question of whether speculation raises volatility is thus an empirical one, but one that is not easily tested. For example, crude-oil-price volatility was much greater in the second half of the 1980s than in the first, and futures-trading volume increased dramatically over the decade. It would be inappropriate, however, to conclude that trading volume caused price volatility, or vice-versa. Rather, both are consequences of underlying shocks and news about future supply and demand changes that will likely affect prices (e.g., reserve discoveries and additions, weather forecasts, rumors of war or peace). Roughly speaking, the larger and more numerous are such shocks, the greater will be both trading volume and price volatility 59. It is possible, however, to investigate these relationships indirectly. For example, Slade (1991b), who uses producer and London-Metal-Exchange price data, finds that the temporal increase in price volatility that shows up in unconditional variances of prices disappears when economic factors are accounted for. In sharp See Hart (1977), Kawai (1983), Hart and Kreps (1986), and Newbery (1987). Tauchen and Pitts (1983) present a model that formalizes these ideas. A survey of the price variability/volume relationship can be found in Karpoff (1987).

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contrast, she finds that prices determined in commodity exchanges are considerably more volatile than prices set by producers, even after conditioning on supply, demand, and market-structure factors. Although this is not a direct test of the relationship between speculation and price volatility, the evidence is consistent with destabilizing speculation. Many market participants also believe that a decline in long-term contracting is destabilizing60. Economists' intuition, in contrast, often tends toward the opposite direction; markets wherein most trade is tied up in long-term contracts can be more volatile than thick spot markets because only a fraction of trade is free to respond to supply and demand shocks. Empirical tests by Hubbard and Weiner (1989) support this intuition. Finally, although it is difficult to establish whether markets 'overreact' to news, Dominguez et al. (1989) show that the variance of daily futures-price changes is significantly greater on days with significant news about the oil market than on nonews days 6 1 . Thus higher price variance tends to be associated with news, indicating that speculation is at most one source of volatility. To summarize, industry participants usually associate the decline of vertical and horizontal integration and the rise of open-market trading with increased price volatility. And economists, long champions of open trade, have started to develop models that raise questions about the effects of speculation and additional markets on price stability and economic well-being6'. The necessary empirical evidence on volatility, however, is not yet in. In contrast, even if not fully informationally efficient, evidence on mineral forward and futures markets suggests that they work well. With the exception of the tin crisis, these markets have operated smoothly under considerable stress.

6. Concluding remarks

Sections 2-4 of this chapter summarize much of the work that has been done in the area of energy and nonfuel-mineral-demand modeling. The record is impressive. The vast majority of the papers cited were published in the last two decades. The explosion in interest in energy and nonfuel minerals that took place in the 1970s resulted in considerable advancement in the state of the art of demand modeling. Many of the papers cited in Section 5 are even more recent. This is perhaps due to the fact that interest in purchases by nonusers such as speculators has grown in One trade-journal article [Roeber (1985)l described term contracts as "redolent of stability, continuity, and reliability" and spot trade as "greedy, frantic, and somewhat sweaty". Moreover, producers view the vertical-regime change as a threat to their market power. 'Significant news' in this case is defined as an article appearing in the Wall Street Journal. 62 For an analysis of the welfare implications of opening new markets, see Hart (1975). 60


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the last decade. In spite of this rapid progress, however, there remain areas where coverage is incomplete and tools are inadequate. In this section we try to identify aspects of theoretical and applied modeling that have received little attention. In many cases, these are not areas where mineraldemand modelers have failed to apply the relevant economic theory but are areas where economic theory is weak or only beginning to move to a position of strength. When there is a lack of adequate theory upon which to base models, theoretical and applied researchers must work together if better models are to be built. Several broad areas of this sort are identified and discussed in turn. 6.1. The treatment of uncertainty

Uncertainty affects every aspect of mineral markets. For example, future-price paths must be forecast, technological developments in using industries must be projected, and insecurity of supplies must be dealt with. Tools for handling these problems exist, but in many cases considerable refinement is required before accurate projections can be made. Expectation formation is an important aspect of dealing with uncertainty. The literature on rational expectations offers insights into the modeling of consistent multiperiod forecasts that are endogenous to the system being model. Mineraldemand modelers, however, have not exploited this source to its fullest. Technological forecasting is still in its infancy. Economists and econometricians can track the progress of changes in technology fairly accurately but offer few theories to explain its evolution. As a consequence, technological developments that differ from historic trends are difficult to project but can be of considerable importance to future consumption. Consumers are aware that mineral supplies may be uncertain in the future. This uncertainty stems from many causes including strikes, embargoes, and political disruptions in producing regions. The techniques of inventory theory offer some help in dealing with this sort of uncertainty but have not yet been fully utilized by demand modelers. 6.2. From individual to aggregate relationships Virtually all demand studies rely on aggregate data. For example, even studies of individual households must aggregate the commodities that households consume. The problems involved in constructing aggregates should therefore not be ignored. When aggregating goods (inputs and outputs) it is possible to test the restrictions required for consistent aggregation. In practice, these tests usually fail. In addition, when aggregating consumers (households and firms) restrictions for consistent

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aggregation are extremely limiting. For example, consumers (firms) may be required to have identical homothetic preferences (technologies) characterized by considerable linearity. It is often felt that these restrictions are inconsistent with empirical regularities in consumer behavior. Because demand modelers must aggregate and may feel that the restrictions for consistent aggregation are very limiting, it is essential to know what sorts of errors are committed when the restrictions are ignored. It is possible that certain violations lead to larger errors in parameter estimates than others, but little work has been done to assess the magnitudes of these effects. 6.3. Temporaiy equilibrium and rationing

Disequilibrium and rationing are caused by many factors, including reduced offerings by producers and temporarily fixed inputs due to adjustment costs or regulation. When producers adopt a policy of maintaining price below marketclearing levels and limiting consumer purchases, estimation techniques developed to deal with limited or truncated variables are appropriate. And when modeling temporary equilibrium and the dynamics of the adjustment process for quasi-fixed factors, adjustment-cost and partial-static-equilibrium models can be used. Because regulation is pervasive and the regulatory environment c h n g e s rapidly, forecasting both the extent and the effects of regulation can be essential to demand modeling. When rationing is due to legal restrictions on input use or output production (environmental regulations, for example), the methods of mathematical programming (constrained optimization) or partial-static-equilibrium (exogenous constraints on factors) seem most useful. Through the use of such techniques, it is possible to obtain appropriate shadow prices for the constrained inputs and outputs, which are prerequisites for reliable demand studies. These techniques have been exploited by mineral-demand modelers. Nevertheless, this area remains one where significant improvement is needed. 6.4. Demanders with price power Traditionally, both theoretical and applied economists spent a disproportionate amount of time modeling the two extremes of perfect competition and monopoly. Most real-world markets however lie somewhere in between. Often. both buyers and sellers have some degree of price power but their power is far fi-om complete. Theories of strategic behavior and game-playing have revolutionized many fields, including industrial organization and international trade. These theories have however not been sufficiently exploited in applied work in any field, including demand modeling.


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Oligopolistic sellers and oligopsonistic buyers cause a breakdown in the duality between production, profit, and cost that so much applied-demand modeling is based on. They therefore present special problems for demand modelers. It is essential to have methods of testing for price-taking behavior in input and output markets. And, when the absence of price-taking behavior is detected, it is equally essential to have methods of constructing theoretically consistent systems of demand equations that do not rely on competitive-market assumptions. Such methods have been developed and applied in the industrial-organization literature but have seen little use in the field of mineral modeling.

6.5. Speculative dynamics A final area for future research is the dynamics of speculative demand. The method under which a commodity is sold can affect the level and the variance of its price as well as the security of the contractual arrangement. Clearly, these factors have ramifications for 'legitimate' consumption. Furthermore, a complicating aspect of this cycle that has received little attention is the possibility of market power and strategic behavior on the part of both producers and traders6'. One has only to look at the history of market manipulations to see that this issue might be important. Nevertheless, there has been even less work on modeling the demands of powerful actors in futures ,markets than in spot markets.

6.6. Model validation

Demand models are based on a multiplicity of assumptions and techniques. Just as methods vary, demand projections from the models vary as well. It is desirable to be able to isolate the factors that are the most important determinants of differences in forecasts. To do this, it is necessary to standardize as many factors as possible so that comparative experiments can be performed. For example, when comparisons are made between models that are different in every aspect, it is impossible to isolate the major causes of differences in model predictions. In contrast, when models differ in only one aspect, differences in forecasts must be attributed to that factor. The Energy Modeling Forum (1980,1981) investigated systematic differences in forecasts due to differences in techniques and assumptions. Because this information is essential to designing better models, it is hoped that this sort of exercise will become more common in the future. For a survey of the relationship between futures-market behavior and imperfectly competitive product markets, see Anderson (1990).

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This chapter devotes many pages to the subjects of model construction and use, but the areas of maintaining, updating, and testing models have been ignored. Commercial forecasting agencies often spend much more time maintaining models than constructing them. Because their models are proprietary, however, results from comparing forecast and realized values are rarely published. In contrast to commercial modelers, academics often spend little time updating models or testing their performance ex post. If we are to learn from our errors, however, it is important to assess where we went wrong. 6.7 Summing up

With the softening of energy and nonfuel-mineral markets in the 1980s, the world turned its attention to other crises, and interest in mineral-demand modeling waned. However, the problems associated with adjustment to lower prices while less publicized are just as real. Moreover, many of the factors that led to the energy crises of the 1970s resurfaced in the 1990s as a consequence of the Iraqi invasion of Kuwait. The need for understanding and forecasting market dynamics is thus just as great now as in the past. In spite of the progress that has been made in energy and nonfuel-mineral-demand modeling and forecasting in the last two decades, there is ample room for improvement. It is therefore hoped that modeling efforts will continue and that as a consequence the decade of the 1990swill prove as productive as the last two. References Acton, J.P., and B.M. Mitchell, 1980, "Evaluating Time-of-Day Electricity Rates for Residential Customers", in: B.M. Mitchell and P.R. Kleindorfer (eds.), Regulated Industries and Public Enterprise (Lexington Books, Lexington, ICY). Acton, J.P., B.M. Mitchell and R. Sohlberg, 1978, Estimating Residential Electricity Demand Under Declining Block Tariffs: An Econometric Study Using Micro-Data, Paper P-6203 (Rand Corporation, Santa Monica, CA). Adams, F.G., and S.A. Klein, 1978, Stabilizing World Commodity Markets (D.C.Heath, Lexington). Adelman, M.A., 1972, The World Petroleum Market (Johns Hopkins University Press, Baltimore, MD). Aigner, D.J., and J.A. Hausman, 1980, "Correcting for Truncation Bias in the Analysis of Experiments in Time of Day Pricing of Electricity", The Bell Journal of Economics 11, 131-142. Almon, S., 1965, "The Distributed Lag Between Capital Appropriations and Expenditures", Economefrica 33,178-196. Anderson, C.J., 1979, Energy Policy Model: A Brief Overview, UCRL-52672 (Lawrence Livermore Laboratory, Livermore, CA). Anderson, R.W., 1990, "Futures Trading for Imperfect Cash Markets7', in: L. Phlips (ed.), Commodity Futures and Financial Markets (Kluwer Academic Publishers, Dordrecht). Anderson, R.W., and C.L. Gilbert, 1988, "Commodity Agreements and Commodity Markets: Lessons From Tin", Economic Journal 93,37@389.


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Chapter 21

MINERAL RESOURCE STOCKS AND INFORMATION DeVERLE F! HARRIS Director of Mineral Economics, Depavtment of Mining and Geological Engineering, University of Arizona, Bldg. #12, Tucson, AZ 85721, USA

1. Introduction

The subject of this chapter is the description and estimation of a nonrenewable stock of naturally occurring substance that serves as a source of an element, e.g. copper or uranium, or chemical compound, e.g. oil, or mineraloid, e.g. coal. These stocks are referred to categorically as mineral resource stocks. When the stock of interest is specific, it is reported as quantity of the element, e.g. tons of copper, or compound, e.g. barrels of oil. Finiteness and potential exhaustibility, which are fundamental features of mineral stocks, constitute the basis for exhaustible resource theory [Gray (1914), Hotelling (1931), Dasgupta and Heal (1979), Herfindahl (1967), Smith and Krutilla (1979)l. These features also motivated important studies of resource scarcity and growth [Barnett and Morse (1963), Barnett (1979), McLaren and Skinner (1987)l. In contrast, this chapter deals with features of mineral stocks that often are treated simply by assumption in economic theory or by scenario in economic analysis, such as the magnitude of stock, quality of stock, quality variation, geological and physical determinants of exploration and exploitation cost, and estimation of these features. Estimates of mineral resource stocks received only casual attention until the OPEC oil embargo focused national attention in the USA on the need to have a better understanding of the nation's energy resources. What was once mainly a geological curiosity (the magnitude and quality of undiscovered resources) became of great interest to economists and to policy analysts. This interest in mineral stocks revealed the need for integration of concepts and information that are geologic with those that are economic. For, on the one hand, estimation of the existence of undiscovered deposits is largely a geological exercise, particularly in totally unexplored regions, but on the other hand to be useful in the examination of societal issues, these geological estimates must be converted to terms that are amenable to economic analysis. Early efforts to integrate geologic and economic information revealed three basic needs. The first one is a rigorous definition of Handbook of Naturnl Resource and Energy Economics, vol. III, edited by A. KKneese and J.L. Sweeney O 1993 Elsevier Science Publishers B. V All rights reserved

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traditional stock measures; the second is new (additional) mineral stock measures; and the third is auxiliary relations that facilitate the transformation of a physical stock, as described by a geologist, to one or more stocks that are of interest to economists. Recognitions of these needs led to the search for order in geological features and economic characteristics, such as production cost and exploration cost and efficiency. 2. Motivations for appraisal of mineral resources

2.1. Resource adequacy

The most apparent motivation for appraisal is the examination of future resource adequacy. It was for this loosely understood concept that the nation's mineral resources were appraised in 1952 by the Paley Commission, that the nation's oil and gas resources were appraised in 1975 by the US Geological Survey, and that the nation's uranium resources were appraised through the NURE (National Uranium Resource Evaluation) program in 1980 by the US Department of Energy (DOE). In reality, the concept of resource adequacy is complex and undefined without a clearly identified structure for resource information and correspondingly well specified future economic circumstances. Complexity stems from several sources, one of which is the role of trade, a determination of which requires the consideration of both economic and national security issues. Another complexity stems from the essentially dynamic process of resource exploitation over long periods of changing materials technology and use, The states of potential and dynamic supply are in part a function of such changes. A motivation for the NURE program, which is the most costly and comprehensive resource appraisal in history, was the "breeder question", which at the time of the initiation of NURE was perceived to be the following: Are our uranium resources large enough to meet the feed required by light water reactors if they were to meet projected future requirements for nuclear generated electricity? Or, are these resources so small that as a nation we should commit heavily to the development of the breeder reactor? While these questions do not seem pressing at this time, they were perceived as urgent during the 1970s, as indicated by the massive effort initiated to appraise the nation's uranium resources. 2.2. Anticipating scarcity

A less dramatic but important motivation for the estimation of mineral stocks is the identification of those mineral commodities whose production costs and prices could increase greatly over the next few decades, barring unforeseen substitution

Ch. 21: Mineral Resource Stocks and Information

1013

or technological advances. As pointed out by Tilton and Skinner (1987), sharp increases in costs are unlikely if production cost rises with output in a continuous manner and at a declining rate, while on the other hand, sharply higher prices could occur if production cost has a discontinuity or rises at an increasing rate over certain segments. The capability of identifying cases of increasing cost would be considerably enhanced if both sound methodology and appropriate data were brought to bear upon the estimation of potential mineral stocks.

2.3. Land management and economic development Probably, future demands for mineral resource information will derive more from efforts to support management of the nation's lands, mineral, and non-mineral resources than from the desire to examine resource adequacy. Management decisions at different levels require the consideration, along with other factors, of "mineral potential". At one level, Congress and the President make decisions on withdrawal of public domain as wilderness areas. At another level, federal agencies, e.g. the US Bureau of Land Management, strive to manage the many parcels of public land and their mineral and nonmineral resources in ways that maximize society's welfare. At another level are land management decisions of states and American Indian Tribes. Consider, for example, current efforts by the Department of Natural Resources, State of Alaska and by Doyon, Ltd, an Alaska Native Regional corporation, to select those unassigned lands having the largest net present values of undiscovered mineral deposits, forest resources, or real estate; this selection is to be based upon resource appraisal [Tom Smith, Alaskan Division of Geological and Geophysical Surveys, and Harold Noyes, Chief Geologist, Doyon, Ltd, personal communications (1991)l. At still another level, a mineral resource appraisal may be performed to support the selecting of optimum development programs. Witness the current use by the Inter-American Development Bank (IDB) of petroleum resource appraisals as inputs to a simulator of petroleum exploration and development to examine the feasibility of IDB loans for the development of the petroleum sectors of developing countries [Powers (1983)j. 3. Notions of supply

3.1. Supply as a flow The magnitude of a mineral resource seldom is the real objective of an appraisal; rather an estimate of mineral resource is a means to an end, which is the estimation of supply, either potential supply or dynamic supply. These supply concepts are not

D.P Hams

1014 PRICE

AS,

Q5

QUANTITY /UNIT TIME (a)

QUANTITY OF STOCK (b)

- - - ns, --- ns, CHANGES IN SUPPLY

c

(c)

Fig. 1. Industry dynamics and potential supply: (a) historical shifting of supply (S) and demand (D) schedules as their determinants change, leading to the current market represented by S3, Dj and P5; (b) the cumulative effect over time of previous market transactions is the depletion of the original stock by the amount labeled cumulative production for a price slightly below P5;(c) future supply (flow) curves developed from the remaining potential supply stock in response to resource depletion and price increases. [From Chavez-Martinez (1983).]

equivalent to either the short- or long-run supply of traditional economic theory. As commonly understood, a supply function describes flow per unit of time for various prices, given fixed determinants such as capacity, number of suppliers, and factor prices. The long run allows changes in these determinants.

3.2. Supply as a stock

Although in graphical or functional form a potential supply curve appears like the economists supply curve, the two curves describe very different things. The potential supply curve describes the size of the stock of material by cost of production. Figure 1 depicts market dynamics - the shifting of supply and demand across time - and how price resolution and market flows are related to stock measures: cumulative production, reserves, and potential supply from undiscovered deposits. Specifically, at a moment in time the market clearing quantity reflects not only current consumer preferences, producer technologies, and growth in the economy, but also the cumulative effect of past economic activities in depleting the original stock of producible material (initial potential supply). The position of cumulative production on the potential supply curve indicates the extent of this depletion.


1015

In the simplified exposition on mineral stocks depicted in Figure 1, produced mineral is no longer available, for scrap recycle, which is an important source of supply for some mineral commodities, e.g. iron, copper, and lead, is intentionally ignored. At current time, given fixed technology and factor prices, mineral will continue to be produced according to S j until the currently available stock, labeled reserves, is exhausted; thereafter, ceteris paribus, production will cease unless net price increases. For current technology, the magnitudes of the stocks that are estimated to be producible at prices above P5 are described by the potential supply curve.

3.3. Future flows Additional production from new deposits will require a higher price than P5 and capital investment in exploration and development to convert part of the potential supply stock to new reserves and a flow according to a new supply function, S', as indicated in Figure lc. Of course, the higher prices required to elicit incremental new supply will also create new reserves in old deposits to the extent that the old deposits contain low-grade material not previously producible economically at P5. This effect is not shown in Figures la-c. It is incorrect to draw a series of shifting (fclture) demands on the potential supply cuwe and read on the price axis the market clearingprice for each successive time shift of demand. This is because a potential supply is a stock, and the quantity consumed in one period is unavailable for the next period. A potential supply curve implies nothing as to when quantities of the metal or compound will be produced, except that they will not be produced now. Current deliverability is not implied by potential supply.

3.4. Dynamic supply Dynamic supply, as the term is used here, refers to supply in response to price across time as deposits are depleted (some exhausted) and replaced by new ones which are of lower quality, meaning higher costs of either production or discovery. Although dynamic supply is a flow, the design of a mineral supply system to generate dynamic supply from mineral stocks, given projected future demand schedules, is a subject of current and future research [Harris and Chavez (1981,1984)l. Dynamic supply models based upon explicit descriptions of mineral stocks, exploration, and production may be useful in examining the effects of wide ranges of price, costs, and technology. Of course, such capability is strongly dependent upon having credible estimates of the mineral stock and credible models of exploration and production.

D.R Hams

4. Stock concepts and measures

4.1. Reserve

The terms most commonly used to convey mineral resource information are reserve and resource. The term reserve is commonly used by mining and geological engineers working with a specific mineral deposit. To them it is understood that an ore reserve is the size of the current working inventory of material that is known to exist and can be produced economically given the costs and prices at the time. When it is desired to specify the inventory by degree of certainty of the quantity having a specific average grade, a modifier is used: proven, probable, possible. However qualified, the critical features of a reserve are that it is known to exist and it is economically producible at current prices and costs. Since delineating a reserve requires investment in drilling, a stated reserve of a mine may be approximately the same over many years. This reflects the planning function of management, who typically desire to have enough reserves to support production capacity for the planning horizon, e.g. 5-10 years. Thus as proven reserves are produced, more may be added by additional drilling. For that reason, it is useful to consider a quoted reserve as the current working inventory. Change in product price or factor cost alters the magnitude of a reserve; this reflects the definition of a reserve by current economics. Reserves, once delineated, do not necessarily exist forever simply because they are known, for if product price falls below break-even costs, the reserve of a mine ceases to exist.

4.2. Resource By the foregoing definitions, the quantity of an element or compound within a known deposit that cannot be produced economically for current economic circumstances is not a reserve. Neither is this quantity a resource at the same low price; it is properly referred to as a resource for the economic conditions that make it profitable to produce. An ore reserve is simply a known quantity of mineral resource that is economically producible under existing economic conditions. If the deposit currently is not economically producible, it is properly referred to as a known resource only at the higher price required to meet production costs (see Figure 2). Resource exists only within an economic and technologic reference. In this sense, a resource is like a reserve; however, when the term resource is qualified only by a specified price, it is understood to refer to the sum of the element or compound in all (known plus undiscovered) deposits producible at that price (ignoring discovery costs), given current and near feasible technology.


Potential Supply (Given stated economic conditions, eo, and specified exploration effort, EX') mic Resources (Reserves)

Economic Resources (Given Current Conditions. eo)

Resources, Given e * (stated economic conditions more favorable than eo)

Mineral Endowment. minimum grade q' minimum tonnage t* maximum depth h ' mode of occurrence

Resource Base

> Mineral Endowment > Resources > Potential Supply > Refewes

Fig. 2. Resource terminology and relations. [From Harris (1978).]

4.3. Potential supply

When the set of deposits that comprises resource is restricted to only those that also are economically discoverable, the sum of the element or compound in these deposits constitutes the stock known as potential supply [Harris (1984a)l. These relations and definitions are shown schematically in Figures 1 and 2.

4.4. Additional stocks: Endowment and resource base

Two additional stocks are required for a comprehensive description of mineral stocks: resource base and endowment. These two stocks differ from reserve, resource, and potential supply in that they are not defined by economics or technology. Resource base is the total amount of an element or compound that is present in the earth's crust within the region of interest. For example, the resource base for copper includes not just copper in ore minerals but copper that substitutes

D.P Hams

1018

for other ions in common silicate minerals. Thus, for resource base, the basis for measurement is molecular, while for resource the basis is mineral, meaning the quantity of the element occurring in ore minerals of the element. Mineral endowment can be considered a component of resource base. If from the earth's crust those occurrences of the element or compound are selected that meet specified minima of concentration and size and a maximum depth within the crust, the sum of the amount of the element or compound in all such occurrences is known as mineral endowment [Harris (1984a, b)].

4.5. A formal statement of stock measures and determinants Consider, for convenience, at a given moment in time, a single element in a single region of the earth, so that notationally time, element or compound varieties, and places can be ignored. Our experience has shown that the ultimate deposit of this element in that region of the earth consists of many smaller deposits occurring in varied geologic environments and possessing various characteristics of grade, size, shape, mineralogy, depth, host rock, etc. Suppose that there are NM deposits and that they constitute set RB: RB = {rl, . . . , ~ N M ) , ri is the ith deposit. Let us represent our knowledge about the ith member of set RB by a set, Zi, of NC characteristics, ki,,, j = 1, 2, . . .,NC:

The set of N C characteristics includes all physical properties of the NM deposits. Suppose that RB were partitioned solely on the basis of only NCM of the NC characteristics, NCM < NC, with no thought given to economics or technology. The set of occurrences so formed is D, and the quantity of the element in D is referred to as m, endowment. Defining function y(Zi) to map the characteristics Zi of the ith deposit (ri) into quantity of the element, metal endowment, m, is defined as follows:

D

where

D is a subset of RB, RB = D u D, such that ri E D requires that k 1..1 . > k J! , j = 1 , 2 ,..., NCM; N C M < N C . Othenvise,ri~~.


1019

Referring to the level of the NCM conditions used to define D as Z', for every ri E D, we have Zi 2 Z'. As the vector Zi is considered to represent all (NC) physical characteristics of r E RB, resource and potential supply stocks are defined by evaluating the implication of Zi, i = l , . . . , NM to discoverability and to production cost, given (1) the states of exploration, mining, processing, and refining technologies; (2) factor prices; and (3) an optimum allocation of exploration effort. So that the nature of the various mineral stocks are well defined, each of them has been described rigorously in a manner similar to the foregoing description of endowment [see Harris (1984a, b) for a complete development].

5. Perspective on resource information

5.1. General The value of mineral resource information is determined by its social cost and by social benefits that derive from improved economic decisions. As societal issues regarding minerals vary in both context and time frame, a universally best level of mineral resource information for all circumstances and policy issues does not exist. Moreover, as some resource information can be obtained indirectly from geologic information and economic relations, there is an optimum information strategy and estimation methodology for each issue and attendant circumstances, and the selection of such should result from the broad evaluation of social costs and benefits.

5.2. The time dimension The relevant time dimension is the time frame of the central policy issue. Consider the case in which the policy issue is one of a short time frame, say two years. For this case, the time frame is not long enough for the initiation of completely new production facilities, which in mining typically take from two to ten years to complete after the deposit has been discovered. Nor is it long enough for the realization of production from significant expansion in reserves of known deposits. Here, if stocks are the central issue, then the relevant stock measure is current reserve, perhaps amplified by a model of conversion of probable and possible reserves to proven reserve. If flows are the issue, then they can be best estimated by conventional econometric modeling or by time-series forecasting methods. A time frame of two to ten years is an intermediate case, for it is not long enough for significant enlargement of stock measures through new exploration. But it is long enough for the expansion of reserves of existing mines and for the

development of new production capacity from the inventory of known (shelf) but undeveloped deposits. It is for this time frame that for some minerals we have considerable institutional capability for estimating potential supplies for various economic scenarios. The Minerals Availability System (MAS) of the US Bureau of Mines is one example of impressive capability [Bennett et al. (1973), Peterson et al. (1981), US Bureau of Mines (1978)l. For some mineral commodities, such as copper, this system documents the physical characteristics of each known deposit, including those not yet producing. Furthermore, the system is replete with extensive engineering costing models for mining, milling, smelting, and refining. For specified economic scenarios, initiation of this system for a commodity produces what is called an availability curve, which describes potential supply from known deposits. Similar capability exists in DOE for estimation of potential supply for uranium and in the US Geological Survey for petroleum from known deposits. Given the long lead times in exploration and development, unless the relevant time reference is at least 10 years distant, economic questions are answerable by consideration of ore reserves and on-the-shelf deposits (deposits held in inventory by mining companies but not yet developed). Our capability to provide credible estimates of future supply from this known stock for specified economic or policy issues is considerable. For Canada, the work described by Williams (1982) and by Zwartendyk (1982) are further examples of the analytical frameworks, the data systems, and the computer systems that have been developed and are being refined for analysis of these intermediate term issues. It is for a time frame of greater than 10 years that the contribution of potential and dynamic supply from currently unknown deposits must be considered. The longer this time frame, the larger the region, and the greater the change in economics, the greater is the possible change in potential supply. Thus, in an a priori sense, the potential of unexplored regions becomes very important in this time frame. Often, it is the relatively unexplored regions that could contribute most to potential supply for this time frame, and ironically, it is for these regions that information often is very limited, that estimation is the most difficult, and that controversy over the best methodology and the usefulness of estimates is the greatest.

5.3. Estimation issues It is both appropriate and useful to consider the magnitude of a mineral or energy resource to be a conditional random variable. In other words, given all available geodata and information at the time of policy analysis, the magnitude of the resource is described by a probability density function. If estimation of potential supply were to follow classical approaches, it would gather sample information as a means of making inference to the population. But, since new sample information


1021

on the presence or absence of mineral deposits is particularly costly, approaches to estimating potential supply have relied upon other kinds of information. Generally, there are two main, very different, approaches: (1) estimation by projecting economic relations [Cargill et al. (1980), Harris (1984a), Hubbert (1969), Lieberman (1976), Roberts and Torrens (1974), Uri (1980)], e.g., life cycles of discovery and production or trends in discovery rates; and (2) estimation based upon inference from related geological information [Agterberg et al. (1978), Eberlein and Menzie (1978), Grybeck and DeYoung (1978), Harris (1968, 1984a), Hetland (1979), Hudson and DeYoung (1978), MacKevett et al. (1978), Miller et al. (1975), Patton (1978)j. A resource appraisal method that directly yields potential supply is of limited value, for it does not provide the description of the physical features of mineral deposits and the interaction of technology and economics with these features. Estimates by life cycle or discovery rate models [Hubbert (1969), Lieberman (1976)l are of limited usefulness, for not only are the physical features of the endowment suppressed, but economic conditions and technology are described only by unstated trends in the response variable. An alternative to these approaches is to estimate potential supply indirectly by first describing the deposits that make up the endowment and then subjecting the endowment to the economics of exploration and exploitation [Harris (1984a), Harris and Chavez (1981), Harris and Euresty (1973), Harris and OrtizVertiz (1981), Harris et al. (1971)l. This latter approach requires that the estimation of potential supply be made by a potential supply system. The main components of a potential supply system, shown schematically in Figure 3, include mineral endowment, exploration, and exploitation models. In practice, such systems range from models which are basically mathematical, e.g., crustal abundance models [Brinck (1974), Drew (1977), Harris (1984a)], to models that include the computer simulation of exploration, disaggregated cost analysis, and mine optimization [Harris and Chavez (1981), Harris and Ortiz-Vertiz (1981)l. Estimation of potential supply by a system leaves open the methodology for estimating mineral endowment. The use of geological information to estimate the magnitude of mineral endowment requires a model which is linked to either number of deposits or total amount of mineral. Basing endowment estimates upon geological models raises the question of credibility, particularly for an appraisal made by elicitation of judgments of experts, e.g., NURE [Vogely (1983)l. The position taken by some analysts is that until direct sample evidence of the existence of a deposit has been obtained, there is no justification for making estimates of potential supply, because these are only "guesstimates". This 'purest' position leads to ignoring geological information about endowment; consequently, it can not be optimal generally; however, about all that usually can be offered by way of assurance is documentation of a well-conceived and executed methodology, supplemented where possible by a documentation of performance on control or

D.11Hams MINERAL ENDOWMENT

Inventory of Deposits Simulation of Exploitation

Given:

4. t

h' modes of occurrence RESOURCES

cally producible if were known, given economics

Stated economic conditions, e. and - that deposits are known

A

POTENTIAL SUPPLY (PS)

Given:

I

I

I I

I Given:

Fig. 3. A potential supply system (model). [From Harris (1978).]

validation areas. For this reason, great emphasis is given to methodology. The following reference goes beyond methodology and uses exploration results, albeit in a weak sense, to comment upon the credibility issue. Consider the judgment about a previously made resource appraisal [Harris et al. (1971)l offered by R.J. Cathro (1983)J at a symposium on predictive metallogeny, a judgment that challenges the purest position:


Fig.4. Geographic distribution of the endowment of tungsten in undiscovered but expected deposits in the Canadian Northwest. [After Barry and Freyman (1970).]

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1024

The results were synthesized [see map of Figure 41 and appear to have been remarkably perceptive. I am sure none of us who took part in that project 15 years ago would have guessed that it would turn out so well. Geoscience, June 1983,p.100 This judgment is particularly noteworthy because it reflects at least a partial test by time (exploration results).

5.4. Resource, information, and policy Expanding the concept of resource information to include geologic information in addition to drilling results and known deposits leads to a more comprehensive examination of policy options. As man can control the detail of geological mapping, the density of geochemical and geophysical surveys, and the density of drilling, he can essentially achieve whatever level of knowledge about mineral stocks he chooses, ranging from complete knowledge to ignorance. Of course, to each level of knowledge there is an associated information cost and a risk of non-optimal decisions. The relevant question is the policy action to be taken given the current state of information. If policy were evaluated according to a decision-theoretic approach, total ignorance about the mineral endowment of a region would be only a special circumstance for the prior probability distribution, and bestpolicy will be made only by considering the prior probabilities (no matter how difise), conditional losses, and the expected value of information for various information strategies . . .), The optimum action, given a comprehensive analysis, could be to postpone an ultimate selection of a policy option until the acquisition of additional data. Ham's (19846)

The policy decision, such as keeping an area open for exploration, should be made only after analyzing the information available at that time, even ifthe state of geological knowledge were that of "total ignorance", for exploration, whether done by government or industry, is the acquisition of information, and this information has a cost as well as an imputed value. No matter how poor the prior information is on potential mineral supply, an optimum decision on land use would at least reflect the expected value and costs of additional information, given the priors. As an introduction to the next section, the hypothetical state of 'ignorance' merits brief consideration. Even when a geologist claims ignorance, suggesting a rectangular probability distribution for mineral or energy endowment, he seldom, if ever, is totally indifferent about the upper limit of that distribution, the maximum endowment of the region; often, neither is the geologist, even in his professed ignorance, indifferent to the minimum endowment. Since the parameters of a rectangular distribution are the minimum and maximum values of the random variable, this is tantamount to being not indifferent about the parameters of the distribution, and to being not indifferent to the expectation for mineral


1025

endowment [Harris (1983a)l. That being the case, are there any regions about which we are totally ignorant? On the contrary, geological information invariably bounds the values of many factors. Of course, the usefulness of geological information rests upon the presence of heterogeneities within the earth's crust, the relationship of these heterogeneities to mineral occurrence, and the capability of man to identify those heterogeneities that are associated with mineral occurrence. The following section examines the macro features of the earth's crust as they relate generally to the formation of mineral deposits. A subsequent section examines deposit features that relate to exploration cost and performance and to production cost.

6. Geology of mineral occurrence

6.1. Crustal abundance of elements - A gross feature of mineral stocks Geoscientists recognize the following structures in the earth's crust, beginning at the center and proceeding outward: inner core(solid), outer core (liquid), mantle (solid), upper mantle (solid), asthenosphere (solid), lithosphere (solid). The lithosphere is the rigid, relatively thin, outer part of the earth and consists of solid rock. The outer portion (5-60 km) of the lithosphere contains the oceanic and continental crusts. It is from the continental crust that man has obtained the bulk of his mineral supply. While this is expected to continue for some time, mineral supply may one day also derive from oceanic crust. For example, the polymetallic massive sulfide deposit in the Atlantis I1 Deep of the Red Sea has received considerable attention not only for its scientific value but also for what it may portend as a future source of metals [Rona (1983)l. The oceanic and continental crusts differ slightly in bulk composition; throughout the remainder of this chapter, any reference to the earth's crust is of the continental crust. In view of the fact that man's mineral supply has derived primarily from the continental crust, it is informative to examine the composition of this fundamental feature of the earth and ultimate source of minerals. The following nine elements account for 99% by weight of this crust: oxygen (45.2), silicon (27.2), aluminum (8.0), iron (5.8), calcium (5.1), magnesium (2.8), sodium (2.3), potassium (1.7), and titanium (0.9) [Harris and Skinner (1982)l. Noteworthy is the fact that all remaining elements, including some that are commonly used and some that are highly prized - copper, lead, zinc, silver, gold, and carbon - account for only one percent of the crust. Given the high concentration (abundance) of oxygen and its tendency to form complex anions with silicon, it follows that the bulk of the

1026

D.P Hams

earth's crust consists of oxide and silicate compounds. The point to be made here is that while the ultimate source of mineral substances is the earth's crust, most of those sought by man to support his economic activities comprise a very small part of crustal material. In essence, most of these substances are present only in 'trace' amounts. Let us refer to the concentration of an element, expressed as a decimal fraction or as parts per million (PPM), within the earth's crust as crustal abundance, A. Then the stock measure known as resource base (RB) is the product of A and W, the weight of the crust within the region of interest:

For example, consider uranium in the US crust. Given that the weight of the US crust to a depth of 600ft (a depth that includes most US uranium deposits) is 4 . 0 6 1015 ~ mt and that A in terms of U3O8 is 3 PPM, which is equivalent to the fraction 0.000003,

This is a staggering quantity in view of 1977 annual consumption of 15900st [US DOE (1978)l. However, if we had to extract this annual requirement from ore having a grade of only 0.0003% U3O8 (average crustal grade), the cost per lb of U3O8 also would be staggering. The average grade of uranium ore produced in the USA during 1977 was about 0.154% [US DOE (1978)l. Thus, those deposits upon which uranium supply is based represent accumulations of uranium that had been enriched during their formation to approximately 500 times the concentration of the common crust. As rock material of the crust, these deposits differ considerably in concentration of U3O8from typical material.

6.2. Across elements relations 6.2.1. Magnitude of stock 6.2.1.1. Simple proportionality to crustal abundance Suppose, as a gross generalization, that a deposit of X tons of an element or compound having low abundance within the earth's crust represents the outcome of a greater number of sequential depletions and enrichments than does a deposit of X tons of an element of high abundance. Then, a deposit of the scarce element that is both large in size and of high grade would be in a relative sense a very rare event.

1027


Deposits of elements having low abundance in general would tend to be of smaller size than those of high crustal abundance. If crustal elements under consideration also were of similar chemical reactivity, then the numbers of deposits of the various elements and their average deposit sizes and grades would be, ceteris paribus, proportional to crustal abundances. 6.2.1.2. Mineralizability and crustal abundance

In reality, elements differ considerably in ionic size, valence, electron potential, and in their geochemical cycle. Consequently, the simple postulated proportionality is deficient as a means of making generalizations about deposits. Suppose, however, that an additional characteristic, d, referred to as the coefficient of mineralizability [Brinck (1971, 1972)l is identified. Consider d to represent the tendency of an element or compound to form accumulations of high concentration in the processible compounds of the element. Then, together, crustal abundance A and the coefficient of mineralizability d should be related generally to the quality and quantity dimensions of a mineral stock. Table 1 Long-term price predictions by crustal abundance relations Metal

A

d

1971 price ($1971/lb)

Actuala Predicted

Copper 70 16 Lead Zinc 8 ~ r a n i u m ~ , 3~ Gold 0.001

0.1981 0.2793 0.2126 0.2003 0.3547

0.514 0.139 0.169 6.069 446.52

0.88 0.176 0.194 8.35 409.00

1979-1982 actual pricesb.c ($1982ilb)

Low

0.54 0.20 0.27 24.86 1353

Averaged

0.98 0.46 0.45 35.00 6402

High

1.78 0.71 0.52 57.64 11865

Predicted priceC ($198211b)

2.67 0.53 0.59 25.30 1353

A: crustal abundance; d : coefficient of mineralizability. a Producers price FOB refinery. Metal Statistics 1983, unless otherwise noted, e.g., uranium. Inflated to $1982 by Producer Price Index for Industrial Commodities. Average of annual averages, where an annual average is simply the average of the low and high for that year. Units of U308. Estimated from various reported prices. g Average of NUEXCO monthly spot prices.

6.2.2. Pricelcost 6.2.2.1. Relation to crustal abundance and mineralizability Suppose further that the crust of a particular region supports a complex economy producing many varied goods and giving rise to derived demands for many materials. Suppose also that demands are either constant over time or shift in unison in a regular way. Suppose further that there is a limited degree of substitutability among the materials factors for at least some final goods and that both final goods and factors are priced competitively. Given these suppositions, there should be, in a broad sense, a relationship between prices of the materials and the two characteristics of their occurrence, A and d: p = y O ~ -e71d, ' p is price in dollars per lb, A is crustal abundance in PPM, d is coefficient of mineralizability, yo,y 1 are parameters. Brinck (1972) estimated yo and yl for several metals and characterized the equation as describing long-term metal prices:

wherep is in 1971 dollars. Table 1 shows A, d , and the average annual and estimated prices for five metals for 1971 and 1983. 6.2.22. Relation to grade and e n e w of chemical bonding Phillips and Edwards (1976) offer the observation that "relative prices of metals are not arbitrary and are related in some way to their scarcity". Acknowledging the possibility that for a given metal noncompetitive factors, e.g. cartels or barriers to entry, may influence prices, they, nevertheless offer the tentative hypothesis that relative prices are dictated by costs on the rationale that few metals are free from competition from substitutes. One component, the cost of metal production, is specified to consist of the costs of discovery, development, mining and milling, and is considered to be a function of crustal abundance of the metal. The second component consists of smelting and refining (including hydrometallurgical recovery) and is denominated in the energy required to liberate the element from its chemical bonding. This energy is represented by the change in Gibbs free energy, a measure known as AG, which can be obtained from a handbook of chemistry and physics. Specifically, Gibbs free energy G is related through a law of thermodynamics to entropy S, absolute temperature T, volume V, pressure P,

1029


P r ~ c e( r US(196B)/kg)

P-

Fig. 5. Predicted prices from trial B plotted against actual price. [From Phillips and Edwards (1976).]

chemical potential of species pk, and number of gram molecules, dqk present of species k:

~G=scIT+v~P+C~~~~. k

At constant temperature and pressure, dG = C p k dqk, the energy involved in the chemical reactions. This measure was taken as a proxy for the energy required to refine the metal, allowing that this is a conservative estimate because of thermal losses in refining [Phillips and Edwards (1976)l. In their investigation, Phillips and Edwards found that the median grade of ores being mined is a better determinant than crustal abundance; consequently, their model for metal prices was accordingly modified, as follows:

D.P Hams

Statistical analysis of prices, grades, and AG's for 23 metals produced the following equation:

q, median grade of ore produced expressed as a proportion, AG, change in Gibbs free energy times a ( - I), expressed as MJ/kg, p, price in 1968 dollars per lb of metal. For example, the median grade (proportion) of all copper ore produced in the world was taken as 0.01305 and a representative value of the change in Gibbs free energy was estimated to be 0.678; these values of the explanatory variables produce an estimated price for copper in $1968 of:

+ 1.0018 x 1oP2(0.678) pcu = 0.9042 x lop2& = 0.6929 + 0.0068 = 0.6990 FZ $0.70/lb. Noteworthy is the fact that for copper, metal price essentially is determined by the first component; this is supported by engineering cost analyses, which show the cost of milling to dominate copper costs. Contrast this with aluminum, for which the above equation estimates a price in $1968 of approximately $0.31/lb, 93% of which, according to this model, arises from refining costs. Using a producer's price index for metals, this 1968 price for copper of $0.70/lb would imply a price in 1983dollars of $1.73/lb. This is quite close to estimates of the cost on the margin for new copper capacity at that time ($1.50-$1.60/lb). Figure 5 shows the plot of observed metal prices with those estimated by the above equation by Phillips and Edwards. With exception of cadmium, cobalt, and antimony, the relationship is remarkable in its description of prices across this large set of varied metals which occur in diverse chemical compounds and geological environments, thus exhibiting wide ranges in deposit size, average grade, and deposit morphology. The foregoing relations are intriguing as descriptions of cost determinants, and it is as such that they are here presented. While Brinck (1972) and Phillips and Edwards (1976) use them to comment upon price, as price relations they are deficient because they do not explicitly consider demand factors. Appealing to longrun equilibrium to equate cost and price is not inconsequential when the relation of cost is across elements among which there is some substitutability. Strong assumptions about product demands, production technologies, and particulars of mineral occurrences (size, depth, grade, grade distribution) are required to consider these relations as describing long-term price.


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6.2.3. Variation in abundance of a single element - A means to gross modeling of endowment Although the evidence of some order in magnitudes of stocks or pricelcost with crustal or deposit features is intriguing, the variation of concentration of a single element has been the focus of most studies of crustal abundance and mineral stocks. Ahrens (1953) found that the concentration of relatively scarce elements, e.g. uranium and gold, in crustal material commonly is distributed lognormally. As the grades of mining blocks of ore bodies of many of these elements also appear to be well modeled by the lognormal distribution, the notion was advanced that element concentration in ore bodies and in common rocks that contain the element only as ionic substitutes within silicate minerals belong to the same parent distribution of element concentration [Brinck (1967), Agterberg (1978)l. Let us consider this further by drawing upon the work of Deffeyes and McGregor (1980), who, after considering the distribution of U3O8 in a number of mining districts and also in the various rocks that comprise the crust, concluded that the distributions of uranium concentrations (grade) are consistent with a lognormal crustal abundance model. Let us consider the crustal abundance of uranium as a percentage (0.0003%) to be the mean of this distribution. Then, let us postulate the following model: A = exp (p

+

g).

The two parameters ( p and a2)have been estimated using DOE's preproduction inventory [Harris and Chavez (1984), Harris 1988)l: p = -9.144 and a2 = 2.065. DOE's production inventory (reserves plus all produced material plus subeconomic resources present in known deposits) shows, for a cut-off grade of 0.06% U308, 677x 106 mt of mineralized material having an average grade of 0.15% U308.The lognormal endowment model indicates the following for the same cut-off grade: Mineralized material: 9.215 x lo9 mt; Average grade: 0.108% U3O8; Amount of U308: 9.95 x lo6 mt. According to the model, approximately nine times the known uranium occurring in accumulations which have grades of at least 0.06% U3O8 remains to be discovered. Thus, if uranium is lognormally distributed and these estimates of parameters of the distribution are reasonable, one must consider the possibility that large quantities exist. Since 0.06% U3O8 is near cut-off grades of some actual operations, we have no compelling reason to expect this uranium to be nonavailable because of its chemical form. For the lowest cut-off grade of DOE's preproduction inventory, 0.01% U 3 0 8 [US DOE (1980)], the lognormal crustal abundance model indicates 2.206 x 1012mt

D.R Hams

1032 Table 2 Crustal abundance model estimate^^.^ 9' (%)

In(q') Probability

Model estimates MM AG

DOE u308

-

From Harris and Chavez (1984). In Q N(-9.144, 2.056). Abbreviations: MM: mineralized material (mt); AG: average grade (%); U30s: Amount of U30s (mt); DOE: US Department of Energy's preproduction inventory of U30s (mt). a

of mineralized material having an average grade of 0.018% U3O8, giving 397.1x106mt of U308, a very large quantity (see Table 2). In 1977 known ~ mt of U3O8. Thus, the model indicates endowment amounted to only 1 . 5 6 4 lo6 that the quantity of U308in material having concentrations of a least 0.01% U3O8 is approximately 254 times known endowment. Geologists are divided on the credibility of endowment estimates made by crustal abundance models. Central to this division is the assumption that the distribution of element concentration in ore minerals and element concentration in common crustal material is continuous and unimodal, as depicted by the lognormal distribution. Skinner (1987) argues on geochemical grounds that this distribution is bimodal, with the major mode representing element concentration in the population of common crustal material, e.g. silicate minerals, and the other mode at higher concentration levels representing element concentration in the population of ore minerals. Although this argument has scientific merit, empirical results generally have failed to document the second mode at higher concentrations [Harris (1984a)l. Geologists who favor crustal abundance models argue that one advantage of the grossness and simplicity of crustal abundance models is that they allow for the presence of an element in modes of occurrence that are not currently recognized

Ch. 21: Mineral Resource Stocks and In formation

1033

by geologists due to the imperfect state of science and inadequate geologic information. In other words, geologists so to speak "see what they are trained to look for", and to the extent that there exist kinds of deposits about which they have no experience, estimates of endowment by geologists are conservatively biased. The desire to subject endowment estimates to economic analysis reveals great deficiencies in the simple univariate crustal abundance model of endowment, because the mineral embodiment of the element is unspecified. Consider, for example, copper that is present in chalcopyrite, a common sulfide mineral in copper orebodies. After mining, the ore is crushed and ground to liberate the chalcopyrite minerals from the gangue and common rock silicates to form a copper concentrate of about 25% copper, and it is this highly concentrated material that is smelted for the extraction of copper. Contrast this to the extraction of copper present only as copper ions substituting for other ions within a silicate crystal lattice. As there are no ore minerals, the copper can not be separated from the common rock silicates, meaning that all of the silicate rock itself must be melted in order to liberate the copper. Besides requiring the melting of a much greater quantity of material, silicates require much higher temperatures to melt than sulfides. Both of these effects make recovery of copper from silicates very costly [Singer (1977)l. To these costs would have to be added the environmental (externality) cost of dealing with greatly increased quantities of processed rock. The desire to subject endowment estimates to eeonomic analysis places great emphasis on describing the mode of occurrence of the element, meaning mineralogical and physical characteristics that relate to exploration, mining, and processing costs. This need leads to the examination of structure within the earth's crust and the relation of that structure to determinants of cost. 6.3. Geologic environments and deposit types - A basis for increasing resource information

Although the notion of crustal abundance is useful as an ultimate determinant of availability of an element or compound, it and its companion stock measure, resource base, can lead to erroneous perceptions, because they treat the crust as a homogeneous mass having the chemical composition indicated by average crustal concentration. In reality, that part of the crust that is exploited by man, the outer two miles of the continental crust, is heterogeneous, and if crustal abundance measures are an accurate description of crustal bulk composition, they are so only for large crustal blocks which average out the effects of heterogeneities. The last three decades have witnessed a great unification of observation and theory in geology via plate tectsnics. Plate tectonics is based upon the established fact that the crust of the earth consists of crustal blocks that are moving. While

the precise energy mechanism driving these movements is not well understood and the subject of controversy, its effect is well documented. Very simply stated, the energy system of the earth creates a recycling of crustal material: ocean floors are spreading; as new crust is formed by upward movement of molten material, crustal blocks move away from the spreading zones. This outward movement causes some crustal plates to collide. At the collision boundary, oceanic sediment may accrete on continental plates and one plate may subduct. The subducted plate may partially melt in response to high temperatures accompanying deep subduction. This melting may give rise to volcanic activity and magmatic intrusions, which may under certain conditions result in the formation of new mineral deposits. Once formed, the metal in these new deposits may be preserved or it may be remobilized by other earth processes (e.g., oxidation, weathering, erosion) and reconcentrated. As with metals, plate tectonics is useful in explaining the macro features of petroleum and gas deposits. For example, fore-arc basins formed on the continental margin as a result of the collision of two plates and subduction of the oceanward plate, may be shallow with irregular basin profiles. Typically, sedimentary rocks include shales, carbonates, and interbedded volcanics. Due to low heat flow, poor reservoir rocks, and a deficit of trapping mechanisms, forearc basins generally offer poor potential for occurrence of productive petroleum accumulations [Klemme (1977)l. Classifications of basins [Reva (1983)l have been related, where appropriate, to plate tectonics. Plate tectonics explains in a fundamental way the existence and formation of geosynclines and basins. Since the different kinds of basins have been observed to vary somewhat systematically in major structural and stratigraphic ways and in petroleum resources, the tectonics associated with plate movements are determinants of petroleum endowments. Of course, petroleum deposits, like metal deposits, may be remobilized, retrapped and upgraded or dispersed by subsequent geologic processes. For a chapter dealing with mineral resource information, a focus for the foregoing discussion may be helpful. Specifically, the major point to be made is that mineral substances of the crust are acted upon by both macro and micro earth processes and often by more than one cycle of them. In a broad and general sense, the result of the sequential operation of these processes is the depletion of an element or compound from some crustal material for the enrichment of other material. Thus, nonhomogeneity of the crust in element concentration is accompanied by nonhomogeneity of geology. As most of man's mineral supplies derive from only the highly enriched material, a task for geoscience and explorationists is to use geologic information to identify those heterogeneities that are associated with enrichment.

Ch. 21: Mineral Resoltree Stocks and Information

6.4. Features of deposits valy by environment and deposit type One result of the study by geoscientists of heterogeneities within the earth's crust is the identification of geologic environments and the mineral deposits types that typically occur in them, e.g., stratigraphic type oil deposits, porphyry copper deposits, sandstone roll-type uranium deposits, etc. Usually, for a given element or compound, there are a number of environments, giving rise to different kinds of deposits. For example, environments for copper include porphyry systems, volcanogenic massive sulfide, sedimentary, replacement, and strataform. For the resource analyst, the importance of this structure and taxonomy is that the different processes that were operative in these environments embodied the enriched crustal material in different chemical and physical forms. The following five characteristics are especially relevant to mineral supply because of their effects on costs: mineralogy; deposit size; intradeposit grade variation;

average grade; depth to deposit.

Although there is much variation in these characteristics within a given deposit type, there also are some general patterns. For example, copper deposits of the porphyry type generally are very large and low-grade, having an average ore tonnage of 548 x 106st and an average deposit grade of 0.63%Cu [Singer et al. (1975)l. In contrast, copper deposits of massive sulfide types are much smaller and higher in grade (3.78%Cu). The important point of this discussion is that ore deposits of a specific kind, e.g. massive sulfide copper, are created from common crustal material by earth processes that are characteristic of that deposit type. Consequently, such deposits exhibit some common characteristics irrespective of where they occur, e.g., in the African or North American continents. Accordingly, the past two decades have witnessed concerted efforts to document the statistical distributions of selected deposit characteristics by deposit type [Cox and Singer (1986)l; these distributions are referred to as deposit models. Thus, possessing both the knowledge of deposit-forming processes for geologic environments and deposit types and statistical distributions of deposit features by deposit type permits the geologist to draw some broad conclusions about the undiscovered mineral deposits of a region from an understanding of the region's geology. This capability is the basis for resource information strategies and resource estimation methodologies, as uncertainties about estimated quantities can be reduced by acquiring more geoscience information.

D.P Ham's

1036

7. A generaiized model of resource by depesit type - A conceptual reference

7.1. Perspective The foregoing section established the notion that deposits of elements or compounds that are mined commercially constitute anomalous crustal occurrences both in terms of amount of metal and of grade (concentration) and that the earth processes that cause these anomalies leave geological signatures. Further, the estimation of a mineral resource is facilitated greatly by structuring the estimation by geological environment, which is detectable from geological information, and by deposit type, as types of deposits differ in important features that influence exploration and exploitation cost. Such structuring facilitates the use of deposit models constructed from data on known deposits and of cost relations that have been determined by deposit type. To highlight the nature of useful relations and their integration for resource estimation, consider the following generalized resource model defined for a single deposit type.

7.2. Model components ~ ef (G("');P) t describe the quantity of crustalmaterial that has been mineralized by earth processes typical of a specific deposit type, where G("') is a vector of geologic variables that influence amount of mineralized rock, and ,B is a vector of parameters. The quantityf (G("');P) is comprised by N deposits of the specific type:

N =

(G(m);'),

I

i = average deposit size (tonnage of mineralized rock).

In the formal definition of mineral stocks presented in an earlier section, each deposit is represented by NC characteristics. Restricting this model to a single deposit type reduces the number of characteristics required for the description of mineral stocks, for some of the characteristics are employed in the taxonomy of deposit type. Let us simplify further by representing each deposit by only four characteristics (features): q : deposit average grade; t : deposit size; h = lld, d is depth to top of deposit. v : intradeposit grade variance; Let X(t, q, v, h ) be the joint probability distribution function (pdf) for these four characteristics. Then,


1037

Consider an exploration model 4 ( X , t, q, h; G(e),E, y), which describes the fraction of the population of deposits having characteristics t, q, and h that is discovered by effortX, given the vector of geological variables G(")and the vector of physical conditions E that influence discoverability, and given parameter vector y. Define unit cost by a(q,t,h,v; W,T), where W is a vector of factor prices and T is technology. Cost function a is derived from a generalized cost function c b , q,t, h, v; W, T), wherey is output rate. Define average unit cost as the value of function E:

Then, as aElay = E1(y, q, t, h, v; W, T), let y* = P(q, t,h, v; W, r ) be the value of y for which tl(y, q, t, h, v; W, T) = 0 and substitute y* for y into c ( y , q, t, h, v; W, T) to describe minimum average cost c*: E* = c ( y * , q , t , h , v ; W , ~ )= E ( P ( q , t , h , v ; W , ~ ) , q , t , h , v ; W , ~ ) = a(q, t, h, v; W,T).

In other words, function a describes average unit cost as a function of q, t, h, and v when production is at the optimum (minimum average cost) rate. The quantity referred to as resource, rs, for price r, given factor prices W and technology 7, is defined as follows:

- f(G(m);8) -

t

J J J 1 tqo(q, t, h, v ; r ) ~ ( tq,, v, hldvdhdtdq, Q

T

H

V

where 1 for r > a(q, t, h, v; W, T), 0 otherwise. The purpose of this description is to highlight model components and their interplay. Clearly f(G("');p), which represents the contribution of geologic data G("') and geoscience to resource appraisal, is a very important component. For given an estimate of ,O and observations G("'), the quantity of crustal material that is mineralized by earth processes relevant to the specific deposit type is estimated simply by evaluating f on the vector of observed geological variables G("'). When the objective is the estimation of resource, the model of deposit characteristics, X(t, q, v, h) and the model of unit cost, a(q, t, h, v; W, T) are

4 9 , t, h, v;r) =

D.P Hams

1038

equally important as is f (G("'); P). For example, Niikl, the number of deposits of size class i, grade classj, nearness class k, and intradeposit grade variance class 1 is calculated simply by N..l ~ k l= f G

)

i

t;'

$ /": $

~ ( t*,, V,h) dv dh dt dq,

h;'

where t(', tj : lower and upper limits of ith size class, q,!,'q,! : lower and upper limits ofjth grade class, h;l,hi : lower and upper limits of kth nearness class (lldepth), ,,I/I ,,I . lower and upper limits of lth intradeposit grade variance class. Of course, cost function cw can be used to estimate Etkl, the minimum average unit cost for each of these combinations:

Finally, when potential supply ps is desired, the exploration model represented by 4(X, t, q, h; G ( ~ )E, , y) is vital, for it is required to determine the fraction of the population of deposits represented by f (G("');p)l t that is discovered by optimum exploration:

$(X* (r; W, r ) , t, q, h; G ( ~ )E, , y)) dv dh dt dq, where X*(r;W, T ) is the optimum exploration for price r, given W and r. In application, optimum exploration is not known a priori and must be computed for specified product price r, given W and 7. Optimum exploration effort X*(r;W, r ) is that level of exploration effort that maximizes expected rent, T :


COMSTOCK EPIMERMAL VEIN

TONNES ( in MIUIONS )

Fig. 6. Tonnages of Cornstock epithermal vein deposits. [From Cox and Singer (1986), fig. 113, p. 1-52.]

The following sections present a partial and select review of some contributions with respect to these component models and the systems designed to integrate them. The first section to follow reviews deposit models, because endowment estimation, exploration modeling, and production cost modeling are by deposit type. This section is followed by cost models, here represented by function a, and by exploration models, represented by function 4. Finally, the section that precedes concluding remarks examines estimation and inferential issues, most of which concern f ( G @ )@)If. ;

D.P Ham's

GOLD GRADE ( in GRAMS ITONNE )

Fig. 7. Gold grades of Comstock epithermal vein deposits. [From Cox and Singer (1986), fig. 114,p. 152.1

8. Deposit models 8.1. Kinds of models

The term deposit models as used here refers to four separate kinds of models. The first is a model of the geology of the deposit type. Constructing this model requires the distillation from the great amount of detailed geologic observations about deposits and their geologic settings to those earth processes or geological conditions that are either critical to or typical of the formation of the deposit type.


COMSTOCK EPITHERMAL VEIN

SILVER GRADE ( in GRAMS /TONNE )

Fig. 8. Silver grades of Comstock epithermal vein deposits. [From Cox and Singer (1986), fig. 115, p. 153.1

The second type of deposit model requires the identification of mineralogical, morphological, and physical features that typify deposits of that type and the identification of deposits around the world that comprise the population of known deposits. The population of deposits identified for the second type of deposit model serves as a basis for statistical compilations and descriptions of selected deposit features: these constitute the third type of model. This third type of model consist of relative frequency plots of selected features, such as ore tonnage, average ore grade, grades

D.R Hams

Undiscovered and non-reported deposits Geologic d e p o s i t

A

I

-\

Ore D e p o s i t

Minimum grade and tonnage economic o p e r a t i o n s

, for

Average grade

Fig. 9. Schematic illustration of truncation and translation of ore deposit to reserves due to economic and technologic effects. [From Harris and Agterberg (1981).]

of associated eiernenis (see Figures 6-4, and the correlations between deposit tonnage and grade and between grades of primary and secondary elements. The fourth type of deposit model describes the variation of grades within the deposit either by the average intradeposit grade variance for deposits of that type or by the distribution of grade variances and the correlation of variance to either deposit tonnage or deposit average grade [Charles River Associates (1978), Harris (1988)l. Deposit models of the first three kinds have been and are being constructed by various individuals and institutions; however, the singly most productive and continuous effort is that by the US Geological Survey [Cox and Singer (1986)], which provides deposit models of the first three kinds for selected deposit types. These deposit models can be very useful in the estimation of endowment, resource, and potential supply. Deposit models of the fourth type, that of intradeposit grade variance, are very scarce, as they require information on the distribution of grades within deposits, which is usually not available to the public. Consequently, there have been few published studies describing this deposit feature [Harris (1988), Agterberg (1978), Charles River Associates (1978)l. While information represented by the fourth


1043

kind of deposit model often has been neglected, it is, nevertheless, very important for economic analysis of resource and potential supply. For, when element concentration within the deposit varies greatly, there exists a cut-off grade for which expected discounted rent is an optimum. Generally, this cut-off grade decreases the amount of mined ore and increases its average grade. This is referred to in Figure 9 as translation. Modeling translation requires not only the tonnage and average grade of the deposit but also the distribution of grades within the deposit. The intradeposit grade variance is useful in modeling this distribution. Suppose, for example, that both deposit tonnage, t, and average grade, q, are known and that previous investigations have shown ore grades to be lognormally distributed: In Q N(p, v). Then, for cut-off grade, q', the quantity of ore, t,,, and average grade, qqt, can be computed, given v, the logarithmic intradeposit grade variance:

-

where y(1nq; p, v) is the normal pdf having parameters p and v, and p = Inq - v/2.

8.2. Contamination of geologic data by economics Because of the importance of deposit characteristics to the estimation of potential supply, many potential-supply models or systems employ distributions of deposit size and grade (quality). Only in the past few years has the information content of such data been critically examined. Use of these data as they are routinely reported may pose some difficulties if economic scenarios very different from the past are to be considered for their impact upon potential supply. From Figure 9, it is apparent that reported data on deposit size and grade reflect the physical attributes of the deposit, the economics of exploration, and profit maximization of deposit exploitation. Modeling endowment by probability distributions constructed from these data tends to overstate the relative frequency of occurrences of high grades and to obscure the relative frequency of deposit size. Such effects can cause distortions in the modeling of exploration outcomes and of reserve expansion in response to improved price. Furthermore, economic contamination interferes considerably with the determination of the presence of dependency between size and grade, an issue of considerable importance in modeling of potential supply and the investigation of resource scarcity. Consider Figure 10, which portrays the truncation effect of economics for fields of the Western Gulf of Mexico [Drew et al. (1982)l. In fact, because of this contamination effect, Drew et al. (1982) proposed that the lognormal distribution,

D.I?Hams

Fig. 10. Schematic diagram of the method used to estimate the part of the field-size distribution below the historical level of economic truncation. [From Drew et al. (1982).]

which long ago was accepted as the cornerstone of petroleum endowment and exploration modeling, should be replaced by a log-geometric distribution because the lognormal model does not explain well the very large numbers of oil deposits


of small sizes: define the random variable X as field size class; then, P(x=X+l)=P(x=~)2-~, P(x=~)=c2-"~; c and 19are parameters.

8.3. The size bias effect with economic truncation

8.3.1. Exploration as a size biased sampling process

As a sampling process, exploration has been represented as being size biased [Drew et al. (1988), Barouch and Kaufman (1976), Long (1988)l and truncated [Drew et al. (1982)l. When this is an appropriate representation, obtaining an unbiased estimate of the population parameters requires the 'undoing' of bias and truncation. This can be achieved by explicit modeling of bias and truncation and the relations of sample parameters to population parameters. Here, we consider truncation at a single known deposit size, although there may be multiple truncations [see Long (1988)l. Letx be the size of an oil pool. Suppose that Y = InX N(p, 02). Represent , Consider the probability that x is discovered to the normal pdf fory as f ( y ; ~a2). be proportional to x" provided that x 3 xc, where x, is the truncation size. Then the pdf for discoveries, f a @ ;p', D ~ , ~ ,is) ,related to the pdf for pool sizes in the following way:

-

- f (y; P + aff2,f f 2 )

k = f T ( ~ ; +p aff2,ff2,yc), yc < Y < The implication of the foregoing is that the population variance a2can be estimated directly from the sample of discoveries using an appropriate estimator for a truncated lognormal population [i.e., Hald (1949)], yielding ji' and d2. But since ji = ji' - a e 2 ,estimation of p requires an estimate of the bias coefficient a. Forman and Hinde (1986) describe a means for estimation of a when it is reasonable to assume that the region is sufficiently explored so that all pools above a known size x* have been discovered [also see Long (1988)l. For example, ji' and e2for discovered pools of the Rimbey Meadowbrook Play of central Alberta, Canada, were estimated to be 8.0832 and 6.3, respectively [Harris (1990)l. Following Forman and Hinde, the size bias coefficient a was estimated to be 0.664. Correcting for

D.11Ham's

1046

truncation and size bias yielded lognormal parameters fi = 3.9 and &2 = 6.3:

-

Thus, lnx N(3.9,6.3) is an estimate of the size distribution of deposits as they occur in nature. 9. Cost models 9.1. Perspective

In the resource model, unit cost was represented by a special cost function a(q,t,h,v; W , T ) .In concept as well as practice, a credible estimation of resource or potential supply requires a credible representation of unit production cost. Although there are many determinants of production cost in actual resource development, cost models for the analysis of undiscovered mineral stocks usually are predicated upon only a few of them. The reason for this is that every determinant of cost used must also be described explicitly in the resource model. The deposit models described in the foregoing section are explicitly for that purpose. Notably, these models typically describe only the major determinants of cost, such as deposit tonnage and grade. An ever present difficulty in the estimation of cost models is the lack of cost data by mine or deposit. When such data are not available, the cost function must be estimated from engineering relations. The following are two selected examples of cost relations that have been estimated and used for the economic analysis of mineral stocks.

9.2. Zimmerman's analysis of coal cost and resources Although the cost model developed by Zimmerman (1981) is simple, it is a valuable demonstration of the use of economic information and theory to derive a cost function, and of the use of the cost function to describe magnitude of coal resource by cost. An estimation of US deep coal resources was based upon production (Q) and cost (TC) functions involving a deposit parameter (thickness, Th) and number of working sections (s) of the mine: Q

= 1597.6~h1.1071 s0.7915

E,

TC = 3914764 + 2 122480 [ ~ ' . ~ ~ ~ ~ ( 1 5 9 7 . 6 ~Eh] ',. ' O ~ ' ) with Th the seam thickness; s the number of sections in the mine; Q tons of coal output; and TC the annualized total cost of mining. E is a lognormally


1047

distributed error term representing those physical features of coal deposits that affect production and cost but are not included in the analysis. By converting TC to average cost, AC, differentiating with respect to output Q and setting the partial derivative equal to zero, the output rate that minimizes average cost can be determined. By substituting this quantity into the average cost equation, a stochastic equation for minimum average total cost AC* can be determined; for deep mining, this procedure produced the following relationship [Zimmerman (1981)l:

Given the assumption that E is lognormally distributed, it has been shown [Zimmerman (1981)] that the distribution of deep coal by cost is also lognormally distributed:

-

lnc ~ ( p c4, , pc = ln 2567 - 1.1071 ln Th, a: = (1.1071)~a:nTI,+ a:,,. Of course, before the distribution of coal resources by cost can be computed, one must have estimates of additional parameters: E, initial coal endowment; PI, TI? and the parameters of the lognormal distribution for thickness; and a:, ,, the variance of the error term representing geologic factors not accounted for. Inspection of a plot [Zimmerman (1981)l of the logarithm of coal seam thickness in Pike County, Kentucky, gives the following:

The regression analysis performed to estimate the parameters of the production function for coal provides a standard error of the regression estimate of 0.98 [Zimmerman (1981)) This serves as an estimate of al,,. Given independence of the error term and thickness, transformation to the cost space is achieved using the following relations:

fit

= In 2567 - 1.1071 x 3.611 x 3.8528,

8: = 1.10712 x 0.0406 + 0.912 x 0.88.

-

Thus, In C N(3.8528,0.88). Production records indicate cumulative production of 4 . 1 2 lo9 ~ tons [cumulative production through 1974 for Kentucky; Schmidt (1979)l. Suppose, for demonstration purposes, that this production were in response to a stable price of approximately $25.00. Then we could estimate the initial coal endowment E from

the basic relations of the model:

lm In 25

4.12 x lo9 = E

f (ln c;3.8528,0.88) d in c o E F(-0.68) o 0.2438E.

Thus, E o 16.6 x lo9 tons. ~ tons, the remaining coal resource Given an initial coal endowment of 1 6 . 6 lo9 ~ tons: for a price of $50/ton is estimated to be approximately 4 . 5 6 lo9

Finally, the coal endowment that is not a resource at $50/ton is estimated to be 7 . 9 2 ~lo9tons. 9.3. Response function of a cost estimation system 9.3.1. Background Typically, information on unit cost, production rate, and cost determinants required to estimate a unit cost function are not available for many types of mineral deposits. In that case, an alternative approach is to use a cost estimation system to estimate unit cost. Regression analysis of estimated unit cost on cost determinants produces an equation that describes generally the response of the cost estimation system to changes in the levels of the cost determinants. Provided that the cost estimation system is well designed and properly used and that the combinations of the determinants are wisely chosen, the estimated response function may be a useful cost model for the economic analysis of mineral stocks. 9.3.2. Special considerations

The use of a cost estimation system as described above to estimate a cost model requires that the system mimics the decisions of a rational economic agent in real world situations. This means that estimated unit cost approximates the unit cost associated with profit maximizing decisions. As discounted rent changes with product price, given factor prices and technology, optimum mine life, cut-off grade, and output rate also change with product price. Thus, besides cost determinants, the response function must include product price and discount rate as explanatory variables. Some deposit types typically contain more than one element of economic interest, and often the contribution to revenue of coproduct or byproduct is the difference between an economic and a noneconomic deposit for anticipated prices.

Ch. 21: Mineral Resource Stocks and Infomation

1049

Thus, for a specific deposit type, the response function will include the grades of by- and co-product metals. When the deposit typically contains more than one metal of economic interest a useful procedure is to define the dependent variable to be the ratio of total cost per unit of major metal to revenue from all recovered metals. Explanatory variables include metal prices as well as the cost determinants, e.g., ore tonnage and grades of the ore in each of the contained metals. As each cost estimate requires the specification of engineering relations and the execution of the cost estimation system, the generation of cost data themselves incurs a cost. When that cost is a significant factor and there are several metals that typically occur together in the deposit type of interest, it may be necessary to specify a base price vector and to limit price variation to a multiplier of the base vector. This reduces the representation of several prices in the cost equation to a single price multiplier, thereby reducing the number of combinations of the explanatory variables for which the system must be executed.

9.4. Cost model for gold in gold-quartz vein deposits -A case study

9.4.1. Approach

Gold-quartz vein deposits typically contain both gold and silver, and when warranted by gold and silver prices and the grades of gold and silver, both metals are recovered. Thus, the cost model for gold must account for silver as well as gold values. Accordingly, letting c be the ratio of unit cost to combined (gold and silver) revenue per unit, the cost model estimated for gold in gold-quartz veins is of the following general form: c = v ( t , q ~ uq, ~ g~, , P A ~ , Pr), A~, c : total production cost divided by total revenue from gold plus silver; t : deposit ore tonnage (1000 tons); d : depth to deposit (ft); q ~ ,:, grade of gold (%); q ~ :, grade of silver (%); PA^ : price of gold ($102); p , ~ :, ~price of silver ($10~); r : discount rate (%). To reduce the number of combinations to be evaluated by the cost estimation system, the assumption is made that gold and silver prices will move in concert. This permits the use of k, a multiplier of base prices in place ofpAuandpAg:

9.4.2. Combinations and cost estimates The method for developing the cost equation was to select deposit sizes and grades that cover their likely ranges in nature. In this study, the 5th, 50th, and 95th percentile values were selected from size and grade frequency plots (deposit models) constructed by the US Geological Survey [Cox and Singer (1986)J based upon worldwide occurrences of epithermal gold-quartz vein deposits (see Figures 6-8). Three depths were arbitrarily chosen; five price levels and three rates of return were selected. These quantities were combined in 22 selected ways so as to represent relevant ranges of physical and economic circumstances for epithermal gold-quartz veins. Each combination was evaluated separately by the cost estimating system (CES) of the minerals availability system (MAS) by Harold Bennett of the US Bureau of Mines, returning several economic measures, among which were net present value, internal rate of return, and the ratio of cost to revenue, c. Base prices for PA" and p~~ of $350 and $15, respectively, were multiplied by five values of the base price multiplier, k, which replaces pA, and pAg in the cost equation. By way of explanation, a value of 1 for k (k3) means that the prices for gold and silver used in the discounted cash flow analysis were the base prices ($350, $15). Accordingly, k = 1.5 gives prices of $550 and $22.50.

9.4.3. Estimation of the cost equation In order to capture as fully as possible the complexities in the relationship of c to the basic variables (t, q, d, k, r), selected transformations (x,,. . .x,;yl, . . .y,;zl, . . .zr) of the basic variables were computed and added to the data set. The entire data set was then subjected to stepwise regression and the equation having the highest coefficient of multiple determination (R2) and acceptable F statistics for all variables was selected (the numbers in parentheses above a coefficient in the following equation are the F statistics) [Harris (1990)l: (126.86) lnc = - 88.3236 - 5 . 1 9 ~ t

(1 16.03)

(41.70)

+ 48.7526q2 + 2.0532~10W4d (148.66) (1 13.23) (29.28) (143.30) + 48.1914k - 321.7689~~ - 1.4292~ 1OP4x3+ 2.7826~10-4x5 (715.27) (91.57) (88.09) (12.29) (155.96) 1 . 0 0 0 6 ~+~2.8413~5- 2 . 6 6 5 4 ~+~7.3098~ 1Op2z3- 52.3444~5

-


R~ = 0.9998, P ( F > f ) = 0.0001. = 3.591 + 0.1592, ~3 = 0.000001(d t), xs = 3.5ql t, yl = ln(3.5q1 + 0.15q2), ys = ln(3.5ql t), 22=Inq1, 23=Inq2, z5=Ink, zb=Inr, XI

27

= (Int) lnd

28

= [In

- :-lor)]

Ink,

29

= (ln k)2.

Given constraints:

As noted, the value of R2 is approximately 1.0, and F statistics for all variables are large, showing that all included variables carry information useful in describing In c. , x~,yl, Substituting the functional expressions for transformation variables X I x3, ys,zz, z3,zg, 26, 2 7 , and ~ ~29, Inc can be written as a function of the basic physical variables (t, ql, 92, d) and the economic variables (k, r): Inc = - 88.3236 - 5.19 x 10W6t + 48.7526q2 + 2.0532 x 1 0 - ~ d+ 48.1914k - 321.7689(3.5q1 + 0.15q2) - 1.4292 x 10-"(dt) + 2.7826 x 10-~(3.5q~t) - 1.0006ln(3.5 q l + 0.15 92) + 2.8413 ln(3.5ql t) - 2.66541 lnql 7.3098 x lop2Inq2 - 52.3444 Ink + 2.7888 x 10-I Inr - 6.8254 x 10-~(lnt)(lnd)

+

+ 1.6570 [In ( l

- :-lor)]

(Ink) - 21.518l(lnk)'.

Suppose that our interest were directed to two mutually exclusive sets, economic and noneconomic deposits. The value of c for the boundary separating these sets is 1.0, for which Inc = 0.0. Therefore, setting lnc = 0.0, d = 1, k = 1, r = 0.12 and 92 = 0.05 describes a filter in t-ql space for deposits at the surface that contain silver grades of 0.05% when gold and silver prices are $350 and $15, respectively, and required return on investment is 12%:

0.00043 < ql ,< 0.0019. This filter is shown in Figure 11 as the curve farthest from the origin. The second curve is a filter derived from the same cost equation, but for higher prices ($420 and $18: k = 1.2) and greater depth to deposit (d=500ft). As shown by the position of the second curve closer to the origin, the increase in revenue from higher prices overwhelms increased cost due to deeper mining; the economic set for the second filter is much larger than for the first, for it includes deposits of smaller size and lower gold grade.

D.P Ham's

1052

t

-37.3011

- 1126.1912q+0.1759

lnq

5.1901429 x

lob6

4x

0.00043 1 q 1 0 . 0 0 1 9 tonnes 5 t S 11.0 x l o 5 tonnes

lo5

............ ........... ............ ........... qAg = 0.05 ............ ........... ............ ........... ............ k=1

, I

k

=1.z

r

=0.12

- 1.0006 I n - 9.7391 x lo-'q

S i l v e r grade (

Base p r i c e m u l t i p l and $15 (Ag)

[ \

1 second

f i l t e r showing e f f e c t of g r e a t e r depth (h = 500) and h i g h e r p r i c e s ( k = 1.2-+ $420 (Au), $18 (Ag)

0.0

l 3

I

l 4

-

RELIABLE DOMAIN O F F I L T E R l

5

l

l

6

l 7

l

8

l 9

l I0

l 11

l 12

DEPOSIT A V E R A G E G R A D E ( X

l 13

l 14

i

-

7 I

1

l 15

l 16

l 17

l 18

I

I I

i 19

q

Aux lo-*)

Fig. 11. Economic filter for epithermal gold-quartz veins. [From Harris (1990).]

10. Exploration models

10.1. General

The generalized model of resource by deposit type includes the exploration model $ ( ~ , t , q , h ; G ( ~ )?), , E , which describes the fraction of the deposits having size t, average grade q, depth d = llh, that is discovered by exploration effort x, given geology G(e) and physical conditions E of the region. Required features of this model include diminishing returns to effort x and increasing returns to t, q and h. These features mimic the documented size bias of exploration [Drew et al. (1988), Long (1988), Barouch and Kaufman (1976)l and the effects of discovery depletion [Harris (1990)l. Exploration models developed so far have not captured all of these features in a single mathematical expression, although all of these features have been collectively represented by separate modeling efforts. Some of these are reviewed briefly in the following section.


10.2. Discoverability, information gain, and depletion 10.2.1. Major concepts

Consider the estimation of potential supply by a potential-supply system in which the earth's crust of the region is seeded with mineral deposits by Monte Carlo sampling of the geologist's probability distributions for N, the number of deposits of the specific type, t, deposit tonnage, q, deposit average grade, and d, deposit depth. Although each of many regions is separately seeded, exploration is to be simulated on the collective region in a way that it mimics industry behavior in at least a few major ways: The effect of deposit features t, q and d on discoverability; The effect of magnitude of endowment, e.g. number of deposits, on discoverability; The information gain that occurs with the initial discovery in a region; The 'play' effect, meaning that firms continue to explore a region even though the large deposits have been found and other unexplored regions are available; The effect of discovery depletion on discoverability of remaining deposits. 10.2.2. Structure of discoverability modeling for a potential-supply system

This approach to modeling exploration in a potential- or dynamic-supply system simulates exploration on the seeded endowment. At every stage of the computer simulation, every seeded deposit that has not been discovered is given an adjusted index of discoverability, I , based upon its features (t, q, d), the number of deposits initially seeded, N, and the number of deposits already discovered, n [Harris (1990)l:

with

1= f (t, q, d),

A = #(N, n),

n

< N;

f : index of discoverability,

I : index of discoverability adjusted for information gain and depletion, N : number of deposits comprising the endowment, n =: number of deposits discovered, 1 for initial discovery,

.={

0 otherwise, A : adjustment factor for previous discoveries.

Deposits are discovered in order of the adjusted index of discoverability I , provided that the exploration expenditure E X = g ( I , t, q) is no greater than available rent. An ever present task in modeling potential supply is the simulation of an economically relevant allocation of exploration expenditures. So far, this allocation in discoverability modeling has been simplistic. As the objective of discoverability modeling to date has been to simulate exploration across a set of regions by an industry of firms, as contrasted to a single firm in a single region, amount of exploration in a specific region has been controlled by the economic rent of the region's deposits. Thus, for a specific region, the nth discovery is made when

where EXi = g(Ii,ti,qi) is the discovery cost for the ith discovery, Ro is a small base value that serves to initiate exploration, and Ri is the economic rent for the ith discovery. Clearly, for this allocation to make sense economically, EX must be normalized to include the costs of unsuccessful ventures leading to discovery. Such allocation implies that the industry is competitive, earning only the return on capital that is consistent with risk to firms in that industry. 10.2.3. US uranium -An example

Use of the model described in the foregoing requires identification of appropriate functional forms for f , q!~ and g and estimation of their parameters. This confronts the analyst with the difficulties of implementation, one of which is that data on discoverability or on information gain are not readily available. Moreover, although number of discoveries n by region is known, seldom is the endowment N known. Consequently, responses of four consultants, each an expert in uranium exploration, served as the data base for estimation of an exploration model for two deposit types: tabular sandstone uranium and roll-type sandstone uranium deposits [Harris and Chavez (1981), Chavez-Martinez (1983)l. Statistical analysis of pooled responses of the four experts yielded the following results: Tabular deposits:

Roll-type deposits:

Ch. 21: Mineral Reso~trceStocks and Information

20000

-

10000

.-

OCCURRENCE CONDITIONS: SIZE(106s.t.ore) AVERAGE GRADE ( X )

LARGE 50.0 0.2

SMALL 1.0 0.2

LARGE DEPOSIT

2

300

0

20 10

SMALL DEPOSIT

500

1000

1500

2000

2500

3000

DEPTH TO DEPOSIT (FEET)

Fig. 12. Discoverability of a large and a small uranium deposit. [From Harris (1987); data from Harris and Chavez (1981).]

Therefore,

As expected a priori, initial discoverability I increases with deposit size t and average grade q but decreases with d (depth to deposit). However, 1 is less than elastic to all three determinants, being most elastic to deposit size and least elastic to average grade. Figure 12 shows the effect of depth on discoverability for a large and a small uranium deposit. Once a discovery has been made, adjusted discoverability is elastic to the number of deposits initially seeded. This result is intuitively satisfying, as it shows in discoverability terms the great information gain and reduction in discovery cost that take place with an initial discovery within a richly endowed region.

D.P Ham's

---

Porphyry copper deposit. 150 million short tons with an average grade of 0.7% Cu

- \

\ \ \

:i

i : \ ;

1000

.........

Massive sulfide deposit. 10 million short tons with an average grade of 3% Cu

Stratiform deposit. 9 0 million short tons with an average grade of 4% Cu

2000

3000

Depth (feet)

Fig. 13. Discoverability of copper deposits using current technology. A discoverability of 1000 implies certainty of discovery given best practice technology. [From Harris and Skinner (1982).]

10.2.4. Discoverability and deposit type - Copper deposits

Although the discoverabilities of tabular and roll-type sandstone uranium deposits were found to be quite similar, that is not generally the case. Different deposit types of the same metal may exhibit very different discoverability because of differences in the geology of their formation and because of different deposit features. Figure 13, which shows the effect of depth on discoverability of a copper deposit, was developed from discoverability equations similar to those shown for uranium [Harris and Skinner (1982)l. Especially noteworthy is that although discoverability for all modes of occurrence decreases as depth of cover increases,

Ch. 21: Mineral Resource Stoch and Information

1057

strataform deposits are much more discoverable than porphyry deposits for all depths up to 1000 ft. Consider a porphyry copper deposit of 150x lo6 st of ore at an average grade of 0.7% Cu. When some part of this deposit is exposed, the explorationist is certain that current exploration practice would discover it, giving it the maximum relative discoverability of 1000. With lOOOft of cover, relative discoverability is reduced to approximately 100. The implication of this figure is twofold. First, considering what has been discovered in light of the rapid decay in discoverability with depth, there probably are quite a few copper deposits remaining to be discovered; second, costs for the discovery of remaining deposits will increase unless there are some noteworthy improvements in sensing technologies or reductions in drilling costs.

10.3. Sequential decisions and valuation of exploration information using capital markets

Mineral exploration is investment in information, an investment that typically is at considerable risk; moreover, risk varies with deposit type. When exploration is conducted by a corporation, the expected value of information can be estimated as the expected change in the value of the firm and of the project net the investment in exploration, as valuated by capital markets. As mineral exploration places capital at risk, exploration in practice is engineered sequentially so that the newly acquired information can be analyzed and the value of information to be acquired in the next stage can be estimated. Conceptually, the next stage of exploration is initiated only when the expected value of information acquired in that stage exceeds cost of acquisition. This perspective leads to the use of statistical decision theory and the explicit modeling of (1) the relationship of the firm's cost of capital to risk, (2) uncertainties about exploration outcomes, and (3) the change in risk and expected value of the firm brought about through investment in the next phase of exploration for a specific target, e.g., gold vein deposits, with explicit consideration given to diversification effects on the firm's cost of capital [Markowitz (1957)l. A highly disaggregated and complex computer simulation model of exploration for roll-type sandstone uranium deposits was designed to have these, as well as other important features [Harris et al. (1981), Harris (1990)l. First, the unknown endowment of the region is simulated by Monte Carlo sampling of probability distributions of endowment descriptors, e.g., number of deposits and deposit features (size, grade, depth, grade variation, etc.). Then exploration for the seeded endowment is simulated sequentially according to the architecture of actual exploration practice, which consists of five stages (phases). Except for the first phase, which consists of the broad geologic analysis required to select the area to be explored, these phases are described in Table 3 in terms of objective, action, state of nature, and degree of

D.P Hams Table 3 Architecture and structure of explorationa Phase

Objective (0)

Action (a)

State of Degree of attainment of ~ature~ objective ( d ) (s)

2

Select a favorable A3

Do geology and geochemistry

L

3A

Find the redox

L

3B

Estimate the general trend of the redox line L

Drill nc drill holes and geologic interpretation Drill nR drill holes and geologic interpretation

4A

Find the deposit: Deposit is defined as a concentration containing material > qmin

Drill f fences and geologic interpretation

4B

Rough evaluation of tonnage and grade (U3O8) of deposit given Q b qmin Continuing evaluation of tonnage and grade (U308 amount) of deposit given

Drill nE drill holes and geologic interpretation

( q n ) wD(qmi,)

Drill n t E drill holes and geologic interpretation

(qmin), wD(qmin)

Q a

L

1(qmin), LD

Do the right selection (if L > 0 or rejection (if L = 0 (binary) Binary: Redox found or not found Percentage of error incurred in redox line length estimate (target percentage error also asked) Binary: Deposit found or not found

Percentage of error incurred (target percentage of error also asked) Percentage of error incurred (target percentage of error also asked)

2 Qmin

From Harris and Ortiz-Vertiz (1981). Symbols: L, length of redox line contained in A3; l(qmin),lenght of target; Lo, search length.

attainment of objective. Exploration was structured in this way so that magnitude of effort (amount of information purchased) could be optimized through an explicit evaluation of the expected net value of information for the next stage of exploration. This contrasts with the more traditional modeling of exploration according to prespecified behavioral rules, with no provision for modification of behavior in response to change in economic circumstances or in uncertainty and in risk.


10.4. The Arps-Roberts exploration process model 10.4.1. Structure

The foundation of this model is the probability for discovery,~,of an oil field having a surface-projected area of a when exploration is performed by drilling randomly selected locations within a basin having an area of B [Arps and Roberts (1958))

This probability is considered to be a special case of the general model p = calB, where c = 1 for random drilling. When geologic information is useful in the preferential selection of drilling locations, then c > 1.0, generally ranging from 1 to 3. Thus, generally,

Defining the probability for no discovery as q = 1 - p, we have by the binomial law that the probability for zero discoveries after drilling x locations is 1 - qx. Substituting 1 -p = 1 - calB for q, the probability for zero discoveries given the drilling of x locations is given by PROB(n = O/x drillings) = 1 - qx = 1 - (1 -

-)

ca B

.

Given that the number of deposits within the basin that have area a is Na(co), the expected number of discoveries of such fields, given the drilling ofx locations, is

When calB is small, the term [1 - (1 -calB)"] 1 - exp(-calB). Thus,

may be approximated by

Suppose that this basic model for deposits of one size and one depth is specified for number of deposits of the ith size class and kth depth interval that are discovered by drilling x locations:

where ck = 1 for random drilling; ck > 1 to the extent that geology improves exploration results (discoveries) beyond those for random drilling.

10.3.2. Perman Basin -An example In a particularly impressive demonstration, the US Geological Survey (1980) used drilling and discovery data only through 1961 to estimate an exploration process model for deposits of size class 10 [1.52x 106 to 3 . 0 4 lo6 ~ bbl of oil equivalent] and depth interval 1 (0-5000 ft):

where Fl,lo(m) is the desired endowment estimate, i.e., the number of deposits discovered when there has been an infinite amount of drilling; B is the basin area; A is the average areal extent of the fields in the given size class and depth interval; w is the cumulative number of wells for the depth interval; and C is the efficiency of exploration: for random drilling, C = 1; if exploration is twice as effective as random, then C = 2. For deposits of the tenth size class and first depth interval in the Perman Basin, there were by 1961 14243net wells, which yielded 59 discoveries. Given this amount of exploration and the basin parameters B = 100000 mi2,A = 2.2 mi2, C = 2.0, we have the following initial endowment estimate for the number of size-class-10 oil fields:

[

59 = F l , l ~ ( m )1 - exp

(

(2.0)(2.2)(14243) 100000

+

F l , l o ( ~=) 126.7.

Therefore, this model indicates that 68 deposits of size class 10 remained to be discovered after 1961. The model was then tested by predicting discoveries for the interval of 1961-1974. Cumulative drilling by 1974 amounted to 25055 net wells for size class 10; thus Fl,lo(25055)= 84.5, meaning that an additional 25.5 fields of size class 10 should have been discovered by 1974. In fact, during this period 25 discoveries were made.

10.4.3. Estimation of marginal cost and potential supply Clearly, this model provides conditional discoveries, conditional upon cumulative drilling. But, an increment of drilling occurs only when its expected benefits outweigh expected costs. Thus, use of this model to estimate potential supply requires (1) explicit consideration of the costs of drilling, developing, and producing deposits of each size class and depth, (2) an estimation of surplus net present value, and (3) a relationship of surplus net present value to drilling effort.


1061

The approach in this study was to develop engineering relations which ascribed either (1) physical parameters, e.g. oil gas ratio, important to costing, or (2) cost estimates for each of a number of cost categories. Thus, by employing these relations, each discovery was given values for the physical parameters and costs required for economic analysis. Potential supply from undiscovered endowment was estimated by finding that level of drilling for which the positive surplus of net present value from the discovered fields just offset the cost of exploration. The results of this analysis were summarized by graphs of marginal cost schedules for each of three rates of return (5%, 15% and 20%). By considering rate of return, r, as a parameter (shift variable in marginal cost), the results can be generalized to the following model of marginal cost of potential supply:

where r is the rate of return on capital as a percentage; ps is the quantity of petroleum (oil+gas) in bbl of oil equivalent; mc(ps; r ) is the marginal cost in dollars per bbl, given a required return of r and a quantity of potential supply of ps. For example, consider a rate of return of 15% and a potential supply of 3 x lo9 bbl:

Marginal cost increases rapidly as the size of the stock increases; for example, if rate of return remains at 15% butps is increased from 3 to 5 bbl, marginal cost triples:

By recasting the data, they can be statistically analyzed to estimate potential supplyps, in which potential supply is a function of the marginal cost for each of three rates of return:

whereps(mc; r ) is the potential supply of oil equivalent, given marginal cost mc and rate of return r, and the mc, are the marginal cost for 5,15, and 20% rates of return, respectively. For example, suppose we wish an estimate of the potential supply of petroleum from undiscovered deposits of the Perman Basin for marginal cost $30/bbl, given a required return on capital of 15%. For this circumstance,

11. Geologic endowment models 11.1. Perspective

The generalized resource model described in an earlier section includes a component that represents the number of deposits, N , of a specific deposit type within a region: N =

(G(m);p) = endowment number, S

where f (G(m);p)is the quantity of rock mineralized by the earth processes of the geologic environment of this deposit type; G(m)is a vector of geologic variables that influence amount of mineralized rock; ,8is a vector of parameters; and j =

L, L, L, I-,

tX(t, q, v, h) dv dh dq dt;

X(t, q, v, h) : joint pdf for deposit characteristics t,q, v, h, t : tonnage, q : average grade, v : grade variance, h = lld, where d is depth. The function f (G("');p) represents generally the use of geological information to estimate endowment when there is no direct evidence of the deposits. This mapping of geologic information to endowment represented by function f in practice has taken various forms, including: (1) multivariate statistical relations [Harris (1966), Harris and Pan (1990), Agterberg et al. (1990), McCammon et al. (1983)l in which a specified equation, usually but not always linear in geological variables, serves as f (G("');p), (2) the subjective evaluation by a geological expert in which the expert's mind, aided by a genetic model of the geoscience of the geologic environment and deposit formation, maps geologic features - lithologies, rock alteration, geologic structure, geophysical properties, e.g. magnetism, gravity, and geochemical values - to endowment [Reed et al. (1989), Finch et al. (1980), Harris (1984), Miller et al. (1975)], (3) a computer expert system in which the inference relations, e.g., decision trees and weights that comprise the system, serve as f and either map directly from observed geologic features to endowment or from genetic conditions interpreted by the geologist from the basic geology to endowment observations [Harris and Carrigan (1980)l. Here, it is understood that there is a different f for every deposit type. The concept of function f requiring a vector of parameters ,fl is generally useful as it focuses on the practice of using observations from an analogue or control area


1063

to estimate p before using f to estimate endowment for the region of interest. Clearly, the formal estimation of ,6 for a multivariate statistical model requires data on endowment and on the quantified geological variables G("').Although the need of statistical control and validation for a geologic expert or a computer expert system is not so apparent as it is for a multivariate statistical model, it is just as real, for geological experts and expert systems both require training, calibration, and the use of analogues to compensate for missing or unobservable geology and for deficiencies in basic scientific knowledge. Basic geoscience education describes the earth processes in both space and time that operate to form mineral deposits. Generally, this follows a materials balance view, in that it accounts for the element from source through the genetic processes to the preservation of deposits enriched in the element. Seldom is a geologist provided enough basic geodata to be able to estimate endowment by material balance accounting. So, he compromises strict materials balance accounting to a combination of genetic principles and empirical observation. Essentially, he draws upon his science and experience and geologic observation to determine if those earth processes required to form the specific kind of deposit did indeed transpire within the region. If so, he then uses endowment densities of known regions (analogues or control areas) that have similar geology to estimate the endowment of the region of interest, making adjustments to these densities to compensate for geological differences in the analogue and the region. 11.2. Institutional use of subjective estimates by experts The earliest efforts to estimate mineral resource stocks were objective and employed multivariate statistical models to relate quantified geologic variables to some mineral resource descriptor, e.g. mineral wealth [Harris (1966)l or number of deposits [Agterberg and Cabilio (1969)], or number of mineral occurrences [Harris and Pan (1990)l. While development of objective geostatistical models has continued off and on over the last thirty years, most institutional and governmental efforts to estimate mineral endowment or resource have been subjective in nature, as they have employed expert geologists to provide probabilities for numbers of deposits [Harris (1973), Reed et al. (1989)l or for other endowment descriptors, e.g., quantity of mineralized rocWunit area and average grade of mineralized rock [US DOE (1980)l. In part, the adoption of subjective methods by institutions reflects the overly simplistic geologic inference of the early multivariate geostatistical models. Although objective and mathematically rigorous, these models were very limited in the geologic information that they utilized. Recognition of this by geologists served to undermine credibility of the models and their estimates. The sampling schemes used to quantify complex geological information and the superficial utilization

1064

D.P Harris

of these measurements directly in linear models failed to match the information generated in the mind of the expert geologist by the interaction of science and experience with the visually sensed information from maps and field observation. Other important factors in the adoption of subjective methods by institutions are (1)the flexibility of the mind of the expert in utilizing different kinds of geodata and geodata that may be uneven in sample density across the region and (2) the savings in time achieved by using experts. Part of this savings arises from the requirement of multivariate models for quantified geologic information; in contrast, an expert geologist can use qualitative or quantitative information. 11.3. NURE - A massive national resource program NURE (National Uranium Resource Evaluation), the largest and most comprehensive of all 'resource appraisals' to date, initially was motivated by questions as to policy vis-a-vis development of the breeder reactor and the processing of plutonium. Political issues ranging from the general capability of meeting future energy requirements and of energy supply independence to security vis-a-vis proliferation of nuclear weapons were involved. The desirability of at least some policy options initially was perceived to be highly dependent upon the magnitude of the nation's resources of U308; consequently NURE was created to provide enlightenment of existing controversies. Besides the initiation of aerorad and hydrogeochemical surveys and the compilation of geological information by quadrangle, NURE geologists constructed genetic models for many types of uranium deposits and identified recognition criteria to aid field geologists in the delineation of map areas favorable for each type of deposit. Deposit models and tonnage grade relations also were developed by deposit type. The approach employed in NURE to estimate uranium endowment combined principles of geological analogy, as evidenced by the effort to describe thoroughly the geology and resource parameters on control areas, with subjective probability [Harris (1980, 1984), US DOE (1980)l. Important modifications over previous practice include the following: (1) estimation by the geologist of U3O8 endowment instead of resource or potential supply, (2) decomposition of endowment into its components A, F, T, G, and Po (see Figure 14), (3) elicitation of subjective probabilities on the components, and (4) the recombining through mathematical analysis of these components to give a probability distribution for E (U308endowment) by the following relationship [US DOE (1980))

where A is the size of a favorable area; F is the fraction of favorable area underlain by mineralization; T is the tonnage of mineralized material per square mile of


Prob Computer Analys~s

t

E=A.F.T.G

Fig. 14. Implicit methodology of US Department of Energy - NURE. [From Harris (1983b).]

favorable area; G is the average grade of mineralized material; and Po is the probability for at least one deposit having at least 10 tons of U3O8given a cut-off grade of 0.01% uranium. Subsequent to their geological investigations, geologists provided most likely plus 5th and 95th percentile estimates for each of A, F , T, and G. They also provided a single point estimate of Po. Distributions were fitted to A, F , T, and G, and these distributions and Po were combined appropriately to yield a probability distribution for uranium endowment (see Figure 14). Although the original design of the appraisal methodology, as shown in Figure 14, treated A as a random variable, as the methodology was applied, only the most likely estimate of A was employed.

C ~ I21: . Mineral Resoclrce Stocks and Information

1067

Potential supply of U3O8 was estimated by analyzing the cost of finding and producing the endowment. The results of the potential-supply analysis are presented in Figure 15; the right-most curve of case d is the probability distribution for E; the remaining curves are potential supply for forward costs of $30, $50, and $100/lb U308. 11.4. Heuristics, hedging, and bias in subjective estimation The pressing economic and policy issues stemming from the OPEC cartel were manifest in two resource appraisals of national scope: NURE for uranium [US DOE (1980)l and the oil resource appraisal resulting in USGS Circular 725 [Miller et al. (1975)l. Both of these appraisals employed (1) subjective geological analysis as a means to estimating the magnitude of undiscovered deposits, and (2) the description of quantitative estimates by subjective probabilities. Because of the urgency of the policy issues that were examined with regard to estimates of the quantity and quality of undiscovered deposits, methodologies were scrutinized more carefully than ever before. Initially, subjective probabilities of an expert were accepted as useful, first because of his expertise and second because of the seemingly reasonable assumption that man functions well as an intuitive statistician, meaning that the expert's perception of likelihood of an event corresponds generally to its relative frequency in nature. Moreover, Delphi methods had become accepted means for treating differences of opinions of experts, having taken for granted that convergence of opinions of members of the group to a single value provided a desirable and useful resolution of differing expert opinion. These perceptions were seriously challenged by the work of Tversky and Kahneman (1972, 1974) and Sachman (1974). Tversky and Kahneman (1972, 1974) identified some of the heuristics used by man to estimate an uncertain event: anchoring and adjustment, representativeness, and availability. These heuristics were found to lead to predictable biases. Psychometricians found that man generally behaves as though he knows far more than he actually does, tending to provide subjective probability distributions that are narrower than they should be by approximately 50% [Slovic (1972)l. This tendency results from the inability of man to image mentally the combinations that result in extreme values of the random variable; heuristics used to approximate actual calculations understate probabilities for events in the tails of the distribution when stochastic events are conjunctive. Sachman's (1974) investigation of traditional Delphi as a means of inquiry found that repeated cycles of estimate and statistical feedback violate blatantly the condition that estimates by individuals be independent in order for statistics such as mean and variance and for relative frequencies of estimates to be

1068

D.P Ham's

statistically meaningful. Moreover, he documented that convergence can be solely a psychological phenomenon and usually is not the result of exchange of factual information and logical deliberation. These findings led to (1) the total elimination of Delphi or the replacement of traditional Delphi by modified Delphi, and (2) the structuring and support of subjective probability estimation so as to improve the use by the expert of his science and available geodata and to minimize the effects of heuristic biases.

11.5. Purposefil hedging - motivational bias Experience with the elicitation of subjective probabilities for states of endowment descriptors, e.g. number of deposits, obtained primarily from NURE and preNURE uranium resource appraisals made by forerunners to the US Department of Energy (US Atomic Energy Agency and US Energy Development and Research Administration) revealed the purposeful discounting of endowment estimates by expert geologists for purely psychological reasons or for personal value judgements unrelated to geological bases for uranium endowment [Harris (1980, 1984a)l. Motivations for hedging include the perception that conservatism is a virtue and that it is better to be always pleasantly surprised than to be occasionally disappointed. Other motivations include the protection of previously established views of the expert, of his superior, or of the firm or institution.

11.6. The Arizona appraisal system - A n expert-like system 11.6.1. Design and estimates The desire (1) to mitigate heuristic bias, (2) to prevent purposeful hedging, (3) to support the geologist's estimation of uranium endowment, (4) to provide a track of the logic and data used in making an endowment estimate, and (5) to assure that endowment estimates by more than one geologist are made by the same logic, led to the construction of an appraisal system. This system consisted of two major components : (i) an expert-like system referred to as a computerized geological decision model that converts the geologist's observations into probabilities for process states and (ii) an endowment model that transforms probabilities for process states to a probability distribution for uranium endowment by first computing a probability distribution for number of deposits from the probabilities for process states and then combining mathematically the probability distribution for number of deposits with distributions for deposit tonnage and grade (the deposit models).

Ch. 21: Mineral Resource Stocks and Infomation

H Y -

1069

IMPLICIT2 probability

w/;::

ARIZONA SYSTEM

Fig. 16. Graphic comparison of estimates of initial U3O8endowment of the San Juan Basin: expected values and 90% confidence ranges. [From Harris and Carrigan (1980).]

For each of five expert geologists, the geoscience of uranium deposit formation was formalized as an inference net which served as the structure for a computerized geologic decision model, a submodel in an endowment appraisal system. Once the geologic model was calibrated on known test areas, the geologist (creator of the model) employed it to make endowment estimates of less well-known areas by answering questions posed by the model about the geology and states of relevant earth processes for each area. The endowment appraisal system then computed from these inputs a probability distribution for each evaluation area. The lower line of Figure 16, labeled SYSTEM, shows probability distributions for the uranium endowment of the entire San Juan Basin of New Mexico that resulted from the disaggregation of estimation and the formalization of geoscience. 11.6.2. An experiment to examine heuristic bias and purposeful hedging A tailor-made appraisal system for each geologic expert provided an excellent opportunity to test for heuristic bias and purposeful hedging in unconstrained and unstructured subjective estimation by expert geologists. Having already reviewed the geology of each appraisal region in depth in responding to questions posed by the system but not having viewed the endowment estimates computed by the system, the geologist was prepared to make subjective estimates simply by estimating fractiles of uranium. These estimates are represented by the line labeled Implicit 1. Implicit 2 estimates are Implicit 1 estimates subsequently modified by the geologist to conform as closely as possible to his intuitive feelings. The

NURE estimate is not strictly comparable to the other three, because it was not made by the five geologists involved in this experiment; it is presented here solely for comparison with the results of the experiment. Basically, this study found that use by geologists of formal and explicitly stated geoscience results in estimates of uranium endowment that are considerably greater that those made by NURE and by Implicit assessment. Howevel; this study also found that there exists much greater uncertainty about the magnitudes of the uranium endowment of this region than hadpreviously been expressed. This experiment verified the heuristic bias reported by psychometricians in that the Implicit distributions are approximately one-half as broad as the System distribution. In addition to this heuristic bias, the experiment revealed a pronounced hedge (motivational bias), exhibited by the shift to the left of expected values and percentile values of the Implicit distributions relative to the System distribution.

12. Concluding remarks The past two decades have brought considerable progress in the estimation and description of mineral stocks. This progress, like that in most research, identifies new questions and offers many challenges for future research. These exist at all levels, ranging from genetic geologic modeling of mineral deposit formation to the use of resource information in optimum policy selection; however, the following comments are restricted to only the few that are either central or critical to the overall study of and use of mineral stocks. A basic and critical task is the geologists' mental mapping from geology, which is three-dimensional, to an endowment descriptor, such as number of deposits or tonnage of mineralized rock. As this is the most difficult as well as most critical task in the geological estimation of endowment, it requires careful and thorough support by data and models relevant to the estimation task. In view of the psychometric properties of subjective estimates made by experts, as documented in the Arizona Appraisal System [Harris and Carrigan (1980, 1981), Harris (1984)], this critical task merits much greater and more specific support than it often receives. There are two levels to this support. One of them is providing the geologist with deposit models, which are probability or frequency models of deposit size and grade by deposit type. While these are useful in endowment estimation and subsequent economic analysis, they provide only marginal help to the geologist in translating three-dimensional geology to number of deposits or to volume of mineralized rock. For this task, deposit models need to be augmented by deposit density models, which describe number of deposits per unit area or volume of crustal rock. Construction of these models confronts the analyst with the exploration issue, meaning that the number of deposits observed is not the total number that occur, because the economics of exploration results in less


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than complete sampling. Thus, support of the geologist's estimation task requires the gathering and description of information on exploration activity as well as information on deposit density. Greater support may be provided by appropriate pre-processing of the analogue data to adjust for economic effects, such as size bias and economic truncation. The analysis and processing of mineral deposit density and exploration information to remove size-bias and truncation effects would be useful in two ways: First, it would lead to descriptions of deposit and density models of endowment, rather than discovered deposits, and this would assist the geologist in his estimation task; second, acquisition of data on deposit density and on exploration effort would also contribute to the design and estimation of improved exploration models, which in turn would improve the estimates of potential supply for a given endowment. Thus, exploration information and exploration modeling can contribute significantly to improved estimates of mineral stocks. Although most institutional estimates of mineral resources have been made by using expert's subjective probabilities, current and future research topics include the design and use of computer expert and artificial intelligence systems and the design and estimation of improved multivariate statistical models as substitutes for informal subjective estimation by experts. Recent examples include multivariate information synthesis and intrinsic sample theory [Harris and Pan (1990)], the use of 'weights of evidence' methods combined with GIs (Geographic Information Systems), image analysis, and expert systems to identify favorable areas for deposit types and overall favorability for deposit occurrence [Agterberg et al. (1990)l. The estimation of resource or potential supply relies heavily upon the availability of cost relations. Only rarely are the necessary data for estimating such relations readily available. Consequently, recent efforts of the US Bureau of Mines [Camm (1989)l to provide simplified cost models that show capital and operating costs for infrastructure, mining, and milling as functions of the major cost determinants (deposit size, grade, and depth) are especially useful. These models can be used directly as elements of a Monte Carlo discounted cash flow subroutine, or they can be used to generate unit cost equations or filters. Most of the preceding comments dealt with mineral stocks per se and their estimation. While potential supply is a useful stock, for the evaluation of some policy options dynamic supply, which is a future flow, would constitute a more comprehensive basis. As dynamic supply resolves resource depletion and future discoveries in response to future economic circumstances, it is in concept more useful than potential supply in the analysis of some policy options. But, dynamic supply systems are much more demanding of economic linkages than is potential supply, for the system must define not only production decisions for existing mines, given projected demand functions, but investment in exploration and exploitation across time. As efforts to model dynamic supply from mineral stocks have been meager so far, there is a great amount of research and development required on

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the economic and systems relations of dynamic supply models if they are to be useful supports for the economic analysis of policy options. References Agterberg, El?, 1978, "Regional Mineral Appraisal: An Analytical Approach", paper presented at the Conference on Techniques of Broad Mineral Appraisal, College of Mineral and Energy Resources (West Virginia University, Morgantown, WV). Agterberg, F.P., and F? Cabilio, 1969, "Two-stage Least Squares Model for the Relationship Between Mapable Geological Variables", Journal of Mathematical Geology 1 no. 2, 137-153. Agterberg, EP., and S.R. Divi, 1978, "A Statistical Model for the Distribution of Copper, Lead, and Zinc in the Canadian Appalachian Region, Economic Geology 73,230-245. Agterberg, F.P., G.E Bonham-Carter and D.F. Wright, 1990, "Statistical Pattern Integration for Mineral Exploration: Computer Applications in Resource Exploration: Prediction and Assessment for Petroleum, Metals and Nonmetals", in: G. Gaal and D.F. Merriam (eds.), Computer and Geology Series, Vol. 6 (Pergamon Press, Riverside, NJ). Ahrens, L.H., 1953, "A Fundamental Law of Geochemistry", Nature 172, (4390), 1148. Ahrens, L.H., 1954, "The Lognormal Distribution of the Elements", Geochimica Cosmochimica Acta 11, 205-212. Arps, J.J., and T.G. Roberts, 1958, "Economics of Drilling for Cretaceous Oil on East Flank of Denver - Julesburg Basin", American Association of Petroleum Geologists Bulletin 42 no. 11,2549-2566. Barnett, H.J., 1979, "Scarcity and Growth Revisited", in: V.K. Smith (ed.), Scarcity and Growth Reconsidered (Johns Hopkins University Press, Baltimore, MD) pp. 163-217. Barnett, H.J., and C. Morse, 1963, Scarcity and Growth (Johns Hopkins University Press, Baltimore, MD, for: Resources for the Future). Barouch, E., and G. Kaufman, 1976, Oil and Gas Discovery Modelled as Sampling Proportional to Size, Sloan School of Management Working Paper 888-76 (MIT, Cambridge, MA) 64pp. Barry, G.S., and A.J. Freyman, 1970, "Mineral endowment of the Canadian Northwest", Mineral Information Bulletin, MR 105 (Mineral Resources Branch, Dept. of Energy, Mines and Resources Canada, Ottawa, Canada) pp. 57-95. Bennett, H.J., L. Moore, L.E. Welborn and J.E. Toland, 1973,An Economic Appraisal of the Supply of Copperfrom Primaly Domestic Sources, Information Circular 8598 (US Bureau of Mines, Washington, DC). Brinck, J.W., 1967, "Note on the Distribution and Predictability of Mineral Resources", Euratom Bulletin 6,4. Brinck, J.W., 1971, "MIMIC, The Prediction of Mineral Resources and Long-Term Price Trends in the Non-Ferrous Metal Mining Industry is No Longer Utopian", Eurospectra 10,4656. Brinck, J.W., 1972, "Prediction of Mineral Resources and Long-Term Price Trends in the Nonferrous Metal Mining Industry", in: Twentyfourth Session International Geological Congress, Montreal, 24th International Geological Congress (Ottawa, Canada) Section 4 -Mineral Deposits, pp. 3-15. Brinck, J.W., 1974, "The Geochemical Distribution of Uranium as a Primary Criterion for the Formation of Ore Deposits", Symposium on the Formation of Uranium Deposits (International Atomic Energy Agency, Vienna). Camm, T., 1989, "Mineand Mill Models for the Juneau Mining District, Open File Report, Western Field Operations Center (US Bureau of Mines, Spokane, WA) p. 33. Cargill, S.M., D.H. Root and E.H. Bailey, 1980, "Resource Estimation from Historical Data: Mercury, a Test Case, Journal of the InternationalAssociation of Mathematical Geology 12 no. 5,489-522.


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Cathro, R.J., 1983, "Invited discussions" (Predictive Metallogeny Symposium), Geoscience Canada 10 no. 2, 100. Charles River Associates, Inc., 1978, "The Economics and Geology of Mineral Supply: An Integrated Framework for Long-Run Policy Analysis, CRA Report No. 327. Chavez-Martinez, M.L., 1983, "A Potential Supply System for Uranium Based Upon a CnistalAbundance Model, PhD Dissertation (University of Arizona, Tucson, AZ). Cox, D.P., and D.A. Singer, eds, 1986, Mineral Deposit Models, Bulletin 1693 (Government Printing Office, Washington, DC). Dasgupta, P.S., and G.M. Heal, 1979, Economic Theory and Exhaustible Resources (Cambridge University Press, Cambridge) 501pp. Deffeyes, K.S., and I.D. MacGregor, 1980, "World Uranium Resources", Scientific American 242 no. 1, 66-76. Drew, L.J., J.H. Schuenemeyer and W.J. Bawiec, 1982, Estimation of the Future Rates of Oil and Gas Discoveries in the Western GulfofMaico, US Geological Survey Professional Paper 1252 (Government Printing Office, Washington, DC). Drew, L.J., E.D. Attanasi and J.H. Schuenemeyer, 1988, "Observed Oil and Gas Field Size Distributions: A Consequence of the Discovery Process and the Price of Oil and Gas", Mathematical Geology 20 no. 8,939-954. Drew, M.W., 1977, "U.S. Uranium Deposits: a Geostatistical Model", Resources Policy 3 no. 1, 60-70. Eberlein, G.D., and W.D. Menzie, 1978, Maps and Tables Describing Areas of Metalliferous Mineral Resource Potential of Central Alaska, US Geological Survey Open File Report 78-1-D (Menlo Park, CA). Finch, W.I., H.D. Granger, R. Lupe and R.B. McCammon, 1980, Genetic-Geologic Models-A Systematic Approach to Evaluate Geologic Favorability for Undiscovered Uranium Resource, Part I, Research on Uranium Resource Models, a program report, US Geological Survey Open-File Report 80-2018A, 5 5 ~ ~ . Forman, D.J., and A.L. Hinde, 1986, "Examination of the Creaming Method of Assessment Applied to the Gippsland Basin, Offshore Australia", in: D.D. Rice (ed.), Oil and Gas Assessment: Methods and Applications, American Association of Petroleum Geologists Studies in Geology, Vol. 21, pp. 101-110. Gray, L.C., 1914, "Rent Under the Assumption of Exhaustibility", QuarterlyJournalofEconomics (May). Reprinted in: M. Gaffney (ed.), Extractive Resources and Tawation (The University of Wisconsin Press, Madison, WI, 1967). Grybeck, D., and J.H. DeYoung Jr, 1978, Map and Tables Describing Mineral Resource Potential of the Brooks Range, Alaska, US Geological Survey Open File Report 78-1-B (Menlo Park, CA). Hald, A., 1949, "Maximum Likelihood Estimators of the Parameters of a Normal Distribution Which is Truncated at a Known Point", SkandinaviskAktuarietidsknlft 32, 119-134. Harris, D.P., 1966, "A Probability Model for Mineral Wealth", Transaction of SME, 199-216. Harris, D.P., 1968, "Alaska's Base and Precious Metals' Resources: a Probabilistic Regional Appraisal", Mineral Resources of Northern Alaska, MIRL Report No. 16 (University of Alaska College, Alaska) p. 189-224. Harris, D.P., 1973, "A Subjective Probability Appraisal of Metal Endowment of Northern Sonora, Mexico", Economic Geologv 68,222-242. Harris, D.P., 1978, "Undiscovered Uranium Resources and Potential Supply", in: Workshop on Concepts of Uranium Resources and Producibility (National Research Council, National Academy of Sciences, Washington, DC) pp. 51-81. Harris, D.P., 1980, Critique of Resource Estimation Methodology, Report prepared for US Department of Energy under Subcontract No. 80-469-S (Grand Junction Office, CO).

Harris, D.P., 1983a, Mineral Resources Appraisal and Policy - Controversies. Issues, and the Future, Prepared for Conference on the Role of Earth Sciences Information in the Mineral Policymaking Process (Carnegie Institution of Washington). Harris, D.P., 1983b, "An Investigation of the Estimation Process of Predictive Metallogeny" (Predictive Metallogeny Symposium), Geoscience Canada 10 no. 2,82-96. Harris, D.P., 1984a,Mineral Resources Appraisal - Mineral Endowment, Resources, and Potential Supply: Concepts, Methods, and Cases (Oxford University Press, Oxford). Harris, D.P., 1984b, "Mineral Resources Appraisal and Policy - Controversies, Issues, and the Future", Resources Policy 10 no. 2,81-100. Harris, D.P., 1987, "Mineral Exploration and Production Costs and Technology - Past, Present, and Future", in: D.J. McLaren and B.J. Skinner (eds.), Resources and World Development, Dahlem Workshop Reports: Physical, Chemical, and Earth Sciences Research Report 6, New York (Wiley, New York) pp. 423442. Harris, D.P., 1988, "Crystal Abundance Modeling of Mineral Resources: Recent Investigations and Preliminary Results", in: D.E Merriam (ed.), Current Trends in Geomathematics (Plenum Press, New York) pp. 207-252. Harris, D.P., 1990,Mineral Exploration Decisions: Guide to Economic Analysis and Modeling (Wiley, New York) p. 425. Harris, D.P., and F.P. Agterberg, 1981, "The Appraisal of Mineral Resources", in: 75th Anniversary Volume, Economic Geology, pp. 897-938. Harris, D.P., and F.J. Carrigan, 1980, A Probabilistic Endowment Appraisal System Based Upon the Formalization of Geological Decisions - Final Report: Demonstration and Comparative Analysis of Estimatesand Methods, Open File Report No. GJBX-383(81), prepared for US Department of Energy (Grand Junction Office, CO). Harris, D.P., and M.L. Chavez, 1981, Crustal Abundance and a Potential Supply System. Part II, Systems and Economics for the Estimation of Uranium Potential Supply, Report prepared for US Department of Energy (Grand Junction Office, CO, Subcontract No. 78-238-E) pp. 385-506. Harris, D.P., and M.L. Chavez, 1984, "Modelling Dynamic Supply of Uranium - An Experiment in the Integration of Economics, Geology, and Engineering", in: 18th International Symposium on Application of Computers and Mathematics in the Mineral Industries (Institution of Mining and Metallurgy, London) pp. 817-892. Harris, D.P., and D.E. Euresty, 1973, "The Impact of Transportation Network upon the Potential Supply of Base and Precious Metals from Sonora, Mexico", in: Proceedings of the 10th International Symposium on Application of Computer Methods in the Mineral Industry (The South African Institute of Mining and Metallurgy, Johannesburg), pp. 99-108. Harris, D.P., and S.R. Ortiz-Vertiz, 1981,Potential Supply Systems based upon the Simulation of Sequential Exploration and Economic Decisions - Systems Designed for the Analysis of NURE Endowment. Part I, Systems and Economics for the Estimation of Uranium Potential Supply, Report prepared for US Department of Energy (Grand Junction Office, CO, Subcontract No. 78-238-E) pp. 9-384. Harris, D.P., and G. Pan, 1990, "Intrinsic Sample Methodology, in: G. Gaal and D.F. Merriam (eds.), Computer Applications in Resource Exploration: Prediction and Assessment for Petroleum, Metals, and Nonmetals, Computers and Geology Series, Vol. 6 (Pergamon Press, Riverside, NJ). Harris, D.P., and B.J. Skinner, 1982, "The Assessment of Long-Term Supplies of Minerals", in: V.K. Smith and J.V. Krutilla (eds.), Explorations in Natural Resource Economics (The Johns Hopkins University Press, Baltimore, MD, for: Resources for the Future) pp. 247-326. Harris, D.P., A.J. Freyman and G.S. Barry, 1971, "A Mineral Resource Appraisal of the Canadian Northwest Using Subjective Probabilities and Geological Opinion", in: Proceedings of the 9th International Symposium on Techniquesfor Decision-Making in the Mineral Industry, Special Volume 12 (Canadian Institute of Mining and Metallurgy, Montreal) pp. 100-116.


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Herfindahl, O.C., 1967, "Depletion and Economic Theory, in: M. Gaffney (ed.), Extractive Resources and Tavntion (University of Wisconsin Press, Madison, WI). Hetland, D.L., 1979, "Estimation of Undiscovered Uranium Resources by U.S. ERDA", in: Evaluation of Uranium Resources, Proceedings of an Advisory Group Meeting (International Atomic Energy Agency, Vienna) pp. 231-250. Hotelling, H., 1931, "The Economics of Exhaustible Resources", The Journal of Political Economy 39 (April) 137-175. Hubbert, M.K., 1969, "Energy Resources", in: Resources and Man (A study and recommendations by the Committee on Resources and Man, National Academy of Sciences National Research Council) (Freeman, San Francisco, for: National Academy of Sciences) ch. 8, pp. 157-242. Hudson, T., and J.H. DeYoung Jr, 1978, Map and Tables Describing Areas of Mineral Resource Potential, Seward Peninsula, Alaska, US Geological Survey Open File Report 7&1-C (Menlo Park, CA). Klemme, H.D., 1977, "World Oil and Gas Reserves from Giant Fields and Petroleum Basins (Provinces)", in: R.F. Meyer (ed.), The Future Supply of Nature-Made Petroleum and Gas (Pergamon Press, New York) pp. 217-270. Lieberman, M.A., 1976, "United States Uranium Resources - An Analysis of Historical Data", Science 192 no. 4238,431436. Long, K.P., 1988, "Estimatingthe Numberand Sizes of UndiscoveredOiland Gas Pools, unpublished Ph.D. dissertation (Department of Mining & Geological Engineering, University of Arizona, Tucson, AZ) 160pp. MacKevett Jr, E.M., D.A. Singer and C.D. Holloway, 1978, Map and Tables Describing Metalliferous Mineral Resource Potential of Southern Alaska, US Geology Survey Open File Report 78-1-E (Menlo Park, CA). Markowitz, H.M., 1957, Portfolio Selection: Efficient Diversijication of Investments (Wiley, New York). McCammon, R.B., J.M. Botbol, R. Sinding-Larsen and R.W. Rowen, 1983, "Characteristic Analysis 1981: Final Program and a Possible Discovery", Mathematical Geology 15,5943. McLaren, D.J., and B.J. Skinner, 1987, Resources and World Development, Dahlem Workshop Reports: Physical, Chemical, and Earth Science Report 6 (Wiley, New York) p. 940. Miller, B.M., H.L. Thomsen, G.L. Dolton, A.B. Coury, T.A. Hendricks, F.E. Lennartz, R.B. Powers, E.G. Sable and K.L. Varnes, 1975, Geological Estimates of Undiscovered Recoverable Oil and Gas Resources in the United States, US Geology Survey Circular 725. Paley, W.S., 1952, "Resourcesfor Freedom, A Report to the president by the President's Materials Policy Commission, W.S. Paley, Chairman. Patton Jr, W.W., 1978, Maps and Table Describing Areas of Interest for Oil and Gas in Central Alaska, US Geology Survey Open File Report 78-1-F (Menlo Park, CA). Peterson, G., R. Davidoff, D. Bleiwas and R. Fantel, 1981, "Alumina Availability - Domestic: A Minerals Availability System Appraisal, NTIS PB82-135468 (US Bureau of Mines, Washington, DC). Phillips, W.G.B., and D.P. Edwards, 1976, "Metal Prices as a Function of Ore Grade", Resources Policy, 167-178. Powers, T.A., 1983, "A Computer Model and Methodology for the Economic Appraisal of Regional Petroleum and Natural Gas Exploration Projects in Frontier Areas", Papers on Project Analysis No. 21 (Inter-American Development Bank, Washington, DC). Reed, B.L., W.D. Menzie, M. McDermott, D.H. Root, W. Scott and L.J. Drew, 1989, "Undiscovered Lode Tin Resources of the Seward Peninsula, Alaska", Economy Geology 84,1936-1947. Riva Jr, J.P., 1983, Worldwide Petroleum Resources and Reserves (Westview Press, Boulder, CO). Roberts, F., and I. Torrens, 1974, "Analysis of the Life Cycle of Non-Ferrous Minerals", Resources Policy 1 no. 1,14-28. Rona, PA., 1983, "Potential Mineral and Energy Resources at Submerged Plate Boundaries", Natural Resources Forum 7 no. 4,329-338.

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Sackman, H., 1974,DelphiAssessment: Expert Opinion,Forecasting, and Group Process, R-1283-PR (The Rand Corporation, Santa Monica, CA). Schmidt, R.A., 1979, Coal In America: An Encyclopedia of Reserves, Production and Use (McGraw-Hill, New York). Singer, D.A., 1977, "Long-term Adequacy of Metal Resources", Resources Policy 3 (June) pp. 127-133. Singer, D.A., D.P. Cox and L.J. Drew, 1975, Grade and Tonnage Relationships Among Copper Deposits, US Geology Survey Professional Paper 907-A, p. Al-11. Skinner, B.J., 1987, "Geochemically Scarce Metals", in: D.J. McLaren and B.J. Skinner (eds.), Resources and World Development, Dahlem Workshop Reports: Physical, Chemical, and Earth Science Report 6 (Wiley, New York) pp. 305-326. Slovic, P., 1972, "From Shakespeare to Simon: Speculations - and Some Evidence -about Man's Ability to Process Information", Oregon Research Institute Monograph 12 no. 12 (April). Smith, V.K., and J.V. Krutilla, 1979, Explorations in Natural Resource Economics (Johns Hopkins University Press, Baltimore, MD, for: Resources for the Future) 352pp. Tilton, J.E., and B.J. Skinner, 1987, "The Meaning of Resources", in: D.J. McLaren and B.J. Skinner (eds.), Resources and World Development, Dahlem Workshop Reports: Physical, Chemical, and Earth Sciences Research Report 6 (Wiley, New York) pp. 13-27. Tversky, A., and D. Kahneman, 1972, "Anchoring and Calibration in the Assessment of Uncertain Quantities", Oregon Research Institute Research Bulletin 12 no. 5. Tversky, A., and D. Kahneman, 1974, "Judgment under Uncertainty: Heuristics and Biases", Science 185 no. 4157,1124-1131. Uri, N.D., 1980, "Crude Oil Resource Appraisal in the United States", The Energy Journal 1 no. 3, pp. 65-74. US Bureau of Mines, 1978, "Minerals Availability System Deposit Information Manual (US Bureau of Mines) unpublished. US Department of Energy, 1978, "Statistical Data of the Uranium Industry, CJO-lOO(78) (Grand Junction Office, CO) p. 8. US Department of Energy, 1980, "An Assessment Report on Uranium in the Unites States of America, Report No. GJO-lll(80) (Grand Junction Office, CO). US Geological Survey, 1980, Future Supply of Oil and Gas from the Permian Basin of West Taus and Southeastern New Mexico, Circular 828 (Government Printing Office, Washington, DC). Vogely, W.A., 1983, "Estimation of Potential Mineral Reserves, and Public Policy", Earth and mineral sciences 52 no. 2. Williams, R., 1982, Uranium Production Capability - Concepts and Procedures, A Seminar Presentation to Uranium Resource Appraisal Group, Energy, Mines and Resources Canada (Ottawa, Canada). Zimmerman, M.B., 1981, The US. Coal Industry: The Economics of Public Choice (MIT Press, Cambridge, MA). Zwartendyk, J., 1982, "Monitoring and Assessing the Mineral Supply Process from Mineral Policy Formulation: The Role of Scientific and Technical Knowledge", Proceedings of the Tenth CRS Policy Discussion Seminar (Centre for Resource Studies, Kingston, Ontario, Canada).

Chapter 22

STRATEGIES FOR MODELING EXHAUSTIBLE RESOURCE SUPPLY DENNIS EPPLE Graduate School of Industrial Administration, Camegie Mellon University, Pittsburgh, PA 15213-3890, USA JOHN LONDREGAN Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, NJ 08544, USA

1. Introduction

The feature that distinguishes markets for exhaustible resources from markets for other resources is that a nonrenewable stock is being discovered, produced, traded, and consumed. Hence, the characterization of this stock or resource base and the factors determining the rate and extent of exploration and exploitation are fundamental to modeling exhaustible resource markets. Our purpose in this chapter is to present alternative strategies that may be employed in providing such a characterization. Thus, rather than cataloging what is known about the supply of various exhaustible resources, we focus on practical methods for modeling the supply of exhaustible resources. Other chapters in this volume address exploration for and extraction of exhaustible resources at a theoretical level. Accordingly, we focus on assessing the extent to which theory has been used and found to be a satisfactory foundation for modeling resource supply1.As this focus on applied modeling of the supply of depletable resources suggests, we do not discuss the preferences that impel demand for these resources nor do we consider research concerned with characterizing intermediate production or the potential for substitution between depletable and renewable resources. We discuss issues that arise in estimation of cost functions for exhaustible resources in Section 2. In Section 3 we discuss computational equilibrium models. We then turn to econometric models of exhaustible resource supply in Section 4.

'

For an earlier evaluation touching on these issues, readers may also wish to refer to Bohi and Toman (1984). Handbook of Natural Resource and Energy Economics, vol. III, edited by A. K Kneese and J.L. Sweeney O 1993 Elsevier Science Publishers B. K All rights reserved

D. Epple and J. Londregan

2. Cost functions for exhaustible resources

The foundation of most models of supply is a characterization of the production technology, either directly, by way of a production function, or indirectly, in the form of a cost function. Most models of energy supply take the indirect route, employing a cost function that embodies the technological and geological constraints on suppliers. In competitive markets for renewable resources, cost functions embody the empirically recoverable structure of the production technology. However, cost functions for exhaustible resources are alloyed with some additional implicit assumptions about the production technology. To clarify the issues that are special to exhaustible resources, this section begins by relating cost functions for exhaustible resources to conventional cost functions. Exhaustible resource supply consists of two interlocking processes: exploration for new reserves, and the extraction of known reserves. In some modeling situations, it is expedient to focus on only one component of this activity, holding the rest in the background. For example, with price-taking producers, supply from a known deposit can be modeled without regard to potential new discoveries. However, a model of exploration requires a characterization of the exploitation of deposits that may be discovered. Cost functions are accordingly tailored to the scope of the analysis: some model the costs of extraction of a known and non-renewable stock, others focus on exploration, while still others are 'vertically integrated', modeling exploration and extraction jointly. Models also vary in their degree of 'horizontal integration': some consider behavior at the reservoir level, while others aggregate across entire geological regions. Models that are appropriate for one level of aggregation (vertical or horizontal) can be misleading if applied to other levels. The model of extraction from a single resource deposit of known size cannot capture aggregate supply when exploration opportunities have not been exhausted. Likewise, a functional form that is appropriate to the cost of extracting a single resource deposit may not be appropriate for an entire geological region. Conventional cost functions are of the general form c = c*(q, w), where q is the output quantity and w is a vector of exogenous prices of all productive inputs. Input prices are unaffected by action on the part of the producer, and are typically common to all producers in a given market. This framework must be modified when we consider exhaustible resources. To begin with, let us consider the exploitation of known reserves in a discrete time setting. As production proceeds, characteristics of the deposit (e.g. pressure in an oil reservoir) change. As a thought experiment, imagine that instead of being intrinsic to the resource deposit, these characteristics were purchased on a frictionless competitive market: so many dollars per foot of width of a coal seam, so much per pound per square inch of pressure in an oil reservoir. The producer would then treat these reservoir characteristics as variable inputs, along with capital

Ch. 22: Strategies for Modeling Exhaustible Resource Supply

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equipment and labor. Conditional on having decided how much of the reserve to extract during the current time period, the producer's cost minimization problem is of the form min wix, x, 31

+ sizt

subject to f (x,, zt) 2 q,,

(C1)

where q, is the desired output quantity,~,is the input of factors that are not peculiar to the reserve being exploited, such as capital and labor, z, is the vector of reserve characteristics purchased by the producer, and wt and st are the corresponding vectors of input prices. The output corresponding to inputs of x, and zt is f (xt,zt). The solution to this problem is summarized by a conventional cost function of the form

Markets for reserve-specific characteristics do not actually exist. Instead, the producer must take the features of a deposit as given. This means that once the desired level of current output has been selected, the producer's cost minimization problem becomes: min wix, Xf

subject to f (x,, zt) 2 qt.

(C2)

We may write the solution to this problem as a function of w,, zt and qt, which yields a sort of hybrid of a cost function, with respect to the variable inputs, and a production function, with respect to characteristics of the reserve. Let us denote this solution by

This hybrid 'cost function', which we shall refer to as the reduced-form costfinction, is perhaps the most popular specification of the cost structure for a resource extractor. Notice that the solution to eq. (C2) implies that the vector of shadow values for reserve characteristics, z,, is given by ~*(qt,xt,zt)= XVZf (x,, zt), where X is the Lagrange multiplier for the output constraint, and will in general depend on qt, xt and z,. In a discrete-time framework, z, is fixed at the beginning of period t , and so is invariant to the rate of exploitation. Thus, if s*(qt,x,, z,) is

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D.Epple and J. Londregan

invariant to qt andx,, then the solution to eq. (C2) will be identical to the solution to eq. (C1) with s = s*(qt,xt,zt) = sO(zt),so that

In this case, the firm behaves as if it were minimizing a conventional cost function, and could purchase reserve characteristics at fixed prices given by sO(z,). The conditions under which cost functions for non-renewable resources mimic conventional cost functions are very special, and often fail to apply. If the production function exhibits constant returns to scale, and additive separability between reserve characteristics and inputs that are purchased or rented directly on the market, then the resource extraction technology can be characterized by a cost function that employs the 'shadow value' of reserve characteristics as their price. This approach is taken by several authors, notably Halvorsen and Smith (1984). In many settings, marginal cost depends on the scale of production, and variable inputs interact with reserve characteristics (e.g., water can be employed to augment natural pressure in an oil reservoir). In these cases the shadow value of reserve characteristics will depend on the current rate and mode of extraction, and hence cannot be taken as a parametric 'price' for these inputs for the purpose of cost minimization. The effect of reserve characteristics is the fundamental difference between cost functions for non-renewable resources and conventional cost functions. 3. Cost functions for non-renewable resources: specification issues

To account for approximation error, and the influence of unobserved factors, the reduced-form cost function is often augmented with the addition of a stochastic vector E :

The most popular versions of the reduced-form cost function assume that all of the shadow prices are functions of one observable. A common choice for this observable is cumulative extraction from the deposit:

For example, we might observe this dependence on past extraction because the highest-quality reserves are extracted first, and then, as extraction continues, 2

That is, ifs4$(qr,xr,zr) = 0 ands:(qt,xr,zr) =

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Ch. 22: Strategiesfor Modeling Exhaustible Resource Supply

progressively lower-quality reserves are brought into use. Here high quality corresponds to low extraction cost per unit of the resource. Formally, these cost functions correspond to

C(q, Z) = m i n x {xi)

Ci

.xi subject to xi

i=l

( Ri

Vi,

and

C xi = q, i=l

where xi is the quantity of reserves currently extracted from the ith reserve stock, ci is the unit extraction cost from the ith reserve, Ri is the total amount of remaining reserves in reserve stock i, and q is total extraction: q = xi. Cost functions of this form imply that the cost per unit of the remaining reserves rises as extraction progresses. Nordhaus (1973a) provides a clear exposition of these issues. Alternatively, the dependence of costs on cumulative extraction may be a consequence of the physical characteristics of a deposit. For example, as a petroleum reservoir is exploited, natural pressure drops, increasing the costs of further extraction. This is not a result of a conscious decision by producers to exploit cheaper reserves first, but an unavoidable entailment of the physical structure of the reservoir.

c;=,

3.1. Cumulative cost functions

An important family of cost functions, often referred to as cumulative cost functions, treat cumulative extraction as a sufficient statistic for the shadow cost of extraction. This means that marginal cost depends only on cumulative production, regardless of the time path over which that cumulative output was realized. Using Nordhaus's (1973a) interpretation, the objective in estimating a cumulative cost function is to provide an enumeration of the available deposits of a resource, to determine their size, and to array them in order of increasing marginal costs of exploitation. The dependence of costs on cumulative extraction may be direct, and independent of whether producers exploit deposits in inverse order of costs. For example, by lowering the pressure of oil occurring in a natural petroleum reservoir, cumulative extraction raises the cost of further exploitation [Livernois and Uhler (1987)l. Examples of creative strategies carefully tailored to the resources being studied are provided by Kaufman and his collaborators [Barouch and Kaufman 1976a, 1976b), Kaufman, Runggaldier and Livne (1975)l and by Zimmerman (1977). These are examples of a family of models often referred to as 'process analysis' models in which the cost function is developed from a characterization of the process of exploration for or exploitation of the resource. We discuss illustrative examples here.

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Kaufman constructs a cumulative exploration cost function for new reserve discoveries. His approach is based on the assumption that the distribution of oil reservoirs in a geologically homogeneous oil-bearing region can be characterized by an appropriate choice of probability distribution, e.g., the lognormal. To this is added the assumption that the discovery process can be characterized by random sampling, without replacement, with probability of discovery of a reservoir being proportional to size. Given a history of drilling and discovery in a region, one can use these assumptions to estimate the parameters of the distribution of deposits. This coupled with information on drilling costs in the region provides the information required to construct a schedule of expected cumulative discoveries versus expected costs 3. Smith (1980) suggests modifying Kaufman's approach by assuming the size distribution of deposits to be discrete. By grouping past discoveries into size categories and employing the assumption that probability of discovery is proportional to size, the number of reservoirs in the original deposition in each size class can be estimated by maximum likelihood. Smith applies this approach to estimate the distribution of deposits in the North Sea. He uses the resulting model to estimate ultimate recovery and to estimate a confidence interval for ultimate recovery. Smith's reformulation of the approach by Kaufman yields an attractive and comparatively straightforward method for estimating a probabilistic model of discoveries in an oil-bearing region. Zimmerman (1977) estimates cumulative extraction cost curves for deep coal (as distinct from strip-mined coal) in the USA. He observes that the key factors affecting extraction cost are seam thickness and depth of the seam. Using available data, he characterizes the distribution of deposits by seam thickness and depth. Using this distribution and information on the costs of production as a function of thickness and depth, he constructs a cumulative cost curve for deep coal deposits in the USA. These studies elucidate the importance of knowledge about the geology of resource deposition and the technology of extraction as a foundation for modeling cumulative cost functions. Interested readers may wish to refer to the results assembled by Nordhaus (1979) and Salant, Sangvhi and Wagner (1979) for summary cost estimates and references for other resources.

Another use of this approach is to estimate the size of the undiscovered resource base. This involves calculating the quantity discovered in the limit as the number of wells drilled becomes large. Smith (1980) is an example of this method of resource-base estimation. For other approaches to resource-baseestimation, see Dolton et al. (1981).


3.2. Issues in spec$cation Cumulative cost function are sometimes expressed in terms of the size of remaining reserves [Solow and Wan (1976), Pindyck (1978a)l rather than cumulative output. Since remaining reserves are simply the total originally in the deposit net of cumulative extraction, this formulation is equivalent to that presented above. To illustrate the equivalence between cumulative and reserve-based cost functions, let R denote remaining reserves, Q indicate cumulative extraction, and q the current rate of extraction. We specify the reserve-based cost function c'(q, R) and the cumulative cost function c2(q,Q). If I denotes initial reserves, then remaining reserves and cumulative extraction satisfy the identityR Q = I, so that the two cost functions are related by the identity cl(q, I - Q) = c2(q, Q). The above equivalence applies when I is the initial reserve stock, both known and unknown. If instead, one used the sum of cumulative production plus known reserves in place of I , the equivalence would not hold since known reserves are continually changing as a result of exploration. Indeed, such a specification would imply that the cost of extracting previously discovered deposits would change as a function of the number of new deposits discovered - a characterization that would rarely if ever be appropriate. Many analysts often impose further restrictions on cumulative cost functions. For example, many theorists work with an 'elbow-shaped' specification of extraction costs, in which extraction costs are constant up to exhaustion, at which point they become (implicitly) infinite. Hotelling's (1931) seminal analysis of resource supply used the specification

+

This makes marginal extraction costs constant (at c) up to exhaustion. More recently Farzin (1984) and Gamponia and Mendelsohn (1985) have used models in which cumulative extraction does not affect marginal extraction costs until the resource is exhausted. Another, somewhat more general formulation is of the form

where z may be a scalar measure of cumulative extraction, as in Weitzman (1976), or the value of remaining reserves, as in Solow and Wan (1976) and Pindyck (1978a). Both the cost functions of the form c(z) . q and the 'elbow-shaped' cost function devised by Hotelling impose constant returns to scale in current extraction. As we will see in the following section, the constant-returns feature of these models implies 'all-or-nothing' supply responses in contrast with most observed behavior.

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3.3. More flexibleformulations of the cost finction To avoid imposing constant returns to scale in the extraction technology some analysts [e.g., Burness (1976), Eswaran, Lewis and Heaps (1983)l have adopted the specification cr(q, 2) = c(q) (up to exhaustion of the resource). This cost function resembles that used by Hotelling in that depletion has an all-or-nothing effect on extraction costs. At a constant rate of extraction the last unit of the resource is as inexpensive to extract as the first. Recent analyses have often incorporated more sophisticated reduced-form cost functions [Levhari and Liviatan (1977), Halvorsen and Smith (1984), Heaps (1985), Hansen, Epple and Roberds (1985)l. These cost functions allow for non-linearities in both the depletion effect, and in the rate of extraction. For example, Epple, Hansen and Roberds use a quadratic cost function of the form4

where Q denotes cumulative extraction, while q is the current extraction rate. The 0 parameter measures economies of scale in current extraction, with 0 > 0 indicating decreasing returns to scale, while 0 < 0 corresponds to increasing returns. Cumulative cost functions, reduced-form cost functions, and cost functions that directly model the dependence of extraction costs on shadow values are equally practical alternatives for the purposes of theory. However, data available often lead empirical modelers to adopt cumulative cost functions, or linear-quadratic specifications of costs, as the only practical estimation strategy. An interesting exception to this rule is by Livernois (1987), who used data from 80 reservoirs in Alberta to estimate a cost function that depends on reserve characteristics, such as the level of water saturation, the thickness of the reserve deposit, and well-head pressure: c*(q, w,s).Pressure in many of the reservoirs in his data set was artificially maintained by water injection. For this set of reservoirs his model identified the shadow value of pressure directly. Livernois found that the marginal value of pressure rose as pressure fell. Holding pressure constant, the null hypothesis of constant returns to scale in the extraction technology could not be rejected. This suggests that for petroleum, costs depend on cumulative extraction because of its effect on pressure, and that non-linear extraction costs in discrete models may be a consequence of time aggregation. To illustrate this, consider the following hypothetical example: suppose that initial well-head pressure for an oil deposit was 1000psi. At a rapid rate of extraction, In this exposition, we reserve the appellation 'cumulative cost function' for functions with the property that the marginal cost depends on cumulative extraction and nothing else. Because the EppleHansen-Roberds function allows for dependence of marginal cost on cumulative extraction and the rate of extraction, we do not call it a cumulative cost function.


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pressure at the end of the month may have dropped to 950 psi, while at slower rates the pressure may fall to only 980 psi. In the first case, average well-head pressure for the month would be 975 psi, indicating higher costs than in the second, in which the average is 990 psi, even though costs only depend on pressure, and not directly on the instantaneous rate of extraction. 3.4. Aggregation While Livernois's findings are of some interest, the detailed reservoir-specific engineering data needed to implement a disaggregated model are often unavailable. In such circumstances it is often sensible to work with reduced-form cost functions. Sometimes even reservoir-specific extraction rates and reserves are lacking. One response to this is to treat an entire resource region (e.g. the North Sea) as a single resource deposit. While this results in a tractable formulation, it is not an innocuous step. As in other economic contexts, the individual level cost functions may fail to aggregate so that the aggregate cost function is an approximation. In addition, care is needed to avoid a fundamental misrepresentation of the producers' objective functions. This is demonstrated by Livernois and Uhler (1987) who use 32 annual observations for Alberta and an aggregate cost function of the form c(q, z), where z represents remaining reserves. They find that costs are an increasing function of aggregate reserves. This illustrates the point made earlier that known reserves can be a misleading indicator of per unit extraction costs. They compare the aggregate cost function with a disaggregated analysis of 166 individual oil pools which uses a cost function of the form c r ( q , z ~ , z ~where ), zl is the fraction of initial reserves remaining in a pool, and 2 2 indicates the order in which the pool was discovered (e.g., for the first pool discovered, 2 2 = 1). The disaggregated cost estimates indicate that c:, < 0. This means that the standard depletion effect was present for individual pools. The reason for the positive coefficient for cumulative reserves at the aggregate level is heterogeneity among pools. Low-cost reservoirs tend to be found first. As exploration progresses, increasingly inaccessible reserves are discovered (with correspondingly higher extraction costs) as implied by standard geological models of exploration (such as that employed by Kaufman and collaborators). More formally, the authors found that ci2 > 0; pools discovered later exhibited systematically higher costs. As the aggregate stock of reserves grew, the average quality of those reserves declined, generating the positive correlation between extraction costs and aggregate known reserves. Not only does the aggregate model, with costs specified as a function of aggregate known reserves, fail to capture the deciine in reserve quality as exploration progresses, it also implies a spurious cost reduction. When new discoveries outpace extraction, aggregate reserves rise. The aggregate reserve-dependent cost function

I

Marginal Cost

Q

,

D.Epple and J. Londregan pri~l

Q

Quantity (Stack)

(a)

Quantity (Flow)

(b)

Fig. 1.

indicates that this leads to a reduction of extraction costs for reserves which have already been discovered. The disaggregated analysis makes clear that larger reservoirs are less expensive to produce. However, they do not indicate interreservoir economies, which are incorrectly implied by the misspecified aggregate function.

4. Equilibrium models

Now that we have discussed methods of modeling costs we turn to the behavior of suppliers. We first consider the competitive model analyzed by Hotelling (1931), which serves as an informative benchmark for other computational models. We then move on to models that depart from the basic assumptions built into this benchmark model.

4.1. Models with price-taking present-value-maximizing producers A benchmark model of extraction was developed in the pioneering work of Hotelling (1931). In his model there is a fixed stock, zero fixed cost of extraction, and constant marginal extraction cost. Hotelling developed his model for the special case in which extraction cost is zero 6 . The cumulative cost curve for such a deposit is shown in panel (a) of Figure 1. When the resource is owned by price-taking producers, the supply relation for such a deposit is a correspondence. To see this, suppose production takes place We focus here on computational models that account for resource depletion. For early papers utilizing static economic theory to model resource markets, see Fisher, Cootner and Baily (1972) and Kennedy (1974). We also do not discuss the 'systems dynamics' approach to modeling resource usage, but refer the reader to Nordhaus (1973b) for an excellent critique. Devarajan and Fischer (1981) provide a review of Hotelling's contributions and an overview of the way in which subsequent theoretical contributions have extended and generalized Hotelling's analysis.

, -y


c

Q

Quantity ~Stoek)

Q

(b)

(a)

Quantity (Flow)

Fig. 2.

in discrete periods. The supply relation is a schedule relating amount produced to current price holding constant other things - including prices in future. Discount price in each future time period back to the present, and let m denote the maximum of these discounted prices. The resource owner will produce nothing today if the current price is less than m, and everything today if the current price exceeds m. If the current price equals m, the resource owner will be indifferent about the amount produced. Hence, the supply relation is as shown in panel (b) of Figure 1. The above intertemporal arbitrage argument also yields a precise prediction about the equilibrium path of prices over the interval of time in which the deposit is being exploited. In particular, it is evident that price must rise at the rate of interest over the interval in which production from the stock is positive. If the marginal cost of extraction, c, from the stock is positive, supply by pricetaking producers is again a correspondence. In this case, discount to the present the difference between price and c for each future period, known as royalty income, and let m denote the maximum of these discounted values. If the current price is less than c + m, nothing will be produced today. If the current price exceeds c + m, the entire deposit will be produced today. If the current price equals c + m, producers will be indifferent about the amount produced. The cumulative cost curve and associated supply correspondence for this type of deposit are shown in Figure 2. Intertemporal arbitrage now implies that, in equilibrium, price net of unit extraction cost must rise at the rate of interest over the period of time during which the deposit is being exploited. If we now think of extraction as taking place in continuous time, and if a positive amount of the resource is extracted in both to and t l , then it must be the case that

applying the rule that the present discounted value of royalties at any time at which extraction is positive must equal m. Rearranging terms, this says that


I

Quantity (Stock)

Fig. 3.

Given the resource price at any given date, the above price relation enables us to recover the entire price path up to exhaustion of the resource. Two alternatives might be used to pin down price at the date of exhaustion of the stock. One is to assume that the demand curve intersects the vertical axis at a finite price. In this case, the price at the date of exhaustion of the stock is the price at which the demand curve intersects the vertical axis. In each period prior to exhaustion of the stock, production must equal demand at that period's price. Moreover, the path of price must obey the relationships derived above. These conditions together determine the date of exhaustion of the stock. For many applications, it is more convenient to think of the exhaustible stock as one of possibly many ways in which the demand for a generic commodity may be met (e.g., oil from conventional sources is one source of energy). An alternative strategy is then to base the price at the date of depletion of the exhaustible stock on the cost of providing the commodity from some non-depleting source (i.e. a 'backstop' price). Thus, nuclear fusion may be the technology determining the backstop price of energy, and extraction of helium from the atmosphere may determine the price of helium once nonrenewable sources (helium found in natural gas) are exhausted. The backstop technology often depends on some of the same inputs as the extractive technology for the resource. Farzin (1984) makes the important point that when the backstop technology is capital intensive the backstop price cannot be viewed as invariant with respect to changes in the interest rate. He derives conditions under which increased interest rates lead to slower extraction of the resource by competitive suppliers. This occurs when the increase in interest rate boosts the backstop price enough to overcome the more rapid depletion that would arise if the backstop price remained fixed as the interest rate rose. This simple representation of cumulative costs is too restrictive for most resources. A more general cumulative cost curve can be constructed by thinking of a stock as being made up of a series of grades with unit extraction costs differing across grades. Thus, as shown in Figure 3, the cumulative cost function for a


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given stock may be represented as a series of cost curves, each of the form shown in Figure 2, with unit costs cl, cl, c3, etc., differing across grades. The preceding discussion applies to each of the grades in Figure 3. In each case, the 'backstop' technology for all but the most expensive grade is given by the extraction cost of the next most expensive grade of the resource. Thus, the supply relation for each is a correspondence. In addition, with price-taking resource owners, price net of unit extraction cost must rise at the rate of interest during the time that a given grade is being extracted. Let the grade with unit extraction cost cl be exploited during time period [to,tl],the grade with unit extraction cost cz be exploited during interval [tl,tz], etc. Letting r denote the rate of interest, the price path must be such that [P(t) - c;] e-" is constant over [ti-,, ti]. Evaluating this expression at dates ti-, and ti respectively, equating the results, and rearranging, one obtains that:

Using the above results, one can, given knowledge of price at the date of exhaustion of the stock, determine the equilibrium price over the entire time interval that the stock is being depleted. Two varieties of cumulative cost curves have been widely used in computational models. Reduced-form cumulative cost functions such as those developed in the previous section are analytically tractable, and are common among theoretical expositions. Step functions of the type depicted in Figure 3 are commonly applied to data because they are easily represented in a linear programming framework, and by choice of a suitably large number of grades, they can approximate an arbitrary cumulative cost curve. One of the earliest and most comprehensive treatments is the model by Nordhaus (1973a, 1979). Extraction costs of nonrenewable stocks for several primary energy resources (oil, natural gas, coal, shale, uranium) for several regions of the world are represented as step-shaped cost functions. The backstop technology is assumed to be either solar energy or fusion. Since the form of final energy consumption (electricity, industrial heat, residential heat, transportation) can be met in a variety of ways from the primary stocks, Nordhaus' model also includes costs of transportation and costs of conversion from the various primary energy forms to various end-use forms. In his model, equilibrium allocations and prices are computed through the date at which nonrenewable supplies are exhausted and the backstop comes into use. One of the many interesting findings of Nordhaus' pioneering work is that the price of oil in the cost-minimizing allocation of energy prices was roughly one-fifth

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the prevailing price. Nordhaus (1979, ch. 6) observes that the implicit assumption of competitive behavior underlying the cost-minimizing computational strategy is moot in the context of the world oil market.

4.2. Non-traditional price-taking models

A serious challenge to any competitive model of the world oil market is the sudden run-up of prices in 1973'. Johany (1978, 1980) and Meade (1979) argue that this was the result of control over the major oilfields in the OPEC countries passing from oil companies to national governments. Anticipating the impending seizure of the fields, so the authors argue, the oil companies applied very low shadow values to reserves underground, realizing that reserves not extracted during the immediate future were likely to be seized. After assuming control of the oil fields, the governments of the OPEC countries applied much lower rates of time discount to the reserves. The price path thus jumped from a price-taking trajectory corresponding to a high rate of discount, and a rapid rate of extraction, to a much lower rate of discount, and correspondingly slower exploitation. This propertyrights hypothesis is consistent with a one-time dramatic jump in the price of oil, and does not require a departure from the assumption of price-taking behavior. Another challenge to the competitive model comes from the observation that several OPEC countries exhibited backward-bending supply curves for oil during the 1980s. A price-taking model that attempts to explain this behavior is the so-called 'target revenues' hypothesis, advocated by Benard (1980), Scott (1981), and Teece (1982). The target revenues hypothesis posits that the oil-exporting countries have fixed revenue objectives, and that revenues beyond these levels are valueless to the exporters. Given that the oil exporters have some degree of access to capital markets, at least for lending, the target-revenue hypothesis is best viewed as a polar alternative to the present-value-maximization hypothesis. A less extreme theory of backward bending supply curves, proposed by Cremer and Salehi-Isfahani (1980) and Salehi-Isfahani (1986) is driven by imperfections in capital markets. These models assume that oil-exporting countries face diminishing returns on foreign lending markets, while they also experience diminishing returns to scale, at least in the short run, in home investment. Salehi-Isfahani (1986) simulates OPEC supply responses and generates backward-bending supply curves in response to price changes that are anticipated to persist, while the response to price changes that are expected to be temporary has a positive slope. While these results are interesting, they rely critically on the controversial assumption of sharply diminishing returns to foreign lending.

'

Gately (1984) provides an instructive discussion of the challenges that modelers confront in attempting to explain prices and producer behavior in the world oil market of the 1970s and early 1980s.


4.3. Market power

Many analysts have turned to noncompetitive models to explain price changes in the oil market. There is no generic formulation of equilibrium in markets where producers exercise market power that commands the general level of acceptance that the competitive formulation holds as a characterization of equilibrium in markets where producers do not exercise market power. Hence, while a single model such as Nordhaus' can serve to illustrate the competitive analysis of the supply of natural resources, no single noncompetitive model will serve to illustrate the analysis of supply of exhaustible resources in noncompetitive markets. Hence, our discussion of this case will illustrate the variety of approaches that have been adopted. 4.4. Monopoly models

The polar case, opposite that of price-taking producers, is that in which a depletable resource is controlled by a single producer. Hotelling (1931) showed that for the cumulative cost curves of the form depicted in Figures 1 and 2, the profitmaximizing production plan for a monopolist implies a price path in which marginal revenue net of marginal cost rises at the rate of interest. Recall that price-taking firms treat price as identical to marginal revenue, so that the price-taking rule is really a special case of the monopoly pricing rule in which the demand curve is viewed by producers as being infinitely elastic. While the monopoly model has considerable pedagogical value, there are no clear-cut cases which literally conform to the model. Actual attempts at monopolization of an exhaustible resource usually fall short of 100% control of the market. However, a non-competitive market structure similar to monopoly does occasionally emerge: a dominant supplier surrounded by a fringe of price-taking rivals.

4.5. Dominant-firm models Nordhaus (1979) investigates the potential monopoly power of OPEC. Since computation of the present-value-maximizing price path for OPEC is very difficult in his model, Nordhaus investigates the potential power of OPEC by computing the price path that would emerge if OPEC production were withdrawn permanently from the market. While this approach gives only an upper bound on the presentvalue-maximizing price path, Nordhaus' model has the virtue of being more comprehensive in treatment of alternative resources than other dominant-firm models.

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Pindyck (1978b) uses the dominant-firm model to place an upper bound on the gains from cartelization in three exhaustible-resource markets: petroleum, bauxite, and copper. H e assumes that extraction costs are a decreasing function of the total resources of the cartel, and completes his model with demand functions and reserve estimates from other sources. He then simulates equilibrium trajectories for prices, output and producer rents for monopolistic and competitive market structures, and for discount rates of r = 0.05 and r = 0.10. Pindyck's model is closed by specifying a simple autoregressive supply rule for the competitive fringe. This produces a Ushaped price path in his simulations. The cartel sets a high initial price, taking advantage of the sluggish response imbedded in the fringe's behavioral rule. A U-shaped price path similar to that generated by Pindyck's simulation emerges from Gilbert's (1978) model of a dominant firm facing a competitive fringe. In Gilbert's model there are parameter configurations for which the fringe are capacity constrained, with the constraint relaxing over time. In this setting, the dominant firm sets a high initial price, which is bid down as the fringe expands its capacity, until the capacity constraint of the fringe ceases to bind. Thereafter, price rises, producing a U-shaped price path similar to that observed in Pindyck's simulations. Salant (1976) constructs a model of the oil industry which consists of a cartel that acts as a dominant firm, and a competitive fringe of other producers. He uses a Nash-Cournot characterization of the dominant firm, i.e., the dominant firm takes the extraction path of the competitive fringe as given. His model predicts a steadily increasing price path once the cartel is organized. In Salant's model the gains from cartelization accrue disproportionately to non-members. The reason for this is simple: the cartel achieves a higher price trajectory by curbing its own production, while non-members free-ride on the higher price - expanding output and collecting greater rents. A model similar to those of Gilbert and Salant, with a competitive fringe that foresees the future price path and responds to it, is estimated by Cremer and Weitzman (1976). They predict an approximately constant price for crude oil for the period 1976-1995. The price trajectory is flattened by the elastic response of the non-OPEC sector during the short run. Beyond 1995 they predict that the non-OPEC suppliers will begin to exhaust their reserves, and the market will increasingly approximate a pure OPEC monopoly. The major difference between the Cremer-Weitzman (CW) trajectory and the Pindyck trajectory seems the be the elastic short-term response of supply by the competitive fringe in the CW model. 4.6. Cartel models Salant (1982) studies oligopolistic production of natural resources in a NashCournot model in which extraction costs are represented as step-shaped cumulative


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cost curves. In the Nash-Cournot model, each producer with market power is assumed to take the current and future production of all other suppliers as given. The equilibrium price path is then one in which marginal revenue net of marginal production cost for each producer rises at the rate of interest during the time that the producer has positive production. Loury (1986) provides additional results on qualitative properties of equilibrium extraction paths in a Nash-Cournot model. An application of this Nash-Cournot framework to the world oil market is presented in Salant (1982). The Nash-Cournot model has the virtue of computational tractability when there are several producers, several grades of a resource controlled by each producer, and several resources. The model can accommodate both price-taking and Nash-Cournot producers. Salant provides a computational model when there are four producers (USA, OPEC, Mexico, Rest of World), several resources (oil, heavy oil, shale, natural gas), and several grades of each resource. Salant's approach to noncompetitive exhaustible-resource markets thus permits generality in treatment of number of resources and number of players that rivals Nordhaus' treatment of the competitive case. Another alternative to the dominant-firm model is implemented by Hnyilicza and Pindyck (1976). In this model, the OPEC cartel is divided into two factions, those with relatively low rates of time discount, the 'savers', and those with high rates, 'spenders'. The Hnyilicza-Pindyck (HP) model goes beyond the standard monolithic cartel model to analyze the give and take among members over output shares, which is assumed to conform to the Nash bargaining solution. Suppliers are assumed to be able to perfectly commit to future price and extraction paths. The H P model generates a 'bang-bang' solution, with the 'spenders' providing the entire supply for the cartel during the short run, while the 'savers' withhold their oil until the 'spenders' have exhausted their entire reserves. The authors caution against literal interpretation of this prediction, but suggest that with heterogeneous members, we should expect the relative output share of the 'spenders' to fall over time. Pindyck (1978b) and Stollery (1983) construct models of extraction of durable, but exhaustible resources, copper and nickel respectively. Pindyck models the supply and demand for copper in much the same way that he does the petroleum and bauxite markets analyzed in the same paper. In addition to incorporating a competitive fringe of producers of newly mined copper, he also accounts for the existing stock of manufactured copper, which is assumed to decay at an annual rate of 2%, absent new production. The potential for speculative holdings is not modeled. In this framework Pindyck concludes that the gains to monopolization of the joint reserves of CIPEC, the official copper cartel, would generate a relatively small increase in rents for members. In part this is due to the relatively small share of copper reserves controlled by the cartel. Monopolists need not extract all of their rents in the form of pecuniary profits. Moran (1982) asserts that the preferred model of OPEC has Saudi Arabia as the

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dominant supplier, surrounded by a fringe. However, he contends that the Saudis have chosen to extract rents in the form of political concessions, rather than in pecuniary profits. While this interpretation has enjoyed wide acceptance in the press, it leaves several important questions unanswered. "Why don't the Saudis also consume some of their rents in the form of cash (as, indeed, they seem to be doing)? Why did the Saudis wait until 1973 to begin to pursue their political objectives, which were at least as pressing during, for example, 1967?" The approach to the internal organization of a cartel taken by Hnyilicza and Pindyck (1976) is not the only one. Commentators in the popular press, for example Friedman (1974), argued that cartels are inherently unstable because of the tremendous temptations to chisel on price and overproduce on quotas. Cheating by cartel members in models of renewable resources has been studied by Green and Porter (1984), Porter (1983a, b), and Abreu, Pierce and Stachetti (1986), but their analyses have not been extended to the case of depletable resources. Such an extension could prove to be quite valuable. While the correct model for market structure in a given industry is not readily apparent, the differences between the models do matter. Comparing the models put forward by, for example, Salehi-Isfahani (1986) and Pindyck (1978b) we observe that not even the sign of the supply response to a long-term increase in demand is the same for the two models. Although identifying the appropriate market structure is a challenging task, as evinced by the wide range of opinion expressed by industry analysts, it is absolutely essential to understanding the behavior of prices and output over time. Griffin (1985) undertakes a comparison of four alternative models of OPEC behavior - a cartel model, a competitive model, a target-revenue model, and a property rights model. He finds no support for the target-revenue model, and little support for the property-rights hypothesis. He finds that the competitive model is rejected for OPEC suppliers but the cartel model is not, and finds the reverse to be true for the non-OPEC suppliers. As Griffin acknowledges, his econometric representations of the various theories are simple, and proponents of various theories might offer alternative formulations. Nonetheless, his results are intriguing, and pose a challenge for alternatives to cartel models of OPEC behavior. If one accepts Griffin's conclusion, much remains to be done in refining and choosing among alternative cartel models.

4.7. The time-inconsistencyproblem

A problem that arises in dominant-firm models of exhaustible resources that does not arise in competitive models is the potential for time inconsistency 8. An optimal For a general discussion of the problem of time inconsistency, see Kydland and Prescott (1977).


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policy regarding future extraction chosen today by a producer with market power will generally be one that the producer will want to deviate from in the future. The reason is as follows. A fringe producer's current extraction decision depends on expectations about future prices. The dominant producer's extraction policy affects the expected future price. Thus, the dominant player's policy regarding future extraction affects the amount currently extracted by the competitive fringe. It is this linkage that gives rise to the time-inconsistency problem in dominantproducer models. As time passes, the dominant producer has an incentive to revise its future extraction policy and thereby manipulate the extraction decisions of the competitive fringe. This is a potential concern for all of the dominant-firm models discussed thus far other than those in which the competitive fringe is assumed to be myopic or mechanistic in its behavior. The models with a forward-looking competitive fringe implicitly assume that the dominant firm can commit to follow the ex ante optimal extraction policy. Since there is no external enforcement authority to guarantee the dominant firm's adherence to the ex ante optimal plan, the assumption of commitment is troubling. A similar problem arises in monopoly and dominant-firm models in which the resource is durable and purchasers of the product are forward looking. The dominant firm's policy regarding future extraction affects buyers' incentives regarding the amount to hold in inventory. Thus, over time, the firm has an incentive to revise its future extraction plans in order to manipulate inventories held by others 9. The time-consistent solution to the dominant-firm model of resource extraction has been provided for the linear-quadratic model by Hansen, Epple and Roberds (1985). In particular, in their analysis extraction costs at date t for a particular producer are assumed to be of the form

Here, q, and Q, are current and cumulative extraction respectively, E, is a random technology shock, and 4, 0 and x are parameters. This cost function captures the effects of depletion by making costs depend not only on the current rate of extraction but also on cumulative extraction. Hansen, Epple and Roberds (1985) derive equilibrium decision rules for extraction for a variety of market structures l o Time-consistency issues for a durable-good monopoly were first discussed by Coase (1972) and later elaborated by Bulow (1982) and Gul and Sonnenshein (1988). Stockpiling of reserves is analyzed by Newbery and Stiglitz (1982). ' O In particular, they present solutions for six alternative characterizations of market structure: competitive suppliers, Nash suppliers, colluding suppliers, one Nash supplier and one competitive supplier, one dominant supplier able to pre-commit to a future extraction plan and one competitive supplier, and one dominant supplier that cannot commit to a future extraction plan and one competitive

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for duopoly models in which each supplier has a cost function of the form above, where the shock E, and parameters 4,6' and .rr may differ across suppliers. Of particular relevance here are the solutions for three characterizations of the dominant firm: the time-consistent case, the time-inconsistent case (i.e., the extraction policy that the dominant firm would adopt if commitment were possible), and the case in which the dominant firm takes the time path of production of the competitive fringe as given [i.e., the Nash-Cournot equilibrium introduced by Salant (1976)l. They contrast the solutions analytically and supplement this analytic comparison with numerical examples. The analytic results compare extraction paths as time grows large. A comparison of the three dominant-firm games reveals that, after a sufficiently long time has elapsed, cumulative extraction is highest for the time-consistent solution, next highest for the Nash case, and lowest for the time-inconsistent solution. In this sense, extraction is most rapid (and, hence, closest to the competitive solution) in the time-consistent case and least rapid (hence, closest to the monopoly solution) for the time-inconsistent case, with the Nash case being intermediate between the other two. The numerical results reveal that the differences in extraction rates among the three dominant-player solutions can be substantial. These results demonstrate that the nature of the solution concept employed in the analysis of dominant-firm models can be quantitatively important. Hence, assuming that the dominant firm can commit to a future extraction path may not be innocuous. This underlines the importance of extending the analysis of the timeconsistent dominant-firm model to cost structures more general than the linearquadratic case.

4.8. Treatment of uncertainty in computational models In computational models in which extraction costs are represented via step-shaped cumulative cost curves, uncertainty may be introduced by assuming a discrete set of possible future values of parameters with probabilities assigned to each outcome. Thus, for example, the backstop cost may be treated as uncertain with new information becoming available at a specified future date that partially or completely resolves the uncertainty. This treatment of uncertainty is implemented in the computational model of Salant (1982). While this approach is, in principle, quite general, it is difficult to treat models with a large number of possible future outcomes. Linear-quadratic models permit introduction of uncertainty about both future demand and future extraction costs [Hansen, Epple and Roberds (1985). However, supplier. These solutions are presented in the context of a duopoly, but, for cases with a competitive supplier, that supplier may be thought of as the entire competitive fringe.


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the comparative ease with which uncertainty can be treated in the linear-quadratic structure is not likely to carry over to more general cost structures. 4.9. Long-run versus short-run analysis

Nordhaus' and Salant's work illustrate that models utilizing step-shaped cumulative cost curves to characterize depletable resources can be powerful vehicles for providing a comprehensive and informative analysis of depletable resources. Models built on this characterization of extraction costs have thus far proven to be better suited to investigating long-term patterns of resource exploitation and prices than short-term patterns. Models using step-shaped cumulative cost curves to characterize resource extraction costs often show relatively dramatic changes during short time periods in the composition of resources being exploited. Such dramatic short-run shifts are rarely observed in practice because of the costs of adjusting from one technology to another. Thus, attempts to use models based on step-shaped cumulative cost curves to analyze short-term changes often yield implausible results. One response to this problem was suggested in our discussion of cost functions for exhaustible resources: make costs a non-linear function of the rate of extraction as well as cumulative extraction: ~ ~ ~Q)( #9 0, [Levhari and Liviatan (1977), Halvorsen and Smith (1984), Heaps (1985), Hansen, Epple and Roberds (1985)l. Implementation of this approach requires information about the relationship of costs to rate of extraction. Lacking detailed information about extraction costs some analysts impose a dynamic adjustment rerationship such as a stock adjustment mechanism to induce sluggishness in the rate of change of output in response to changes in incentive variables. For example, this approach is used to characterize the competitive fringe in Pindyck's (1977) model of the world bauxite market. There is, of course, a degree of arbitrariness in constraining quantity adjustments in this way - as there is in imposing direct constraints on output [Manne (1976), Modiano and Shapiro (1980)l. In either case, results can be very sensitive to the imposition of such constraints. 4.10. Concluding remarks on computational models

An inevitable concern about any large-scale computational model revolves around the extent to which the results are valid empirically. While individual model parameters may potentially be the subject of formal empirical estimation, formal testing of the overall properties of a large-scale computational model is, in principle, a difficult undertaking. Hence, judgment about the validity of the findings

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generally rests on an evaluation of the theoretical soundness of the model structure, the fit of the model to the question being studied, and the care with which values of model parameters are chosen. Most computational models that provide an in-depth treatment of exhaustible resources typically contain a simplified treatment of the non-energy economy. The discount rate is treated as constant in real terms. The costs of extraction are commonly expressed in the form of foregone consumption of an endowed numeraire commodity. On the other hand, models that treat exhaustible resource and economy-wide interactions in greater detail [e.g., Hudson and Jorgenson (1974), Despotakis and Fisher (1988)l often model resource production as exhibiting constant returns to scale, thus neglecting the effects of resource depletion. These models also typically assume that producers have static expectations in contrast to the perfect-foresight or rational-expectations approaches of most models discussed in this section. There is thus a good deal of room for unifying the treatment of computational models of depletable resources and computational general equilibrium models.

5. Econometric models

An early and highly influential econometric model of resource extraction is due to Fisher (1964). Fisher models oil discoveries in the USA as the outcome of three equations. One determines the number of wells drilled, a second determines the success rate per well, and a third determines average amount discovered per successful well. Among the right-hand-side variables included in his equations are the price of oil, the price of natural gas, a variable to capture regulatory restrictions on production, measures of geological and geophysical exploration efforts, well depth, and lagged values of the dependent variables. Erickson and Spann (1971) extend Fisher's model by including an additional equation to model average natural gas discoveries. Khazzoom (1971) adopts a somewhat different approach to modeling natural gas, using amount discovered per year as his dependent variable and including oil and natural gas prices, the price of natural gas liquids, and the lagged dependent variable as right-hand-side variables. MacAvoy and Pindyck (1973, 1975) build a more comprehensive model of the natural gas supply process from exploration through production, transportation, and distribution. Their approach to modeling outcomes of exploration is to use dependent variables similar to those developed by Fischer. Their right-hand-side " In the discussion that follows, we focus on models of resource exploitation. Hence, we do not review

research on various strategies for measuring of resource scarcity. Readers interested in this topic may wish to refer to reviews by Fisher (1981) and Smith (1980) and to recent contributions by Devarajan and Fisher (1982) and Halvorsen and Smith (1984,1986).


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variables include cumulative drilling to reflect the effects of depletion, an issue not addressed in earlier models. Detailed comparison of the models by Erickson and Spann, Khazzoom, and MacAvoy and Pindyck, is provided by Pindyck (1975). He reports results on sensitivity of parameter estimates to changes in the sample used for estimation, and he provides a comparison of forecasts from the three models. He finds that the parameter estimates of the Erickson-Spann and Khazzoom models are quite sensitive to time period of estimation, and that the three models give very different predictions about the effects of changing prices. Neri (1977) compares the MacAvoy-Pindyck model to a model developed by the American Gas Association and finds great divergence in forecasts from the two models. Fisher's (1964) model and subsequent models that build on his framework rely on an intuitive appeal to economic theory in choosing functional form and variables to appear in the equations being estimated. Models based on an intuitive appeal to theory typically are less computationally burdensome than models formally derived from theory. Against this advantage must be weighed the costs of using a specification that lacks the discipline and relatively sharper testable implications that models formally derived from theory provide. Given the divergent predictions of the models compared by Pindyck (1975) and Neri (1977), this is an important concern 12. An alternative approach is to begin with a formal specification of the objective function of resource suppliers and deduce the equations to be estimated from the solution of the producers' objective function. Cox and Wright (1976) derive their econometric model from a specification in which price-taking firms maximize the present value of revenues net of costs of acquiring and exploiting reserves. In their formulation, the cost of acquiring reserves may change exogenously over time, but the cost is not a function of depletion of the resource stock. Thus, while they motivate their econometric analysis with a dynamic model, intertemporal tradeoffs associated with depletion of the stock are not captured in their formulation. A test of the competitive theory of resource depletion is presented by Farrow (1985) 13. He uses data for a single mine, thus avoiding potential aggregation problems that might arise from combining data from heterogeneous mines. The theoretical formulation that he adopts is a non-stochastic continuous-time model l 2 In our discussion of econometric models thus far, we have focused on models of oil and natural gas supply. Oil and natural gas have been the subject of much more extensive econometric investigation than other resources, and more information is available about the comparative performance of these models. However, aside from models to be discussed below, econometric analyses of other exhaustible resources exhibit problems of incomplete treatment of intertemporal trade-offs and expectations similar to those manifest in models of oil and natural gas supply. l3 An alternative approach to testing resource depletion theory relies on data on resource prices or n~ While discussion of this work would take us too far afield, value of r e s o ~ r c e - ~ % d u c iproperties. interested readers may wish to refer to Heal and Barrow (1980) and Miller and Upton (1985).

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in which the firm makes its decisions taking account of the effect current extraction has on future costs. In deriving an empirical counterpart to the theoretical model, Farrow adopts some simplifying assumptions including treating certain shadow prices that vary with time in the theoretical model as constants in the empirical analysis. His empirical results lead to rejection of the theoretical model. This work highlights the importance of empirically testing the foundations of the theory of depletable resources. As Farrow points out in his conclusion, his work underlines the need for development of econometric models that provide a more general treatment of expectations and uncertainty 14. Stollery (1983) investigates resource depletion theory with an application to the nickel industry. He assumes that the dominant producer, INCO, can be treated as a monopolist in the nickel market for the period 1952-1972. A non-stochastic continuous-time theoretical model is developed. The empirical analysis focuses on assessing whether the shadow price of the resource rises over time in conformance with the predictions of the model. He finds the results to be broadly consistent with theoretical predictions. Cairns (1985, 1986) challenged the optimizing models applied by Campbell (1980) and Stollery (1983) to INCO, the dominant supplier of nickel. Cairns asserts that a myopic pricing rule consisting of a fixed markup above extraction costs tracks the nickel supply data equally well. Stollery (1985) responded to Cairns' criticism by testing the myopic pricing model against the Hotelling model, and found that his estimates of the shadow price of nickel ore had a significant coefficient in the nickel pricing regression equation, as it would if the Hotelling model were correct, and contrary to its expected coefficient of zero in the simple markup pricing model. While Stollery's analysis is instructive, use of a non-stochastic theoretical model raises difficulties in formulating an empirical counterpart to the model, and necessitates assumptions about revision of expectations and replanning that are not addressed by the theoretical model. Thus, it would be desirable to derive a test more directly from a stochastic model of resource depletion. Roberds (1984) investigates equilibrium in the world nickel market using the stochastic formulation of the linear-quadratic model of Hansen, Epple and Roberds (1985). He investigates several of the alternative characterizations of market structure studied by Hansen, Epple and Roberds (1985). He finds it necessary to impose a priori constraints on values of some parameters in order to obtain convergence in estimation. Thus, while his analysis yields insights about both the nickel industry and the fit of the model to data for the nickel industry, his comparison of alternative industry structures is conditional on a priori restrictions on model parameters. Farrow also notes the need for more general models that allow for heterogeneity of ore within a given deposit - an issue addressed in Farrow and Krautkraemer (1988).

l4


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In Epple (1985), the competitive version of this model is extended to the case of jointly exploited resources, and the model is estimated for oil and natural gas supply in the USAIS. The intercept in the marginal cost function is found to be negative and significantly different from zero. This suggests that the linearquadratic functional form may be too restrictive for this application. Walls (1987) suggests an alternative formulation of the linear-quadratic structure in which the cost function is expressed in terms of drilling inputs, and a stochastic process relates amounts discovered to amount of drilling undertaken. She estimates the model using data on natural gas supply for the USA. The model fits the data quite well. However, Walls also obtains a negative value for intercept in her marginal cost function. The cost specifications in Hansen, Epple and Roberds (1985), Roberds (1984), and Epple (1985) assume that quantity to be extracted (or discovered) is chosen by the producer and that costs are stochastic 1 6 . In some contexts, this is quite natural. In others, it is more natural to assume that the producer chooses the amount to spend on exploration or extraction in a given period, and that the amount discovered or produced is stochastic. That is, in the first alternative, quantity is set deterministically by the producer and costs are stochastic, while in the second cost is set deterministically and quantity is stochastic. If under the second alternative, one assumes that the producer's choice variable is expected quantity, then the equation to be estimated is the same as under the first alternative except for heteroskedasticity in the error term. Thus, the linear-quadratic specification can potentially be applied to quite diverse resource exploration and extraction contexts. The close similarity between the estimating equations for these alternatives is a special feature of the linear-quadratic functional form, and it will not apply to most other specifications of the cost function. Both Epple (1985) and Walls (1988) obtain a negative value for the intercept of the marginal cost of production. This negative value, implying negative costs at low output levels, points to the need for models with less restrictive cost structure. Their findings highlight the gain from estimating equations derived from a model of the optimization problem being solved by producers. Without the tie to the underlying theoretical model, no difficulty with the equations estimated for the linear-quadratic structure would have been evident. Hendricks and Novales (1987) examine exploration for oil and gas in Alberta. They estimate a dynamic costs of adjustment model with a stochastic return per unit of drilling effort. Rational expectations, and dynamic optimization of a quadratic Is Differences in the quality of deposits of different vintages are captured by making development costs a function of cumulative reserves discovered. l6 In Walls (1988), the firm chooses the amount of drilling rather than the amount to be discovered. However, the amount discovered as a function of the amount of drilling is known to the producer at the time the drilling decision is made. Hence, her model also shares the feature of a known quantity discovered with stochastic cost.

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objective function by oil explorers, lead to a second-order difference equation in measured drilling effort (number of exploratory wells) with the return per unit of drilling effort as the 'forcing variable'. They estimate this model using Hansen and Singleton's (1982) 'method of moments' technique. Their results fail to reject the hypothesis that there are significant adjustment costs, nor can they reject intertemporal optimization, though the small size of their data set limits the power of these tests. Hendricks and Novales do not model the effect of current drilling on the stochastic discovery process, taking it to be exogenous. Thus, in their formulation, land owners do not consider the intertemporal trade-offs associated with choosing the date at which to undertake exploration of their property. Another feature of their analysis is that they treat the value of a barrel of oil in the ground as the same for all known deposits in Alberta during a given year. This could result in measurement error if the expected cost of extracting reserves from newly discovered (and presumably smaller than average) deposits were higher than the cost of extraction for pools already being exploited. In the analysis of Devarajan and Fisher (1982) the return to exploration comes through reduced extraction costs. In their analysis, newly discovered reserves reduce the cost of extracting reserves from all deposits - even previously discovered deposits. This is a troubling assumption. While reserves in a given pool are inversely related to extraction costs for that pool, reserves in newly discovered pools do not affect the physical characteristics of pre-existing ones. Thus, a technological link between the magnitude of new discoveries and the cost of exploiting previously known pools is unsatisfying. For competitive suppliers, new discoveries elsewhere affect the extraction path for known reservoirs only if they affect the expected path of future prices. Pesaran (1990) uses an optimizing framework to study exploration and extraction in the North Sea. Rather than explicitly introduce adjustment costs, he instead uses an 'error correction7 model, in which the actual setting of the control variables by agents is a weighted average of the desired level implied by the model, and the previous period's actual level. Thus, his model limits the extent of agents' optimizing behavior by imposing restrictions on the way in which agents adjust over time. He experiments with two models of expectations formation: the Rational Expectations Hypothesis (REH), and a version of the Adaptive Expectations Hypothesis (AEH). He obtains a better fit to the data with the AEH. In addition, the REH model produces the 'wrong' sign for his reserves variable. However, as in Devarajan and Fisher (1982) and Pindyck (1978b), the cost of exploiting known reservoirs is reduced by exploration in Pesaran's model. This linkage may give rise to the unsatisfactory performance of Pesaran's R E H model. The objective of estimating supply functions for exhaustible resources has proved challenging. However, as the preceding section indicates, considerable progress


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has been made. Further progress is likely to result from dynamic models allowing greater flexibility in the form of the underlying cost functions. We have seen that careful attention must be paid to the specification of the aggregate cost function to avoid seriously misleading conclusions. 6. Conclusion

For many years after Hotelling's (1931) initiation of the study of depletable resources, theoretical developments outpaced empirical application. Indeed, it is only comparatively recently that resource depletion theory has been used as a foundation for developing applied models. Much progress has been made in recent years, but room for considerable additional work remains. On the econometric front, work is needed in developing and testing models of cartel behavior. Related to this is the task of developing dynamic stochastic models that extend the range of empirically testable cost and demand structures beyond the current state of the art represented by linear-quadratic models. Much progress has also been made in analyzing cost functions for exhaustible resources. Empirical research has highlighted the potential pitfalls in aggregating across deposits found at different points in time. Creative and innovative methods have been found for estimating cost functions for a variety of resources. Equilibrium models provide a vehicle for unified analysis of exhaustible resource markets. Improved estimates of cost functions for exhaustible resources provide an enhanced base for computational equilibrium models. Among the remaining challenges for research on computational equilibrium models are developing improved methods for capturing short-run dynamics and finding improved ways of testing the models. Further integration of the depletable and non-depletable sectors of the models is another area of potential additional research. Ideally, one would hope that the distinction between computational equilibrium models and econometric models would eventually disappear so that estimation, testing, and simulation of equilibrium outcomes are entirely unified. While this is feasible for relatively small models, it is not on the immediate horizon for very large-scale models. Fruitful roles for both approaches to applied modeling remain for the foreseeable future. References Abreu, D., D. Pierce and E. Stachetti, 1986, "Optimal Cartel Equilibria with Imperfect Monitoring", Journal of Economic Theory 39,251-269. Barouch, Eytan, and Gordon M. Kaufman, 1976a, Oil and Gas Discovery Modelled as Sampling Proportional to Random Size, Working Paper WP888-76, December (MIT Sloan School of Management, Cambridge, MA).

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Levhari, David, and Nissan Liviatan, 1977, "Notes on Hotelling's Economics of Exhaustible Resources", Canadian Journal of Economics 10 no. 2 (May) 177-192. Livernois, John R., 1987, "Empirical Evidence on the Characteristics of Extractive Technologies: The Case of Oil", Journal of Environmental Economics and Management 14 no. 1 (March) 72-86. Livernois, John R., and Russel S. Uhler, 1987, "Extraction Costs and the Economics of Nonrenewable Resources", Journal of Political Economy 95 no. 1 (February) 195-203. Loury, G.C., 1986, "A Theory of 'Oil'igopoly: Cournot Equilibrium in Exhaustible Resource Markets with Fixed Supplies", International Economic Review 27,285-301. MacAvoy, Paul, and Robert S. Pindyck, 1973, "Alternative Regulatory Policies for Dealing with The Natural Gas Shortage", The Bell Journal of Economics and Management Science 4 no. 2 (Autumn) 454-498. MacAvoy, Paul, and Robert S. Pindyck, 1975, The Economics of the Natural Gas Shortage (19601980) (North-Holland, Amsterdam). Manne, Alan S., 1976, "ETA: A Model for Energy Technology Assessment", The Bell Journal of Economics 7 no. 2 (Autumn) 379-406. Meade, Walter J., 1979, "The Performance of Government Energy Regulations", American Economic Review Proceedings (May). Miller, Merton, and Charles W. Upton, 1985, "A Test of the Hotelling Valuation Principle", Journal of Political Economy 93 no. 1 (February) 1-25. Modiano, Eduardo M., and Jeremy F. Shapiro, 1980, "A Dynamic Optimization Model of Depletable Resources", The Bell Journal of Economics 11 no. 1 (Spring) 212-236. Moran, Theodore, 1982, "Modeling OPEC Behavior: Economic and Political Alternatives", in: James M. Griffin and David J. Teece (eds.), OPECBehavior and World Oil Prices (Allen & Unwin, London). Neri, John A,, 1977, "An Evaluation of Two Alternative Supply Models of Natural Gas", TheBeNJournal of Economics 8 no. 1 (Spring) 289-302. Newbery, David M.G., and Joseph E. Stiglitz, 1982, "Optimal Commodity Stock-Piling Rules", Oxford Economic Papers 34 no. 3 (November) 403-427. Nordhaus, William D., 1973a, "The Allocation of Energy Resources", Brookings Papers on Economic Activity, pp. 529-570. Nordhaus, William D., 1973b, "World Dynamics: Measurement without Data", Economic Journal 83, 332 (December) 1156-1183. Nordhaus, William D., 1979, The EfJicient Use of Energy Resources, Cowles Foundation Monograph 26 (Yale University Press, New Haven, CT). Pesaran, M. Hashem, 1990, "An Econometric Analysis of Exploration and Extraction of Oil in the U.K. Continental Shelf ",he Economic Journal 100,367-390. Pindyck, Robert S., 1974, "The Regulatory Implications of Three Alternative Models of Natural Gas", The Bell Journal of Economics and Management Science 5 no. 2 (Autumn) 633-645. Pindyck, Robert S., 1977, "Cartel Pricing and the Structure of the World Bauxite Market", The Bell Journal of Economics 8 no. 2 (Autumn) 343-360. Pindyck, Robert S., 1978a, "The Optimal Exploitation and Production of Non-Renewable Resources", Journal of Political Economy 86,841-861. Pindyck, Robert S., 1978b, "Gains to Producers from the Cartelization of Exhaustible Resources", Review of Economics and Statistics 60,238-251. Porter, Robert H., 1983, "A Study of Cartel Stability: The Joint Executive Committee, 1880-1886", The Bell Journal of Economics 14 no. 2 (Autumn) 301-314. Roberds, William, 1984, "Essays on the Econometric Application of Dynamic Game Models", Ph.D. Thesis (Graduate School of Industrial Administration, Carnegie-Mellon University). Salant, Stephen W., 1976, "Exhaustible Resources and Industrial Structure: A Nash-Cournot Approach to the World Oil Market", Journalof Political Economy 85 no. 4 (October) 1079-1093.


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Salant, Stephen W., 1982, Imperfect Competition in the World Oil Market: A Computerized Nash Cournot Model (D.C. Heath and Co., Lexington, KY). Salant, Stephen W., A. Sangvhi and M. Wagner, May 1979, "Imperfect Competition in the World Oil Market: A Computerized Nash-Cournot Model", Report submitted by ICF Inc. to U.S. Department of Energy. Salehi-Isfahani, Ojavad, 1986, "Oil Supply and Economic Development Strategy", Journal of Development Economics 21, 1-23. Scott, B., 1981, "OPEC, the American Scapegoat", Harvard Business Review 59 no. 1. Smith, James L., 1980, "A Probabilistic Model of Oil Discoveries", Review of Economics and Statistics 62 no. 4 (November) 587-594. Solow, Robert M., and Frederick Wan, 1976, "Extraction Costs in the Theory of Exhaustible Resources", The Bell Journal of Economics 7 no. 2 (Autumn) 359-370. Stollery, Kenneth R., 1983, "Mineral Depletion with Cost as the Extraction Limit: A Model Applied to the Behavior of Prices in the Nickel Industry", Journal of Environmental Economics and Management 10 no. 2 (June) 151-165. Stollery, K.R., 1985, "User Costs Versus Markups as Determinants of Prices in the Nickel Industry: Reply", Journal of Environmental Economics and Management 12,110-1 13. Teece, David, 1982, "OPEC Behavior: An Alternative View", in: J.M. Griffin and D. Teece (eds.), OPEC Behavior and World Oil Prices (Allen & Unwin, London). Walls, Margaret A., 1987, "Petroleum Supply Modeling in a Dynamic Optimization Framework: Forecasting the Effects of the 1986 Oil Price Decline", mimeograph (Resources for the Future, Washington, December). Weitzman, Martin L., 1976, "The Optimal Development of Resource Pools", Journal of Economic Theory 12 no. 3 (June) 351-364. Zimmerman, Martin, 1977, "Modeling Depletion in a Mineral Industry: The Case of Coal", The Bell Journal of Economics 8 no. 2 (Autumn) 41-65.


PART 3

APPLICATIONS TO POLICY AND FORECASTING ISSUES


Chapter 23

NATURAL RESOURCES IN AN AGE OF SUBSTITUTABILITY* PARTHA DASGUPTA

Faculty of Economics and Politics, University of Cambridge, Sidgwick Avenue, Cambridge, United Kingdom CB3 9DD

1. Introduction

All human activity is based ultimately on resources found in nature. Whether it is consumption, production, or whether it is exchange, the commodities involved can be traced always to constituents provided by Nature. A tractor requires for its manufacture iron and steel, rubber, plastics, nonferrous metals, labour of various skills, factory-machinery, water and so on. Of these, to take an example, the steel requires for its production iron-ore, coal, furnaces, water, labour, and so forth. The furnaces in turn require for their manufacture, among other things, iron ore, brick-works, and labour. One can thus break down any produced good into the inputs involved in its manufacture and one can metaphorically trace them ultimately to a combination of labour and natural resources. Of course, labour too is produced and sustained by natural resources. So ultimately all commodities and services can be traced to natural resources. The morphology of produced goods and services does not lead to a resourcetheory of value. Like Marx's labour theory such a construct runs quickly into analytical difficulties. Nevertheless, there is an advantage of noting the origins of all produced goods and services. It encourages us to assume a materialistic tone so that one may in an unhampered way view natural resources in the light of their use to us in running our lives. This is not an entirely defendable perspective, but we will find it useful to strike this attitude in this chapter. I shall concentrate on the instrumental value of natural resources. It is usual, and convenient, to divide natural resources into two classes; exhaustible (such as coal, oil and natural gas) and renewable (such as fisheries, aquifers, forests and woodlands, and soil quality). On the face of it, the classification is misleading, because even renewable natural resources are in danger of * This is a much-revisedversion of a non-technical paper titled "Exhaustible Resources", in: R. Laskey and L. Friday (eds.), The Fragile Environment (Cambridge University Press, Cambridge, 1988).

Handbook of Natural Resource and Energy Economics, vol. III, edited by A.KKneese and J.L. Sweeney O I993 Elsevier Science Publishers B. K AN rights reserved

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exhaustion if they are harvested at too fast a rate. But the idea behind the distinction is clear enough. Resources such as fossil fuels enjoy growth rates which operate only over geological time. Their stock cannot increase. It can only decrease, or if none is mined for a while, stay constant. Improvement in technology - for example, learning to drill offshore - can increase the useable stock. But this is a different matter. Then again, discoveries of new deposits increase the known available stock. That too is a different matter. What has been just said about fossil fuel is true also of recyclable material like metals. The redoubtable Second Law of Thermodynamics ensures that we will never recover an entire ton of secondary copper from a ton of primary copper in use, or an entire ton of tertiary copper from a ton of secondary copper in use. There is leakage at every round, and a simple multiplier formula, based on compound decay, tells us how much copper can be used from the initial stock once one knows the recovery, or recycling, ratio. In a more sophisticated exercise we would make the recycling ratio an increasing function of costs, and we would then determine the ratio adopted in the economic environment we happen to study.

2. History

Fear of the impending exhaustion of natural resources would seem to be a periodic state of mind, and it is not always prompted by good reasons. The worldwide concern over the availability of fossil fuels in late 1973 was in great part occasioned by the four-fold price increase in Gulf-oil. But this increase ought not to have been seen as a signal for increased resource scarcity. Worldwide reserves had not suddenly shrunk. Nor had demand without notice all at once jumped. The rise in price was rather the exercise by OPEC as a cartel of its market power. The consequences to the world economy have been enormous [see Bruno and Sachs (1985)l. But it had nothing to do with resource exhaustion. One sees this vividly today, in that with the weakening in cohesion among OPEC members energy scarcity has disappeared from the agenda of public anxiety. This is not to suggest that societies have not faced resource scarcities in the past, nor that they have not done something about it. Indeed, one can look at history as a relentless pursuit of new, substitute resource bases for existing, vanishing ones. These substitute resources are sometimes present in ready-made form, sometimes they are not. In either case it is a matter of devising ways of using them, and by this I mean economically feasible ways of using them. This is the hard part. It involves research and development (R&D). The basic ingredients of all present and future commodities and services are present today. It is only when we learn to make use of them, or when we start expecting to make use of them, that they attain some economic value. Then we take an interest in them. To put it in the words of Zimmerman (1964), "Resources are not, they become."

Ch. 23: Natural Resources in an Age of Substitutability

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To cite a concrete episode, a number of historians have seen the Industrial Revolution as a response to a concern with the supply of raw materials, especially sources of energy. Preindustrial societies were dependent upon wind, water and animal power. Above all, they were dependent upon wood, not only as a building material, as an industrial raw material and as a source of chemical inputs, but also as a source of fuel. The need for finding substitutes for wood-fuel was being signalled in England as early as in the Elizabethan period. The signal was a secular increase in fuel prices which, as it happens, rose during this period three times as fast as prices generally. The Industrial Revolution in Britain involved a substitution of cheap coal for wood as a source of fuel and power, and an abundant source of iron for vanishing timber resources. The process was slow, because this substitution was fraught with technical difficulties, but it happened. An extreme version of this viewpoint was expressed by Thomas: In the second half (of the eighteenth century) Britain experienced an energy crisis.. . After the middle of the eighteenth century there was a growing general shortage of timber and especially charcoal, whereas coal was relatively plentiful . . . (the problem) could only be resolved by switching the energy base from wood to coal . . . but this could not be done until a fundamental innovation had been made.. . At the beginning of the 1780s Britain was in trouble, a special kind of trouble which no other country faced at that time . . . she was in a severe energy crisis, dangerously dependent on wood fuel . . . In the previous twenty five years as many as thirteen inventors had attempted to overcome the technical difficulties. It was not until 1784 that the problem of refining pig iron with coal or coke was finally solved by Henry Cort's process . . . the Industrial Revolution occurred in Britain at the end of the eighteenth century not because Britain was 'well endowed' in various respects, but because she was 'illendowed' in one fundamental respect - she was running out of energy and had to do Thomas (1980) something about it. France had no such problem.

The point of view is single-minded,but the thesis is at the very least suggestive. In the United States, where resource endowments were quite different, the temporal pattern of resource-use was also different. In the early part of the nineteenth century, wood in America constituted an abundant and cheap fuel. Consequently its use continued long after England had ceased to rely on it and had adopted coal. In 1850, mineral fuels supplied less than 10% of all fuel based energy in the United Stated, whereas wood supplied 90%. By 1915 wood had declined to less than lo%, whereas coal accounted for 75%. The story since the end of the First World War has largely been one of a move away from coal to oil and natural gas as sources of energy. [See Rosenberg (1976), ch. 14.1

3. Resource substitution as the key process

This example of alternative energy sources and the reasons underlying a move from one source to another with the passage of time is indicative of an elementary but important truth: demand for minerals is for the most p r t derived demand; it is derived from our demand for final goods and services. It is not the materials per se which are necessary for the production of final goods and services, it is certain key properties, or characteristics which are required, and it is these we seek in minerals. The properties I have in mind are familiar; for example, tensile strength, conductivity - or lack of it, durability, porosity, texture, specific gravity - high or low, colour, magnetism and so forth. To take an example discussed by Scott (1962) in a most interesting article on resource substitution in the past, no one cares for the metal 'tin' as such. One does care for certain of its properties. It make copper harder and iron resistant to corrosion. It is also durable, light and malleable, and this makes it a convenient constituent of containers for food. Each of these functions can now be performed by other means. Tin's hardening of copper can be achieved by other metals. Glass jars have replaced tin cans in many circumstances. The basic constituent for glass is sand, available in vast quantities, and glass requires for its manufacture less expenditure of energy than does the extraction of tin, when the latter is sought in low-grade deposits containing minute quantities of the stuff. This is why glass jars have replaced tin cans for so many purposes. Lead and mercury are being replaced in a similar way. And so on. What are the innovative mechanisms, the characteristics of technological change, which bring forth such resource substitution as I have been discussing? They would appear to be nine in number, often overlapping, and often simultaneously occurring I . There is, first of all, the sort of innovation which enables a given resource to be used for a given purpose, that is, to use once again Zimmerman's aphorism, the kind of innovation which enables a resource "to become". The development of techniques for using coal in the refining of pig-iron is a classic example of this. To give another example, research and development aiming at the control of nuclear fusion is designed to bring forth this sort of innovation. There is, secondly, the development of new materials, such as synthetic fibres. Thirdly, there are technological developments which increase the productivity of extraction processes; or in other words, make extraction of certain minerals cheaper. (To cite an example, in the early part of this century the manufacture of large earth-moving equipment made possible the strip-mining of very low-grade ore deposits.) Fourthly, there are scientific and technological discoveries which make exploration activities cheaper. Developments in aerial photography and seismology have been crucial here. Fifthly, there are technological developments

' For a formal account of this, see Dasgupta and Heal (1979).


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which increase the efficiency in the use of resources. To give an example, during the period of 1900 to the 1960s, the quantity of coal required to generate a kilowatthour of electricity fell from nearly seven pounds to less than one pound, a more than seven-fold reduction. Sixthly, there are developments of techniques which enable one to exploit low-grade, but abundantly available deposits. For example, the discovery of the technique of froth-flotation allowed low-grade sulphide ores to be concentrated in an economical manner. Seventhly, there are constant developments in techniques of recycling materials, lowering its cost, thereby raising the effective stock in the manner I indicated earlier. There is an eighth mechanism, much more prosaic, and unconnected with any new technological development. It consists of the substitution of lowergrade resources for vanishing high-grade deposits. In early years, when high-grade deposits are amply available, there is no need to exploit lower-grade ores. Being exhaustible, the superior deposits eventually get depleted. This is then the time to move on to inferior deposits, for which extraction and refining costs are higher. Examples of this abound. And finally, there is a ninth mechanism, much explored by economists [see, e.g., Dasgupta and Heal (1974), Solow (1974), Stiglitz (1979)l. It is the substitution of fixed, manufactured capital for vanishing resources. Such possibilities are limited. Beyond a point fixed capital in production is complementary to resources, most especially energy resources. Asymptotically, the elasticity of substitution is less than one. [See Dasgupta and Heal (1979), ch. 7.1 All this looks like pure taxonomy, and taxonomy induces boredom. Fortunately, there is a single organizing idea behind all these substitution mechanisms. This enables one to study the economic process of resource exhaustion and substitution within a single analytical framework. I will give an outline of this presently. For the moment, note that each of the first seven mechanisms in the foregoing list is triggered by technological discoveries. Only the eighth and ninth mechanisms involve no new knowledge; resource substitution in these mechanisms being occasioned by the economic use of existing knowledge. That the ninth mechanism is formally akin to the eighth was transparent in the papers I have just cited above. That the first, second and sixth mechanisms can also be understood in terms of the eighth was shown by Dasgupta and Heal (1974). Subsequently it was demonstrated by a number of authors, including Dasgupta, Heal and Majumdar (1977), Hoe1 (1978), Arrow and Chang (1980), Dasgupta and Stiglitz (1981), Dasgupta, Gilbert and Stiglitz (1982,1983), and Gallini and Ware (1983) that the third, fourth, fifth and seventh mechanisms can also be understood in terms of the eighth. For analytical purposes the eighth mechanism is the key one. This is comforting, because even at first sight the eighth mechanism is the simplest to understand: it does not involve the production and use of new knowledge. As it happens, the economic analysis of the eighth mechanism had been presented, and presented to all intents and purposes in a complete form, in

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Hotelling (1931). So far as I can tell his article went pretty much unread, presumably because the timing was wrong: it was the beginning of the Great Depression. In any event, no progress in the analytical economics of exhaustible resources was made for over forty years subsequent to the publication of Hotelling's classic. Now, the reductionism just alluded to - the reduction of the first seven and the ninth economic mechanisms to the eighth - may appear to be a sleight of hand. New knowledge by definition must in some sense be unpredictable, and in extreme cases we may not even have a language to discuss it prior to its acquisition. So then how can one analyse and plan for resource exhaustion and substitution on the basis of our taxonomy? The answer is that in discussing the means of resource substitution we are not required to concern ourselves with the exact nature of future discoveries. If we needed to we would be caught in the sort of dilemma the Greeks found irresistible: to know something now we will only know in the future. So we do not try doing that. What we instead try to do is to identify the economic characteristics of possible discoveries. Thus, for example, we may not now possess the technology for mining deep-sea nodules from the middle of the Pacific. But technologists may have good reasons to be sanguine that if so much research attention is given to the problem, within twenty years' time there is a good chance economically viable techniques will have been developed. The key term here is 'economically viable', and one can see that it is the characteristics of certain operations which are relevant, to wit: finding cheap ways of operating equipment several miles below the ocean's surface over vast tracts of the ocean floor and lifting the nodules to the surface. Technologists may be able to predict with fair accuracy the time and effort needed to bring this about even though they do not know today how to do it. The point is that all research is goal-oriented. Increases in productivity are obtained not only through expenditure on research and development, they occur also through the process of resource-use, what we call learning-by-doing, or learning-by-using. Getting children to learn their tables is proto-typical learning-by-doing: repeated use teaches a person to do arithmetic operations mor e efficiently. Similarly, past experience is often a reliable guide to the extent of future learning through doing, or through using. We thus see that there is, to put it metaphorically, a constant tension between forces which raise extraction and refining costs, and those which reduce such costs. The former set of forces is occasioned by the depletion of high-grade deposits, the latter by discoveries of newer and newer technological processes and materials. It is the net effect of the two sets of forces which determines the evolution of extraction and refinement of exhaustible resources. All of this is influenced by policies affecting extraction rates and R&D expenditure. As it happens, in the aggregate extraction costs fell steadily over the first forty years of this century [see Barnett and Morse (1963)l. There are reasons for thinking, however, that costs have been rising slowly during the past few decades. [See Brown and Field 1979).] We will study the implications of this.


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Technological improvements and their influence on resource substitutability are a key to understanding the economics of exhaustible resources. We can therefore understand why people often suggest that future generations need new knowledge and capital equipment from us more than vast quantities of currently useable resources. The idea here is that technological improvements will enable future generations to exploit currently unusable resources. But for technological discoveries to occur there needs to be a motive, and thence an incentive. If serendipity is the drug which induces new discoveries, potential profits provide the far more reliable carrot and stick. These profits can be private or social, depending on the agency instituting the research: the lone inventor, the giant corporation, the private consortium, the government, or whatever. As we may infer from our seven-fold list of discoveries, these profits may be generated by the discovery of new deposits, or from discovering ways of better using existing deposits. In short, there are profits to be had from expanding the resource base. Since research and development involves the expenditure of resources, not all research is worth conducting. To strike an appropriate balance in scientific and technological research, the expected costs of research and development must be compared with the expected benefits (or profits) to be enjoyed from them. And when we try to estimate expected benefits we need to know the resource base and its economic characteristics. It is the size of the existing useable stock and not the current resource price which influences the expected profitability of a new technological discovery. As we noted earlier, the four-fold price increase of crude oil in late 1973 was not signalling impending resource depletion. It was a message that a cartel was exercising its market power. Nevertheless, we may imagine that as a resource gets depleted its price rises, reflecting growing scarcity. Were this so, then ignoring such exceptions as resource cartels coalescing effectively, price increases are the signals the market provides for profit-seeking inventors, firms and governments. As it happens, this is not precise enough. The matter is not difficult to fathom, but it is a good deal deeper. So we turn to the behaviour of market prices of exhaustible natural resources, to see which price we ought to monitor, and why.

4. Analysis of resource prices

A pool of oil, or a vein of iron or a deposit of coal in the ground is a capital asset to society, and to its owner if the deposit is owned by an individual agency. The deposit draws its value, say a market value, from the prospect of extraction and sale. In the meanwhile, as a renowned economist aptly marked, the resource owner is looking

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down at his mine and asking "What have you done for me l a t e l ~ ? There "~ are two ways an asset can yield a return to its owner: by appreciating in value (capital gains), and by earning a dividend. Most assets offer a combination of both. (Of course, assets are all too often known to depreciate in value - they are capital losses - but this is merely the negative of appreciation, and so falls within the same category.) The fundamental point about an exhaustible resource deposit lying untapped,is that the only way it can earn a return for its owner is by appreciating in value. It cannot earn a dividend. It cannot because we are talking about that portion of the deposit lying untapped. We must now ask by how much the deposit should appreciate in value over time in order that investors would be willing to hold a mixed portfolio of shares in this deposit and shares of other market assets. This is easy to answer. If the rate of return on any other capital asset in the same risk-class is given, the rate of price appreciation (i.e. the rate of capital gains) of the untapped deposit must equal this rate of return. To see why this must be so, notice that if the expected price appreciation on the resource deposit were greater than the expected rate of return on other assets in the same risk category, no one would wish to hold these other assets in their investment portfolio: all would wish to unload these assets and move exclusively towards buying shares in the resource deposit. Contrariwise, if the expected rate of price appreciation on the resource deposit were less than the rate of return on other capital assets in the same risk category, no one would wish to hold a share of the resource deposit in his investment portfolio. All would wish to unload. We conclude that in order for people to wish to hold a mixed portfolio of assets - inclusive of the resource deposit - the expected capital gains on the resource deposit must equal the expected rate of return on other capital assets in the same risk class. This is the fundamental principle of the economics of exhaustible resources, and is today referred to by economists as the Hotelling Rule, in honour of the man who first deduced it in a rigorous manner in the process of analysing the eighth mechanism in my earlier list. The capital gains I have been talking of is the rate of appreciation in the value of the resource deposit underground. It is the rate of capital gains on the value of the mine. It is thus the rate of appreciation of the ground rent, or royalty, on the mine. The Hotelling Rule states that the expected rate of capital gains on the mine will - under equilibrium conditions - grow in a compound manner at a rate given by the expected rate of return on any other capital asset belonging to the same risk class. Now it should be remembered that the royalty is not the final sales price of the extracted or refined ore. It is less, sometimes far less, because extraction, refinement, and transportation involve costs. If the resource market is approximately competitive at all stages, the final sales price of the extracted The economist is Robert Solow, whose Richard Ely lecture to the American Economic Association [Solow (1974)l is a classic exposition of the subject matter of this essay.


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resource (and by this I mean the extracted, refined, and transported resource) must approximately equal the sum of its ground rent (or royalty) and its extraction cost 3 . So there it is. The expected royalty on a resource deposit grows at a compound rate equal to the expected rate of return on assets in the same risk category. But the final sales price of a unit of the extracted ore at any date is the sum of the ground rent and extraction costs. The current ground rent on an abundant resource would be small. In the extreme it would be nil, as with air. For scarce resource deposits it would be large. In order to formalize this let me, for ease of exposition, assume away uncertainty, so that the expected prices are realized. Let us take 1991 to be the base year, and let q, denote the market price of the extracted, refined and transported resource in year t , where t = 1991,1992,1993,. . . , and so on. Let P~~~~ be the ground rent on a unit of the resource in the base year, and let c, denote the cost of extraction, refinement and transportation of a unit of the resource in year t . Finally, let r be the rate of'return on any asset in the same risk class as the resource in question. For convenience of exposition we may think of r as the real interest rate on long-term government bonds. By assumption expectations are always realized, and so from our previous arguments we can conclude that if the resource market is approximately competitive the various prices and costs defined above will be related by the formula

The first term in the right-hand side of this expression is the royalty, increasing at the compound interest rate r; and the second term is the cost of extraction, refinement and transportation 4. Of these, only the royalty in the base year, ~1991, needs explanation. Unlike r and c,, it is not part of the 'data'. One needs to estimate it from data pertaining to the resource market. Its value depends on current and estiinated future demand for the resource, available and potential resource deposits, the availability of near-substitutes, and so on. Other things being the same, the larger are available deposits (or expected future discoveries), the smaller isp1991 in relation to ~ 1 9 9 1 .In extreme cases it may be nil 5 . The simplest general case to study is one where the unit cost of extraction is constant over time. The final sales price of the extracted ore is then a constant amount in excess of the royalty, which as we have seen, grows at a compound rate equal to the rate of return on other assets. The final sales price qt of the refined I should add that the story would be somewhat different if the resource market were not competitive and were instead controlled by a friendly neighbourhoodmonopolist. But the difference is not sufficient to justify my not assuming a competitive economic environment for the purposes of this chapter. In what follows I will collapse these items and refer to them together as extraction costs. For details of this kind of calculation, see Dasgupta and Heal (1979).

I? Dasgupta

Royalty, or Ground Rent Price of Extracted

Extraction Cost

Fig. 1. Competitive price path of exhaustible resource: constant unit extraction cost.

ore in this case grows at a rate less than r. Figure 1 displays the price trajectories of such a resource. Now, one would not expect extraction costs to remain constant, for reasons we have already discussed. If unit costs of extraction are expected to grow because society will be forced to mine more and more inferior grades, the final sales price will rise, now for two reasons, rather than the single reason prevailing if unit extraction costs remain constant. But if technological advances lower extraction costs at a sharp enough rate the final sales price would indeed fall. But it cannot fall forever, because extraction costs have a floor to them, namely, zero. Eventually the final sales price must rise, and rise at nearly a compound rate, for the ground rent term will eventually come to dominate. (See Figure 2.) The key word here is 'eventually', and I shall come back to it. Let me summarize what we have learnt about price paths of exhaustible natural resources. The market price of a resource is made up of two components: extraction cost and ground rent. The latter grows at a compound rate. If the existing, useable, deposit is large, the ground rent will initially be low relative to extraction costs. As the deposit eventually gets depleted the ground rent comes to dominate. This conclusion holds even if new deposits are continually being discovered through the process of research. That an untapped deposit cannot yield a dividend continues to hold even when new deposits are being discovered in a predictable way. The Hotelling Rule is robust against this form of generalization. Matters are different if there is uncertainty in the discovery process. Discoveries are then not predictable, In this case expected prices are not necessarily realized - the size of newly discovered deposits may be larger or smaller than anticipated. If discoveries over a period happen to be systematically larger than anticipated the realized ground rent will decline over the period. Nevertheless, even in the face of


Unit Extraction

Price of Extracted

Ground Rent

t Fig. 2. Competitive price path of exhaustible resource: variable unit extraction cost.

uncertain discoveries a modified version of Hotelling Rule will hold, the Rule now pertaining to the ground rent which in some sense is expected to prevail, not to that which is ultimately realized 6 .

5. Royalties as a measure of resource scarcity

Data on ground rents are hard to come by. Nevertheless, there have been several analyses of time series of extraction costs and final sales prices of exhaustible resources. In their well-known work, Barnett and Morse (1963) argued that with the exception of timber, both extraction costs and final prices of natural resources displayed a secular decline during the first half of this century. If true, this must have been due to a combination of our first seven mechanisms. Barnett and Morse concluded from this that resources were not getting scarcer; on the contrary, they were getting less scarce. This is an incorrect conclusion to draw. We have noted that if extraction costs fall fast enough the final sales price will fall for a while even if there were a single deposit and no discoveries in sight. We would hardly say that the resource was in this case getting less scarce. So then which price signals growing scarcity? The ground rent of course: its 'expected' value grows at a compound rate, signalling the expected growing value of the resource. Ground rents, as a fraction of extraction costs, say, are a true index of resource scarcity. If deposits are initially very large, the ground rent is initially tiny, and it is many years before the rent rises to appreciable For exact statements, see Dasgupta and Heal (1974,1979) and Arrow and Chang (1980).

Table 1 Real price of selected minerals using the price of capital as a numeraire; selected years, 1920-1950a Mineral

Real price

Coal Copper Iron Phosphorus Molybdenum Lead Zinc Sulphur Aluminium Gold Crude petroleum a

From Brown and Field (1979).

figures. Even at 5% per annum (a generous figure for the real interest rate) a penny takes about 120 years to become a five pound note. Compound interest is no doubt remorseless. But it can at the beginning be slow if what is compounded is very small to start with. In any case, time series of resource prices are not ambiguous. Estimates of the behaviour of resources prices tend to vary from study to study. In ,a recent work Brown and Field (1979) assessed different estimates and showed that the prices of a selected group of key minerals did not display a secular decline during the first half of this century. Indeed, for one set of data (see Table 1) given for three selected years, prices display a U-shaped path.

6. Transition from exhaustible to durable resource base I began by suggesting that it is not specific resources we care for, it is certain characteristics we seek, certain services we need and desire. A wide variety of resources may offer the same set of services. This is why substitution is the key concept is resource economics. Timber, coal, oil and natural gas are all sources of free energy. (By 'free' I mean free in the thermodynamic sense, not in the economic sense.) So is uranium-238 a source of free energy today, although it was not so fifty years ago. If at some future date nuclear fusion comes to be controlled at an acceptable risk, or if solar energy comes to be tapped in large quantities at reasonable cost, we will have at our disposal vast new deposits of free energy, so vast that to all intents and purposes we will have a renewable source, which is to say that the royalty on such sources, when they become technologically and economically

Ch. 23: Natural

?sources in an Age of Substitutability Market Price ( = Unit Production Cost) of Durable Energy Source Market Price of Extracted Fossil Fuel

Ground Rent on Fossil Fuel Unit Extraction Cost of Fossil Fuel

I

-

w

T

t

Fig. 3.'Date of substitution of renewable energy source for non-renewable source.

viable for exploitation, will be tiny for a while. But the economical availability of such renewable sources is at the moment conjectural. Provided resources are diverted'towards research and development of these alternative sources, we may expect to develop them some time in the future, the greater the R&D effort, the earlier the expected date of success. Meanwhile we have to rely on finite resources. What then will be the price trajectory of the service provided by such resources? In Figure 3 I present the competitive price path of a service, such as say energy,when it has to be obtained from a finite deposit, and where it is expected that a renewable source will become available at a date T somewhat far away in the future7. The expected date of completion of the R&D programme on the alternative energy source influences the current and future resource price. Moreover, the size of existing deposits of fossil fuels influence the rate of R&D effort, and thus the expected date of completion. These mutual relationships can be analyzed, and there is m a substantial body of literature which does this, and they have taken into account such obvious extensions as uncertainty in research completion times and in the cost of energy obtainable from these future technologies Figure 3, describing a possible time profile of energy price, is stylized to indicate the crucial 'features. The transition from the exhaustible (fossil fuel) base to the more durable, renewable (nuclear or solar) base will, unlike in Figure 3, not be dramatic. If and when such renewable sources are put into operation alternate sources will co-exist, possibly for quite some time, as indeed they do now. Prices will not display the discontinuity suggested in Figure 3, because the diagram has not recldoned for the feature that new technologies inevitably suffer from teething trouble. Production costs usually fall with growing experience, and plants take time to build. In short, transition from an exhaustible resource base to a durable, renewable resource base can always be expected to be gradual.

'

For simplicity of exposition I assume away uncertainty once again, so that expectations are realized. See Dasgupta and Heal (1974) for an analysis of the case where T is uncertain. See Dasgupta, Heal and Majumdar (1977) and Dasgupta (1982).

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The nagging question remains: isn't all this too fanciful? We began by discussing exhaustible resources, we are now making the mental transition to durable resource bases. Is this the right conceptual framework? In any case, we have been talking so far about energy resources. Why should we think this is the only biting constraint, the most important resource to discuss among geological resources?

7. Prospects for transition to the age of substitutability

Such questions as these can only be broached by physical scientists. To the best of my knowledge Goeller and Weinberg (1976) was the first empirical cut at such issues. There are many shortcomings in this article. Nevertheless, the spirit of the exercise is just right. Goeller and Weinberg went through the periodic table, examining all the elements and then some important compounds, such as hydrocarbons; noted their world-wide use in the year 1968 - the authors' base year - and estimated for each item its global presence, having entertained an extremely generous notion of what constitutes potential resource deposits. The deposits included the atmosphere, the oceans and a mile-thick crust of earth. Their attitude towards what constitutes a resource is light-years away from the attitude I have taken in this chapter. They make only cursory reference to costs of resource extraction. They concern themselves mainly with their physical presence, not with their economic availability. For example, a given quantity of resource may be thinly distributed over the earth's crust, in which case extraction costs will be very high. Alternatively, the same amount may be present in highly concentrated forms. In this latter case extraction costs will be low. This, as we have noted, can make an enormous difference. To illustrate the point I am driving at, consider the fact that soil erosion (that is, loss of top soil) is today a major form of environmental degradation, a serious loss in world-wide agricultural output. The quantity of soil in the atmosphere, the seas and a mile-thick crust of the earth remains pretty much the same. But the soil has got 'relocated', it has got 'blown away'. This matters greatly. Goeller and Weinberg treat such considerations lightly. Nevertheless theirs is a rough starting point for charting possibilities. There is a good deal more work to be done. I shall first give an idea of our current use of exhaustible materials. In Table 2 world demands in 1974 of the major non-renewable materials are presented. In terms of quantity, far and away the most important are sand, stone and related products (accounting for nearly 60%), and this is followed by fossil fuels (nearly 37%). These materials, plus iron, aluminium and magnesium, and eight of the other most widely used elements constitute more than 99.5% of all nonrenewable materials currently used by society. When we include prices and their In this article we are ignoring the biological sphere. It raises a different set of issues.

Ch. 23: Natural Resources in an Age of Substitutability Table 2 World demand for non-renewable materials, 1974a Material

Total world demand % of total quantity (by weight) % of total demand (by value)

Fossil fuels (CH,) Coal and peat Petroleum Natural gas Subtotal Sand and gravel ( S O z ) Crushed stone (CaC03) Clay, gypsum, pumice Subtotal Iron Aluminium & magnesium Subtotal Other major material Chlorine Sodium Nitrogen Sulphur oxygen Hydrogen Potassium Phosphorus Subtotal All other a

0.38

9.10

From Goeller (1979).

relative importance in value terms, fossil fuels leap to the first place, accounting for nearly 55% (right-hand column), building materials plummet to a rock-bottom place, accounting for under 5%, and iron, aluminium and magnesium jump to a second place at nearly 27%. In value terms these principal materials account for over 90% of all non-renewable materials currently used by society. I now come to the Goeller-Weinberg estimates. Table 3 provides data on the hydrocarbons and a few of the more notable elements. The most revealing column

II Dasgupta Table 3 World availability of the most extensively used elementsa Element CHx C (oxydized) Si Ca H Fe N Na 0 S C1 P K A1 Mg Mn Ar Br Ni a

Resource

Tons available

R/D year^)^

coal, oil, gas limestone sand, sandstone limestone water basalt, laterite air rock salt, seawater air gypsum, seawater rock salt, seawater phosphate rock sylvite, seawater clay (kaolin) seawater seafloor nodules air seawater peridotite

From Goeller and Weinberg (1976). RID is the resource-to-demand ratio in 1968.

is the last one. For each resource it presents the total stock in the atmosphere, the oceans and a mile-thick crust of the earth, divided by the 1968world demand for it. In short, the column presents the number of years each resource can be expected to last at the 1968 rate of world use. (The underlying assumption is that recycling is not possible.) As incomes rise and population grows demand must surely be expected to grow, though not necessarily at the same rate for all resources. And I will come back to the adjustments required to account for such changes. But note first that the only cause for worry are the phosphates (a mere 1300 years of supply), fossil fuels, labelled CH, (some 2500 years), and manganese (about 13000 years). The rest are available for more than a million years, which is pretty much like being inexhaustible. More particularly, Goeller and Weinberg argue that with the exception of phosphorus, some trace elements needed for agriculture (notably zinc and copper), and fossil fuels (hydrocarbons), the essential raw materials are in effect in infinite supply. As the world exhausts its non-renewable raw materials it can move to lower-grade inexhaustible resources. The increase in energy required to extract and process these low-grade materials is not huge. Goeller and Weinberg present crude estimates of the ratio of the energy required to extract a ton of some of these low-

Ch. 23: Natural Resources in an Age of Substitutability Table 4 Energy requirements for the production of abundant metals and coppera Metal

Source

Magnesium ingot

seawater

Aluminium ingot

bauxite clay

Raw steel

magnetic taconites iron laterites

T i b u m ingot

rutile ilmenite titanium-rich soils

Refined copper

porphyry ore, 1% Cu porphyry ore, 0.3% Cu

Gross energy (kWh/ton of metal)b

EL/EH'

From Goeller and Weinberg (1976). Gross energy is estimated at 40% thermal efficiency for generation of electricity. EL/EHis the ratio of energy required to extract a ton of metal for low-grade ores (EL) and for highgrade ores (EH). With carbon. With electrolytic hydrogen. a

grade abundant metal ores to that required to extract a ton of high grade ores. In none of these cases does the ratio exceed 2. (See Table 4.) So the problematic resources are phosphorus, some trace elements needed for agriculture, and fossil fuels. The solution for phosphorus and the trace elements must then lie in recycling. Indeed, H.G. Wells, in his book, The World Set Free, had suggested that phosphorus is in limited supply, and that we may need to recycle it as fertilizer by crushing bones! The supply of hydrocarbons, adjusting for population growth, which Goeller and Weinberg take as 10 billion in the long run, will only last a few hundred years, a good deal less than the 2500 years estimated on the basis of 1968 demand. So then this is the fly in the ointment, the bottleneck, the binding resource: limited hydrocarbons, currently the main source of energy. In a sense we are back, full circle, to where we began in this chapter, the exhaustibility of energy resources. Here Goeller and Weinberg have an interesting suggestion. They observe that both carbon and hydrogen are abundant in oxidized form, specifically in the form of carbon dioxide and water, respectively. They also note that there are a number of known technical processes which allow us to reduce carbon dioxide and water to hydrocarbons needed for transport and

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II Dasgupta

energy. The trouble is, these processes in turn require a good deal of energy! So there we are, back to the 'ultimate' resource: cheap and non-risky sources of useable energy. In an interesting work The Next Million Ears, C.G. Darwin (grandson of Charles Darwin), saw the only possible source of unlimited energy in nuclear fusion. Today we think of other inexhaustible sources: solar, geothermal and clean nuclear breeder reactors. Goeller and Weinberg see the pattern of future resource-use as consisting of three stages. The first, lasting for another thirty to forty years at least, would be a continuation of present patterns of use of exhaustible resources. The second, lasting several hundred years, would be one where society depends mainly on coal (there would be little oil and natural gas left). Less reliance would be placed on nonferrous metals, more on alloy steels, aluminium, magnesium and titanium. Beyond that is the third stage, the Age of Substitutability, by which time fossil fuels will have been pretty much exhausted. In this final Age, economic activities will be based almost exclusively on materials that are virtually inexhaustible, with relatively little loss in living standards. Goeller and Weinberg speculate that the Age of Substitutability will be based largely on glass, plastics, wood cement, iron, aluminium and magnesium. Difficult to imagine perhaps. But then, eighteenth century society would have found it difficult to imagine us today, certainly they would be astonished at the resource base upon which modern economic activities rest. The details of the Goeller-Weinberg speculations are not of importance, nor would they, I imagine, wish to emphasize them. But we need something like this sort of exercise to back up the analytical literature we sketched earlier. And yet, talk of controlled nuclear fusion and clean breeder reactors, smacks of the futurology, wishful thinking. If such technological possibilities appear now to be remote, and this remoteness a cause for anxiety about the future, we should remember that even in the second half of the nineteenth century thoughtful people worried about declining energy sources and saw no way out. In a famous chapter on possible substitutes for coal, the economist, W.S. Jevons, in his book The Coal Question, published in 1865, expressed deep concern about the future of British industry. And he wrote: I draw the conclusion that I think anyone would draw, that we cannot long maintain our present rate of increase of consumption; that we can never advance to the higher amounts of consumption supposed ... the check to our progress must become perceptible considerably within a century from the present time; that the cost of fuel must rise, perhaps within a lifetime, to a rate threatening our commercial and manufacturing supremacy; and the conclusion is inevitable; that our happy progressive condition is a thing of limited duration.

That Britain's 'commercial and manufacturing supremacy was under threat cannot be doubted, since the supremacy did not last. But the price of fuel had nothing to do with it. It may be argued that economists are prone to making rotten


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predictions, scientists are better. This is not quite true. Here is an editorial comment in the 1876 issue of the ScientiJicAmerican: A recent lecture was given by Professor Foster, F.R.S., at South Kensington on 'Electricity as a Mode of Power.' Dr. Siemens, F.R.S., took the chair. Professor Foster first showed with a number of experiments that by very simple arrangements light bodies can be moved by electricity .. . Although we cannot say what remains to be invented,we can say that there seems no reason to believe that electricity will be used as a practical mode of power. There is always power lost by the inverse current. Work of some kind must be done to produce electricity, and this can more economically be done by employing that power directly. Scientific American, 1876 The moral is banal. We are all given t o myopia.

References Arrow, K.J., and S. Chang, 1980, "Optimal Pricing, Use, and Exploration of Uncertain Natural Resource Stocks", in: P.T. Liu (ed.), Dynamic Optimization and Mathematical Economics (Plenum Press, New York). Barnett, H.J., and C. Morse, 1963, Scarcity and Growth: The Economics of Natural Resources Scarcity (Johns Hopkins University Press, Baltimore, MD). Brown, G., and B. Field, 1979, "The Adequacy of Measures for Signalling the Scarcity of Natural Resources", in: V. Kerry Smith (ed.), Scarcity and Growth Revisited (Johns Hopkins University Press, Baltimore, MD). Bruno, M., and J. Sachs, 1985, The Economics of Worldwide StagfIation (Basil Blackwell, Oxford). Dasgupta, I?, 1981, "Resource Pricing and Technological Innovations Under Oligopoly: A Theoretical Exploration", Scandinavian Journal of Economics 83, 289-318. Dasgupta, P., 1982, "Resource Depletion, Research and Development and the Social Rate of Return", in: R. Lind (ed.), Discounting for Time and Risk in Energy Policy (Johns Hopkins University Press, Baltimore, MD). Dasgupta, P., and G. Heal, 1974, "The Optimal Depletion of Exhaustible Resources", Review of Economic Studies, Symposium Issue, pp. 1-23. Dasgupta, P., and G. Heal, 1979, Economic Theory and Exhaustible Resources (Cambridge University Press, Cambridge). Dasgupta, l?, and J. Stiglitz, 1981, "Resource Depletion Under Technological Uncertainty", Econometrica 49,85-104. Dasgupta, I?, G. Heal and M. Majumdar, 1977, "Resource Depletion and Research and Development", in: M.D. Intriligator (ed.), Frontiers of QuantitativeEconomics, Vol. I11 (North-Holland, Amsterdam). Dasgupta, P., R. Gilbert and J. Stiglitz, 1982, "Invention and Innovation Under Alternative Market Structures: The Case of Natural Resources", Review of Economic Studies 49,567-582. Dasgupta, ,.'F R. Gilbert and J. Stiglitz, 1983, "Strategic Considerations in Invention and Innovation: The Case of Natural Resources", Econometrica 51,1439-1448. Debrajan, S., and A.C. Fisher, 1982, "Measures of Natural Resource Scarcity Under Uncertainty", in: V. Kerry Smith and J.V. Krutilla (eds.), Explorations in Natural Resource Economics (Johns Hopkins University Press, Baltimore, MD). Gallini, N., T. Lewis and R. Ware, 1983, "Strategic Timing and Pricing of a Substitute in a Cartelized Resource Market", Canadian Journal of Economics 16,429-446.

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Goeller, H.E., 1979, "The Age of Substitutability: A Scientific Appraisal of Natural Resource Scarcity", in: V. Kerry Smith (ed.), Scarcity and Growth Reconsidered (Johns Hopkins University Press, Baltimore, MD). Goeller, H.E., and A.M. Weinberg, 1976, "The Age of Substitutability", Science 191 (February 20) 683689. Harris, D.P., and B.J. Skinner, 1982, "The Assessment of Long-Term Supplies of MineralsV,jn:V. Kerry Smith and J.V. Krutilla (eds.), Explorations in Natural Resource Economics (Johns HopkinsUniversity Press, Baltimore, MD). Hoel, M., 1978, "Resource Extraction, Substitute Production and Monopoly", Journal of Economic Theory 19,28-37. Koopmans, T.C., 1980, "The Transition from Exhaustible to Renewable or Inexhaustible Resources", in: C. Bliss and M. Boserup (eds.), Economic Growth Resources. Vol. 3: Natural Resources (Macmillan, London). Rosenberg, N., 1976, Perspectives on Technology (Cambridge University Press, Cambridge) chs. 12 and 14. Scott, A., 1962, "The Development of Extractive Industries", Canadian Journal of Economics 28,70-87. Slade, M.E., 1982, "Trends in Natural-Resource Commodity Prices: An Analysis of the Time Domain", Journal of Environmental Economics and Management 9,122-137. Solow, R.M., 1974, "The Economics of Resources, or the Resources of Economics",American Economic Review 64 (Papers and Proceedings) 1-21. Stiglitz, J., 1979, "A Neoclassical Analysis of the Economics of Natural Resources", in: V. Kerry Smith (ed.), Scarcity and Growth Reconsidered (Johns Hopkins University Press, Baltimore, MD). Thomas, B., 1980, "Towards an Energy Interpretation of the Industrial Revolution", Atlantic Economic Review 8, 1-15. Zimmerman, E.W., 1964, Introduction to World Resources (Harper and Row, New York).

Chapter 24

NATURAL RESOURCE CARTELS* DAVID J. TEECE Haas School of Business, University of California, 554 Barrows Hall, Berkeley, CA 94720, USA DAVID SUNDING Law and Economics Consulting Group (LECG), Parker Plaza, 2560 9th Street, Suite 212, Berkeley, CA 94710, USA ELAINE MOSAKOWSKI Graduate School of Management, University of California at Los Angeles (UCLA), 6359 Anderson, 405 Hilgard Avenue, Los Angeles, CA 90024-1482, USA

1. Introduction

The defining characteristic of cartels is that they involve explicit communication and agreement among competitors to control output and price. Various synonyms are commonly used to describe these arrangements, including combine, conference, and syndicate. The loosest form of cartel is a 'gentleman's agreement' to fix prices and/or control output. A tighter form would involve separately owned, independent or public enterprises unified under a formal charter or agreement to engage in restrictive practices. The cartel concept as defined does not include collusion which is merely tacit and which does not involve an agreement, although it is recognized that the market outcomes associated with tacit collusion may sometimes be quite similar to those obtained from cartelization. A cartel, if it is to be successful, must confront and surmount several organizational and market challenges. The external challenge is to discourage and, if possible, prevent production by non-members. The internal challenges are more numerous, although arguably not so severe: to calculate the optimal level of production and prices for the commodity being cartelized; to allocate that production, or the returns from it, among the members of the cartel; and to detect and punish cheating. * We thank Robert Pindyck and James Griffin for helpful criticism. This paper was drafted in 1984 and revised in 1992. Handbook of Natural Resource and Energy Economics, vol. 114 edited by A. VKneese and J.L. Sweeney O 1993 Elsevier Science Publishers B. V All rights reserved

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Conventional textbook theory teaches that cartefs are inherently unstable because of the difficulties associated with sharing, detecting and punishing. Unless the cartel members have identical cost functions, discount rates, and a host of other common attributes, profit-maximizing members will disagree about the appropriate level of cartel output and the division of that output among the cartel members. When government entities are involved, with discount rates set by political whim rather than by objective market consideration, this later problem will be particularly serious, as many observers, including Osborne (1976) and Griffin and Teece (1982, ch. 1) have indicated. Those members that judge the production agreement as unfair will cheat on that account alone, while all members will have an incentive to cheat if they believe that deterrence is weak. In the standard formulation, cheating dominates over observing the agreement; so the cartel collapses, assuming it were ever to become established in the first place. The traditional cartel theory based on maximizing behavior of cartel members tends to be somewhat strained. Both the creation and maintenance of cartels is difficult, though not impossible, to explain. Game theory addresses some of these deficiencies. The most important results in this recent effort stem from 'Folk Theorems' for repeated games such as that described by Fudenberg and Maskin (1986) and reputation models of the type formalized by Kreps et al. (1982). These theorems show the types of cooperative behavior that are attainable with repeated contact when cartel members employ sophisticated monitoring and punishment strategies. Their results indicate that in theory cartels can achieve a high degree of cooperation, thus laying a foundation for the treatment of cartels as cooperative institutions. In Section 2 we consider the major classes of theories of cartel objectives and behavior. Whether cartels can solve their problems in principle is not as interesting as the question of whether they can solve their problems in practice. Some clearly have, at least for certain periods. Successful cartels include a number of exhaustible resource cartels. Section 3 presents a number of theoretical and empirical results on the durability of cartels. In Section 4 we consider some propositions concerning the welfare implications of cartels. The typical argument treats cartels as monopolists, and concludes that cartels subtract from social welfare by choosing suboptimal extraction paths. While we largely agree with this treatment of the problem, we also consider conditions under which such cooperation is socially beneficial. Finally, in Section 5 we discuss in detail some natural resource cartels and use this evidence to assess the cartel theories presented in Section 2. We consider the international oil, mercury, uranium, and diamond cartels.

Ch. 24: Natural Resource Cartels

2. The cartel problem

There are three major classes of theories concerning the nature of exhaustible resource cartels: (1) The behavior of resource cartels can be described by a simple welfare diminishing monopoly model or by treating a subset of producers (or countries) as a dominant firm, with the remaining producers behaving as a competitive fringe. (2) Cartel behavior can be described by non-traditional objectives, particularly satisfaction of target revenue requirements. (3) Cartel behavior can in some circumstances generate positive welfare gains. We consider (1) and (2) below. In Section 3 we briefly touch upon (3).

2.1. Monopoly

The behavior of a cartel can be considered to approximate a single-firm monopoly. This is a rather extreme characterization of cartel behavior, but is nevertheless a useful starting point. Thus consider a natural resource cartel in which the decision to produce today does not influence future production costs. Even in this simple world it is important to recognize that the decision to produce today precludes the possibility of producing at some time in the future. In effect, there is an opportunity cost, or user cost, associated with the decision to produce. Harold Hotelling (1931) first articulated the intertemporal conditions for profit maximization in extractive industries. Hotelling chose to make the simplifying assumption that marginal production costs are zero. His now-standard arbitrage rule holds that prices will rise at the rate of interest under competitive market conditions, or

where P,is the market price in period t , and r is the (common) rate of discount. For the monopolist (or the cartel), marginal revenues, which are less than price as in the static case, will rise over time at the rate of interest, or

We should note that eq. (2) is bath a flow and a stock equilibrium condition, as discussed by Solow (1974) and Dasgupta and Heal (1979). Monopoly prices determined by eq. (2) obviously rise over time with marginal revenue, but the rate of increase depends on the characteristics of the market demand curve. It is natural to investigate the competitive and monopoly price paths

D.J.Teece et al.

t

*

time

Fig. 1. Alternative price paths for an exhaustible resource.

governed by eqs. (1) and (2), respectively, by making alternative assumptions about how the elasticity of demand varies along the demand curve. In the case of a constant elasticity of demand, the depletion policy undertaken by a cartel is identical to that undertaken under perfect competition. The intuition is simple: the price resulting from an intertemporal competitive equilibrium rises at the rate of interest, while under monopoly marginal revenue rises at this rate. Marginal revenue is proportional to price when the demand function has constant elasticity, so eqs. (1) and (2) imply the same extraction paths. A more plausible situation is one in which the elasticity of demand increases with the price of the resource. This may arise, for example, when there exist actual or potential substitute technologies for the resource in question that are viable at high prices or, somewhat more mechanically, when the cartel faces a linear demand curve. In this case, the monopoly price path is always flatter than the competitive price path, and must cross the competitive price path once from above. Figure 1 contrasts the price paths. This argument illustrates the adage that "The monopolist is the conservationist's best friend". The monopoly extraction agreement distorts the socially optimal pattern of resource depletion by encouraging too much conservation initially, that is before t* in Figure 1. Hotelling's arbitrage principle provides the most fundamental characterization of the behavior of resource cartels as monopolies. It is not, however, sufficient to describe the behavior of even a simple monopolist in several significant and realistic cases. Perhaps most important is a situation in which there exists a 'backstop technology7. In this case, it is common to assume that there is some price above which the resource cannot be sold. The optimal monopoly price trajectory may


time before exhaustion

Fig. 2. Alternative price paths with backstop.

then be derived by working backwards from the backstop price with the arbitrage condition. To determine the date of exhaustion under these conditions, it is analytically convenient to move backwards through time from the date at which price equals its maximum and note that the price falls for reasons just discussed. Price determines consumption at each date, and also cumulative consumption. The time to exhaustion is simply determined by stopping the clock when cumulative consumption equals the total stock. Figure 2 gives price and depletion paths for a monopoly cartel and a competitive industry in the presence of a backstop technology for the case of a linear demand curve. This analysis highlights the fact that resource cartels are even more difficult to form and maintain than are collusive institutions in the more familiar static case. Members must agree on the size of the total stock, future demand conditions, substitute goods, and discount rates; otherwise they will disagree as to the optimal price path. In some cases, however, the problems faced by resource cartels may not be so different from those faced by static cartels since Hotelling rents are small for many commodities in relation to costs. In this event, agreement on depletion rates will not be an empirically decisive factor in determining cartel behavior or success. A closely related class of models of cartel behavior envisions the cartel as consisting of a core number of firms or countries acting cooperatively in the presence of a competitive fringe. These models typically treat the cartel as a Stackelberg leader that announces a timqpath of prices. The fringe reacts to this announcement by choosing a profit-maximizing extraction path. Papers in this genre include Salant (1976), Gilbert (1978), Lewis and Schmalensee (1978, 1982), Ulph and Folie (1980), and Ulph (1982). The analysis in this case is considerably

D.J. Teece et al.

I

I TI

I

TI

time

Fig. 3. Limit pricing.

more complicated than in the case of either perfect competition or monopoly. The previous section indicated that the extraction behavior of a monopoly cartel could be described by the Hotelling rule and, where necessary, by consideration of the constraints imposed by a backstop technology. In the case of a dominant firm facing a competitive fringe, the relationship between price and marginal revenue becomes more complex. We illustrate some of the complexities here by considering one important, although admittedly special, case: limit pricing. Suppose that a cartel must decide on an extraction plan in the presence of a fringe that supplies elastically above a certain price, sayp. The cartel's marginal revenue schedule then has a kink a t p since it cannot feasibly set a higher price and faces no competition at lower prices. Suppose further that the demand function is iso-elastic and has greater than unitary elasticity belowp*. There is a familiar equilibrium in this case shown in Figure 3. Initially the cartel prices belowp* and prices rise at the rate of interest. Between T I and T 2the cartel sells its remaining stock atp*. Finally, the fringe produces atp* until its stock is exhausted. Gilbert (1978) and Dasgupta and Heal (1979) consider the more complex cases of unitary and inelastic demand atp*. This core-fringe market structure highlights another important problem faced by a resource cartel in addition to those faced by static cartels: the possibility of the dynamic inconsistency of extraction plans derived via the maximum principle. Our analysis to this point has assumed that all members of the cartel, and indeed all fringe firms, commit to extraction paths and do not deviate from these plans. Modelling cartel behavior with commitment is equivalent to assuming the existence of well-functioning futures markets wherein producers can contract with consumers for current and future delivery of the resource at prespecified prices. In the


Rate of Return

I I I'

Investment

Production

Fig. 4. Target revenue model: (a) investment determination; (b) output determination.

absence of futures markets, commitments to price paths are typically not credible. Newbery (1981) and Ulph (1982) were among the first to show that there is an incentive to deviate from these plans derived from the maximum principle in a number of realistic cases. In particular, they show that the problem of dynamic inconsistency is especially important in the case of a cartel facing a competitive fringe. Computation of dynamically consistent plans, defined as extraction plans and implied price paths that maximize discounted profit for each firm at each date, imposes a significant burden on industry participants. To the extent that these plans differ from desired behavior at any instant in time, dynamic inconsistency is a basis for conflict.

D.J. Teece et al.

2.2. Target revenue models Target revenue models depict resource cartels as a collection of firms whose production decisions are made with reference to budgetary requirements. As described in Teece (1982), these budgetary requirements are, in the case of nationstates, determined by absorptive capacity and other macroeconomic concerns. More formally, cartel revenues can be considered as the source of funding for potential investment projects, which can be arrayed along a representative marginal efficiency of investment schedule (see Figure 4a). If a country is unwilling to invest for return less than r* then investment needs are limited by I*.In Figure 4b, if production decisions are made in order to meet the investment objective represented by I * , then increases in the world price (from Po to P') in the current period will tend to result in reduced production (Qo to Q') in the current period, and conversely. The supply schedule thereby generated will have the 'wrong' slope; that is, it will be backward bending, at least over the relevant range. This property also exists in Cremer and Salehi-Isfahani's (1980) consideration of OPEC and in Griffin and Steele (1980) I . An intertemporal dimension can be readily added: economic development can be viewed as expanding investment opportunities and thereby raising the revenue target. Consequently, any specific backward-bending supply curve is dependent on a given level of infrastructure. Given adjustment time, the target revenue can rise substantially; so the target revenue model might be thought of as a more adequate description of cartel behavior in the short run than in the long run, and more for economies highly dependent on oil revenues than for economies that are diversified. However, it can be argued that the target revenue model has long-run predictive implications for countries with more limited potential for expanding domestic investments. Earnings from current investment activity may generate sufficient returns to partially finance future investment plans, enabling a lower dependency on revenues for domestic investment programs.

3. The durability of cartels

The cartel problem involves surmounting both external challenges (production by nonmembers) and internal problems (calculating the optimal cartel production, allocating production, detecting cheating, and deterring cheating). In this section we examine factors which seem to influence the ability of producers to meet these challenges. In short, we examine conditions that favor cartel formation and factors which contribute to cartel durability.

'

The target revenue model and the backward sloped supply schedule were first put forward by industry economists in the 1970s.


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We begin by noting that the answers to these questions are complex and not well understood in any systematic way.'Nevertheless, received theory does provide some valuable insights. In a strictly rational world where cartel agreements were enforceable a cartel would be undertaken if and only if the present value of the cartel's joint profits from monopoly pricing exceeded the present value of the expected cost of operation and enforcement. In such a world, the formation of potentially profitable cartels is blocked only by its lack of inventiveness with respect to mechanisms for detection and deterrence. In reality, the existence of net gains from cartelization will generally not suffice to enable a cartel to be formed. Cartel formation is often hampered by the inability of the potential cartel members to strike a deal, and to manage a deal once it is struck. For an efficient cartel, it is not enough to divide markets or agree on a common price. In order to minimize the aggregate cost of producing the joint profit-maximizing output, it will ordinarily be necessary to devise some revenuesharing scheme involving side payments. Without side payments, the feasible locus of efficient profit outcomes will contain points inconsistent with joint profit maximization. Thus, an important potential limit on the ability of producers to reach an agreement is posed by contractual difficulties and uncertainty. Differences in sellers' objectives (assuming they ,are not strict profit maximizers) and their forecasts of market demand contribute to these costs. Where a depletable natural resource is involved in which user costs are substantial, then differences in discount rates and forecasts of future reserve additions compound the problem. Oligopoly theory in the Fellner (1965) and Williamson (1975, ch. 12) tradition recognizes how such inconsistencies prevent cartels from ever simulating pure monopoly outcomes. In an interesting paper, Cramton and Palfrey (1990) highlight the difficulties posed by asymmetric information about cost and demand for cartel members bargaining about production and revenue-sharing rules. They show that, for at least some common environments attaining in the absence of collusion, the excess payments necessary to induce truth-telling in the revelation mechanism with incomplete cost information are larger than the gains from collusion when the number of industry participants is sufficiently large. The opposite result holds for the common value situation of asymmetric demand information. Even though theory indicates that cartels fall short of complete joint profit maximization, they can extract monopoly rents of nontrivial magnitudes, and the industrial organization literature has endeavored to identify the structural conditions and sellers' strategies capable of sustaining a noncooperative market bargain. It emphasizes the importance of market structure and the fewness and similarity of producers. Few sellers are a necessary but not sufficient condition for collusion; many sellers are a sufficient though not necessary condition for competition. It also emphasizes the importance of inelastic demand, not so much because it implies that the monopoly price premium is larger the more inelastic the demand, but because it suggests the absence of competition from outside the

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industry that might tend to upset and undo the collusive deal worked out among the industry participants. Economic theory emphasizes the fragility of cartels in the face of the temptation which every member has to cheat by surreptitiously providing the market with a little extra production. The size of the temptation swings on at least three classes of factors, which we now examine. The first is the behavior of short-run marginal cost in the neighborhood of the individual firms post cartel level of output. If the gap between marginal cost and price is large and if marginal cost continues to fall for the individual producer, the per unit profit is likely to be substantial and the incentive to cheat enormous. The second factor is the elasticity of the individual producer's demand curve. This determines the responsiveness of sales to whatever discounts the cheater offers to move his output. Obviously, the more elastic the demand, the less the discount that must be offered and the greater the incremental profit. The less the product differentiation, the higher the elasticity. The ability of the cheater to price discriminate also affects the profitability of this behavior. If clandestine price cuts can be offered to lure new buyers while preserving the price structure in place to existing buyers, then cheating is especially seductive to the producer. A third influence on the incentive to cheat is the probability of detection and the costliness of the punishment which the other cartel members are able to impose. Orr and MacAvoy (1965) have developed a model in which the price information is transmitted only with a lag so that the price cutter enjoys some increased profits before discovery, although reduced profits afterward. If enforcement takes the form of matching the cheater's price cuts, the potential cheater can calculate the optimal price cut. The present value of the profits expected from cheating will exceed those of remaining loyal if the lag before detection is long enough. Besides the lag, the price cutter's expected return depends on the likelihood of detection, which depends upon the form in which information passes through the market. The 'trigger price' literature [most notably Stigler (1964), Green and Porter (1984) and Abreu, Pearce and Stacchetti (1985)l reinforces the difficulty of collusion when prices are imperfectly known. A system of open price quotas often confounds cheating as the same price will generally have to be offered to all buyers and will become known to all sellers simultaneously. If price quotations are made on a customer-by-customer basis, several outcomes appear possible. The buyer with the special deal may wish to cooperate in keeping it secret, fearing that if other buyers hear of it they will demand equally favorable terms. This is likely if the cartel commodity is an intermediate product, the acquisition price of which affects the buyers' competitive position in downstream markets. It is possible, however, that the buyer may judge the best course of action to be playing one cartel member off against another in the hope of getting a better price. This runs the risk, however, of providing other cartel members with the information they need to share in order to discipline the cheater.


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Obviously, the most likely outcome is difficult to predict except upon various assumptions about the internal structure and operating mechanisms of the cartel. The fundamental tension in cartel arrangements is that there are incentives for firms both to form and to undermine cooperative institutions. There has been a great deal of attention paid in the last few years to models that exploit these incentives to predict when in the business cycle cartels are most likely to occur. Stigler (1964) and Green and Porter (1984) note that when prices are not directly observable and demand is subject to random fluctuations, undercutting an agreement on prices is observationally equivalent to an inward shift of the demand curve. When cartel members see market price falling below a certain level (the trigger price), they rationally respond by expanding their own outputs for a finite period of time, even if there has been no cheating and members know there has been no cheating! Despite the eventual occurrence of this unwarranted punishment, a trigger price scheme is attractive to the cartel since a sufficiently long reversion phase will deter cheating. The empirical implication of the trigger price mechanism is that cartel agreements are more likely to break down when demand is falling, as during business cycle downturns. Recently, Rotemberg and Saloner (1986) have argued that they expect exactly the opposite result: cartels are more likely to fail when demand is rising since this increases the benefit from cheating. Thus, while theory has identified economic fluctuation as an important determinant of cartel durability, it is unable to predict the direction of incentives in this case; we must rely on empirical evidence to sort things out. In an important test of these competing theories and other predictions about cartel behavior, Suslow (1992) examined the durability of international cartels in 45 industries between 1920 and 1939. During this period cartels were often overt, with European firms taking the lead due to relatively lax antitrust laws. Most of the cartels considered were governed by formal contracts between members, with United States participants being an occasional exception. Suslow finds that the average non-censored cartel episode lasted 2.8 years, and the longest episode was more than 13 years. Censoring in this case means that the cartel agreement was cut short by an exogenous factor. Table 1 lists the reasons, endogenous and exogenous, for the demise of cartels studied by Suslow. The number of firms comprising the cartel appears to influence durability. Information on firm membership was available for 41 episodes; of these 64% had five or fewer members, and 83% had 10 or fewer members. Further, "formal cooperation, rather than tacit coordination, is chosen in markets with relatively few firms." [Suslow (1992) p. 121 Another significant finding of Suslow's study is that longer-lived cartels tended to employ more complex and specialized governance structures. In particular, there seems to be a requirement that successful cartels put production quotas and punishments into the contract.

D.J. Teece et a!.

1142 Table 1 Reasons for termination of cartel contracta Cause of termination Cheating on agreement Defection of important cartel member Fringe production undermines agreement Tariff Direct government intervention Antitrust indictment World War I1 Total a

Frequency

-+ 71

From Suslow (1992), p. 42.

Finally, economic activity appears to be an important factor governing cartel durability. Using indices of industrial production for the United States, the United Kingdom, and France, Suslow concludes that economic volatility, or positive and negative 'surprises', contributes to the collapse of cartels. Her results also indicate that sub-trend economic activity tends to decrease cartel survival. Suslow's investigation thus lends empirical support to Green and Porter's characterization of cartel behavior.

4. Welfare implications of cartels

In standard treatments, the welfare implications of cartels are usually presented in a fairly straightforward and unambiguous fashion: cartels, to the extent to which they are successful, promote adoption of suboptimal extraction plans. In short, cartels are typically folded into the standard treatment of market power with the associated deadweight losses. However, the literature does contain threads of arguments indicating that the negative welfare implications of cartels rest upon the assumption that in their absence competition would reign and moreover would yield a superior allocation of the economy's resources. We outline these arguments below and use them to argue that the received doctrine is probably correct, but that under certain conditions cartels may in fact augment, rather than subtract from, economic efficiency in a laissez-faire economy.

4.1. The coordination of complementaly and competitive investments The ideal state to which cartels are usually compared is that of the perfectly competitive economy in equilibrium. Serious scholars have questioned the ability


1143

of an economy to reach this state. The justification for use of the concept is the supposed tendency toward equilibrium, which is, however, an empirical rather than a theoretical proposition. Indeed, G.B. Richardson (1960, pp. 1-2) argues that "the general equilibrium of production and exchange.. . cannot properly be regarded as a configuration toward which a hypothetical perfectly competitive economy would gravitate or at which it would remain at rest." His argument is the obvious one, that for equilibrium to be attained, firms need information about each other's investment plans. In the absence of the sharing of investment plans, however, this is not going to be fully and accurately revealed. Accordingly, "it is difficult to see what but an act of faith can enable us to believe that equilibrium would be reached" [Richardson (1960) p. 111. Indeed, as Hahn (1973) has pointed out, the basic purpose of the Arrow-Debreu model of equilibrium is to show why the economy cannot be in this state. As explained by Richardson (1960, p. 36), the problem with the model of perfect competition is that it contains no special machinery to ensure that investment programs are made known to all concerned at the time of their conception. "Price movements, by themselves, do not form an adequate system of signalling" (p. 37). Koopmans (1958, pp. 146-147) recognizes the same deficiency in competitive theory noting that "To my knowledge no formal model of resource allocation through competitive markets has been developed, which recognizes ignorance about decision makers' future actions, preferences or states of technological information as the main source of uncertainty confronting each individual decision maker and which at the same time acknowledges the fact that forward markets on which anticipations and intentions could be tested and adjusted do not exist in sufficient variety and with a sufficient span of foresight to make presently developed theory regarding the efficiency of competitive markets applicable." It may be that certain kinds of cartel arrangements, particularly those that involve the disclosure of information on investment plans, and perhaps even the coordination of them, may contribute to rather than subtract from economic welfare. Demesetz (1982, p. 50) has suggested that a similar quandary exists with respect to the role of trade associations which distribute price information among their members. Recent economic theory lends some credence to this assertion, particularly regarding the welfare-enhancing effects of information exchange. While the literature has pointed out that the type of competition (Bertrand vs. Cournot) and uncertainty (private values vs. common values) have pivoted importance in explaining the incentives for information exchange, Vives (1990) has shown that exclusionary disclosure is much easier to motivate than nonexclusionary disclosure. That is, if information can be limited to a subset of firms, then exchanges (via institutions such as cartels or trade associations) is easy to explain. Vives also points out that, at least under Cournot competition, exclusionary disclosure increases total surplus.

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The notion that cartels may perform a socially beneficial function in this regard is closely akin to arguments commonly advanced in favor of indicative planning [Meade (1970)l. Indicative planning has been used in France and other countries in an attempt to improve the information available to decision makers, supposedly reducing uncertainty [Cohen (1969)l. The questionable success of the process may not be so much the result of a flawed concept as of flawed implementation. For instance, if the important competitive factors are international, an indicative planning exercise which is domestic in scope is doomed to failure. However, it does seem possible, theoretically at least, that a cartel could inspire efficiency relative to alternatives if it could select and trace an expansion or contraction path for industry capacity that was more closely matched to long-run demand than a laissez-faire competitive economy without cooperation could generate. Our position in this regard is very tentative and is best viewed as a hypothesis. The literature on the issue is extremely sketchy, although earlier treatment of cartels did distinguish between 'cartels of conditions' and those that regulate output, sales, and prices. 'Cartels of conditions7 [Plummer (1951) p. 181 include agreements relating to information exchange, product standardization, patent exchanging and pooling, and the like. According to Plummer, "Standardization, cooperative research, and similar arrangements help to increase efficiency and economy; and therefore little or no objection can be raised to 'cartels of conditions,' unless patents are deliberately acquired and put into 'cold storage' to keep them from producers not in the cartel, or similar policies, advantageous to the private interests concerned but against the public interest, are pursued. But we must not overlook the fact that cartels of the first type can pave the way to those of the second type, so that 'closer cooperation' may ultimately evolve out of an apparently harmless 'cartel of conditions'." If advantages do exist from cartelization, the welfare analysis is not simple. Our point is that the case against all forms of industry coordination and cooperation among competitors is rather weak and is based on the assumption that the available adjustment processes enable equilibrium conditions to be selected and implemented in a frictionless fashion - or at least more efficiently than an alternative process based upon cooperation and coordination [Jorde and Teece (1992)l. 4.2. Price stabilization cartels

A discussion of cartels would not be complete without mention of international commodity agreements, which often have many cartel-like features. They are often directed at stabilizing export prices, if not export receipts, for countries whose exports are specialized in the traded commodity in question. Economists generally view such arrangements with great suspicion because the implicit agenda is often


1145

to raise as well as stabilize prices. To the extent that the objective is to raise prices, the analysis of cartels presented above seems to be applicable. The more intriguing questions relate to whether price stabilization can augment economic welfare. Once again the answer swings importantly on the alternatives. If it is the model of perfect competition with fully developed futures markets and mechanisms to attain instant equilibrium, then the welfare implications would appear to be negative. On the other hand, if futures markets are nonexistent or highly incomplete and price information is the only investment signal available to producers, the results may be quite different. As Behrman (1978) suggests, the issues are empirical rather than theoretical. Given that the empirical base which affords commentary is rather thin, we simply note this is a relatively unexplored area and an important direction for future research.

5. A synopsis of some natural resource cartels 5.1. Cartel issues raised with respect to world oil in the immediate post-embargo period

Two decades after the first oil shock of 1973-1974 there remains disagreement about the reasons for the price increase and the role that classical cartelization had to play. Aside from political explanations of what went on, there are three main classes of economic explanation that have been advanced. They are labelled here as the cartel explanation, the competitive explanation, and the target revenue explanation. Each is briefly surveyed below. More complete surveys can be found in Griffin and Teece (1982) and Teece (1983). 5.1.1. The cartel explanation The view most widely accepted by economists is that OPEC effectively cartelized the world oil market, fixing prices above competitive levels and restricting output to support the common price. There are many early statements of this view, but the representation by Pindyck (1978) of OPEC as a monopolist is perhaps the starkest and most precise. In other versions, the dominant producer, Saudi Arabia, sets the price, allows the other OPEC producers to sell all they want, and supplies the remaining demand. Saudi Arabia is thus the 'balance wheel' or 'swing producer', absorbing demand and supply fluctuations in order to maintain the monopoly price. Such an arrangement creates no cartel problems. However, it does run the risk of inducing sufficient new production outside of Saudi Arabia to make the strategy nonviable for the Saudis. The stability of OPEC turns on whether world supply and demand at the monopoly price results in sufficient demand for Saudi oil to satisfy Saudi objectives. Put another way, the world price does not necessarily depend

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upon the strengths and weaknesses of cartel cohesion. In the simplest version of this model, the dominant producer chooses the best price from its own viewpoint, taking into account both present and future demand and supply of the competitive fringe at whatever price the dominant producer may choose. The problem facing Saudi Arabia is to choose a price path which maximizes its wealth over time. If the price set by the dominant producer is high enough to let fringe producers earn monopoly rents, they will have an incentive to expand their capacity. Also, new entrants will be attracted into the fringe. This causes a reduction in the residual demand confronting the dominant producer. If Saudi Arabia adopts a high discount rate, implicitly setting a low value on future profits, the dominant producer selects a higher initial price and makes room for an expanded competitive fringe, earning higher profits initially than later on. Its high prices and profits in the current period set into motion a chain of repercussions reducing the dominant producer's market share in future years. In many instances, there is only one way for the dominant producer to avoid this outcome: it must adopt a lower discount rate, reducing its current price to a level at which new entry and the expansion of fringe members are discouraged. An overly simple but useful first approximation is to view the dominant producer's decision problems as dichotomous: either it sets high prices and accepts declining future market shares and profits, or it sets low current prices to deter all entry and expansion by fringe competitors. The latter strategy is commonly referred to as limit pricing, in that a price is selected which limits entry to zero. In reality, depending on the rate of discount, intermediate outcomes between these two extremes may well be chosen. Limit pricing is particularly germane with reference to synthetic oil production from shales, tar sands, and coal liquefaction. Since these fuel sources can be likened to a backstop fuel, available in elastic supply, a wealth-maximizing dominant producer with huge reserves would probably choose a price path below the price at which large quantities of synthetic fuels would be produced. To introduce collusive elements into the model, a number of variants of the dominant-producer model have emerged, with a group of OPEC producers acting essentially as the single dominant producer. One popular view is that there is a 'cartel core' (e.g., Saudi Arabia, the United Arab Emirates, Kuwait, Qatar, and Libya) which behaves like a dominant firm. Analytically, this model is basically the same as what we have just described. The only significant difference is that the 'cartel core' version depends on cooperative behavior within the core; the dominant-producer version does not depend on collusion, explicit or tacit, for the generation of rents. This difference is important for assessing the stability of the cartel arrangement. Models of this genre are the conventional wisdom among most economists. Adelman (1982), an influential disciple of this traditional view, has set forth the factual argument in support of this genre of models. Milton Friedman appears to adhere to it, as he predicted that OPEC will quickly go the way of other cartels


1147

and collapse, and along with it the price of crude oil. (Having been awarded a booby prize for his prediction by the Society for the Promotion of Humor in International Affairs, Friedman has confessed to a predictive error in timing, but not direction. The cartel will collapse 'sooner or later' according to his March 21, 1980 Newsweek column.) 5.1.2. Competitive views

An alternate view, advanced in one form by MacAvoy (1982) and in another by Johany (1978) and Mead (1979), is that the price increases merely reflect a shift in underlying supply and demand conditions. MacAvoy argues that a tight market with minimal excess capacity in 1973 and spot prices above contract prices was pushed over the brink by demand growth coupled with the embargo. MacAvoy (1982, p. 57) concludes that because of politically induced supply interruptions (the 1973-1974 embargo and the turmoil in Iran and Iraq during 1979-1980) "prices would have risen to four-fifths or more of preSent prices under open market conditions. This would have required a tripling of constant dollar crude prices. The operations of an open market would have been subject to fundamental constraints in accumulation of reserves and to income determined increases of year-to-year demand. The conditions, and not OPEC caused most of the crude oil price increases in the 1970's" (emphasis added). The argument is buttressed by an econometric model of the world petroleum market using parameter values derived where possible from the pre-1972 era. The model is then used to predict demand, supply, and price in the post-1973 era. The difference between simulated prices based on 'market fundamentals" and prices simulated with actual OPEC production is then attributed to cartel behavior. While MacAvoy7sconcept of market fundamentals is never fully explained, it turns out to be critical to the interpretation and evaluation of his study. He hints that it is a market 'without cartels', one characterized by an 'open markeP2. If this is the case, then a price path generated by market fundamentals need not be a Hotelling-type competitive price path calculated on the basis of known reserves, reasonable discount rates, and expectations as to future oil demand and reserve conditions. It is simply one generated in the absence of collusion and coordinated behavior. Such a price path might be well above or well below the (Hotelling) competitive path, especially if the production decisions of some producers are made with reference to revenue targets, as emphasized below. It seems important to know not only whether OPEC is a cartel, but also whether the price is above or below the Hotelling price path as this path is likely to be close to what would be observed were producers to behave according to the classical competitive model. MacAvoy does Further confusing the issue is mention that OPEC could conceivable "have been a factor in determining the fundamentals" [MacAvoy (1982) p. 31.

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not distinguish between the two concepts, and this carelessness is likely to mean that too few readers will realize that the market fundamentals concept may refer to a set of conditions quite different from the usual conception of a competitive market. The MacAvoy argument can be labeled as a competitive interpretation of the world crude market. In another version, henceforth labeled the property-rights view, Johany (1978) and Mead (1979) argue that the price regimes prevailing before and after 1973-1974 are best explained by appealing to the change in ownership patterns that transpired in the early 1970s. Until that time, the concessions granted by the producing countries to the oil companies permitted the companies to make unilateral production decisions. Accordingly, since production policies were essentially the prerogative of the companies, discount rate assumptions were made on the basis of the companies' perceptions of the future. Since expropriation risk was nontrivial in many countries in the 1960s, the wealth-maximizing strategy for the companies involved a high discount rate and rapid depletion. This was fueled by forever escalating royalty and tax demands by producer countries, which further served to reinforce expectations that profits would decline in the future. The result, according to Johany, was that the companies produced as if there were no tomorrow, depressing world crude oil prices in the process. According to the property rights view, the events of 1973-74 marked a watershed in the world oil market, principally because of the transfer of control over production policies that occurred at that time. As Johany (1978, p. 107) explains it, "the oil producers decided to determine the price of their oil unilaterally rather than through negotiations with the oil companies as had been done in the past. Once the host countries became the ones who decided the rate of oil output and its price, the role of the companies had been essentially reduced to that of contractors. That amounted to a de facto nationalization of the crude oil deposits." This reassignment of property rights was significant because the companies and the host countries had different discount rates and that implied different rates of output [Johany (1978) p. 1071. These differences would be traced to intrinsic differences in the discount rate, as well as to differences in risk evaluation. With lower discount rates, current production would fall, thereby driving up the world price. At the time of the transition, production would drop sharply, causing a switch to the higher price path. According to this line of reasoning, 1973-1974 represented such a transition period and switching to a higher price path. The property-rights interpretation of the transformation of the world oil market is consistent with the observation that the world price during the 1970s did not appear to be threatened by cheating - such as the granting of secret price concessions by some members of OPEC in order to capture market shares from the others. Furthermore, there is evidence that the companies considered the expropriation risk in the 1960s to be real. In fact, significant episodes took place in Algeria, Iraq, Egypt, Iran, Libya, and Peru. These episodes illustrated the latent


1149

power of governments over the companies and the reality of the political risks inherent in the industry. The nationalization of foreign oil companies was an appealing way for governments to develop government-owned enterprises and to win popular support. Implicit threats of expropriation stood behind many less extreme forms of regulation. It is instructive to set forth the major inadequacies of this theory. The most obvious inadequacy is that most oil-producing countries in the 1950s and 1960s were demanding that the companies expand production. The Shah of Iran pushed hard on the companies to expand production. This is completely at odds with the property-rights model. However, Iran might be considered an exception as the Shah's lust for current revenues was legend. Unfortunately, one is never likely to be entirely sure as to the relations between the companies and the countries as 'behind the doors' manipulation is likely to have been of some importance. Still another objection is that while this theory could presumably explain a portion of the 1973-1974 price increase, it offers no obvious interpretation to the doubling of prices in 1978-1979. As the transfer of ownership had long since occurred, further reductions in the discount rate are not apparent. Similarly, the rationale for changed expectations in other factors that could allow competitive prices to double is not apparent. It is not obvious that producers altered their long-run expectations in 1978-1979 regarding future reserves, future demand growth, the price of the backstop fuel, and so forth. Rather, following the rationale of a competitive model, one would expect that following the 1978-1979 price rise due to short-run supply constraints, the price would return to the initial price path, with an easing of these constraints. 5.1.3. The target revenue model

In its pure form the target revenue model explanation depicts OPEC, or at least its principal members, as a collection of nation states whose oil production decisions are made with reference to the requirements of the national budget. Budgetary needs are in turn a function of absorptive capacity which is limited where the economy is small in relation to oil revenues or where the infrastructure is inadequate to support rapid escalation in consumption and investment levels. A challenge can be mounted to the target-revenue approach on grounds that it is unrealistic to assume that foreign investment is not a viable alternative to domestic investment, for this is the assumption implicit in the analysis. One reply is that for various periods of history OPEC producers have perceived foreign investment to be unattractive, not only from perceived low returns (generally when the dollar was depreciating in relation to other key currencies and producers held dollardenominated assets) but also because of political risks. These risks are of several kinds. One is the risk that the nation in which the funds were deposited might confiscate, freeze, or otherwise manipulate financial assets for political reasons.

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The other is that the existence of huge external liquid assets might facilitate the survival of revolutionary regimes, which if successful in displacing existing governments would have command over liquid assets that could be used to placate friends and buy off enemies. While admittedly such risks exist, it seems highly implausible that wealth-maximizing agents in selecting a portfolio of assets would limit those portfolios to oil in the ground and domestic investments. As the Iranian experience proves, the latter are not devoid of their risks. A portfolio including foreign debt and equity securities would presumably both increase the expected return and reduce the overall risk of the portfolio. In view of these considerations, our interpretation of the target revenue model is that it eschews wealth-maximizing behavior. An important implication for OPEC, as explained in Teece (1982), is that prices can rise above the Hotelling competitive price path even in the absence of coordinated action by OPEC members. If an event such as the embargo brings current oil revenues into the target revenue range, there is no desire for individual producers to cheat by expanding production. Conversely, if demand reduction or rapid expansion in absorptive capacity creates a situation in which revenue needs are not met, then the producer in question will expand production until revenue objectives are satisfied. With these characteristics of instability, the model allows for behavior by a number of producers which could lead to a collapse of the cartel price. 5.1.4. Evidence

It is perhaps amazing that such a variety of models can exist contemporaneously, and sometimes contemptuously, without much in the way of serious empirical efforts to select among them. As Gately (1984) points out, initially there was much optimism that the wealth-maximizing approach would help us understand OPEC behavior. But disillusionment has set in. It seems that from a theoretical point of view, models of OPEC oil pricing have reached practical limits as tools of analysis [Pindyck (1982) p. 1091. The normative sensibility of such models has been questioned by many, including Teece (1982) and Gately (1984). In addition to the formulation of more robust models of the world oil market, the predictive power of existing models needs to be tested. This task has been much neglected to date, the standard practice being to validate the choice of model by arbitrarily pointing to selected events which are consistent with the model and then ignoring anomalies. Such an approach is obviously unscientific. Part of the difficulty is in specifying a valid test. Considerable progress in this direction has recently been made by Griffin (1985). To test competing models, he focuses on each individual country's production decision. The determinants of each OPEC country's oil production (Q) are formalized based on various competing models of OPEC behavior. These determinants are then systematically


Table 2 Hypothesized coefficient signs of various models. [Source: Griffin (1985).] Modela I. Cartel model: In Q;,, = a , 1. Strict market sharing 2. Market sharing

Sign Pi

Sign y;

Pi = 1 Pi = 1 Pi > 1

y .' < -0

Sign 6;

Sign q5i

+ Pi In Q:: + -yj In P,

3. Partial market sharing

n=O >

y.I > 0
0

Symbols: Q: production in barrels per day; production of OPEC oil less that of the ith producer; P: price of Saudi Light 34" API; G: government production divided by total production; I: gross fixed capital formation. a

eoO:

assessed with respect to their conformity with resulting hypotheses. The advantage of focusing on the individual country's production behavior, as Griffin points out, is that "each model yields quite disparate hypotheses about the determinants of production. The emphasis here is on testing the simplest version of the model, necessarily omitting nuances which would improve the explanation power of the model" [Griffin (1985) p. 2). Table 2 summarizes Griffin's formulations and the signs of the hypothesized coefficients. The simplified models were then tested with quarterly data for the period 1971:I through 1983:1113for the 13 OPEC countries with the exception, for data availability reasons, of Ecuador and Gabon. For Iran and Iraq, respectively, the sample is truncated to delete the period following the revolution in Iran (78:III) and the beginning of the IranIIraq war (80:III). Griffin's results (summarized in Table 3) are suggestive, if not instructive. Cartellike behavior was rejected for Iraq only, classical competitive behavior was rejected for six of the 11 countries, the property rights model rejected for eight of the 11 countries, and the target revenue approach was rejected for all but Algeria. However, if the sample is restricted to the period 74:1 to 81:IV, the target revenue hypothesis cannot be rejected for four of the 10 countries. Clearly, this model seems to work best when prices are rising. However, Griffin concludes that "the results The exception was the property-rights model.

D.J. Teece et al.

1152 Table 3 Results of tests: four models of OPEC behaviora Country

Partial market sharing cartel

Classical competitive

Property rights (competitive)

Target revenue

Saudi Arabia Kuwait Qatar UAE Iraq Libya Algeria Iran Nigeria Indonesia Venezuela Adapted from Griffin (1985), Tables 2-5. Codes: R, hypothesis rejected; NR, hypothesis not rejected.

a

give considerable support to the cartel model. Not only does this model apply to a greater number of countries modelled, but the overall level of explanation dominates other models" [Griffin (1985) p. 241. The principal weakness of the above approach is that the results are somewhat dependent upon the particular test devised for each model. The burden, Griffin claims, rests upon the advocates of particular models to specify precisely the criteria by which these models should be accepted or rejected. Another weakness of the approach is that certain models are empirically more demanding that others so that the comparative nature of the tests must be viewed cautiously. For instance, the target revenue model is empirically the most explicit and demanding. At the other extreme is the classical competitive model which needs only a positive price coefficient coupled with a positive investment coefficient, as is required for the target-revenue approach. The analysis has thus not entirely laid matters to rest. This is especially so as OPEC's behavior may well be changing over time. This simply reflects the complexity of the problem and the necessity for approaching modeling exercises with temerity.

5.2. Cartel experience in the world merculy market The international mercury market displays a long history of cartel activity. A recent study [MacKie-Mason and Pindyck (1987)l identifies a long period of successful This section draws heavily on the excellent treatment in MacKie-Mason and Pindyck (1987).


Table 4 World price and production of mercury (1972$/flask of 76 Ibs, and 1000 flask^)^ Year

Price

Spain

Italy

USSR

Mex.

USA

Chinab Yug.

Alg.

Total

1951-1980 prices taken from 1981 Commodity Yearbook (Commodity Research Bureau, 1981); 1981 prices from Minerals Commodity Summaries 1982 (US Bureau of Mines, 1982). Abbreviations: Mex., Mexico; Yug., Yugoslavia; Alg., Algeria. Data for China are estimates for 1949-1967. Output of India mine (Yugoslavia) included with Italy through 1945. Estimates. a

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two-country cartelizations by Spain and Italy (1928-1972) followed by years of unsuccessful many-country attempts at price king. Spain and Italy were the dominant producers, at least up until 1960, because of their low production costs. The potential for industry cartelization was enhanced by the small number of firms in each producing country and by the willingness of governments in the producing nations to exercise control. There were just a few mines in each country (Spain, Italy, Yugoslavia, Algeria, and the Soviet Union) that were wholly or partially state owned. Production and price data are contained in Table 4. The formation of Mercurio Europeo by Spain and Italy in 1928 marked the emergence of the cartel. These two nations accounted for more than 80% of world production at that time. Buttressed by an understanding with Mexico, the cartel was apparently very successful until 1950 [Hexnes (1945)l. A market-sharing arrangement, by which Spain supplied the USA and Italy supplied Europe, was part of the cartel agreement. The agreement was formally terminated by Spain in January 1950 after Monte Amiata, the largest Italian mine, sold 80 000 flasks of mercury to the US government stockpile in 1949. Spain replied with a price cut, but cartel pricing, albeit informal, was soon restored. Prices rose sharply in 1950, and a formal cartel was secretly re-established in 1954. Prices peaked in 1965 as the US government began to stockpile. The cartel's market share peaked in 1950 and fell to 32% in 1970, by which time, according to MacKie-Mason and Pindyck (1987, p. l l ) , its effectiveness had largely ended. Subsequently, several producing nations, including Spain, Italy, Algeria, Yugoslavia, Peru, and Turkey, have attempted to recartelize the industry, but without apparent success. In any case, MacKie-Mason and Pindyck (1987, p. 12) argue that in the past war period the external market conditions "explain mercury price movements in the last three decades, price movements which cannot be explained by (and in fact often run counter to) changes in internal cartel organization." In support of a general thesis that once minimal conditions of market concentration have been met, the controlling factors in cartel success or failure are not the internal problems of organization, but the external constraints imposed by the market, the Italian 'cheating7incident of late 1949 is cited: Italy's sale to the U.S. Government stockpile was two-thirds as large as the entire world output of mercury in 1949. The Mercurio Europeo agreement was terminated, and for about ten months Spain tried to retaliate by undercutting Italy's price. Spain offered mercury to the market at $120 (1972 dollars), approximately equal to Italy's cost of production. One might think that this apparent collapse of the cartel would lead to depressed, competitive pricing. In fact prices began to rise during the summer of 1950. Spain stopped undercutting and increased price to $385 in January 1951. Prices and profits reached historical highs just one year after the cartel's 'demise'. The average price for 1951 was $368, and it stayed near that level through 1953. The high prices of the early 1950s were the result of the extremely low short-run elasticities of supply and demand. When Spain tried to undercut Italy in 1950, its production

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capacity, combined with that of fringe suppliers,was too constrained in the short run to fulfill demand at the low ($120) price. Italy was able to sell at higher prices in the disequilibrium of the market; demand held strong as Italy gradually raised price. As long as the market was unresponsive, it was in Spain's interest to raise its price, which it did, and Italy followed suit. Thus any internal problems the cartel faced were irrelevant to its success in exploiting market power to obtain excess profits. None of the internal problems were overcome: Spain and Italy did not reach a new agreement until 1954, cheating was not deterred, and retaliation was unsuccessful. If anything, these events made the cartel more aware of its strength. MacKie-Mason and Pindyck (1987, pp. 17-18)

This outcome is very similar to that which was obtained in the world oil market after the Doha meeting in 1978, where a two-tier price structure prevailed as Saudi Arabia tried to keep prices down for various economic and political reasons. The Saudis could not prevail because they had insufficient spare capacity to impact the entire price structure through increased production. However, neither incident supports the inference that the internal mechanisms of cartelization are unimportant and that external market factors are deterministic. Clearly the market is a tremendous force to be reckoned with, and attempts to tamper with it through complex forms of collusion are often fragile, though not totally ineffective. Inelastic demand and inelastic supply from non-cartel fringe producers are almost always necessary conditions for effective cartelization, but they are not sufficient. Some form of internal organization is also needed unless producers are satisficing, as is postulated in the case of the target revenue model of OPEC outlined earlier.

5.3. Cartel experience in the world uranium markets

From 1972 to 1976, the price of uranium ore rose from $6/pound to over $40/pound. Following this price increase, the existence of a secret international uranium cartel was revealed and a cross-fire of investigations and legal battles began. Although all the effects of the uranium cartel are unclear at best, its existence has significantly affected energy markets and the future of the nuclear industry. This case is an interesting illustration of the interaction between privately held firms, host governments, and public interest concerns involved with a natural-resource cartel. It also illustrates many of the mechanisms necessary for the formation and maintenance of a cartel. The active participation of host governments, the cartel's secret and illegal status, and the use of national security reasons as a disguising mechanism all contribute interesting complexities to the case. The attempt to cartelize the uranium industry in the early 1970s seems to have been triggered by an overabundance of mining and milling capacity in relation to

D.J. Teece et al. Table 5 US reserves and potential resource estimates (January 1, 1977)a Cost per pound U3O8 cost category

Tons of U3O8 potential resources Reserves

Probable

Possible

Speculative

$10 $10 to $15 increment $15 $15 to 30 increment $30 $30 to $50 increment $50 a

From US Department of Energy.

demand. Price competition, led by the French, was forcing producers to sell at prices covering only their marginal costs, around $5/pound in 1972. The USA has the largest known uranium deposits in the world. Over 25% of 'reasonably assured' world reserves reside in the USA [Taylor and Yokel1 (1979)l. US resources can be categorized by their estimated costs of production, which are known as 'forward costs'. Forward costs are essentially marginal costs and do not include fixed costs (such as exploration and mine development if these costs have already been sunk) or the user costs discussed in Section 2. DOE estimates of US uranium reserves categorized by their forward costs are shown in Table 5. It can be seen that the forward costs were and still are significantly above the prices quoted in 1972. If forward costs are expanded to include user costs, the depressed situation of the industry in 1972 is readily apparent. Estimates of potential reserves have been subject of much debate in the industry. Resource estimates have grown each year as new exploration and drilling have uncovered new deposits. In addition to holding the largest known reserves, the USA is also the world's largest producer of uranium ore. However, while US uranium reserves are large, they are and have been significantly more costly to produce than Australian, Canadian, or South African uranium. The USA has the strictest safety requirements and high labor costs. In addition, US deposits are not so rich as those of other producers and thus they are more costly to extract. The international uranium cartel commenced with meetings in 1972 among uranium producers from France, England, Canada, Australia, and South Africa. It continued with meeting of a 'policy committee' and an 'operating committee' and with the support of a 'secretariat' to compile and circulate data. Some or all of these operations were taken over in 1975 by 'The Uranium Institute', headquartered in London, after its formation by the cartel participants.

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A stated purpose of the series of producer meetings begun in Paris in February 1972 was "to discuss ways and means of assuring an adequate price of uranium in order to attract sufficient investment into the industry." With the existing price at "about U.S. $4.5 per pound", an initial proposal was to set the price at "$6.25 per pound U308 in 1975" and that the 'Club' thereafter "agree upon a price for uranium from time to time .. . " 6 . An elaborate cartel agreement was in fact arrived at during meetings in Johannesburg, South Africa, in June 1972. A written summary of the agreement worked out at the Johannesburg meetings was approved at the Paris meeting on July 6,1972 '. Among the constituent agreements were those relating to: (1) "Market quotas7'as follows: Country

1972-1977

Canada South Africa France Australia RTZ (Rio Tinto Zinc)

33.50% 23.75% 21.75% 17.00% 4.00%

1978-1980

(2) Sales to be allocated among members on the basis of "contracted tonnages" and "each group's quota to be filled at a uniform rate", with 'the Secretary' to report quarterly "on markets, contracts, deliveries and positions vis-a-vis quotas", and to "distribute price and quantity information to members on a routine basis". (3) "Minimum prices" for all future bids as follows (with prices for customers in Japan, Taiwan, and Korea to be $0.20 per pound higher)

(4) Quotations beyond 1978 to be no lower than the minimum prices or based on "world market price", with the "maximum validity period for any quotations" to be 90 days. Report of the Discussions in Paris on the Uranium Industry, Feb. 14,1972. See previous footnote. The Report of the Discussions in Paris on the Uranium Industry, Feb. 1-4, 1972 and Notes of the Johannesburg Meeting of the Uranium Producers Club were released publicly by California officials on August 29, 1976. The documents were obtained from the files of an Australian uranium producer, Mary Kathleen Mines. They constitute some of the minutes and detailed reports of the 'Club'. The following points are extrapolated from the 'Notes'. The rationale for price discrimination appeared to be that these countries were pursuing large, wellpublicized nuclear expansion programs and had few domestic sources as substitutes. Their demand could therefore be inferred to be more inelastic, thereby supporting a higher than competitive price.

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(5) No uranium sales contract to contain a "consequential damage clause" and no producer to "waive a force majeure condition for any period in order to guarantee delivery". (6) A leader and a runner-up to be selected by the Secretary for each bid after consultation with the (Operating) Committee, with the leader having the right to quote the appropriate minimum price; the runner-up having the right to quote only the minimum price plus 8c/lb, and with all others having the right to quote the minimum price plus 15cIlb. (7) "If a supplier not associated with the organization should quote under the minimum price, the leader will not match that quotation and the Operating Committee will review the situation and decide on a course of action as soon as possible". Further meetings in Johannesburg on January 28 through February 1, 1974, led to additional increases in the agreed schedule of minimum prices previously increased three months earlier. The ninth session of the uranium producers 'Operating Committee', held at Las Palmas (Canary Islands) on November 23, 1973, adjusted upward the quota for the Australian group of producers for the period 1978-1980 because the political situation in Australia made it impossible for the Australian producers to sell their assigned quota for the period 1972-1977. The evidence and information publicly available amply demonstrate the existence and operation of the cartel, but they do not constitute a complete set of the minutes of the many meetings held over a five-year period or a complete record of the cartel's activities. In connection with the impact of the cartel on the US market, it is clear that parties recognized early on that in the colluding formation of their cartel coordination with US uranium producers was necessary to ensure their overall objectives of raising prices and dividing the market. Beginning with contacts by Louis Mazel of Rio Tinto Zinc at least as early as the fall of 19721°, foreign producers increased the tempo of their coordination efforts with US producers to demonstrate the higher prices foreign producers were charging and to assure the US producers that foreign uranium would not be sold in the USA at prices below the US prices. The leader runner-up system was an attempt to make the bids look competitive when in fact they had been rigged. 'O Louis Mazel of Rio Tinto Zinc in London addressed a meeting of US uranium producers in Washington, DC, in late 1972 on 'supply and demand'. On November 29, 1972, following the meeting, he wrote the secretary of the trade association which sponsored the meeting: "I would like to thank you for the pleasant and interesting breakfast at the Shoreham Hotel and I hope that my remarks on the foreign U3O8 supply and demand were not too shocking for some of the Mining and Milling Committee members. Nevertheless, we sincerely believe that an exchange of information, and consequently an understanding of one another's position, will be helpful in solving problems which exist both in the USA and non-USA U3O8 market."


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The cartel also refused to deal with so-called 'middlemen', like Westinghouse Electric. Apparently the foreign uranium producers were annoyed at the sale of uranium by Westinghouse at prices that were considered too low. Westinghouse was selling uranium forward in order to sweeten the sale of nuclear reactors to electric utilities. However, the producers were upset because in their view the effect of Westinghouse activities was to withhold demand from the market just at a time when the producers were hurting the most. Producers therefore agreed to deal with end-users only. The ownership structure of the industry outside the USA seemed to favor cartelization. The number of parties was limited by the small number of commercial deposits and the cooperation that various governments were prepared to offer to help the cartel become effective. In addition, the demand facing uranium producers was very inelastic in the short run due to the high switching costs and long lead times associated with nuclear- and power-plant production. Finally, the USA had placed an embargo on the enrichment of foreign uranium, and this effectively protected the international market for US competition. At the very inception, the cartel agreed that secrecy was a necessity. Violation of US antitrust laws was a danger, especially for those firms with US subsidiaries. Also, the US government might retaliate by withholding enrichment services to international producers. In addition, antitrust action was possible in other countries where the uranium was sold. Governments actively participated in the cartel alongside the companies. The Canadian government was especially enthusiastic. The Canadian uranium industry suffered after the USA stopped purchasing foreign uranium in 1957, and the government had to step in with over $100million to avert the collapse of the industry. However, because of this strong government participation in the cartel, the domestic markets of the four producing nations were initially excluded from the cartel-set price. The cartel was not insensitive to monitoring and enforcement needs. Stringent disclosure requirements and selective punishments were established. All contracts, letters of intent, inquiries, quotations, and delivery invoices had to be turned over. If any were not, the offending producer was to be called before the Operating Committee which met bimonthly. Such checks were designed to eliminate overt cheating. To prevent more covert actions, the cartel used the governments as an enforcement mechanism. In France and South Africa, marketing was controlled through a single corporation with government participation. In Canada and Australia, the government used the technique of withholding export licenses to ensure that no company exceeded its quota. This was possible because uranium was declared a commodity with national security implications. Price (the cartelset price) was then incorporated as one of the criteria for government approval.

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Infractions did occur. They were penalized by selectively levying a "fine" on the offendingparty that took the form of a reduced quota. As mentioned earlier, one potential problem arose when Australian producers discovered new, low-cost sources of uranium. These new deposits threatened to undercut the existing cartel mechanism unless some entry was allowed on relatively good terms. The Australians threatened to stay outside, undersell the cartel, and capture an even larger market share unless accommodated. The cartel's response was twofold. First, Australia's entry was accommodated slowly by using a dual quota system. Australia was given a lower (ranging from 7% to 17%) market share for 1972-1977 and a larger one (from 24% to 28%) for 1978-1980. Second, existing producers forced the government to "institute some control to prevent new producers from coming into production too early" and exceeding the quotas set in the dual system. The result was that the government denied several export licenses. An interesting but difficult question to answer about the cartel is whether it affected the price of uranium. Prices did rise in the 1972-1976 period, but it is not clear what if any part of this escalation was due to the cartel. During the period 1972 through 1976, production costs were increasing, supply uncertainties were exacerbated, and demand for international uranium was rising because of increased restrictions in US government enrichment policies. Whether the cartel had much impact in relation to these other factors is yet to be firmly established.

5.4. The diamond cartel The monopolistic and cartelistic features of the diamond industry are more sensational than they are typical, but underlying and buttressing observed behavior is one fundamental fact: there is no close substitute for diamonds, especially for ornamental (gem) uses, but to a lesser degree for industrial uses as well. Nevertheless, the internal organization of the cartel appears intriguing. The formal organization of the cartel was established in 1934under the rubric of a trade association, the Diamond Producers' Association of London. The members of this trade association included representatives from the governments of the Union of South Africa and the Administration of Southwest Africa. The most significant member of this association was De Beers Consolidated Mines, LtdH, which was the controlling shareholder of the Diamond Corporation. De Beers was, and still is, the most important producer of diamonds. In fact, of all the world's major commodity markets, the market in diamonds comes nearest to being a monopoly. The world diamond industry might arguably be better read as a study in monopoly In the nineteenth century, Cecil Rhodes amalgamated the Kimberly diamond fields into de Beers Consolidated.

l1

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South African and Namibian

Cunwactual snlcs by forcign

Opcn market competitive sales &West African sales

Diamond Corporation (1W% Dc Rccrs) also buys and sclls industrial production of SA/ Namibia

I Diamond Trading Company (DITRA*). De Beers conuols DlTRA indirectly lhrough Anglo American Corp. Takes a conuactual 2% profit on

Diamonds sold to South African cutters in sights a1 10% discount on world priccs

Diamond Producers Assoc. (DI'A): Principal members arc De Beers; the SA govemmen~;the Namibia adminiswation and the

. Diamond Corporation

The Diamond Purchasing and Trading Co. (I'UKTKA*). 50% held by Dc Rccrs. Takcs a contrac~ual10% profit on CSO salcs.

DITRA branch in London* hofit margin on open market and West African purchases

world markets. especially

*part of Ihc Ccnlral Sclling Organization (tlm CSO)

Fig. 5. The De Beers supply and marketing system. (From The Economist, February 23,1980, p. 102.)

than as a study in cartelsI2. Still, there are enough aspects of coordination amongst governments and independent private entities to warrant categorizing the industry as one organized as a cartel with a dominant player - De Beers. Since the 1930s, De Beers has operated an elaborate apparatus of stockpiling and distribution under the Central Selling Organization (CSO). The CSO is an inextricably complex group of London-based companies, the major elements of which are controlled either directly by De Beers itself or by Anglo-American (Anglo-American and De Beers are both chaired by Harry Oppenheimer, whose shareholdings interlock in a group called E. Oppenheimer & Sons). Figure 5 sketches the companies involved in the distribution system. The CSO, backed by De Beers, attempts to regulate prices to the benefit of De Beers, its dealers, and probably the producers as well. This involves adjusting stocks of diamonds to meet demand at smoothly rising prices and tightly managing the distribution system so as to exert maximum control over the way diamonds are distributed and priced. An important part of the apparatus in this regard is the Indeed, de Beers Chairman Hany Oppenheimer would seem to agree, stating: "We are a monopoly of the most unusual kind - you can say we handle at least 80% of the diamonds of the world." Forbes, May 28,1979, p. 45. l2

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fashion in which De Beers conducts sales, or 'sights' as they are called in the trade. These sales are by invitation only, and denial of access means that a dealer must buy from other dealers at prices considerably above De Beers' prices. De Beers thus uses access to their supply to 'bribe' dealers into 'responsible' behavior. The threat of black-balling can be serious. The dealers who are provided access are expected to avoid hoarding for speculative reasons and to accept consignments almost sight unseen. Price chiseling with De Beers is also unacceptable. In fact, Epstein (1982, ch. 6) identifies six 'rules of the game' that have been established by De Beers. Rule one: No one may question the authority of the diamond trading company to decide who gets which diamonds (a block consignment rule). The De Beers director of operations is the sole arbiter of both the number and quality of the diamonds offered to each dealer. This enables Oppenheimer to largely control both the volume and profitability of the dealer's business. Rule two: There shall be no haggling over price. De Beers is the sole arbiter of price, and it is able to do so since the price it charges averages about 20-25% below the wholesale price. Refusal to pay the price may foreclose future purchase opportunities. This effectively prevents price competition and helps De Beers stabilize the market so the profit margin provided to the dealers seems to vary with the business cycle. Rule three: Take the entire offered arrangement, or none of it. This appears to be a form of price discrimination akin to the economics of block booking in the movie business. Rule four: No client may resell the diamonds in his consignment in their uncut form without a special dispensation from the director of operations. To manage its international monopoly over the supply of diamonds and to maintain control over prices, De Beers needs to control the world stockpile of uncut diamonds. If it permitted its clients to resell their boxes, some outside party could amass its own stockpile of uncut diamonds. Rule five: Clients will supply De Beers with whatever information it needs to assess the diamond market. Before attending a 'sight', a client must provide detailed information on the number of uncut diamonds in inventory, the number in the process of being cut, the number previously sold, forecasted sales, and the relevant details of his business. In fact, clients must also be open to a De Beers audit at any time. This information is obviously quite critical to maintaining control over supply and hence prices. Rule six: Diamonds must never be sold into 'weak hands'. Since the marketing strategy of De Beers involves portraying diamonds as steadily appreciating in value, it is important to avoid 'fire sales' and the like. For this and other reasons, De Beers clients are prohibited from selling their diamonds to any wholesale or retail jewelers who undercut retail prices. De Beers clients are thus "forced to be silent partners with De Beers in maintaining an orderly retail market" [Epstein (1982) p. 641.


1163

The penalty for violating the rules is either refusal to deal at all or refusal to deal in terms quite as favorable. Typically, the quality of the consignment is degraded for minor offenses, and refusals to deal are reserved to punish more severe departures from expected behavior. These rules could not be imposed but for De Beers's considerable control over production, which seems to have been maintained through nationalization and changing governments in the producing nations. Even production not under De Beers's ownership seems to have been controlled by the company. According to Epstein (pp. 97-98), Oppenheimer negotiated a series of secret arrangements to block the availability of diamonds from the sources that his company did not directly own or control. In South Africa and the Belgian Congo, he pressed the governments into passing laws that forced independent prospectors and diggers to sell their diamonds only to government-licensed diamond buyers, who in turn contracted to sell their diamonds to De Beers's subsidiary, the Diamond Trading Company. In British colonies, such as the Gold Coast (now Ghana) or Sierra Leone, he contracted to buy whatever diamonds were unearthed from British mining companies, such as the Selection Trust, which held the mining concessions there. In South America, where the alluvial diamond fields are scattered over vast areas, he arranged his deal with local buying agents. In all cases, Oppenheimer required that the total production of diamonds be turned over to De Beers or its subsidiaries at an agreed-upon price. In recent years, De Beers's production has been increasing much faster outside South Africa than within it, at a time when political alignments are changing fast. A large and growing proportion of De Beers's production comes from Namibia and Botswana. In fact, Namibia is now the most important single source of gemstones. Yet De Beers seems to have moved successfully against potential competitors. Marine Diamond Corporation, a new entrant which obtained a concession in Namibia, was unable to market its production profitably when De Beers unloaded from its stocks sufficient diamonds of similar size and grade to depress the market segment upon which Marine Diamond depended. By 1965, this had deprived the fledgling enterprise of cash and made it an easy buy-out for De Beers [Epstein (1982) pp. 212-2131. Attempts by others to obtain concessions in Angola and elsewhere similarly ran up against the economic and political ability of De Beers to foreclose them. The Soviet Union, on the other hand, was not driven out but accommodated when it began to sell its polished diamonds in the 1960s. According to Epstein, the Soviets became partners in the cartel (p. 255) and have relied upon the De Beers distribution system. As De Beers's upstream position has now eroded through the entry of the Soviet Union and the shifting political winds of Africa, De Beers has attempted to integrate downstream into cutting, distributing, and wholesaling. One reason was to monitor market conditions more closely, but another may have been to obtain market power in various downstream positions, an inherently difficult objective to attain.

D.J. Teece et al.

6. Conclusion

The markets examined here - oil, mercury, uranium, and diamonds - are characterized to a greater or lesser degree by external market environments in which demand elasticities, as well as supply elasticities of non-members are relatively low. Still, success for the cartel seems to depend on a viable internal 'structure' - such as the CSO in the case of diamonds, and a 'club' in the case of uranium - bolstered by governments in all cases. The cartels selected seem to indicate that the external market environment molds the outcomes associated with attempts at cartelization, but that internal structure also matters. However, the need for tight internal governance is softened if the producers are satisfiers, as may be the case with certain OPEC producers. The welfare implications of the four cartels examined were addressed only superficially. Effects on price are often difficult to ascertain, particularly in the case of natural resource cartels, where the calculation of monopoly rents requires measurement of user costs. Further, to the extent that cartels lower the adjustment costs associated with competitive markets, deadweight-losscalculations from monopolization fail to capture the totality of normative considerations. Economists, however, seem reluctant to address disequilibrium phenomena, and so our understanding of the causes and consequences of cartels is likely to be incomplete for quite some time. References Abreu, D., et al., 1985, "Optimal Cartel Equilibria with Imperfect Monitoring", Journal of Economic Theory 39,251-269. Adelman, M.A., 1982, "OPEC as a Cartel", in: J.M. Griffin and D.J. Teece (eds.), OPEC Behavior and World Oil Prices (Allen & Unwin, London). Behrman, J.R., 1978, "Simple Theoretical Analysis of International Commodity Agreements", in: Development, the International Economic Order and Commodity Agreements (Addison-Wesley, Reading, MA). Cohen, S.S., 1969, Modem Capitalist Planning: The French Model (University of California Press, Berkeley, CA). Cremer, J., and I. Salehi-Isfahani, 1980, "Competitive Pricing in the Oil Market: How Important is OPEC?", CARESS Working Paper 80-4 (University of Pennsylvania, Philadelphia, PA). Dasgupta, P.,and G.M. Heal, 1979,Economic Theory and Exhaustible Resources (Cambridge University Press, Cambridge). Epstein, E.J., 1982, The Rise and FaN of Diamonds (Simon & Schuster, New York). Fellner, W., 1965, competition Among the Few (Augustus Kelley, New York). Fudenberg, D., and E. Maskin, 1986, "The Folk Theorem in Repeated Games with Discounting and Incomplete Information", Econometricn 54 (May) 533-554. Gately, D., 1984, "ATen-Year Retrospective on OPEC and the World Oil Market", JoumalofEconomic Literature 22 no. 3,1100-1114. Gilbert, R., 1978, "Dominant Firm Pricing in a Market for an Exhaustible Resource", Bell Journal of Economics 9,385-395.


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Green, E., and R. Porter, 1984, "Non-Cooperative Collusion under Imperfect Price Information", Economehica 52,82-100. Griffin, J., 1985, "OPEC Behavior: A Test of Alternative Hypotheses", American Economic Review 75, 954-963. Griffin, J.M., and D.J. Teece, eds, 1982, OPEC Behavior and World Oil Prices (Allen & Unwin, London). Hahn, F., 1973, On the Notion of Equilibrium in Economics (Cambridge University Press, Cambridge). Hexner, E., 1945, International Cartels (University of North Carolina Press, Chapel Hill, NC). Hotelling, H., 1931, "The Economics of Exhaustible Resources", Journal of Political Economy (April). Johany, A.D., 1978, "OPEC Is Not a Cartel: A Property Rights Explanation of the Rise in Crude Oil Prices", unpublished doctoral dissertation (University of California, Santa Barbara, CA). Jorde, T.M., and D.J. Teece, 1992,Antitrust, Innovation, and Competitiveness (Oxford University Press, New York). Koopmans, T.C., 1957, Three Essays on the State of Economic Science (McGraw-Hill, New York). Kreps, D. et al., 1982, "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma", Journal of Economic Theory 27,245-252. Lewis, T., and R. Schmalensee, 1978, "Cartel and Oligopoly Pricing of Nonreplenishable Natural Resources", in: I? Liu (ed.), Dynamic Optimization and Application to Economics (Plenum Press, New York). Lewis, T.R., and R. Schmalensee, 1982, "Cartel Deception in Non-renewable Resource Markets", Bell Journal of Economics 13 no. 1,263-271. MacAvoy, P., 1982, Crude Oil Prices as Determined by OPEC and Market Fundamentals (Ballinger, Cambridge, MA). MacKie-Mason, J., and R. Pindyck, 1987, "Cartel Theory and Cartel Experience in International Minerals Markets", in: R. Gordon et al. (eds.), Energy: Markets and Regulation (MIT Press, Cambridge, MA). Mead, W.J., 1979, "The Performance of Government in Energy Regulations", American Economic Review 69 (Papers and Proceedings, May) 352-356. Meade, J.E., 1970, The Theory of Indicative Planning: Lectures Given in the University of Manchester (Manchester University Press, Manchester, England). Milgrom, P., and J. Roberts, 1982, "Predation, Reputation, and Entry Deterrence", JournalofEconomic Theory 27,280-312. Newbery, D., 1981, "Oil Prices, Cartels, and the Problem of Dynamic Inconsistency", Economic Journal 91,617446. Orr, D., and P. MacAvoy, 1965, "Price Strategies to Promote Cartel Stability", Economica 32, 186-197. Oshorne, D.K., 1976, "Cartel Problems", American Economic Review 66,835-844. Pindyck, R.S., 1978, "Gains to Producers from the Cartelization of Exhaustible Resources", American Economic Review 60 (May) 238-251. Pindyck, R.S., 1982, "OPEC Oil Pricing and the Implications for Consumers and Producers", in: J.M. Griffin and D.J. Teece (eds.), OPEC Behavior and World Oil Pnces (Allen & Unwin, London). Plummer, A., 1951, International Combines in Modem Industry (Pitman, London). Richardson, G.B., 1960, Information and Investment (Oxford University Press, London). Rotemberg, J., and G. Saloner, 1986, 'A Supergame-Theoretic Model of Price Wars During Booms", American Economic Review 76,390-407. Salant, S., 1976, "Exhaustible Resources and Industrial Structure: A Nash-Cournot Approach to the World Oil Market", Journal of Political Economy 84,1079-1093. Solow, R., 1974, "The Economics of Resources or the Resources of Economics", American Economic Review 64,l-14. Suslow, V.Y., 1992, "Cartel Contract Duration: Empirical Evidence from International Cartels", submitted.

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Taylor, J., and M. Yorkel, 1979, Yellowcake: The International Uranium Cartel (Pergamon Press, New York). Teece, D.J., 1982, "OPEC Behavior: An Alternative View", in: J.M. Griffin and D.J. Teece (eds.), OPEC Behavior and World Prices (Allen & Unwin, London). Teece, D.J., 1983, "Assessing OPEC's Pricing Policies", California Management Review 26 (Fall) 69-87. Ulph, A., 1982, "Modeling Partially Cartelized Markets for Exhaustible Resources", Economic Theory of Natural Resources (Physica-Verlag, Vienna). Ulph, A,, and G.M. Folie, 1980, "Exhaustible Resources and Cartels: An Intertemporal Nash-Cournot Model", Canadian Journal of Economics 13,645-658. US Bureau of Mines, 1960 and 1965 editions, Mineral Facts and Problems (US Government Printing Office, Washington, DC). US Bureau of Mines, Various years, Minerals Yearbook (US Government Printing Office, Washington, DC). US Bureau of Mines, Various years, Commodity Data Summaries (US Government Printing Office, Washington, DC). US Congress, 1939, Hearings Before the Temporary National Economic Committee, 76th Congress, 1st Session, Part 5. Vives, X., 1990, "Trade Association Disclosure Rules, Incentives to Share Information, and Welfare", RAND Journal of Economics 21 no. 3,409-430. Williamson, O.E., 1975, Markets and Hierarchies (Free Press, New York).

Chapter 25

THE ECONOMICS OF ENERGY SECURITY: THEORY, EVIDENCE, POLICY* MICHAEL A. TOMAN** Energy and Natural Resources Division, Resources for the Future, 1616 P Street, NW, Washington, DC 20036, USA

1. Introduction Relatively few events in recent economic history have generated the quantity of scholarly writing, policy analysis, and public debate that have resulted from the 'oil shocks7of the 1970s and 1980s. Those events directly stimulated the rapid growth of literature on a number of the topics discussed in this volume. The purpose of this essay is to review the state of analytical knowledge with regard to two such topics: the relationships between oil imports and economic well-being and the nature of economic adjustment costs imposed by rapid energy price changes. The chapter provides a review of scholarly research concerning (i) the functioning of world oil markets, (ii) the consequences of import dependence and instability in energy markets for aggregate economic well-being, and (iii) the policy options available for addressing these concerns. The review is limited to issues faced by industrialized, market-oriented economies . Conclusions emerging from the review of the literature are mixed. Despite a large application of analytical and financial resources, there remain important gaps in knowledge and understanding which hinder effective policy making. These range from general issues concerning the behavior of petroleum demand and

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Of the many colleagues who deserve thanks for their help in preparing this paper, I would particularly like to express my appreciation to Douglas Bohi and Hillard Huntington. I also have benefitted from careful comments on earlier drafts by Robert Deacon, William Hogan, James Sweeney, and Margaret Walls. In addition, I am grateful for the assistance of Caroline Bouhdili, Andrew Jones, Andrew Plantinga, and Gayle Killam in assembling the facts and data used in Section 2 of the chapter, and Kay Murphy in preparing the manuscript. Responsibility for errors and opinions is mine alone. * * Senior Fellow, Energy and Natural Resources Division, Resources for the Future, Washington, DC. The preparation of this review has been aided by several earlier works concerned with various aspects of energy security. See, e.g., Plummer (1982), Alm and Weiner (1984), Hubbard and Weiner (1985), Bohi and Toman (1986), Gately (1986), and Horwich and Weimer (1988). These surveys provide many other references in addition to those given here.

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Handbook of Natural Resource and Energy Economics, vol. III, edited by A. K Kneese and J.L. Sweeney O I993 Elsevier Science Publishers B.K All rights reserved

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supply to the design of specific policy instruments, such as the draw-down of strategic petroleum stocks. While energy security is seen by many analysts to be a serious policy issue, the literature to date has not provided an entirely convincing argument for the existence of market failures warranting substantial government intervention, or for an effective design of policy measures if such intervention is found to be warranted. To set the stage for the review, the balance of this section seeks to provide a more precise statement of the nature of the energy security problem.

1.1. Overview of the energy security problem To identify the energy security problem more precisely, we must consider how market failures may arise. One such externality is the well-known 'monopsony wedge' in the international trade literature. A large oil-importing country may face a higher marginal cost of oil purchases, taking into account how increases in its collective purchases raise the world price, than the cost reflected in the world price. For many commodities this effect is only a pecuniary spill-over, but because oil is not priced in perfectly competitive markets, action to exploit a monopsony wedge for petroleum could be justified in terms of recapturing monopoly rents. Some observers have argued that there are other social costs of oil imports which reflect their deleterious long-run impacts on inflation and the trade balance. An energy security problem also may arise from interactions between energy price instability and economic performance in modern economies. Rapid increases in energy costs and declines in energy use not only reduce potential economic output - an unavoidable cost, even in an idealized textbook economy - but also may reduce actual output below its potential because of market rigidities and adjustment costs. These adjustment problems could include, for example, unemployment and reduced output when labor productivity drops with lower energy use but real wages do not correspondingly adjust. Such adjustment problems depend on the level of oil consumption, not on imports per se 2. These costs can be and in practice are mitigated by a variety of private-sector activities. For example, investors or firms can store petroleum for speculative or precautionary purposes and hedge short-term price risks in futures or forward delivery markets. Portfolios can be designed which balance assets whose values are raised and lowered by high energy prices. Firms (and others to a lesser extent) can invest in production technologies that allow easier substitution between

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In addition to internal macroeconomic adjustments, oil-exportingcountries confronting an oil price shock also may face changes in the overall terms of trade that have adverse effects on industrial activity. A full discussion of this so-called Dutch disease is not included here; see, for example, Bruno and Sachs (1982).

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oil and other energy sources or between energy and non-energy factor inputs. Notwithstanding these possibilities for reducing the consequences of uncertainty and instability in energy markets, many analysts maintain that energy shocks are likely to have serious macroeconomic consequences. The energy security literature has focused mainly on two types of policy measures for dealing with the externalities noted above. One measure is oil import restrictions through tariffs or quotas to mitigate the costs associated with longterm foreign oil dependence. Other types of policies that can limit imports also have been considered, though less frequently. These include alternative forms of energy taxation (such as a gasoline tax or other levies on consumption), increases in domestic energy supply and fuel substitution capabilities, and non-price measures to promote energy conservation. The other type of policy that has received much consideration is the accumulation and release of oil stockpiles to dampen the size, duration, or likelihood of price shocks and thus lower economic adjustment costs. Policies that try to offset the adjustment costs themselves, rather than trying to cut the size of the oil price shock, also have received consideration [Hogan (1981), Gilbert and Mork (1984), Hickman, Huntington and Sweeney (1987)l. An example of such a policy would be cuts in payroll taxes during a shock to lower employer labor costs and thereby offset any tendency for the shock to aggravate unemployment. However, such fine-tuned macroeconomic policies generally are ignored in the energy security literature or viewed as too difficult to use in practice 3 . Accordingly, we will not examine them in this review. Because oil is a fungible commodity, changes in energy markets and energy policies inherently are experienced worldwide. This policy interdependence expands the scope of the energy security problem by raising questions about whether and how effective agreements for coordinating policies can be structured. Because the benefits of policies spill over to all oil-consuming nations, individual countries' incentives to undertake energy security measures unilaterally will be weaker than in a cooperative arrangement 4. In practice, however, cooperation requires credible agreements - arrangements which serve the participants' own self-interests. It also requires the implementation of policies which are capable of actually contributing to enhanced energy security.

A number of studies do emphasize the importance of having sound monetary and fiscal policies in response to a disturbance as a complement to energy policies. There also are examples of 'beggar-thy-neighbor' policies in which negative spill-overs are ignored in the absence of cooperation. For example, a variable import fee which stabilized the domestic oil price in one country would increase the variability of price elsewhere. Encouragement of inventory accumulation during a crisis to satisfy one nation's precautionary oil demand will raise prices for other countries.

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1.2. Energy security reconsidered: Lessons porn the 1980s

The behavior of the world oil market during the 1970s basically involved two large and somewhat persistent price explosions separated by a period of stable or decliningreal oil prices. The experience of the 1980swas quite different: stagnant or slipping prices punctuated by the price collapse of early 1986, followed by a period of partial recovery and oscillation. Events since 1980force us to reconsider previous conceptions of the energy security problem in several ways5. First, the events of the 1980s highlight uncertainties about underlying demand and supply behavior in energy markets. A practical consequence of these uncertainties is that the ability to estimate the social costs of oil imports or of adjustment to disturbances also is limited. By the early 1980s it had become clear that inexorable growth in energy demand and greater opportunistic control of world oil markets by a few non-US suppliers were not preordained. Demand adjusted to higher prices, the Organization of Petroleum Exporting Countries (OPEC) experienced serious disarray, and other sources of supply assumed greater prominence. In the wake of the 1986 oil price drop, still other questions about the market have arisen. For example, recent experience leaves doubts about any simple theories of OPEC behavior, and even about the degree of OPEC's market power (issues also discussed in chapter 24 of this Handbook, by Teece et al.). Similar uncertainties arise in defining and assessing risks of market disturbances. The price drop of 1986 reminds us that oil price uncertainty includes the possibility of decreases as well as increases, much as with any other commodity. This view is quite different than that built into much (though not all) of the analytical work of the 1970s and early 1980s, which assumed only the possibility of price increases relative to a normal-market level. The fragmentation and increased competitiveness of world oil markets make it even more difficult than before to gauge the variability of oil prices or to draw simple conclusions about conditions under which OPEC could assert control over the market. There also continues to be uncertainty about whether surges in demand during a crisis will exacerbate any future supply disruptions.

1.3. Plan of the chapter

The balance of the chapter is divided into five parts. The next section provides a historical overview of recent oil shocks. Section 3 reviews some of the literature on world oil market behavior. Section 4 examines some potential externalities associated with foreign oil dependence and adjustment to energy shocks. Section 5 The need for reconsideration was only amplified by the events following the Iraqi occupation of Kuwait in August 1990.


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Fig. 1. Spot and official oil prices, 1973-1974 (prices in nominal dollars). (From Petroleum Intelligence Weekly, various issues.)

considers the implications for policy options, specifically import restrictions, oil stockpiling, and international cooperation. The sixth and concluding section briefly summarizes the study's findings and lists some future research directions.

2. Recent experience with oil shocks

Disturbances in world oil markets in the 1970s and 1980s are associated with four events: the 1973 'Arab Oil Embargo', the 1979 Iranian Revolution, the start of hostilities between Iran and Iraq in 1980, and the precipitous 1986 drop in oil prices. The first three events were quite different in their abruptness, duration, and price impacts; the last event was a vivid example of a negative price shock. The discussion below provides a brief summary of these episodes to set a context for the review in the next section of analytical work seeking to explain the functioning of world oil markets. The discussion is not intended to be a comprehensive history; further details can be found in the references cited. The first oil supply disruption began with the outbreak of the Yom Kippur War in October 1973. Later that month, Saudi Arabia and other Arab states proclaimed an embargo on oil exports to the USA and the Netherlands in response to these countries' support for Israel. Actual free world oil production declined from 47.8 mmbld (million barrels per day) in September 1973 to 43.2mmbld in November, a 9.6% decrease. In December the production cuts were partially rescinded, and in mid-March of 1974 the Arab oil ministers agreed to restore production to pre-October levels. As shown in Figure 1, the spot price of Arab Light oil on the Rotterdam market increased sharply in the first two months of the

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Fig. 2. Spot and official prices, 1978-1979 (prices in nominal dollars). (From Petroleum Intelligence Weekly, various issues.)

disruption and then, as the disruption ended, leveled off at over three times the pre-disruption price. Four years of stability followed the 1973-1974 oil embargo, with oil prices decreasing in real terms. This stability eroded after the strike of Iranian oil workers began in October 197B6.Iranian production subsequently declined to zero in late December as the revolution against the Shah unfolded. At first, the price impact of this disruption was not great (see Figure 2) because other countries (especially Saudi Arabia) increased their production to make up for the lost production from Iran, and product stocks within the Organization for Economic Cooperation and Development (OECD) were modestly drawn down. Indeed, total free world oil production was 1.4mmbId higher in the fourth quarter of 1978than in the third quarter. However, in the first quarter of 1979, Saudi Arabia limited its oil production and a significant rebuilding of OECD product stocks began. By March 1979, when Iranian production resumed at a reduced level, the average spot price was 60% above the October 1978 level. While official prices also rose, they lagged substantially behind spot values; in March 1979 they were only 7% above their October 1978 level. Prices and inventories continued to rise through 1979. By the end of 1979, spot prices had increased 200% and official prices 100% above their October 1978levels. These price increases occurred despite the fact that the actual cuts in production experienced were much smaller (in percentage terms) than those that had occurred in the 1973-1974 disruption. Part of the higher volatility of spot prices reflected a The discussion which follows draws on Badger and Belgrave (1982), Mork (1982), Verleger (1982), Bohi (1983), and Charles River Associates (1986).


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Fig. 3. Spot and official oil prices, 1980-1981 (prices in nominal dollars). (From Petroleum Intelligence Weekly, various issues.)

drying up of volumes on what was, at that time, a relatively thin market even under normal conditions. In particular, there appeared to be little attempt to arbitrage gaps of up to $20/bbl between spot and official prices. The lack of arbitrage may have reflected both proscriptions on resale and the likelihood that actual sales by OPEC members were made at effective prices greater than official levels. The first nine months of 1980 were relatively calm: OPEC production declined in gradual steps and final demand also fell, though stocks continued to be built up at an unprecedented rate. Spot prices of Arab Light declined, and the gap between official prices and spot prices was narrowed (Figure 3). In September 1980, war broke out between Iran and Iraq. By November, all oil exports from Iraq and a portion of Iranian exports were halted, leading to a total reduction of 3.6 mmb/d (from 59.5 to 55.9mmbld) in free world production. As a result of this cut, spot prices of Arab Light reached $40/bbl in mid-November,but official prices increased only slightly to $32/bbl. The spot price increases were short-lived; spot prices gradually decreased to their 1980 levels by May 1981. One important difference between this episode and the 1978-1979 crisis, in which a smaller production drop led to a larger and more persistent price hike, was that stocks were above normal at the outset and were drawn down, rather than built up further as the disruption continued. Moreover, oil consumption fell rapidly during this period (faster, in fact, than stocks were being drawn down). The end result was that spot prices fell below official prices by 1981. The overall experience of 1978-1981 with OECD product inventories over 1978-1981 is puzzling, since the observed pattern of accumulation and release was both destabilizing and counter to the maximization of inventory profits.

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Fig. 4. Spot oil prices, July 1985-June 1986 (prices in nominal dollars). (From Petroleum Intelligence Weekly, various issues.)

The price collapse in early 1986 represented yet another twist in the evolution of the oil market '. Prices were steady or declining during the four years preceding the drop, as non-OPEC supplies increased and purchasers reacted to the previous price hikes by completing investments in greater energy efficiency. Indeed, this period included the first drop in the official OPEC selling price (by $5 per barrel) in March 1983. However, as the volume of spot trading grew substantially the official price increasingly became just a lagging indication of spot values. During the four years prior to 1986 the real dollar price of oil dropped roughly 40% 8. OPEC output began to increase in August 1985; by August 1986 it was 25% above its previous year level. Saudi Arabia was responsible for the largest share of the increase, though some other countries also raised national production while still other countries reduced output somewhat. The last quarter of 1985 also saw increased use of 'netback' pricing by OPEC members, whereby the official price was set based on the prices that could be obtained for products less refining and transportation margins. In effect, this move substantially relinquished control of pricing to the market. The direction of the effect on prices of expanded production was predictable, even if the exact timing and duration were not. The spot price dropped by roughly SO%, from $26/bbl to $13/bbl, between late 1985 and early 1986, and dipped below $10/bbl in mid-1986 before recovering to around $17/bbl in mid1987 (see Figure 4). Through 1989 the oil price level fluctuated significantly,though the price remained primarily in the $14-18 range. The Iraqi invasion of Kuwait on August 2, 1990 resulted in the immediate reduction of 4.3mmbld of crude oil normally supplied to the world oil market

' The discussion which follows is drawn from Gately (1986). The real cost to countries other than the USAduring this period dropped less because of depreciation of other currencies relative to the dollar [Huntington (1984), Gately (1986)l.


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Fig. 5. Daily spot oil prices, 30 July 1990-24 May 1991 (prices in nominal dollars). (From New York Mercantile Exchange.)

from the two countries, or nearly 18% of OPEC exports and nearly 10% of total world supply. The spot price of crude oil in US and world markets rose from $21 per barrel the day before the invasion to $28 per barrel within a week afterward (an increase of 33%). In the ensuing weeks, the price of oil fluctuated with changes in expectations about war risks and with increases in production from other sources (see Figure 5). The crude oil price rose dramatically in the last week of September, for example, in response to Saddam Hussein's threat to destroy Kuwaiti and other Middle Eastern oil fields if war should begin. By the end of November, oil production in Saudi Arabia and other countries had increased by enough to offset the original 4.3 mmb/d interruption in supply. Saudi Arabia also announced plans for further production increases, including the development of a newly discovered giant oil field, that were expected to raise Saudi output an additional 1mmb/d by March 1,1991. The crude oil price remained below $30/bbl during December and January, until just before the start of allied air strikes on January 16,1991. The next day witnessed a record one-day drop in spot oil prices, and within five days the price of most crude oil was below $20/bbl.

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The Iraqi war provided the first opportunity to observe oil futures market behavior during a market crisis9. It is of interest to note that throughout the conflict, the futures market consistently discounted crude oil prices for future delivery relative to spot prices. The price for delivery in one month was often $l/bbl below today's price, the 2-month price was another dollar cheaper, the 3month price was cheaper still, and so on for 12-18 months into the future. This pattern of price behavior indicates that the market regarded the effect of the war to be temporary with no major impact on the long-term level of prices. It also indicated that traders with ongoing oil purchase requirements could significantly reduce their costs relative to spot prices by buying forward. The collapse of the oil price immediately after the start of hostilities is consistent with the view that the crisis would soon end. The war also gave us our first experience with the use of the Strategic Petroleum Reserve (SPR). On September 6, President Bush responded to growing pressures to sell SPR oil by ordering a one-time test sale of 5 million barrels from the reserve. The announcement not only failed to reduce oil prices, prices actually rose the next day. Soon after the beginning of hostilities on January 16, the USA proposed selling over 22 million barrels from the SPR within one month. However, the rapid drop in oil prices after January 16 eliminated any interest in the sale.

3. Oil market behavior

In this section we review studies concerned with long-run world oil supply and OPEC behavior, changes in market institutions, and short-run inventory and market dynamics in a crisis. Long-run studies attempt to shed light on the longrun path of the market. Understanding this path is important for determining what policies (if any) are needed for coping with long-run oil dependence and the danger of opportunistic pricing by suppliers. Studies of changing market institutions and of short-run market responses to disturbances attempt to shed light on the causes and consequences of oil price fluctuations. Understanding these issues is an important prelude to assessing the size of the economic adjustment burden caused by abrupt changes in oil market conditions.

3.1. World oil supply and OPEC decisionmaking Most of the discussion in this section is concerned with analyses of OPEC behavior. This emphasis reflects both the importance of OPEC as an oil supplier and The New York Mercantile Exchange did not begin significant trading in oil futures until 1980.


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the uncertainty which exists regarding OPEC behavior lo. Before examining the literature on OPEC decisionmaking, however, we should note that there is also uncertainty about non-OPEC supply behavior. Numerous econometric and simulation studies of US petroleum supply have been undertaken, but that research has not yet generated wide agreement concerning the characteristics of US supply behavior [Bohi and Toman (1984)l. A few studies of petroleum supply in Canada and the North Sea also have been undertaken. Outside of the market economies, very little is known about petroleum supply ' I . Theories of OPEC behavior have run the gamut from a cohesive cartel to a political aggregation of competitive actors. Most analysts would subscribe to the view that OPEC could exercise significant market power, enough to yield outcomes where the price of oil exceeds its full marginal cost (including the cost of reserve replacement). However, there is disagreement about the degree of market power OPEC has exerted. Some analysts have argued that factors other than market power may explain observed behavior. Even adherents to the view that OPEC possesses significant market power would not describe the organization as a stable, monolithic dominant actor; such a view could not be sustained in light of actual experience. Instead, the prevailing hypothesis (with several variants) is that OPEC is a looser entity that constantly struggles to balance the profit interests of individual members against the need for collective output discipline 12. OPEC theories also attempt to explain divergences in the interests of individual members or groups in higher prices, higher output, or more conservative prices and outputs. These differences typically are attributed to differences in revenue requirements, absorptive capacity, and social discount rates [Bohi and Russell (1975), Eckbo (1976), Teece (1982)l. MacAvoy (1982) takes issue with the conventional wisdom that observed petroleum prices and quantities reflect significant exercises of seller market power. He expresses the view that the price explosions of the 1970s primarily reflected individual political events and demand-side responses, not concerted OPEC decisions. He also asserts that OPEC was not the prime force behind the sustaining of price increases in the mid-1970s; instead, he attributes the market responses primarily to a burgeoning of world petroleum demand, significant declines in non-OPEC production, and some adjustment of production plans by In the first half of 1989 OPEC oil production was over one-third of the world total; its reserves were over two-thirds of known world reserves. Broadman (1985) describes an effort to better understand the geological, economic, and institutional forces influencing oil exploration in non-OPEC developing countries. l2 Some studies model intertemporal OPEC decisionmaking and, in some cases, use game theory to describe strategic interactions between producer and consumer countries. See, e.g., Newbery (1981), Gallini, Lewis and Ware (1983), and Hillman and Long (1985). In these studies, however, OPEC is typically treated as a monolithic actor. Moran (1981) argues that all economic models of OPEC behavior are inadequate and proposes some political theory in an attempt to fill the gap. lo

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individual OPEC members. OPEC's inability to control the market effectively is further highlighted, MacAvoy argues, by its inability to offset subsequent stagnation of demand and non-OPEC production increases in the wake of the price jumps during the 1970s. MacAvoy attempts to support his argument about market scarcity with a very simple simulation model showing that price increases much like those observed in the 1970s would have emerged even under an extrapolation of OPEC behavior from the 1960s, a period of less collusion than that which occurred in the 1970s. Unfortunately, attempts to statistically estimate coefficients in the model fare very poorly, and even with judgmentally specified parameters the model is not too successful in tracking actual market outcomes through the 1970s. Thus, while MacAvoy's assertions about market influences may be plausible conjectures, they receive fairly little empirical support in his study. Teece (1982) presents another argument for petroleum prices remaining above competitive levels in the absence of concerted exercises of market power - the socalled target revenue theory. According to this view, once petroleum prices rise to the point where further revenues no longer could be comfortably absorbed by the exporting country, further price increases would cause a reduction of supply. Revenue absorption levels, in turn, are complex dynamic functions of national development objectives, the size of national oil reserves, the returns to foreign investment of oil proceeds, and political risks. With a backward-bending supply curve, prices which have fortuitously risen above the marginal cost of reserve production and replacement - the standard for price behavior in a competitive market [Bohi and Toman (1984)l- may remain so even without collusive output restrictions because individual suppliers have no incentive to expand output and put downward pressure on the price. Producer rivalry would emerge only as revenues are eroded over time by demand stagnation and growth of non-OPEC supply. Teece presents a substantial amount of factual and anecdotal evidence which he interprets as explaining observed petroleum market behavior during the 1970s. In a series of papers, Adelman (1980, 1986, 1990) presents the more widely accepted view that OPEC has exercised market power, though he readily acknowledges that it has functioned only as a 'clumsy cartel'. The core of Adelman's argument is a set of calculations attempting to measure the marginal cost of producing and replacing reserves, which is the standard for a competitive price as noted above. From his calculations Adelman concludes that the gap between the world oil price and the marginal cost of oil supply in OPEC is too large to be explained by market forces. Thus, he concludes that output restrictions must be in place to explain the excessive prices. He makes a similar argument in comparing the spread in marginal costs between OPEC and high-cost producers in the USA. Adelman views the target-revenue argument with disdain, arguing that countries like Saudi Arabia with vast reserves inherently earn a higher return on money in the bank than from leaving the oil in the ground. However, this argument presumes


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that individual OPEC members can be characterized as seeking to maximize the present value of financial wealth. As Teece suggests, a variety of economic and non-economic factors may explain exporters' propensities to hold petrodollar balances 13. In addition, Adelman attributes all of the differences between oil prices and his measures of marginal supply cost to cartel rents. He does not give much weight to the possibility that the gaps could also represent scarcity rents. For example, OPEC countries may not have been in a position to rapidly expand output after the first oil price increase because of deliverability constraints. More recently, Saudi Arabia has attached a high value to its associated natural gas deposits and probably has limited oil production until productive uses of the gas (e.g., petrochemical plants) are more fully developed. Griffin (1985) econometrically tests several different categories of hypotheses about the behavior of individual oil-producing countries inside and outside of OPEC. These hypotheses include variants of market-sharing cartel behavior; competitive price responsiveness; the target revenue theory, which states that countries adjust production to observed prices along a backward-bending supply curve to achieve a desired revenue flow; and a 'property rights' hypothesis that observed price increases in the 1970s resulted from a transfer of oil resource ownership to host countries who collectively had a lower discount rate, and thus a lower proclivity for current output versus future output, than the former oil company owners. Griffin's principal conclusion is that OPEC seems to most closely resemble a partial market-sharing cartel: individual member outputs are sensitive to other countries' shares, but the output responses to changes in price are not strictly proportional. In contrast, output decisions in a group of non-OPEC countries appear to be competitively determined by prices. Griffin rejects the property-rights theory, while his findings concerning the target-revenue explanation of OPEC behavior are inconclusive 14. Griffin's results extend only to 1983.A more recent paper by Jones (1990) extends Griffin's analysis to include behavior after the 1986 price drop. His results are basically in agreement with Griffin's regarding OPEC and non-OPEC behavior before and after the price drop, though Jones finds slightly less support for the partial market-sharing hypothesis. While Griffin's results are provocative, they have some weaknesses which point to the need for further investigation of the issues raised in his paper. As Griffin points out, the partial market-sharing cartel also cannot be rejected for many Constraints on absorptive capacities could affect not just income streams but also the propensity to hold wealth, whether as liquid balances or in situ oil reserves. This could at least partly explain Saudi unwillingness even to delineate areas where oil reserves are likely to be found. l 4 The individual explanatoryvariables often are statistically insignificant, but the combined significance of the variables cannot be rejected in most cases. l3

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Fig. 6. Price reaction curve. (From Hogan (1989).)

non-OPEC oil-producing countries, though in these regressions the individual coefficients frequently are insignificant and the overall explanatory power of the cartel model does not substantially exceed the competitive model. It is difficult to draw sharp distinctions on the basis of these models since both the independent variables - price and other countries' output - are likely to move together. The same could be said of the independent variables - price and investment expenditure - in the target revenue model; the revenue target likely is endogenous to market conditions. Further research that considered different formulations would help to clarify these issues Is. Experiments with different combinations of hypotheses also might be interesting. Most numerical simulation models of OPEC behavior rely on some variant of what is usually called the 'price reaction curve'. This simple reduced-form model specifies a positive relationship between the annual rate of oil price change and the degree of OPEC capacity utilization (OPEC being the residual market supplier). Stable prices are often presumed to occur at a capacity utilization rate of around 80%. Below this utilization rate prices fall, though the rate of decrease remains relatively small even for fairly low utilization rates. Prices rise rapidly when Is These efforts could include specifying separate relationships for market share and absolute output and additional testing of nested hypotheses, rather than the approach of testing separate models used by Griffin in obtaining most of his results. One practical problem that arises in the type of analysis carried out by Griffin derives from the nature of oil price behavior observed over most of the sample period: since the price exhibited little variability outside of the episodic disturbances discussed in the previous section, its ability to explain observed production is limited. Including other variables to capture growth in demand and address the simultaneity problem might be useful. This is particularly important when one considers the importance of inventory demand to price formation over 1978-1981, as noted above.


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demand for OPEC output goes above the stable-price utilization rate. In short, the price reaction curve is taken to have a generally hyperbolic shape. Figure 6 illustrates a typical price reaction curve, taken from a study by Hogan (1989). Several features of the diagram illustrate the limits of the approach, and thus the difficulties in finding reliable rule-of-thumb descriptions of OPEC behavior. Note first that the indicated price response as the market tightens is based on experience in 1979-1980 16. Given the previously mentioned anomalous behavior of the market in those years (particularly with regard to inventory demand), the curve may not provide reliable guidance to future market outcomes with rising demand for OPEC output. Secondly, the curve does not capture the experience with oil prices in 19861987. If we view these years as also being anomalous, along with 1979-1980, then the picture of the oil market that emerges from the scatter of price and capacity utilization is different than the conventional description. Rather than prices being set to capitalize on tight markets, we see capacity utilization adjusting to stagnant prices except during occasional market disturbances. Many of these practical uncertainties regarding OPEC and non-OPEC oil supply are vividly illustrated by results of studies that compare different models [Energy Modeling Forum (1982), Gately (1986)l. These studies compare model outputs for a variety of scenarios. The scenarios differ in their assumptions about demand elasticities, 'backstop' energy resources, oil import reduction policies, and risks of price shocks. The models themselves vary greatly in their structural assumptions regarding OPEC and non-OPEC supply, demand, energy-economy interactions, and level of aggregation. As might be expected, the results for both OPEC and non-OPEC production and for world oil prices vary considerably across the models for a given scenario. Part of the differences reflects different structural assumptions about demand in the models. However, the models also show marked differences in outcomes when comparing scenarios involving changes in demand. This is an indication that disagreement among the models as to supply behavior plays a considerable part in explaining differences in the model results.

3.2. Changes in market institutions

Until the 1970s, most world oil trade moved through the internal channels of vertically integrated international petroleum companies. In response to the l 6 William Hogan has pointed out to me that the 1973-1974 experience is difficult to include in a price reaction curve because of uncertainty about oil production capacity at that time, but that including 1973-1974 likely would imply an even more rapid growth of oil prices as capacity utilization rises than the curve shown in Figure 6.

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greater market uncertainty that began in the 1970s, two institutional developments have occurred that have important consequences for price behavior and market efficiency. These developments are the rapid growth in the volume of spot market trading for petroleum, and the rise of organized futures and forward markets for crude oil and refined products. As noted in Section 2, during the 1978-1979 disturbance transactions on the spot market all but dried up, and this illiquidity may have contributed to the price and inventory instability of the period. Whereas the spot market served a narrow balancing function at that time, representing less than 10% of total traded volumes, it is now a ready source of supply used for half or more of total traded volumes. This suggests that the spot market would be far less likely to experience any destabilizing illiquidity than in the past. Behavior in the spot market, and the overall efficiency of spot and contract trading institutions, obviously depend in part on the nature of the differential between spot and contract prices. In equilibrium these differentials will depend on such factors as the relative risks and enforcement costs associated with the respective transactional arrangementsI7. Changes in these factors, e.g., less price reliability with long-term contracts or greater exercise of producer market power, will alter spot/contract differentials, as will changes in total excess demand on the market. There has been surprisingly little empirical investigation of observed disparities between spot and contract oil prices and their implications for market efficiency. Green and Mork (1991) test for the presence of 'informational inefficiency' in these prices - significant, persistent gaps beyond what could be justified based on relative transactions costs. They find that such inefficiency was present but decreased over 1978-1985. This result is consistent with our earlier intuitive discussion of market changes. An extension of this analysis beyond 1985 probably would strengthen the conclusion. Active futures trading for heating oil began in 1978, with crude oil futures beginning to be actively traded in 198318. These markets primarily serve to exchange risks, in that actual delivery of oil at the maturity of a futures contract is rare (less than two percent). Instead, contracts usually are settled by repurchase. Forward trading for oil cargoes, notably from the North Sea, also has become quite active [Weiner (1989)l. These markets serve a mixed function, satisfying both physical delivery requirements and desires for risk trading. The growth of futures and forward trading has raised two basic questions about the functioning of oil markets. The first question concerns the informational

l 7 See Williamson (1979) for a general discussion of 'transaction cost' explanations for different exchange institutions. l 8 Futures markets now also include other commodities, such as gasoline, as well as options contracts.


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efficiency of market prices. The second question concerns whether the growth of futures trading stabilizes or destabilizes spot prices. As to the first question, Bohi and Toman (1987) conclude from the data that heating oil futures prices are only weak forecast tools for spot prices from month to month and that more distant futures prices do not perform that well from month to month as predictors of more recent futures prices. In these results the time to maturity is fixed but the maturity date varies across the sample 19. Weiner (1989) and Dominguez (1989) find that futures and forward prices do perform efficiently when one considers the time series of daily price changes toward a fixed maturity date: today's futures or forward price for the contract in question is the best predictor of tomorrow's price 20. Much of the general literature on futures markets has been concerned with identifying conditions under which futures trading might stabilize or destabilize spot prices. However, there has been little empirical application of this material to oil markets. Dominguez (1989) shows that futures prices and spot prices tend to react with roughly comparable volatility to market events. She also finds that longer-term futures prices are less volatile than shorter-term prices, and that futures prices generally are less volatile than spot prices. These results do not suggest a built-in tendency for the market to overreact with futures trading, but they leave open the question of whether spot prices would be less volatile if there was no futures trading.

3.3. Short-run market reactions to a market disturbance

Understanding how oil prices may behave in response to a market disturbance is of obvious importance in gauging how policies should be implemented to reduce whatever adjustment costs may result. Given the premise that total enduse consumption demand for oil products is relatively inelastic in the short run, the dynamics of prices during a disturbance will depend primarily upon the nature of the shock, the pricing behavior of producers, and the nature of oil inventory responses. As to the first point, oil shocks may best be viewed as random events rather than purposeful cartel actions. Thus the emphasis here is on work seeking to explain the reaction of prices and inventories to different disturbances. Verleger (1982) examines the dynamics of the oil market disturbances of 19781980. Verleger proposes and tests three basic hypotheses: Bohi and Toman argue that the results reflect the omission of effects from inventory changes in simple forecasting formulas, and they construct a simple rational expectations model that illustrates the interdependencies among spot prices, futures prices, and inventory changes. Their results are expressed in terms of changes relative to the spot price to avoid estimation problems associated with nonstationarity of the price series.

l9

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(a) a supply disruption causes a surge of demand on the spot market and a jump in the spot price; (b) official prices adjust slowly in response to a spot price rise; (c) the gap between spot and official contract prices induces inventory holders to add stocks in anticipation of future speculative profits, thus further destabilizing the market. Unfortunately, this explanation of 1978-1980 market dynamics turns out to be lacking in several respects, particularly as a guide to current and prospective market conditions. The estimated lag for adjustment of contract prices to spot prices is implausibly long, particularly when one considers the changes in market institutions and pricing behavior since 1980. As noted in the previous section, spot trading has grown enormously and contract prices much more closely follow spot prices. The same institutional changes call into question the assumption that inventory holders will naively speculate on gaps between spot and contract prices by adding to stocks, without seeking to arbitrage the gaps or recognizing the opportunities for profit-taking inventory release that would dampen prices. In any event, Verleger is not able to empirically substantiate his inventory hypothesis even for the 19781980 period. Subsequent research has sought to avoid these difficulties, but its ability to explain past behavior or project future market responses remains limited. Bohi (1983) presents some evidence that the 1978-1980 experience resulted from consumer 'panic buying' rather than refiner inventory building. However, Bohi's empirical results also are mixed and, as he notes, his explanation depends on refiners mistaking the nature of the panic demand by not temporarily reducing inventories. Again, it is questionable whether such mistakes would be repeated in the future. Hubbard (1986) offers a theoretical rational expectations model of price formation during a disruption which shows how the price effects of a supply shock can be magnified and prolonged by stickiness in contract price adjustment. However, Hubbard's analysis embodies some of the same disadvantages found in Verleger's formulation: there is a sharp dichotomy drawn between spot and contract prices, and all the short-run adjustment burden is borne by the spot market -contract prices only adjust slowly to spot price movements. In addition, Hubbard does not address the dynamics of inventory demand. Hubbard and Weiner (1986) present and estimate a model of inventory adjustment for the 1974-1981 period, with inventory changes depending on changes in sales and the inventory-to-sales ratio. While the model appears to generate a significant statistical fit, it is unable to explain inventory behavior during the 1978-1979 market disturbance. Research to date does not identify a unique paradigm for the behavior of oil markets in the wake of a shock. Two extreme cases which seem to bracket the range of possibilities can be specified. On the one hand, future disturbances (supply or demand shocks) could evolve much as in the past, with sticky prices and


I'

l"

Quantity

Fig. 7. Illustration of the monopsony wedge tariff.

inventory responses causing disturbances to persist. However, given the changes in the market which have occurred since the 1970s, it seems equally plausible that future disturbances could be similar to the shocks studied in agricultural markets: random perturbations of limited duration, to which the market (at some cost) can adapt without fundamental institutional hindrances.

4. Possible energy security externalities

In this section we summarize various possible costs of oil use that may not be fully reflected in the market price of oil. We begin with long-run costs associated with oil imports. We then discuss the costs associated with oil market disturbances and the costs of risk-bearing in the presence of oil market uncertainty. The section concludes with a discussion of international spill-overs.

4.1. Oil imports and the monopsony wedge

The most commonly identified long-run externality associated with oil imports is the monopsony wedge. This effect is illustrated in Figure 7. If an oil-importing country has a large enough share of world oil trade that it faces an upwardsloping supply curve for imports, then an incremental expansion in total national oil imports will raise the world price of oil. This will raise the nation's total oil import bill by more than the expenditure on the additional imports; payments for inframarginal quantities also will rise [Bohi and Montgomery (1982, ch. 2)].

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The marginal cost of imports to private actors in the oil-importing country is the market price, indicated by the height of the inverse supply curve for imports in Figure 6. The social marginal cost of imports, including higher payments for inframarginal quantities, lies above the inverse supply curve as shown in the diagram. The difference between social and private costs, indicated by the vertical distance between the two schedules, is the monopsony wedge. It can be shown that the size of the monopsony wedge is equal to the ratio of the world price to the elasticity of the import supply schedule. Thus, if P is the world price and n1 is the elasticity, the wedge is given by PlnI 2 1 . The elasticity of import supply depends in turn on the elasticity of total world export supply and on the demand elasticity for imports by other countries. Specifically, it can be shown that nl satisfies n1 = nxXII + e R I R / I where , n x is the elasticity of world export supply, e ~ is the absolute elasticity of import demand by other oil-importing countries, I is home imports, I R is other countries' imports, and X is total world exports [Bohi and Montgomery (1982, ch. 2)]. Note that as n1 gets larger, the monopsony wedge PlnI goes to zero: a country facing a perfectly elastic import supply schedule has no influence over the world oil price. From the formula given above, it also follows that nl for an individual importing country or a group of importers is inversely related to its share of total oil trade (IIX),and it is positively related to the (absolute) elasticity of other countries' import demand e ~ and the elasticity of world supply n x . Thus, even if n x and e ~ are fairly small, nl will be large if the individual country's or group's share of total world imports is small. The USA faces a fairly elastic import supply curve, even though its absolute level of oil consumption is high, because its import share is relatively low given a substantial volume of domestic production. Even a country with 100% import dependence will face a high import supply elasticity if its import volume relative to the size of the market is low. Conversely, a group of importers with a high collective market share will possess a larger monopsony wedge than an individual country with the same demand and supply elasticities. The dependence of nl on n x and n ~ as well as P also illustrates how the monopsony wedge varies with market conditions. In particular, the wedge can be expected to increase, possibly substantially, in a disrupted market when the price rises and the elasticity of import supply declines. The import supply elasticity would decline relative to its long-run value because short-run world supply and rest-ofworld demand elasticities are lower than long-run values. Note that the definition of the monopsony wedge depends on the existence of a stable positive relationship between the volume of imports and the world price of oil, whether that relationship is a standard competitive supply curve or a relationship derived from a price reaction function for world oil supply as shown in Let P ( I ) denote the inverse import supply schedule, so that the total import bill is C ( I ) = I P ( I ) . Differentiating with respect to I , it is easy to show that C 1 ( I )= P + IP' = P + ( P l n ~ ) .

21


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Figure 6. If, on the contrary, import supply is backward-bending because of revenue targets sought by oil exporters, then the magnitude and sign of the monopsony wedge depend on the location of the market equilibrium; the wedge will be negative along the backward-bending branch. Specifying the wedge also is complicated by the possibility that exporters possess enough potential market power to shift the relationship between price and imports. To illustrate with an extreme case, if any attempt to exploit monopsony power by reducing import demand is met with a corresponding supply cut by an oil-producing cartel, then the wedge cannot be defined as in the preceding paragraphs and monopsony power would not be effective. While the existence of a monopsony wedge means that an importing country or group of countries may be paying more than is necessary for imports, this could be taken simply as a pecuniary externality in the world petroleum market. The existence of a pecuniary effect does not itself justify restrictions on oil imports. Most analyses that favor import restriction [e.g., Hogan (1981), Broadman and Hogan (1986, 1988)l counter this point by arguing that the monopsony wedge is a pecuniary externality that is appropriate to exploit in light of market failures on the supply side stemming from oil exporters' market power 12. To be sure, this argument is a two-edged sword in that emphasizing exporters' market power also introduces the prospect of supplier retaliation to neutralize monopsony power. Moreover, the extent of exporter market power remains uncertain, as noted above. Numerous estimates have been made of the monopsony wedge for the USA, most dating from the 1970s. As Broadman's (1986) survey points out, these estimates have varied widely but most tend to be $10/bbl or above. More recent estimates have tended to be much more conservative, recognizing the moderate US share of the world oil market and the relatively high price elasticity of oil import supply to the USA. For example, Broadman and Hogan (1986) calculate a monopsony wedge of $1-4/bbl depending on market condition^^^. Walls (1990) is even more conservative, calculating a wedge of under $l/bbl.

4.2. Otherpossible costs of long-term oil import dependence The literature identifies several more indirect sources of external social cost beyond the monopsony wedge that could arise from import dependence [e.g., Hogan (1981), Bohi and Montgomery (1982), Broadman and Hogan (1986,1988)l.. Some of these potential externalities have a stronger conceptual basis than others. This reasoning is consistent with general arguments in the 'strategic trade' literature [e.g., Grossman and Richardson (1984)l. I3 These figures reflect an optimal tariff for internalizing the wedge; the size of the wedge prior to imposing import restrictions would be somewhat larger. I2

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In addition, the empirical significance of these possible spill-overs remains open to debate. An increased transfer of wealth abroad through higher petroleum imports and prices may retard long-term capital formation. Higher oil prices also could slow growth by reducing long-term factor productivity. In addition, oil importers facing a larger trade imbalance from high oil costs could experience a currency depreciation which raises the real cost of non-oil imports, depending on the response of capital flows. Conceptually, these effects do not introduce a new category of externality. Rather, they are different facets of the monopsony wedge already discussed. If this wedge is estimated using an oil demand curve which reflects general equilibrium consequences of oil price changes and intertemporal consumption-investment tradeoffs, then all these effects will be reflected in the wedge. In practice, such an approach is complicated to say the least. An alternative approach would entail estimating the direct wealth transfer with a partial equilibrium model of the oil market and then separately estimating indirect effects (while taking care to avoid double counting). There are empirical questions about the significance of the indirect effects. Long-term adjustments in energy-related investment and innovation could have significant productivity effects [Jorgenson, Gollop and Fraumeni (1987), Jorgenson (1988), Hogan and Jorgenson (1991)l. However, the link between energy costs and factor productivity remains murky [Bohi (1989)l. Nor is it clear that productivity effects reflect market failures as opposed to cost effects that are internalized in private transactions. The argument that higher oil prices translate into depreciation of the dollar at first seems intuitively appealing. An increase in the price of oil means (assuming oil demand is price-inelastic) that total payments for oil rise and (assuming all other trade is fixed) the current account will move toward deficit. A current account deficit leads to an overall balance of payments deficit (assuming no change in capital flows) which in turn implies an excess supply of dollars in foreign exchange markets. Consequently, the international value of the dollar will fall and all US imports will be more costly - the USA must export more goods to buy the same amount of imports. While this is a pecuniary effect, it could be viewed as relevant to US national welfare in the same way that US interests are related to monopsony power - limits on US oil imports could curb the cost. However, while the argument may have appeal, the necessary sequence of assumptions is not likely to hold. The conclusion of two complementary approaches to the analysis of the balance of payments effects on prices, and the behavior of exchange rates after each oil price shock, is that it is inappropriate to attribute an exchange rate externality to oil imports. One analytical approach is concerned with real terms-of-trade effects of higher oil prices, as in Marion and Svensson (1986). The terms of trade refers to the amount of imports a given unit of exports will command in the international


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market; thus, a rise in the price of oil means that the USA must export more goods to buy the same amount of oil. Marion and Svensson demonstrate that the termsof-trade effect of higher oil prices can be positive or negative for any individual oil-importing country, depending on special circumstances for each country 24. The second analytical approach looks at the effect of oil prices on the monetary exchange rate, as in the work of Krugman (1983). Like Marion and Svensson, Krugman shows that the relationship between a country's exchange rate (or, for that matter, its current account position) and the price of oil is ambiguous in general. All oil-importing countries will experience an initial current account deficit when the price of oil rises, but the effect on exchange rates among oil-importing countries will depend, initially, on the willingness of the oil-exporting countries to hold different foreign currencies (that is, on relative capital flows). If oil exporters prefer to hold more dollars than other currencies, for example, the dollar exchange rate will rise. Over time, the exporting countries will spend their foreign currencies on goods or assets, and the countries of preference for these expenditures will experience currency appreciation. A study of exchange rate behavior by Trehan (1986) finds only weak empirical support for the view that higher oil prices lead to an appreciation of the dollar. A more defensible conclusion, in view of the weak statistical results, is that the price of oil is a poor predictor of the dollar exchange rate, either positively or negatively. A look at the history of the dollar/SDR exchange rate in Figure 8 corroborates these findings. The SDR is representative of a composite of other currencies. The figures suggest that the value of the dollar is not harmed by oil price increases nor helped by oil price reductions. Some analysts also suggest that increased oil imports could aggravate general price inflation, if increased demand for imports gave rise to a higher long-term trend growth in oil prices which was in turn manifested in higher general inflation through some 'cost-push' channels. However, this effect is suspect on several grounds. Aside from lingering general uncertainties about the significance of costpush inflation, there is little clear evidence of any effect of oil imports on long-term oil price Even if such an effect did exist it would have to be very large to have much significance for general inflation, given the fairly small share of total Their analysis includes the counterintuitive result that those countries least able to adjust to higher oil prices (because of rigidities in the way oil is used in their economy) will tend to experience the greatest reductions in domestic output and, assuming other factors constant, will experience an improvement in their terms of trade. This outcome is reached because a decline in home output relative to that of other countries means that there is now a relative shortage of home country goods in world markets. The relative shortage will cause an improvement in the home country's terms of trade. This is one way in which the terms of trade may be inversely related to economic performance (the improvement in the terms of trade presumably is of cold comfort to the country experiencing the deeper recession). 25 Depletable-resource theory predicts a long-term upward trend in oil prices. However, this trend depends on interest rates and on prospects for expanding supply (through new resource discoveries) or altering total demand (the conflicting effects of GNP growth and enhanced energy efficiency), not on 24

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Fig. 8. US dollar1SDR exchange rate and average refiner acquisition cost for imported crude oil, 19741991. (From International Financial Statistics, International Monetary Fund, and Monthly Energy Review, US Department of Energy, Energy Information Administration.)

energy payments (let alone oil payments) in GNP. Finally, for this effect to be a significant social cost one would also have to assume that high costs of tolerating or suppressing inflation were incurred. It is possible that an ongoing bout of inflation could result from an overzealous monetary authority who is seeking to accommodate a rise in oil prices. The monetary authority could err in estimating what is required to adjust to a higher level of oil prices, thereby setting in motion an inflationary spiral that requires a deflationary jolt to the economy to stop. However, inflation scenarios that rely on planning errors by the monetary authorities can be triggered by any number of events, and to focus policy on the triggering event rather than the cause of the problem seems misguided at best. Nor is there a reasonable second-best argument for attaching an inflationary spill-over cost to oil prices, since the firstbest alternative of educating the monetary authority is feasible and more likely to avoid further costs than a policy aimed at oil prices or imports. In short, any connection between oil prices and inflation seems dubious and would reflect at most a policy failure, not a market failure. imports. Stronger imports might enhance exporter market power, but in this case theory would predict a slower growth in oil prices [Bohi and Toman (1984)l.


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Externalities also could arise from the risk of costly disturbances in petroleum markets. For example, if reduced long-term import demand left world oil production capacity idle and available to offset the effects of a supply disruption or a sudden surge in demand, then the import reduction could function as a form of insurance. However, given the complexities and uncertainties in petroleum markets discussed in Section 3, this form of insurance seems problematic at best. Another insurance argument is that reduced long-term oil use lessens exposure to the costs of market disturbances - both the direct costs of increased wealth transfers to oil exporters and indirect macroeconomic costs discussed below. While this argument has some conceptual validity, the costs to be avoided depend only partly on oil import volumes; the indirect costs reflect total oil and other energy consumption in the economy. Attributing to oil imports all the costs of exposure to energy market disturbances is especially misleading for a country like the USA which has substantial domestic energy resources. For a country like Japan which depends essentially totally on energy imports, the distinction between imports and consumption is not important but the distinction between oil and total energy use remains relevant in the calculation of indirect costs of market disturbances. In both cases the actuarial soundness of such insurance - accepting the continuing costs of oil import restrictions to lessen the cost of occasional market disturbances remains uncertain. In particular, it depends on how costly oil price shocks are to the economy (see Section 4.3, below). Estimates of indirect external effects of oil imports for the USA are more sparse than estimates of the monopsony wedge. Most estimates focus on inflation and balance-of-payments effects. The survey of estimates from the late 1970s by Broadman (1986) indicates a cluster of estimates in the $10-40bbl range. To obtain cost figures this large, one must assume that an increase in wealth transfers for oil imports causes a significant increase in domestic price inflation and a significant depreciation of the domestic currency, that the costs of reducing inflation and adjusting to a devalued currency are substantial, and that macroeconomic policy is highly non-accommodating. Aside from uncertainties about the macroeconomic assumptions, we noted above that assumptions of a large unfavorable effect of oil imports on inflation and the exchange rate are open to dispute. Broadman and Hogan (1986) are more conservative about these elements, attributing to them a value of roughly $2-3bbl. However, they also attach a significant value - $7-8ibblto the value of reduced oil use in lessening macroeconomic costs of oil price shocks, and the value of excess world supply capacity in lowering disruption risks. One other concern over dependence on foreign oil supplies that has been raised is the threat of predatory pricing by foreign suppliers against the US petroleum industry, which some observers saw behind the 1986 oil price drop [Singer (1988)l. This potential problem is very different from those discussed above in that it does not arise from high import volumes and costs, but rather from low import prices regardless of import volumes. Predation is seen to raise the financial risks of

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competitive fringe producers like the USA, threaten premature abandonment of marginal oil-producing properties ('stripper' wells), and imperil industry-specific human capital employment. The recommended response is the maintenance of a domestic oil price floor to avoid an unfair weakening of domestic suppliers as part of the competitive fringe. Evidence in support of this argument is limited, however. Even at the low oil prices observed in the mid-1980s, the volume of oil reserves threatened with abandonment probably was modest. Moreover, the threat of significant reserve abandonment from a temporary oil price drop requires an assumption of relatively myopic optimizing behavior by petroleum companies (perhaps because of high debt burdens). More generally, the extent to which cyclic risks in the petroleum sector give rise to market failures remains open to question. Even if such market failures could be demonstrated, alternative co-insurance schemes (e.g., changes in tax treatment) could have lower cost than a domestic oil price floor.

4.3. Macroeconomic costs of oil price shocks A sudden increase in world oil prices increases the flow of real resources from domestic final goods in oil-importing countries to higher payments for oil imports and greater resource use in domestic energy production (if any). However, the size of this cost is limited by the relatively low ratio of energy expenditures to the value of national output 26. Increased energy costs alone do not appear to fully explain the sharp drops in economic performance experienced by the USA and other countries, including net oil exporters like the United Kingdom, in the wake of the two oil shocks of the 1970s. This gap has motivated several studies seeking to theoretically explain and empirically assess the indirect effects that energy price shocks may have on macroeconomic performance. Unfortunately, this literature has given rise to thickets of definitional and measurement questions. We first attempt to review different potential causes and interpretations of these costs. We then discuss efforts to gauge their magnitude 27. Our concern here is primarily with the macroeconomic costs of oil price increases; we briefly consider the impacts of abrupt price declines toward the end of the subsection. For the USA the cost share of all energy has ranged between 4 and 9% since the early 1970s [Alterman (1985)l. The cost shares of oil consumption and oil imports are lower still. Other industrialized countries have even lower basic energy intensities (though higher degrees of import dependence). 27 The discussion which follows draws from Mork (1985b), Huntington and Eschbach (1987), Leiby and Lee (1988), and Bohi (1989). I also have benefitted from the advice of Hillard Huntington.in developing these arguments. 26


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To understand the macroeconomic costs of an oil market disturbance, we must first identify the metric used for gauging these costs. Most studies use some measure of GNP or GDP as a proxy for national well-being. GNP is a value-added measure of national output: it can be expressed as total national output less payments for intermediate goods, including energy, or as total payments to domestic factors of production (labor and capital). We ignore for the moment various index number problems that arise in defining aggregate measures of national output or inputs, and the question of how accurately GNP represents national well-being; these topics are addressed below. With these observations as background, we can discuss the various effects that oil price shocks may have on national income. Consider first a situation where labor and capital resources remain fully employed after an oil price jump, and all domestic factor markets clear with inputs receiving the real values of their marginal products. Then, to a first approximation, the decline in real GNP is equal to the sum of the reduction in final goods output from reduced total energy consumption, the reduction in final goods output from diversion of inputs to increased domestic energy production (if any), and the increased cost of inframarginal oil imports28. Note that the decline in final goods output from diversion of inputs to domestic energy production has an offsetting effect in that the drop in energy consumption is less than the drop in oil imports. Thus the decline in GNP we are considering here also can be expressed as the sum of the decline in final goods output from reduced oil imports and the increased cost of inframarginal oil imports 29. The GNP change just discussed is sometimes referred to as the decline in potential GNP resulting from an oil price shock. Since other factors of production are assumed to be fully employed, this change can be calculated as a consumer surplus loss in a partial-equilibrium microeconomic model of the energy market. In fact, if domestic energy production is fixed in the short run (or zero), this GNP loss is just the increase in the wealth transfer already discussed previously in connection with the monopsony wedge. The decline in actual GNP could exceed the decline in potential GNP for several reasons which are as varied as the different general theories about macroeconomic behavior that can be found in the literature. On the supply side, an oil price shock If the oil price shock triggers a change in the real price of non-oil imports relative to exports, a further adjustment is needed to capture this terms-of-trade effect. 29 See Leiby and Lee (1988), Appendix C, for details. The equivalence of the two formulations can be derived from the equilibrium conditions that the marginal cost of domestic energy production equals its price, and that the marginal rate of substitution between energy and other inputs in producing final output equals the factor price ratio. Note also that the characterizations of GNP change in the text are first-order approximations for non-marginal oil price changes. For a marginal oil price change, the change in energy imports and final goods output also are incremental, so the value loss is the product of two increments; in the limit, as the size of the oil price shock shrinks, the GNP loss reduces to the social marginal cost of oil imports. 28

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could cause increased unemployment because the marginal product of labor drops with a decline in oil use but real wages are slow to adjust. An oil shock also could cause a reduced flow of capital services from accelerated obsolescence of energyusing capital stock30. Still another possible source of supply-side GNP loss from an oil shock is adjustment costs incurred by all sectors, whether otherwise favored or harmed by the relative factor price change, as inputs are reallocated to match changes in demand for goods. Finally, short-run GNP losses could be experienced because of a Keynesian aggregate-spending shortfall if oil exporters (or domestic energy producers) have higher propensities to save than energy consumers. The distinctions among these theories are of more than academic interest from the standpoint of designing energy policies to cope with macroeconomic disturbance costs. Private actors can be expected to take a variety of steps in response to disturbance risks to minimize the expected costs they individually bear. These steps would include, for example, investments in reduced long-term energy consumption and greater flexibility in energy use, along with oil storage and the design of wealth portfolios to hedge financial risks. The role for government policies in mitigating disturbance costs is to account for externalities. As noted above, some decline in potential GNP from an energy price shock is inevitable. Government policies to lower these costs are futile (though distributional policies to shift the burdens could be warranted). Externalities in macro costs can arise from the presence of an enlarged monopsony wedge and from market failures which cause actual GNP losses to exceed potential GNP losses. However, not all the reasons why actual GNP falls short of full-employment potential GNP necessarily constitute market failures. For example, imperfectly flexible factor input employment contracts may in part be a rational method for limiting transaction costs, even if they also magnify adjustment costs during periodic episodes of price instability [Mankiw (1990)l. However, some portion of unemployment in the wake of a price shock may well reflect market failure. Similarly, efficient hedging investments in more flexible capital stock or private energy storage facilities may be limited by tax policy or other distorting effects on private discount rates [Lind (1982)l. Even where market failures related to adjustment can be identified, it is not immediately obvious that they represent energy market failures. Short-term Keynesian spending effects, to the extent they are relevant, are best handled by monetary and fiscal policies. Problems in factor markets related to relative price adjustments are more problematic since the first-best options - more flexible factor prices and employment decisions - generally are seen not to be readily attainable3I. Thus adjustment problems related to energy price changes become This effect is likely to be much more important when the shock is perceived to be enduring rather than transitory. 31 For a discussion of approaches like countercyclical payroll taxation see Gilbert and Mork (1984). 30

Ch. 25: The Economics of E n e w Security

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linked to energy markets in that the second-best policy may involve damping energy price fluctuations. These distinctions among the various types of macro costs, and the degree to which they constitute externalities, often are not drawn in studies of energy security policies. Instead, aggregate summary measures of GNP loss are used to describe the macro consequences of an energy price shock. The goal of policy then is stated as minimizing the size of this loss by limiting the energy price disturbance. To this point we have considered theoretical definitions of changes in GNP resulting from an oil price shock. A problem arises in assessing these costs using data from the national income accounts, regardless of the theoretical explanation. Measured GNP in the national income accounts basically is equal to the total income (or product) of labor and capital valued at a base-year set of prices". Thus, measured GNP does not reflect the increased real cost of oil used in producing final output when relative oil prices increase. In fact, if total employment of capital and labor services are unchanged after an oil price shock then measured GNP will show no decline. In particular, measured GNP losses from an oil price shock will not include the real output loss and wealth transfer from a higher real cost of imports. To integrate measured GNP losses with microeconomic measures of wealth decline from an oil shock, one must add to the measured GNP loss a terms-of-trade loss that corrects for increases in real import costs. The combined loss represents the decline in domestic absorption of national income. This approach can be implemented with a detailed macroeconomic model based on measured GNP. The disadvantage of this approach, however, is that it is not readily applicable without access to a full macro model. An alternative approach uses a simple loss function that approximates the loss in actual GNP relative to potential GNF', and then adds in the microeconomic losses from reduced oil use and costlier inframarginal imports33. Variants of this latter approach are used in several of the strategic oil stockpiling analyses discussed in the next section. Keeping these measurement problems in mind, we turn next to empirical evidence on the size of GNP effects from energy price shocks. The view held among many energy economists is that these effects are large. This view is supported by an extensive simulation analysis carried out by the Energy Modeling Forum (EMF) [Hickman, Huntington and Sweeney (1987)]34.This study compares the effects on US GNP of different oil shocks as indicated by a variety of macroeconomic Measured GNP also includes capital depreciation and indirect business taxes. Leiby and Lee (1988), Appendix C, argue that measured GNP losses already include the reduction in the value of final goods output from reduced energy consumption and diversion of inputs to domestic energy production. Their loss representation combines a macro loss function with the increase in total import payments, rather than with the total surplus loss. 34 See also US DOE (1988). Broadman and Hogan (1986,1988) calculate a macroeconomicdisturbance premium of around 10% of the normal-market oil price, though the basis for their calculation is different and they mistakenly attribute the premium to oil imports rather than energy consumption. 32

33

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models, including standard large-scale models used by forecasting and consulting companies. While there is considerable variation among the findings of individual models, several interesting general results emerge from the study. The EMF study considers two price increases, of $18/bbl and $7/bbl, along with a $7/bbl price drop. These figures represent 50% and 20% of the base price of $36/bbl used in the study. Within this range of price fluctuations, each model finds the relationship between the percentage oil price change and the percentage change in (measured) real GNP to be approximately linear (i.e., the GNP elasticity with respect to the oil price appears to be roughly constant). The models differ in their estimate of this relationship, however. For an $18/bbl oil price increase maintained over four years, the median estimate of the percentage GNP decrease after one year relative to the no-shock growth path is about 1.4%, or $47 billion (1983$). This amounts to roughly $2.5 billion for each $1 increase in the oil price. The distance between the first and third quartiles around the median percentage GNP drop is about 1.0%. The percentage GNP decrease for the second year of the oil price shock is much larger, about 2.9%. Even after four years the lingering effects of the oil price shock are significant (the percentage GNP drops in years 3 and 4 are about 2.5 and 2.1% respectively) 35. These estimated losses only reflect measured GNP, as discussed above. After correcting for the real decline in terms of trade caused by higher oil price, the full losses are found to be roughly 40% higher than the declines in measured GNP. The authors of the EMF report take pains to enumerate caveats which must be borne in mind when evaluating the study results. The individual model results vary significantly, reflecting differences among the models with respect to the relationship between GNP and the overall price level and the link between oil prices and the general price level. On the other hand, most of the models have similar basic mechanisms for the transmission of energy shocks. Increased energy costs cause firms to increase their price mark-ups, which depresses aggregate spending. Reduced aggregate spending causes higher unemployment because of sticky wage adjustment. Microeconomic elements related to relative price changes are largely absent. In addition, the models used in the study employ parameters estimated over the period from roughly the mid-1950s to 1980. During this period real oil prices were stable or falling except for the two brief explosions during the 1970s. Thus the conclusions of the models regarding the relationships between oil price increases and GNP will be heavily colored by the two recessions that followed the price shocks of the 1970s, even though this experience represents only a relatively small part The EMF study does not report quarterly GNP declines, but Huntington (1985) shows a pattern of mean GNP drops beginning at 0.8% in the first quarter after the shock to a peak of 2.7% in the sixth quarter, and then remaining above 2% through the sixteenth quarter.

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of the sample. The EMF study also focuses primarily on US economic models, though one Canadian model also is included. It is of interest to know whether the experience of other industrialized countries with energy shocks is similar to the US experience, particularly given the widely held view that energy security is an important worldwide problem. The direct econometric evidence on the causes and consequences of macroeconomic disruption costs is surprisingly mixed. Using a reduced-form time series model of the US economy, Hamilton (1983) concludes that most postwar US recessions through 1980 are explained at least partly by oil price increases. Mork (1989) extends Hamilton's findings to include post-1980 experience, including the period bracketing the 1986 oil price drop. However, Mork, Mysen and Olsen (1989) conclude from the same type of analysis that West Germany, and especially Japan, show far less sensitivity to oil prices than the USA. They find the aggregate sensitivity of the United Kingdom, a net oil exporter, also to be lower, presumably reflecting offsetting effects in oil-producing and oil-consuming sectors of the economy. Bohi's (1989, 1991) study of microeconomic links between energy price shocks and economic performance concludes with a large amount of skepticism about the macroeconomic importance of energy price disturbance^'^. Bohi surveys previous studies and examines disaggregated industry data for the USA, Germany, Japan, and the United Kingdom, noting that these countries experienced different consequences from the 1973-1974 and 1979-1980 shocks. After showing that the direct effects of increased energy costs on production and employment are not that important, as would be expected given energy's small cost share3', Bohi turns to potential indirect effects: employment losses due to wage rigidity, reduced capital formation, or adjustment costs arising from changes in the composition of final demand. The spread of an energy price shock to other input markets depends crucially on the signs and magnitudes of substitution elasticities among capital, labor, and energy inputs. However, Bohi points out that the empirical literature on these elasticities remains inconclusive; thus it is difficult to say, for example, whether an increase in the price of energy will cause equilibrium demand for labor services to rise or fall. Nor is the literature able to disentangle the effects of energy prices

ASBohi notes, concerns about the importance of energy relative to confounding factors in explaining stagflation also have been expressed by macroeconomists [Sachs (1982), Helliwell (1988)l. 37 Bohi points out that industry-level changes in production and employment during 1973-1975 and 1978-1980 do not appear to be very strongly correlated to energy intensity (the same result is obtained using the cost share of all intermediate inputs). He also notes that in very many cases the same industries in the same countries showed very different responses in the two periods of disturbances. This finding contradicts the seemingly apparent relationship between energy and economic performance in aggregate macroeconomic data. 36

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from other influences on factor productivity. Evidence on wage rigidity also is inconclusive. If energy price shocks do adversely affect economic performance significantly, then the effects of these shocks should be more pronounced in more energyintensive sectors. However, Bohi's analysis of industry data in the four countries listed above does not support this conclusion. There do not seem to be strong negative correlations between energy intensity and changes in employment or capital formation. Nor does the evidence support the existence of more severe adjustment costs in energy-intensive industries from changes in the composition of final demand. Finally, changes in real wages appear to vary negatively with energy intensity in the two shock periods, suggesting that where the adjustment burden in labor markets might have been more serious, wages were more responsive. Based on these and other contrary or inconsistent findings, Bohi concludes that energy prices had little to do with macroeconomic failures during the 1970s. He advances the alternative hypothesis that the industrialized countries already were seeking to combat inflation during the periods of the oil price shocks, and except for Japan in 1979 they tightened their macroeconomic policies further after both the price shocks to mitigate increases in their general price levels. According to this view, deleterious macroeconomic impacts of an energy price shock may be avoided by following a monetary policy that accommodates a one-shot increase in the price level after an oil price While Bohi's analysis does not represent the last word on the subject, it does shift a considerable burden of proof to those who would favor a strong link between energy price shocks and macroeconomic losses. We conclude this discussion with a brief mention of evidence on macroeconomic response to energy price decreases, a subject of some interest in the wake of the 1986 oil price collapse. As noted above, the Energy Modeling Forum simulation study suggests that price drops have a salutary effect on the economy of equal magnitude to the cost of a comparable oil price increase, at least for moderate shocks. Tatom (1987) reaches the same conclusion. In contrast, Mork (1989) finds evidence that the negative effects on US GNP of an oil price increase are far larger in magnitude than the beneficial effects of a price decrease. This conclusion is consistent with the observed response of GNP after the 1986 oil price drop. Mork, Mysen and Olsen (1989) confirm this finding for the USA but achieve mixed results for other OECD countries, with less significance generally between GNP and oil prices. Thus the evidence on this issue also remains inconclusive. The success of this policy depends on the degree of real wage indexation and on whether the monetary authority can credibly undertake a one-shot accommodating policy without giving rise to expectations of persistent price inflation. If the oil price shock or the monetary response create a self-sustaining inflationary cycle, with its attendant costs, then oil price shocks can be seen as indirectly giving rise to macroeconomic costs because of the limited options available to policymakers for controlling inflation. However, this hypothesis is fairly convoluted and requires more substantiation.

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4.4. Cost of risk-bearing Unpredictable fluctuations in energy markets can impose utility losses on riskaverse private actors who must bear the risks of wealth variability. The extent to which there are significant risk-bearing costs associated with energy market instability - the size of the 'risk premium' - depends on both the variance of wealth caused by energy prices and the degree of risk tolerance (a higher degree of risk aversion implies a higher premium). The extent of energy-related wealth variance depends in turn both on the variance of energy prices and on the correlation between energy prices and wealth. Other things equal, a higher variance of energy prices increases the variance of wealth, but this variability is blunted by various forms of hedging that reduce the correlation between energy prices and wealth. Opportunities for hedging include both financial strategies (e.g., purchasing oil futures contracts) and physical capital investment (e.g., holding oil stocks or installing dual-fuel equipment). Macroeconomic externalities related to energy price fluctuaiions could spill over to cause the social risk premium associated with energy price uncertainty to exceed the risk premium perceived by private actors. The social premium includes the variance of income changes indirectly caused by energy price fluctuations (e.g., losses due to increased unemployment after an energy price shock) which are not fully included in private decisions, and covariance between direct and indirect income losses caused by energy price shocks. A consequence of this possible gap between the premia would be lower investment by the private market in hedges against energy price fluctuations than is socially efficient. The practical importance of risk-bearing costs associated with energy price instability is open to dispute. Dominguez (1989) uses regression techniques from portfolio analysis to conclude that investing in oil futures contracts can provide an effective hedge against oil price fluctuations. On the other hand, Strong (1989) concludes that holding equity shares of petroleum companies is a poor hedging strategy. Toman and Macauley (1986) use some simple calculations based on a twoperiod conceptual model to conclude that the private risk premium associated with oil stockpiling is extremely small, and that the social premium, while larger, also is only on the order of 10% of the price of oil. These results suggest that the costs of risk-bearing are minor. However, Toman and Macauley admit that many elements of their analysis are ad hoc.

4.5. Policy coordination spill-overs Since petroleum is traded on a single world market, any action an oil-consuming country takes to alter the price of oil, either in the long run or during a market disturbance, spills over to other nations. Since countries must bear all the costs of

their policies but cannot appropriate all the benefits, the stage is set for a freerider problem: all countries would benefit from coordinated action, but no nation individually has an incentive to do so [Olson and Zeckhauser (1966)l. The ability to form effective agreements for policy coordination is constrained by the sovereign power of each participating country. For agreements to be effective, it must be in the self-interest of each participant to carry out their terms. International policy agreements can serve this end in several ways. At the simplest level, an agreement can simply specify a set of actions which all countries prefer, if they are carried out, with the threat of collapse of the agreement functioning as a deterrent to defection [Schelling (1960), Friedman (1977), Hardin (1982)l. A somewhat wider view of international agreements recognizes their ability to create mutual expectations which foster cooperative behavior [Runge (1981, 1984)l. Of course, for an agreement to be effective, the prescribed policy actions must have the capacity to produce beneficial effects in the oil market. In many ways the need for international coordination of energy security policies parallels the need for individual government intervention to offset the energy security externalities not captured in private-sector behavior. Just as the government of a single oil-importing country can use its collective monopsony power to recapture supracompetitive earnings in the world oil market, a confederation of importing countries willing to restrict imports can exert greater monopsony power than would result from uncoordinated actions by individual nations. Similarly, because the benefits of oil stockpiling to mitigate energy price shocks and macroeconomic disturbance costs flow to all oil-consuming countries, agreements to coordinate the size of stocks and their use in a crisis can yield greater benefits than is possible with uncoordinated policies. Analytically, these policy interactions can be illustrated using game-theoretic constructs. Given international spill-overs of benefits from long-term import reduction and the use of petroleum stocks to combat disturbances, the noncooperative outcomes will be inferior to the results obtained with policy coordination that internalizes the spill-overs. The nature of the inefficiency depends on the policy under consideration. Generally, import restraints and stockpile sizes will be lower in the absence of cooperation [see, e.g., Chao and Peck (1982)l. Uncoordinated stockpile releases are less rapid than the efficient outcome when a disruption is expected to worsen, and too rapid when a crisis is expected to improve [Hubbard, Marquez and Weiner (1985), Devarajan and Weiner, 1989)l. We further discuss these policy lessons, and the implications for developing institutions to foster international cooperation, in the next section of the chapter.


5. Policy issues

In this section we consider the implications of previous discussions in this chapter for the design of energy security policies. We focus in turn on long-term oil import restrictions, the creation of strategic oil stocks and their use during market disturbances, and the establishment of institutions to foster international policy coordination.

5.1. Long-term oil import constraints Three basic questions arise in considering policies for long-term restraint of oil imports. (a) How large are the potential externalities which would provide the rationale for government intervention? (b) What are the potential risks or limitations of import restrictions? (c) What instruments are best suited for undertaking the import restrictions? The discussion in Sections 4.1 and 4.2 suggests that even for a large oil importer like the USA, the size of long-run externalities related to oil imports is uncertain and could be very small. The capacity to unilaterally reduce the direct costs of oil imports by depressing world oil prices is modest given limited national market shares and relatively high elasticities of import supply (this capacity would be larger for a substantial consortium of oil importers, however). In addition, the case for substantial indirect long-run cost spill-overs is problematic on theoretical and empirical grounds. A useful methodology for confronting these uncertainties is the 'risk analysis' used by Broadman and Hogan (1986,1988). They first posit subjective probability distributions for key parameters influencing the degree of cost spill-over from oil import dependence (e.g., the effect of rising oil prices on general price inflation). They then calculate an 'optimal tariff' for a random sample of parameter values. The resulting probability distribution for the calculated optimal tariff gives some idea of the sensitivity of their findings to variability in the external cost components. It should be noted that Broadman and Hogan's actual calculations assume relatively significant spill-overs, even in the low ends of the subjective probability distributions for the input parameters. If one allows for a probability that several components are nugatory [as Hogan (1981) seems to suggest], then the corresponding optimal tariff values will be lower than those computed by Broadman and Hogan. There are two main risks or limitations associated with oil import restrictions. The first is that such efforts could galvanize oil exporters into a more cohesive group capable of neutralizing (or retaliating against) the hostile trade actions. The second limitation is the fact that exempting 'friendly' foreign oil suppliers weakens the potency of the import constraints [Broadman and Hogan (1986,1988),

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Sweeney (1990)], perhaps even to the point where any benefits are outweighed by deadweight losses; yet the political economy of oil import constraints may require such exemptions". If oil imports are to be restricted, the issue of how such restrictions should be implemented recalls several standard points in trade theory. For example, a quota would imply less a priori uncertainty about the import volume than a tariff, but a quota requires more administrative machinery - the establishment of secondary markets for import rights - in order to be cost-effective. In addition, a quota can enhance exporter market power by reducing the price elasticity of import demand [Honvich and Miller (1988)l. If a tariff is used, an ad valorem levy has some advantages over a fixed fee [Broadman and Hogan (1986,1988)l. The ad valorem tariff diminishes incentives for producers with market power to raise prices, and it may better approximate changes in cost spill-overs with fluctuating demand. However, unless the ad valorem fee is capped it could rise to an undesirable level in a market disturbance. Another set of measures that could be pursued to limit long-term petroleum imports is the development of alternative energy sources. These could include domestic petroleum supplies, or alternative sources such as natural gas, methanol, or ethanol fue140. The alternate sources could be imported or domestically produced and still generate declines in oil import demand and prices. Of course, if the alternates are imported then the benefits from reducing the wealth transfer will be less. Moreover, the development of substitutes does not reduce total energy demand and thus may not contribute greatly to reducing the economy's vulnerability to macroeconomic disturbances from energy price shocks. Whether this vulnerability is reduced depends on the supply elasticities of the existing and alternative sources, the elasticities of substitution among energy forms, and the substitution elasticities between energy and other inputs [Mork (1985a)l. The substitution of other energy supplies for imported petroleum introduces no fundamental policy issues related to energy security - other than the size of the potential security gains - if the alternatives are cost-competitive. Policy issues arise when the alternatives require the absorption of social costs in excess of the market price of petroleum. Possible examples include environmental degradation from new petroleum development, or the imposition of subsidies to bring down the price of high-cost alternatives. Such excess costs can be justified on energy security The oil tariff literature includes mention of other possible drawbacks, e.g., the competitive effects on domestic export industries which are energy-intensive. These effects are best considered part of the uncertainty about the external cost components discussed in Section 4.2 above. One additional argument that has been made against import restraints is that the resulting macroeconomic disturbance costs will outweigh the gains [US DOE (1987)], but this depends on the erroneous assumption that the economy never adjusts to the constraint [Hogan (1987), Huntington (1988)l. 40 This argument also applies with some caveats to investments in energy efficiency, but we do not pursue that topic here. 39


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grounds only if they result in the avoidance of even higher external costs associated with oil import dependence. Since the external costs of oil imports may well be quite modest, as noted previously, the case for absorbing excess costs of substitutes on energy security grounds also may be limited. A different set of questions arises in considering public policies to support research and development into alternative energy sources. Government support of R&D generally is considered to be desirable, given the existence of externalities in knowledge acquisition and dissemination. The costs of such efforts also are different than the costs of restricting oil imports through taxes or quotas. The latter policies require incurring ongoing deadweight losses to reap benefits of lower imports over time. If the benefits of import reduction are low relative to the deadweight losses then deferral of the import limits would be warranted. Development of substitutes for oil imports requires incurring up-front costs to generate a stream of benefits. Even if the current benefits of oil import displacement are quite modest, current R&D efforts could be justified in anticipation of future market conditions (e.g., greater OPEC market power) when the social cost of imports would be higher.

5.2. Strategic oil stocks Three key questions can be identified for the analysis of national policies to build and use strategic petroleum reserves to combat the effects of oil market disturbances. (a) How large should a reserve be? (b) When and how should the stocks be used? (c) What institutions are desirable for use of the reserves? There are at least two possible reasons why a private-market equilibrium may generate levels of inventories that are smaller than an economically efficient outcome. One reason is that the return to private inventory holders from selling stocks after a price shock depends on the market price spread, while the social return depends on the spread of marginal social petroleum costs. If there is substantial monopsony power over imports, the latter spread may exceed the former and the efficient stock level would then exceed the private market outcome. In addition, private stocks will be smaller than the efficient level in the presence of significant macroeconomic disruption costs that can be ameliorated by stock release but which are not fully reflected in private inventory decisionmaking. Broadly similar arguments apply to differences between the efficient timing for release of stocks and the market equilibrium release profile chosen by private competitive actors. In this case, however, the direction of the bias depends on the expected time path of a market disruption. In cases where a disturbance is expected to intensify and the gap between private and social costs is expected to grow, private actors will fail to recognize all the advantages of carrying over stock to subsequent periods, and the release profile will be inefficiently tilted toward the present.

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Conversely, where a disturbance is expected to ebb the market equilibrium, stock decision will ignore some gains from more rapid release and thus will be too slow 41. Numerous studies have been undertaken to assess the efficient size and release of government-controlled stocks in light of these possible shortcomings in the private market equilibrium. Most of these studies have been concerned with the US Strategic Petroleum Reserve (SPR). Some studies also consider interactions among the stockpile decisions of different countries under various assumptions about international policy coordination. Those issues are reviewed in Section 5.3, below. Several factors influence the efficient size and draw-down of a national strategic petroleum reserve. These include the severity of economic disturbance costs to be mitigated by stockpile policy, and the nature of disturbance risks (the probability, size, and duration of potential shocks). As emphasized by the historical review in Section 2, the nature of oil market behavior - both supply and demand - is of critical importance in addressing oil shocks. Another important factor is the nature of interactions between the strategic reserve and private stocks. For example, if a government storage program is perceived to lessen potential capital gains from private inventory holding then private stock volumes held for speculative purposes will be reduced. Similarly, an aggressive early release of government stocks during a market disturbance may limit private draw-downs (or even encourage private stock building) if the stock is perceived to be long-lived. The issue of efficient reserve size can be addressed using at least two different methods. One approach is stochastic dynamic programming, where the size of the reserve is one argument of the social value function (other arguments would include the 'state' of the market and the size of private stock^)^'. The value function in this case represents the expected present value of economic welfare, including surplus levels in the petroleum market and indirect effects of energy prices on the economy. This approach can be used to compute both an efficient stockpile size and an efficient draw-down policy for each possible stock level. The disadvantage of this approach is that it requires fairly simplistic modeling of oil market dynamics to be tractable 43. This argument holds constant the level of stock at the start of a disturbance. Given a bias toward too little stock accumulation in the private market equilibrium, and given draw-down decisions that are positively related to stock size, it is more likely that the private stock release is inefficiently small. Note that gaps between market equilibrium and socially efficient inventory also may arise in practice from expectational errors, e.g. 'speculative panic.' We return to this point below. 42 Transitions among market states are represented by a Markov process [Karlin and Taylor (1975)], which indicates the one-step-ahead probabilities of different market shocks. 43 For example, lagged responses of supply, demand, inventories, oil prices, and economic adjustment costs can in principle be represented in a dynamic programming model by expanding the number of market states, but this approach quickly becomes unwieldy computationally. 41


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An alternative approach avoids the burden of recursively optimizing draw-down policies by positing a rule of thumb for stockpile releases, and then experimenting with different stockpile levels to determine a volume which maximizes the expected present value of economic welfare. This approach generates an efficient stockpile size conditional on the assumed rule of thumb for stockpile release. The simplification of the optimization allows one to use a more complex model of the petroleum market in a computational analysis. Sensitivity analysis also is somewhat easier. The literature contains several studies of both types. Unfortunately, however, few concrete conclusions can be drawn from these analyses. Early dynamicprogramming studies [e.g., Teisberg (1981), Chao and Manne (1982)l suffered from various limitations in the specification of oil import supply, possibilities for market disturbance, economic costs of a disturbance, and responses of private inventory holders. More recent dynamic-programming and size-optimization studies [e.g., Charles River Associates (1986), Murphy, Toman and Weiss (1986), Leiby and Lee (1988,1989)l correct some of these limitations, but nothing close to the definitive analysis has been completed. One important conclusion, particularly emphasized in Leiby and Lee (1988), is that the benefit of a public stockpile is highly sensitive to assumptions about oil supply behavior, disturbance probabilities, and the price elasticity of domestic oil demand44.This observation is especially important since most studies find that a very large reserve (over 1 billion barrels for the USA) is warranted. At the risk of some overgeneralization, these studies tend to assume that oil market disturbances are fairly likely and that the oil market does not respond to disturbances very smoothly. If these assumptions need to be re-examined, as suggested by the discussion in Sections 2 and 3, then so do the above-mentioned conclusions about stockpile size. The sensitivity of the efficient stockpile size to the severity of economic disturbance costs also is of interest, given the questions regarding the importance of these costs that were raised in Section 4.3. Most stockpile studies which include macro adjustment costs simply posit that they are substantial 45. Leiby and Lee (1989) find that a smaller reserve is indicated in the absence of macro costs unless there is a significant probability of a severe oil price shock. Murphy, Toman

Leiby and Lee (1989) use the risk analysis method employed in Broadman and Hogan's (1986,1988) tariff study to analyze the sensitivity of stockpile size to market conditions. They do not actually report their probability distributions on stockpile size, but judging from the findings in Broadman and Hogan and in Hogan and Leiby (1985), it appears that the distributions are skew with long upper tails to reflect lower-probability, higher-severity damages to the economy from an oil shock. This finding also reflects the sensitivity of stockpile benefits to market conditions. 45 Some earlier studies did not include such costs. However, there are too many other differences to draw a conclusion about the importance of macro costs by comparing these studies to later efforts. 44

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and Weiss (1985a) find that the efficient reserve size without macro costs may be only one-half or less of its efficient size with significant macroeconomic impacts46. Even less is known about the importance of public-private interactions to the efficient size of a strategic reserve. One methodological question concerns whether to represent these interactions as a multiperiod Nash equilibrium or a Stackelberg equilibrium. The choice of methodology may significantly affect conclusions, as Wright and Williams (1982) point out. In addition, dynamic consistency issues [Newbery (1981)l may militate against the Stackelberg approach4'. The empirical basis for evaluating public-private stockpile interactions is sketchy. Modeling studies by Charles River Associates (1986) and Murphy, Toman and Weiss (1986) suggest that private speculative stocks (that is, stocks in excess of normal working inventories) built prior to a disruption may be small, in which case crowding out is unlikely to be a serious problem. However, there are few data available to judge this claim48.Even less is understood about the causes of 'panic' inventory building in a disturbance and the impacts on this behavior of public stock availability 49. Compared to the analyses of stockpile size, with all their gaps and uncertainties, even less can be gleaned from the literature about efficient stockpile release profiles. The dynamic programming models generally are handicapped by the use of an annual decision period, even though the interesting dynamics of oil shocks have been well under a year in duration (see Section 2). Generally, efficient release rates in the models tend to be approximately linear functions of stock on hand given a particular market state and a private inventory response. However, the slope of this response function may be very sensitive to the market state (e.g., slower release if a crisis is expected to persist), and there may be important nonlinearities such as a rapid release policy which exhausts all stock on hand quickly in the event of a severe shock. Rapid stock release also is likely to be more desirable to forestall transient surges in private incentives early in a disturbance Ironically, the authors of this study omitted these results from the published version [Murphy, Toman and Weiss (1986)l in the belief that they were only of narrow academic interest. 47 See chapter 19, by Karp and Newbery, of this Handbook. Wright and Williams ignore macroeconomic disturbance costs and focus on the threat of future price controls as the deterrent to efficient private stockpiling; they also assume a dynamically optimal tariff. Thus their actual numerical results are not comparable to other studies and may be of limited policy relevance. 48 One confounding influence through much of the 1970s and 1980s was a consolidation and restructuring of the refining industry (e.g., closing of inefficient smaller refineries) which produced a trend drop in private inventory levels. 49 Surges in inventories may reflect private perceptions of increased 'convenience yield' values of stocks on hand, for example, to avoid costly refinery curtailment [Charles River Associates (1988)l. This point is illustrated by dynamic programming results in Murphy, Toman and Weiss (1986) and by simulation results in Hubbard and Weiner (1986). As already noted, however, the latter study is based on an estimated inventory equation which does not explain behavior during the 1978-1979 disturbance, while the former study is entirely ad hoc. 46


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Yet another concern is the design of practical institutions for the use of strategic petroleum reserves. Most studies of government stockpile policy include the implicit or explicit assumption that released oil will be sold in a sequence of spot transactions. This is consistent with current policy for use of the US SPR, which involves periodic sealed-bid auctionssi. However, private oil markets contain a wealth of institutions for meeting disparate transactional needs of suppliers and for allocating risks. For strategic stocks to complement private market forces, it may be useful to consider release mechanisms other than spot sales. Alternative mechanisms also may serve important political economy goals. Several studies have proposed alternative mechanisms for effectuating SPR sales. Devarajan and Hubbard (1984) suggest using forward sales (which they mislabel futures sales) as a way to reduce future uncertainty about SPR release and thus about the price of oil. However, the degree to which forward sales would reduce price uncertainty depends on specific characteristics of oil demand and supply, while the extent of inventory dampening depends on behavioral motives which are poorly understood. Horwich and Weimer (1984) and Kelman (1984) propose the sale of options to purchase oil from the SPR at predetermined strike prices. An option would entitle the holder to receive a stream of SPR oil at a cost equal to the strike price, at or before the expiration date. By setting the number of options to be sold at each strike price, the government essentially would be putting a floor under the SPR release rate to be undertaken in the event that spot oil prices rise above various thresholds. Options of different terms and maturity dates would be sold, with original prices set by sealed-bid auction. Under normal conditions the prices paid for options would be low, though these prices would rise as market conditions tightened. A secondary market for trading these options also could be instituteds2. One advantage cited for an options mechanism is its ability to reduce speculative inventory building by providing greater assurance of SPR release (in increasing volumes) as prices rise. As already noted, this benefit is difficult to evaluate

These auctions are close to spot sales, though given administrative and delivery lags of a month or so it might be better to think of them as near-term forward contracts. The auctions are designed to charge each winning bidder its individual bid price. This system may raise more revenue from the sale, but it is more prone to opportunistic price manipulation than a single-price competitive auction in which all bidders pay a price equal to the lowest winning bid. In the discriminatory auction each bidder knows that its bid price equals the price paid if the bid is successful, so all bidders have an incentive to shade their bids. AS Kelman (1984) notes, there are trade-offs involved in establishing a secondary market. For example, such a market would improve liquidity and raise demand for options; it would also provide an avenue for profit-taking on temporary price blips without triggering SPR release. However, with a secondaly market it is also possible to see the options price bid up in tandem with a rise in the spot price, postponing the exercise of the options until expiration and thereby retarding SPR release when it is socially desirable.

'*

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given our limited understanding of inventory dynamics in a disruptions3.Another argument for an options approach is that it would reduce political obstacles to SPR use54. Up to the amount of SPR release implied by the number of outstanding options, use of the reserve would be brought about automatically by market incentives. However, it is also important to preserve some policy flexibility to address externalities that cause differences between private and social incentives for stock use. Accordingly, options trading might best be used for only a portion of the SPRss.Where the line should be drawn is open to debate.

5.3. Internationalpolicy coordination As already noted, in many ways the need for international coordination of energy security policies parallels the need for individual government intervention to offset energy security externalities not captured in private-sector behavior. International policy interactions can be illustrated using game-theoretic constructs. Outcomes in the absence of cooperation can be described as a Nash equilibrium or as a Stackelberg leader-follower equilibrium if there is an obvious candidate for the leader role. With international spill-overs of benefits from policies, non-cooperative outcomes will be inferior to the results obtained with policy coordination that internalizes these spill-overs. A complication that arises in comparing cooperative and non-cooperative outcomes concerns the precise definition of cooperation. Most studies of international energy policy coordination define the cooperative outcome as a set of policies that maximizes the sum of net economic surplus for the participating countries. Aside from problems in measuring benefits and the issue of noneconomic objectives, focusing on outcomes which maximize a benefit sum across countries implicitly assumes the ability of countries to make side payments for redistributing the surplus. A more general definition would use a Pareto criterion with a continuum of outcomes where no country can be made better off without reducing the benefits garnered by others. The specific choices made among these The options approach also is advocated as a source of information about private market expectations that can be used by the government in tailoring its own policy response over time. Even with the emergence of futures markets, additional information could be obtained from SPR options trading given the existence of daily limits on price movements in futures contracts. For the SPR options to provide this information function in practice, however, secondary trading would be necessary. 54 Current policy calls for a Presidential declaration of a national emergency before SPR release can be initiated. Thus. the decision to use the reserve at all is a highly political act, as was seen in the wake of the Iraqi attack on Kuwait. s5 It should also be noted that in all contracts the government preserves a sovereign right to unilaterally reduce or cancel its obligations. This adds to the market uncertainty associated with both spot and options arrangements for SPR release. 53


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alternatives for policy coordination would emerge from some sort of international bargaining process. With these observations as background, we turn to the two main questions to be addressed in this subsection: (a) What are the capacities and shortcomings of existing international institutions for coordinating energy security policies? (b) What other options could be pursued to strengthen coordination? The main formal means for international energy policy coordination among the industrial countries is the International Energy Agency (IEA), an offshoot of the OECD formed after the 1973-1974 disturbancess6. The IEA agreement does not specifically coordinate long-term import policies, but it does contain measures for responding to market disturbances 57. The formal aspects of the IEA crisis-response provisions can be divided into two parts. The agreement includes requirements and exhortations for member countries to curb oil demand in a crisis through stock release and demand restraints. However, the description of goals and instruments is fairly ambiguous, and there are no explicit mechanisms for policy coordination. Thus the measures applied may be ineffective, and the agreement does not provide strong assurance of cooperative behavior by others. The provisions for joint action also involve a complex plan for sharing oil supplies to even out the burden of a disruption. This plan was designed to respond to successfully targeted embargoes. Given the fungibility of world oil trade, however, the oil-sharing plan at best would replicate the free market, and at worst it would exacerbate disruption burdens [Bohi and Toman (1986), Honvich, JenkinsSmith and Weimer (1988)l. Moreover, both oil sharing and the individual-country requirements for demand reduction are triggered by quantitative assessments of supply shortfall, rather than as responses to market prices. This further diminishes their potential effectiveness. The likely ineffectiveness of the oil-sharing plan raises doubts about whether it would ever be used in a crisis. This means the primary burden of crisis response through the IEA falls on the individual country requirements for demand reduction, and on more informal understandings among member governments. Some progress has been achieved recently in strengthening these provisions. For example, there appears to be a greater recognition of the need for expanding strategic stocks and using them in a disturbance. However, these understandings continue to be concluded in fairly circumspect terms, and the IEA continues to The 21 IEA members include all OECD members except Finland, France, and Iceland. Norway (a major oil producer) maintains a special status in the IEA which involves abstaining from many crisisresponse measures. s7 The IEA also undertakes many cooperative ventures directed ai longer-term issues, such as technical improvements in energy use. In addition, it undertakes data collection and dissemination to provide information about market conditions. See Willrich and Conant (1977) for a fuller description of IEA programs. Dyne (1989) examines cooperative R&D efforts with the IEA. 56

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struggle with the concept of policies that respond to price shocks versus perceived quantity changes58. Consequently, the ability of existing IEA agreements to reinforce mutual expectations of cooperative behavior by member governments is open to question. The ability of the agreements to assure the private sector that appropriate actions will be taken, thus lowering the risk of demand surges as individuals hedge against market disorder, is even more unclear 5 9 . In light of these deficiencies, it is useful to consider various recommendations that have been studied as complements or alternatives to the existing IEA disruption-response program. Many studies have pointed to the potential benefits from international coordination of stockpile policies6O. For example, Hogan's (1983) dynamic programming analysis indicates that full coordination among OECD members allows smaller total stocks and lower aggregate costs than under unilateral actions while yielding total gains from stockpiling that are roughly comparable to the sum of US and other-OECD gains when each of these groups acts unilaterally 61.Leiby and Lee (1988) find that stock expansions in the USA and other OECD countries would benefit both the OECD as a whole and the USA. Several other studies suggest that cooperation in stockpile release among the USA, Germany, and Japan - the three largest oil-importing countries in the IEA and the only nations with significant strategic stocks - could be almost as effective as IEA-wide cooperation in mitigating the effects of a disturbance [e.g., Devarajan, Hubbard and Weiner (1983), Hubbard, Marquez and Weiner (1985), Murphy, Toman and Weiss (1985b)l. These studies also point to the importance of the petsistence of price shocks over time in

Periodically the IEA conducts logistical simulation tests of its system for sharing information and oil supplies in an emergency. Despite the obvious need for assessing how policies might affect oil prices and vice versa, there is a recurrent debate in the experiments on even stipulating what might happen to oil prices in a disturbance. Clearly, this issue continues to be a political football. 59 At the conclusion of their volume, Honvich and Weimer (1988) argue that the USA should formally withdraw from the IEA oil-sharing plan, while continuing to participate in other activities, as a way to avoid the potential costs of oil sharing and galvanize efforts to achieve a better agreement. 60 Other studies, such as Chao and Peck (1982), Manne (1982), and Rowen and Weyant (1982) assess the gains from international tariff cooperation. Even if there are substantial potential gains from tariff cooperation, however, it is unlikely that such agreement will be achieved in practice. A tariff structure including refined products would run afoul of efforts to reduce trade barriers among industrialized countries (especially in Europe). It would also have obvious complicating consequences in relations with the United Kingdom and Noway, two major oil exporters. Hogan also analyzes non-cooperative stockpiling using the Stackelberg leader-follower formulation. Unfortunately, Hogan does not report welfare gains in these cases, thus precluding a comparison of cooperative and non-cooperative outcomes. One interesting result he does report is the sensitivity of the Stackelberg outcome to the market share of the designated leader. When the USA has this role it tends to shirk stockpiling. A rest-of-OECD collective, with a larger market share, does not find this strategy profitable. In practice, given that other OECD countries do not form a monolith, Hogan's result buttresses the observation that most smaller OECD members have little or no strategic stocks. 58


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determining the benefits of policy coordination: with more transitory shocks, the benefits are lower. These studies address the desirability of stockpile coordination, but not how such an agreement might be achieved. Salant (1984) suggests establishing a selfenforcing agreement, with prior understanding on stock sizes and use plus a stipulation that all participants would revert to non-cooperative behavior if any country deviated from the plan. The long-run cost of bringing down the agreement would deter ~hirking6~. However, IEA members probably would not agree to such a non-discretionary system. In addition, such an approach would constrain adaptive learning about the appropriate policy direction over the course of a disruption, and the cost of monitoring compliance would be substantial 'j3. Gibson (1984) proposes an approach in which agreement is sought primarily among the USA, West Germany, and Japan. This smaller sphere of coordination would reduce monitoring costs while still reaping the bulk of potential benefits realizable through IEA-wide coordination. Gibson also suggests a flexible approach to the design of policies whereby participants would agree in advance to target stockpile sizes and relative draw-down rates. Actual draw-down volumes could be negotiated monthly during a crisis (with a default level in the event of deadlock) to respond to changing circumstances. To achieve such agreements, Gibson proposes the use of negotiation methodologies suggested by Raiffa (1982). As pointed out by Gibson (1984) and by Charles River Associates (1986), a fundamental obstacle to the achievement of more coordinated stockpiling is a significant divergence of views among the USA, Germany, Japan, and other IEA members concerning the desirability of stockpiling and other policy measures for responding to disruptions. The USA and Japan hold the largest stocks and have expressed the greatest willingness to use them promptly in a crisis, though the Japanese policy seems more circumspect than the US policy 64. Germany appears to be more inclined to use demand restraints, and in countries with little or no strategic reserve restricting demand is the only option. Moreover, the restraints under consideration primarily involve non-market measures (e.g., driving day restrictions or formal rationing) rather than market-oriented measures such as tariffs or excise taxes. Starting from this diversity of preferences, Bohi and Toman (1988) propose the use of a mixture of strategies by IEA members, with the USA relying on stockpile use while other countries rely to a greater extent on credible and effective demand All parties would find it in their self-interest to act non-cooperatively if other countries defected from the agreement, so the threat of the agreement collapsing is credible. 63 Accurate assessment of compliance is critical if defection literally could wipe out the agreement. A less draconian approach with lower monitoring burden would involve a finite period of no agreement to 'punish' defectors, but this would also weaken incentives for maintaining the agreement. 'j4 The Charles River Associates study also suggests that the United Kingdom would act to compel private stock use in a disruption. 'j2

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restraints. Such an approach, while theoretically inferior to joint stockpiling, could provide practical assurances of cooperative behavior and thus avoid even greater losses associated with inaction based on political reactions to free-riding. In particular, the approach could provide greater assurance of prompt SPR use in a crisis. For this approach to be successful, however, the demand restraint programs agreed to by other TEA members must be both credible and effective. The study by Charles River Associates (1986) reviews a number of non-price demand controls and finds that their effectiveness in actually cutting demand significantly is likely to be limited. Indeed, such proposals are likely to be counterproductive in that the resulting market distortions will increase supply uncertainties and encourage inventory panics. The study also suggests that the economic costs borne by countries imposing (market or non-market) demand restraint policies may be large 65. These results raise questions about the credibility of policies intended to constrain demand in a crisis, and thus about the potential for effective international agreements involving such policies. We are left, then, with a dilemma regarding the design of agreements for international coordination of energy security policies. The most cost-effective policies seem to run afoul of political constraints, while politically acceptable policies seem to lack credibility because of their costliness or amorphousness. 6. Concluding remarks

Given the possible economic consequences of energy insecurity, a better understanding of how government policies can ameliorate the costs clearly is desirable. However, it is difficult to escape the conclusion that the need for additional policy analysis is overshadowed by more fundamental uncertainties about world energy markets and about the importance of spill-overs from energy markets to the economy. The presence of these uncertainties gives rise to a considerable risk of irrelevant policy analysis based on an incomplete or erroneous conception of the energy security problem. Sections 3 and 4 of this chapter identify several areas where better understanding of energy markets and of energy-economy interactions are necessary. Important topics related to energy markets include long-term oil pricing behavior and the influence of oil-exporting countries; short-term inventory demand behavior in a crisis; and the effects of changes in market institutions. With regard to energyeconomy interactions, there is significant uncertainty about both the size of There are several reasons to think these costs might be overestimated in the Charles River study. Aside from the general uncertainty about the size of macro costs resulting from oil disturbances, the cost estimates in the study are based entirely on reductions in oil consumption rather than cuts in panic inventory surges.

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adjustment costs engendered by an oil market disturbance and the long-run costs of oil import dependence. Studies of long-term oil market behavior and of the effects of import restrictions also would be enriched by introducing the dynamics of depletable resource supply behavior 66. As for policy responses, the case for restricting oil imports remains unresolved. More analysis is needed to thoroughly demonstrate that there are conceptually justified and empirically substantial external cost spill-overs associated with import dependence. A somewhat stronger case may be possible for governmental strategic oil stockpiling as a disruption-response measure, because the external costs of adjusting to an oil price shock could be large and because the ability to garner arbitrage profits by sales of the stockpile during a market disturbance can limit the potential cost of the policy measure 67. However, there is enough uncertainty about the magnitude of the adjustment cost spill-overs, and the need for use of strategic stocks to lower these costs rather than simply deploying better macroeconomic stabilization policies, that a major expansion of US strategic reserves beyond existing targets would be premature without further study of the benefits. Further investigation also is needed before methods for using market information to influence stockpile release, like the sale of options, can be recommended. Even though the USA possesses the largest strategic stocks of any industrialized country, its response to an oil crisis easily could be dwarfed by contrary policies of other governments or a worldwide panic surge in oil inventory demand. We already have noted the need to better understand inventory behavior in a crisis, including the extent to which different policies mitigate or exacerbate undesirable demand responses. A better understanding of the prerequisites for more effective international cooperation on energy security, and how such cooperation can be put into practice, is no less important. Collaborative research by economists and political scientists on this subject would be quite fruitful. To conclude on a methodological note, given all the uncertainties that bedevil analysis of energy security policies a careful investigation of the sensitivity of conclusions to assumptions is essential. In the context of simulation analyses, the risk analysis methodology mentioned in Section 5 seems to provide a valuable way to explicitly introduce uncertainty about assumptions and to gauge the consequences of this uncertainty for the model outputs. Further development and application of this methodology, particularly in integrating it with optimization models for policy design, would increase the degree of confidence that can be ascribed to the model results. Initial efforts to this end have been undertaken by Tolley and Wilman (1984), Nesbitt and Choi (1988), Walls (1990), and Yiicel and Dahl(1990). 67 This latter point assumes that the government can judge when to sell high and buy low. In practice, such an assumption cannot be made automatically. Even if this were possible, disturbance risks and thus arbitrage profits could be so low that only a small reserve would be justified. 66

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Chapter 26

NATURAL RESOURCE USE AND THE ENVIRONMENT CHARLES D. KOLSTAD Department of Economics and Institute for Environmental Studies, The University of Illinois, 1101 West Peabody, Room 352, Urbana, IL 61801, USA

JEFFREY A. KRAUTKRAEMER Department of Economics, Washington State University, Pullman, WA 99164-4860, USA

1. Introduction

The organization of this Handbook reflects the common notion that while natural resource and environmental economics are closely related, they are distinct subjects. In general, economic and policy issues are either environmental in nature or resource-related. However, there is an important overlap between the two fields, and that is the subject of this chapter. Resource use, particularly energy use, almost invariably is accompanied by significant environmental effects. Further, a large proportion of environmental problems can be traced directly to resource use. Thus, attempts to correct environmental externalities inevitably impact the resource sector. This inseparability between certain resource and environmental issues leads to a number of unique theoretical, empirical and policy questions, which in turn constitute the subject matter of this chapter. The interaction between resource and environmental economics is strongest at the points of resource extraction and resource use. When resources are extracted from the earth there are many environmental effects, ranging from the release of short-lived pollutants to irreversible changes in natural environments. Environmental effects include the permanent and near-permanent loss of aesthetic resources or productive land due to mining as well as the possibly catastrophic climatic effects of elevated C 0 2 levels in the atmosphere due to the burning of fossil fuels. There is an important dynamic interplay between the irreversibility of some environmental impacts and the exhaustion of natural resources. In general, economic benefits from resource extraction occur in the present, while environmental disbenefits occur in the future. As resources are extracted, stocks * This chapter was prepared in 1983 and revised in 1989 and again in 1991. Handbook of Natural Resource and Energy Economics, vol. III, edited by A. K kheese and J.L. Sweeney O I993 Elsevier Science Publishers B. K All rights reserved

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become depleted, leading to rising production costs (in the absence of technical change). Further, as lower-grade ores are extracted, one can expect environmental effects per unit of output to increase. Thus there are subtle and important economic questions related to the dynamics of resource extraction in the presence of irreversibilities of environmental effects. In contrast to intertemporal issues associated with the optimal use of resources in the presence of environmental externalities, many economic questions arise in a static context where pollutants are short-lived and the effects are reversible. Analysis of such situations is simplified because costs and benefits are generally incurred at the same point in time. A very large proportion of all environmental issues can be traced directly to the extraction or use of resources, particularly energy resources, including mining and fuel combustion. Further, concern for the environment has had great impact on resource industries. While fewer theoretical issues arise in the static context, more applied work is static because of the real need to shape public policy governing current resource extraction and use and environmental protection. Applied work has focused on the design of optimal regulation within an often complex institutional setting. The remainder of this chapter is divided into three parts. In the next section we present background on the nature of the interaction between resource and environmental economics and policy. The subsequent two sections provide a synthesis of past work in resource and environmental economics. Our intent is to include work that contributes to not one or the other, but both of these fields. Thus we will omit environmental economics that is only indirectly related to resource use, and similarly omit resource economics that does not have an environmental component. The presentation is divided into two parts, one concerning economic questions that are primarily static in nature, with a particular emphasis on applied analyses of resources and the environment. The second of the two sections concerns dynamic aspects of the intersection of resource and environmental economics. 2. Resource-environmental interactions

Environmental resources are used extensively in the extraction, processing, and consumption of nonrenewable natural resources. Indeed, the extraction or use of natural resources is the source of many major environmental problems, including acid rain from sulfur emissions, climatic change from carbon dioxide emissions, and the loss of preserved natural environments. Consequently, regulatory efforts to protect the environment can have significant effects on resource industries. This section presents an overview of resource-environmental interactions and presents some illustrative examples from the energy sector. The natural environment is used at both ends of production and consumption activities. That is, the environment is both the source of material inputs into the

Ch. 26: Natural Resource Use and the Environment

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economy and the 'sink' that receives the waste products of economic activity. The environmental impact of natural resource use can be divided into two broad categories: (i) the loss of environmental amenities when natural resources are extracted from preserved natural environments to be used as inputs in production, and (ii) the physical effects of emission into the environment of the waste residuals of production and consumption activities. The extraction of natural resources frequently results in significant physical disruption of the natural environment where the resource is found. The stripmining of coal or the damming of a river to produce electricity are obvious examples. This physical disruption of the natural environment often results in significant loss of environmental amenities - the scientific, recreational, and aesthetic values generated by preserved natural environments1. The reduction, and possible extinction, of salmon populations in the Columbia River basin is an obvious example. Natural environments also can be disrupted by the transportation of natural resources as in the case of the Amoco Cadiz or Exxon Valdez oil spills, or even by exploration for natural resources 2. The physical disruption of the environment is often irreversible and the loss of environmental amenities is often permanent. The environmental impact of resource use does not end here. The physical law of the conservation of mass establishes a close relationship between the rate of natural resource use and the rate at which waste products are emitted into the environment. Since matter is transformed rather than consumed by consumption activities, the mass of residuals generated by production and consumption activities is approximately equal to the mass of materials used as inputs for production and consumption. This link between resource use and the environment provides the basis for 'materials balance analysis', an analytical framework that views the generation of waste residuals as a joint product of production and consumption activities [Ayres and Kneese (1969), Kneese, Ayres and d'Arge (1970)l. Essentially, materials balance analysis simply requires that all of the materials extracted from the environment and used in the economy are accounted for by remaining somewhere in the economy or the environment -either as durable goods, recycled inputs, or waste products deposited into the air, land, or water. Materials balance, then, recognizes a physical constraint on the production possibilities available to the economy. There is no free disposal of materials in that all materials that leave the economy must return to the environment. The flow of materials from the economy back to the environment can be reduced through greater efficiency in the use of raw materials, improved durability of products, A comprehensive treatment of the economics of natural environments is given by Krutilla and Fisher (1985). Environmentalists currently are concerned about the environmental impacts of exploration for oil and gas in the Arctic National Wildlife Refuge, including the potential effects on caribou herds.

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capital accumulation, and perhaps most importantly, the recovery and recycling of materials. Nevertheless, the volume of residuals generated approximately equals raw resource use. Although some wastes are clearly less harmful than others, this illustrates the close connection and inseparability between resource and environmental economics. A variety of factors affect the environmental impact of the waste products returned to the environment. Waste emissions are absorbed, dispersed, degraded, decomposed, or combined with other chemicals in the environment. The type of wastes emitted and the assimilative capacity of the natural processes at work determine the concentration of pollutants, or ambient condition, that results from a given level of waste emissions in a particular area and environmental medium. The concentration of pollutants has physical effects such as reducing the yields of agricultural crops, soiling and corroding materials, impairing human health, and obscuring scenic vistas. Some of these effects are reversible and can be viewed in a static context. For example, if sulfur emissions from coal-fired power plants are reduced, most problems associated with sulfur pollution also will be reduced in a relatively short time period. On the other hand, some pollutants, carbon dioxide for example, will persist for a relatively long time period and must be viewed in a dynamic context. The energy sector provides some of the most striking examples of the interaction between natural resource use and the environment '. The environmental impacts of coal consumption range from the strip-mining of vast tracts of land to the climatic effects of atmospheric accumulation of carbon dioxide. Strip-mining of coal results in at least temporary loss of the productive services of the land, including the loss of environmental amenities. In some cases, the toss of these services may be irreversible since the ability to reclaim strip-mined land is not certain, particularly in arid regions [Atwood (1975)l. The extraction of coal in underground mines also can cause environmental damage in the form of spoil heaps that cause acidic drainage or surface subsidence from subterranean mine collapses. The sulfur contained in coal that is burned to generate electricity provides an illustrative example of materials balance and the variety of possible environmental outcomes. Materials balance requires that the sulfur in coal remains in the environment in some form. A solid sulfur product is obtained if the sulfur is washed from the coal before it is burned or if it is removed from the waste gases by smokestack scrubbers. Any sulfur that escapes the smokestacks takes the form of sulfur dioxide and sulfur particulates. About 70 million pounds of sulfur dioxide are emitted per year from a 1gigawatt coal-fired plant under an emission standard of 1.2pounds of sulfur dioxide per million Btu [Ramsay (1979))

In 1976,60% of the total weight of the flow of materials in the USA originated in the energy sector [Kneese (1976)l.


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High concentrations of sulfur dioxide and particulates in the vicinity of a plant can irritate lungs and contribute to respiratory illness. The impact on the population in the vicinity of the plant can be reduced by dispersing the waste gases more widely with higher smokestacks. However, the sulfur dioxide in the atmosphere is oxidized to sulfates that eventually are deposited out of the atmosphere as acid rain, perhaps hundreds of miles from the power plant. The sulfates are acidic and leach nutrients from the soil, damage plant life, and alter, or even destroy, water ecosystems with adverse impacts on fish and other water species. Elevated sulfate levels also may impair visibility over large regions resulting in serious aesthetic damage in areas where long-range visibility is valued. Carbon dioxide is another important waste product generated by a coal-fired power plant. The combustion of coal generates carbon dioxide at the rate of 8-3million metric tons per year for a 1gigawatt power plant. Carbon dioxide is not ordinarily a hazardous gas, but the accumulation of carbon dioxide in the atmosphere may trigger significant changes in global climate as a result of its 'greenhouse effect'. Much of the energy from the sun is able to pass through the atmosphere and is absorbed by the earth and radiates back through the atmosphere. The wavelength of radiated energy differs from that of the incoming solar energy and carbon dioxide traps some of the radiated energy in the atmosphere just as the glass in a greenhouse allows solar energy to pass through but traps radiated energy in the greenhouse. Consequently, accumulation of atmospheric carbon dioxide could result in a significant warming of the atmosphere. It is estimated that atmospheric carbon dioxide has increased by 25% over the last century4. The future concentration of atmospheric carbon dioxide depends upon both the rate of fossil fuel consumption and what happens to the carbon dioxide after emission. Unfortunately, the exact nature of the carbon cycle is not precisely understood and so there is uncertainty about the link between emissions and atmospheric concentrations. For example, there is a fair degree of uncertainty about the ooeanic absorption of carbon dioxide under different physical conditions such as higher temperature and higher concentrations of carbon dioxide. In addition, other factors, including deforestation and changing agricultural patterns, affect the accumulation of carbon dioxide. The link between carbon dioxide and global temperature is also highly uncertain. The global mean temperature has risen by about one degree centigrade in the last one hundred years, but this increase is well within the bounds of historical natural variation in temperature. Other pollutants also affect global climate, and some, such as particulate emissions, may act to lower global temperatures through the reflection of solar energy. Given the complexity of the problem, it is not possible to predict with great precision the effect of carbon dioxide emissions on global See Rosenberg et al. (1989) for a recent evaluation of the prospects for global warming and its impact on the environment and resource use.

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mean temperature. One recent review of the global climate models suggests that the effect of a doubling of carbon dioxide on global mean temperature would range from +2 to +5OC [Schneider and Rosenberg (1989)l. Regional temperature changes could range from - 3 to +10"C, with the greater temperature increases occurring at higher latitudes. A warmer global climate has a variety of impacts on the use of natural resources, including agricultural [Easterling et al. (1989)], forest [Sedjo and Solomon (1989)], and water [Frederick and Gleick (1989)l resources. In the case of agriculture, the variation in regional temperature combined with shifts in the pattern of global precipitation means that some areas of the world can expect to become more amenable to agricultural production while other areas will suffer. A higher global mean temperature also affects coastal land resources through its impact on the polar ice cap and the attendant rise in the level of the oceans. Estimates of the increase in sea level over the next 100 years range from 0.6 to 4.0 meters [Hekstra (1989)l. Of course, the economic impact of these changes depends upon how rapidly they occur and the speed with which economic activity can adapt to the changes. Given the uncertainty about the ultimate physical effects of carbon dioxide emissions, any estimate of the economic impact of global warning must be seen as indicative at best 5 . Other sources of energy have their own environmental impacts. The production of oil and natural gas requires exploration, extraction, and transportation activities that can disrupt sensitive natural environments as in the case of oil spills from well blow-outs, such as occurred in the Santa Barbara Channel, and tanker accidents, such as the Exxon Valdez. The refinement of crude oil generates air pollution in the form of sulfur dioxides, nitrogen dioxides, carbon monoxide, and hydrocarbons. The combustion of refined petroleum products also generates serious air pollution. Nuclear-generated electricity has significant environmental impacts, from the radioactive mill tailings left by extraction and processing of uranium to the potential for catastrophic accidents at operating plants to the problem of long-term storage of high-level radioactive wastes. Even alternative energy sources have potentially severe environmental impacts. The construction of dams to generate hydroelectric power irreversibly transforms natural environments resulting in the loss of recreational, aesthetic and scientific values. Salmon populations in the pacific Northwest have been reduced dramatically by the dams on the Columbia and Snake Rivers that obstruct the migration of the fish to and from their spawning grounds. Widespread use of solar energy may require large amounts of land and although the technology is not fully developed, solar collectors might require a significant amount of materials. Geothermal energy For example, an early study of the global economic effect of a doubling of atmospheric carbon dioxide gave a range of estimates from a pessimistic loss of 12% of world output to an optimistic gain of 5% of world output [Nordhaus (1980)l.


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produces thermal pollution and its production can have significant amenity impacts. The use of geothermal energy in the area surrounding Yellowstone National Park could disrupt the sensitive system of geysers that is one of the chief attractions of the park 6 . One can conclude from this discussion that the extraction and use of energy resources inherently involves extensive impacts on the environment. The wide variety of resources that can be used and the wide variety of the subsequent effects on the environment means that there are trade-offs between economic costs and environmental costs, between material goods and resource amenities, between current and future environmental impacts, between current and future resource costs, between impacts on different environmental resources, and between environmental impacts with different degrees of uncertainty. The energy sector illustrates this variety of trade-offs. At one time, the primary environmental concern of coal consumption was the health effects of sulfur dioxide emissions. This concern led to standards for local ambient conditions. As mentioned above, one method for improving the air quality in the vicinity of a coalfired power plant is to disperse the sulfur dioxide by building a taller smokestack. However, this dispersion affects acid deposition down-wind from the plant so that local health improvements come at the cost of materials damage and the disruption of ecosystems in other locations. The sulfur dioxide can be removed from the waste gases by smokestack scrubbers which increase economic costs and leave the problem of what to do with the large volumes of solid scrubber waste. An alternative to smokestack scrubbers is to burn coal with a lower sulfur content. Low-sulfur coal generally has a lower heat content and the economic cost of electricity is greater. In addition, the low-sulfur coal in the USA is found predominantly in the western states and occurs in broad seams with little overburden so it is amenable to strip-mining. The strip-mining, of course, can have significant environmental impacts on the land, and reclamation activities are hindered by the region's arid climate. The substitution of nuclear power plants for coal-fired plants would reduce the problem of carbon dioxide and sulfur emissions at the expense of greater economic cost and the environmental impacts of nuclear power. There is a static trade-off between the health effects of coal combustion and the risk of reactor accidents at nuclear power plants. In addition, there is the trade-off between the long-term effects of atmospheric carbon dioxide and the storage of high-level radioactive waste. A market economy is one institutional mechanism for making trade-offs between alternative uses of resources. Given the standard assumptions of perfect competition, a market economy is able to arrive at an efficient allocation of resources. However, many of the amenities generated by preserved natural environments can be characterized as open-access resources or public goods. See OECD (1988) for further discussion of the environmental impacts of alternative energy sources.

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Similarly, many of the environmental impacts of pollution can be characterized as public bads. The public good and open-access nature of environmental resources implies that the market will fail to allocate these resources efficiently. In particular, the market under-values the use of environmental resources, which results in excessive use of these resources. In addition, if there are external environmental costs associated with the extraction, refinement, and consumption of natural resources, then these resource stocks will be depleted too rapidly. The failure to price environmental resources correctly also provides insufficient incentive for recovery and recycling of materials and other activities that reduce the flow of material inputs through the economy. Government intervention is required for market prices to reflect the full social cost of natural resource use. The correct prices would result in greater conservation of natural resource stocks, increased recycling, and improved environmental quality. Because of the inherent interaction between natural resource use and the environment, natural resource policy and environmental policy also interact. Therefore, it is important that these policies be well conceived and well coordinated. Unfortunately, this is not always the case. Many resource policies, such as depletion allowances and preferential rail rates, actually encourage the use of virgin materials and discourage recycling [Page (1979)l. This increases the use of materials in the economy with subsequent detrimental effects on the environment. Environmental policy often is formulated without consideration of the impact of the policy on the use of natural resources. For example, regulations on automobile emissions make it more difficult to achieve fuel economy standards. However, in other situations, environmental policy has been shaped with explicit attention to resource markets. For instance, the fact that standards for sulfur dioxide emissions for power plants can have significant impact on the regional pattern of coal extraction has been a prime factor in shaping portions of the Clean Air Act and associated regulations [Ackerman and Hassler (1981), Dowlatabadi and Harrington (1989)l. Policies designed to correct market failures resulting from resource-environmental interactions also must deal with significant distributional issues. These include important income, inter-regional, international and intergenerational conflicts. Distributional goals often conflict with efficient resource allocation. For example, the use of low-sulfur coal could be the least-cost way to reduce sulfur emissions from coal-fired power plants; but the use of low-sulfur coal would decrease the use of coal from the midwest and eastern states and increase the use of western coal. Ackerman and Hassler (1981) discuss how this distributional issue influenced the development of the Clean Air Act. It is difficult to overstate the significance of distributional impacts. Distribution also can be said to dominate the recent debate over acid rain legislation [Kolstad (1990a), Dowlatabadi and Harrington (1989)l.


3. Static resource-environmental interactions

Much of environmental economics has been motivated by residuals generation in resource industries. However, much of this work is applicable to residuals generated by any source, resource-related or otherwise. It is in a dynamic setting that natural resources most clearly distinguish themselves from other factors of production. Thus, most of the interesting theoretical findings concerned with both resource and environmental economics are based on the interplay between the exhaustion of natural resources and the irreversibility of environmental damage. In other words, the intertemporal nature of the problem is central to the intersection of resource and environmental economics theory. Take away dynamics and most theoretical issues become classic environmental issues regarding the proper management of externalities. While a large proportion of the theoretical environmental economics literature regarding residuals generation in a static context is particularly applicable to resource industries, these results are reviewed elsewhere in this Handbook. However, there is a large body of empirical work involving resource and environmental economics. Empirical work has been concerned with properly representing the complexity of the static interaction between resource markets and the environment. The spatial character of this interaction has been a particular focus of the literature. Extracted resources are generally bulky and thus costly to transport. Sensitivity of the environment to degradation can vary greatly from location to location and pollution can be transformed as it travels through the environment. Thus space plays nearly as dominant a role in empirical work as does dynamics in theoretical work. Over the past two decades, much of the empirical literature in the overlapping areas of resource and environmental economics was related to energy resources. This occurred because of the simultaneity of the radical shifts in energy markets and the elevated social concern with environmental quality. As mentioned earlier, a large proportion of all environmental issues can be traced directly to the extraction or use of energy resources - coal strip mining, fuel combustion for electricity generation or industrial processes, or waste from nuclear power generation. Disruptions in the international energy market have resulted in an increased emphasis on domestic energy production. Much public policy has been concerned with achieving the proper balance between the fundamentally conflicting goals of enhanced environmental quality and increased energy production and consumption. This fertile policy arena has spawned many empirical economic analyses. In general, empirical work is concerned with one question: efficient public management of environmental resources. Recognizing the public-good nature of environmental quality, that either decentralized or centralized regulation is necessary for efficiency,work has focused on the design of optimal regulation within

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an often complex institutional setting. Such work can be roughly divided into three categories. One body of literature is concerned with measuring the economy's response to specific environmental regulations. Since in practice environmental regulations are complex legal instruments, it is often unclear a priori what may be the economic or environmental consequences of a regulation. In the USA, much of this regulatory analysis work has been concerned with the effect of the Clean Air Act on the coal and electric power industries, the two industries directly or indirectly responsible for much of the air pollution generated in the USA. Regulatory analysis in these industries is complicated both by the highly spatial nature of the markets and by the complexity of the environmental regulations. Recently, work has focused on the economic effects of controlling COz, a cause of global warming. A second body of literature focuses more on measuring the social disbenefits of specific environmental externalities that are associated with resource use. A number of studies have concerned the value of long-range visibility in the western USA [for a review, see Graves (1991)l. Good visibility is often considered to be important in order to appreciate the scenic vistas of the West. Visibility is impaired by air pollution from electric power generation and copper smelting. Other studies have been concerned with externalities associated with coal surface mining. A third body of literature can be characterized as costbenefit analysis and thus, in a sense, is a synthesis of work on the economic effects of regulation and the valuation of damage from externalities associated with resource use. Much of the costbenefit work has been concerned with determining economically efficient emission levels for individual coal-fired electricity generating stations. 3.I. Direct costs of environmental regulation

Much of the applied work in environmental economics has involved quantifying the direct costs of complex regulations. Nearly all of such work related to resource industries, at least in the USA, has been concerned with the coal and electric power industries and air pollution. The US Clean Air Act establishes a variety of requirements on the sulfur content of fuels, abatement technologies and emission rates. The debate over the Clean Air Act has concerned the precise form of regulations within the Act. Because of the spatial distribution of coal resources in the USA, variation in the form of the regulation can have significant distributional impacts, particularly in terms of the coal industry. For instance, an economically efficient regulation may require that coal consumers shift to low-sulfur coal. This would result in greatly increased production of low-sulfur coal (located mainly in the western USA) and decreased use of high-sulfur coal (located mainly in the midwestern USA). This would result in


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obvious income and employment shifts at the expense of the midwest. Alternatively, regulations that require the use of particular abatement capital regardless of emission levels may better preserve existing coal production patterns, albeit at higher overall cost. If exit gases are highly purified through the use of capital, then the sulfur content of the fuel makes much less difference - it becomes efficient to use high-sulfur coal if it is only a little cheaper than low-sulfur coal [e.g., see Dowlatabadi and Harrington (1989)l. Thus an inefficient approach may be adopted on distributional grounds. But a secondary distributional question concerns who bears the additional costs associated with a second-best approach. By requiring the use of abatement capital, the additional costs may be borne most heavily by electricity producers that normally use clean coal - principally electricity producers in the western USA. Thus the effect of alternate air pollution regulations becomes a complex spatial issue involving considerations of efficiency and distribution. The common approach to measuring the response of coal and electric power industries to various air pollution regulations is to formulate a spatial partial equilibrium model of those industries and impose various pollution regulations on the model. If demand for electricity on a regional basis can be characterized by integrable inverse demand functions, if cost functions for producing coal and electric power are known on a regional basis and if interregional transportation costs are known, then a partial equilibrium in these markets can be computed by maximizing total producer and consumer surplus. This was shown initially by Samuelson (1952) and was further developed by Takayama and Judge (1971), among others. There are two principal justifications for such models of the coal and electric power markets. One justification is that the structure of these markets suggests the applicability of the competitive model. There are many coal producers and electric utilities, none of which have a sizeable share of even regional markets (particularly in the case of coal producers). The second justification for such an approach is that the market is highly spatial with the relationship between regional coal prices at the mine and delivered coal prices changing over time depending on demand, supply and transport costs. Thus a nonspatial representation of the market is likely to be unsatisfactory. The spatial-equilibrium approach can be criticized on a number of grounds, including (a) the assumption of marginal cost pricing on the part of electric utilities (as opposed to average-cost pricing used in actuality); (b) the generally assumed myopic behavior on the part of agents in the market; (c) the general lack of simultaneous estimation of supply and demand relationships, relying more on engineering estimates of supply and inelastic demand; and (d) the dominance of single transporters in certain regional markets. Implicitly, these shortcomings are assumed to be of secondary importance since the spatial equilibrium approach is widely utilized in examining coal and electric power markets [Wood (1987)l. The


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use of the approach for these markets dates from Henderson's (1958) seminal study of the US coal industry. 3.1.1. A modet of regulatoiy response

Because of the dominance of this approach in evaluating air pollution regulations let us consider a prototypical spatial model of coal and electric power. Suppose there are i = 1,. . . ,I regions where coal can be produced and j = 1,. . . ,J regions where coal is.consumed for electric power generation and other uses. The coal production possibilities in each region are characterized by an upward-sloping long-run supply curve. By representing the electricity production processes in each demand region, demand for coal becomes an endogenous, derived demand based on the demand for electricity. For simplicity, we will neglect other demands for coal. The cost of electric power production is a function of coal use, electricity output and the level of emissions control on coal-fired facilities. Demand for electricity in each region is represented by a single inverse demand function. Let supply (marginal cost) curve for coal in region i; quantity of coal transported from region i to region j; unit cost of transporting coal from region i to region j; inverse demand for electricity in region j; production of electricity in region j; sulfur emissions in region j; sulfur content per unit of coal in region i; cost of producing electricity (from coal and other fuels) in region j (excluding the cost of coal).

Note that the cost of producing electricity, q,, is a function of total coal used, tq, emissions of sulfur, e,, and the sulfur content of fuel, pit;,. Implicit in this cost function is the cost of producing electricity by means other than coal as well as the price of other factor inputs. A partial equilibrium in this market (in the absence of air pollution regulation) is found by maximizing surplus over the non-negative vectors t , e and q:

xi

xi

This expression is simply total consumer and producer surplus. The last term in the braces represents the cost of producing coal; the last term inside the brackets


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represents the cost of moving the coal to market. The remainder of the expression in brackets is the area under the inverse demand curve less electricity production costs (excepting coal costs). The electricity production function has been totally absorbed in the cost function. That the maximization of this overall expression results in the same allocation as that of a partial equilibrium can be seen very easily by examining the firstorder optimality conditions for eq. (1). The first-order conditions are precisely the conventional equilibrium conditions of a competitive market. Obviously, since eq. (1) excludes any sort of air pollution regulation, an equilibrium will occur at el = C, p, q,],provided marginal costs of abatement are positive. Let us now consider how air pollution regulations might be represented in such a market. Very generally speaking, there are two basic approaches to regulation: decentralized economic incentives and centralized .command and control regulations. 3.1.1.1. Economic incentives

Economic incentives are well-known to economists and embrace the two (usually) symmetric concepts of Pigouvian fees to correct an environmental externality and the establishment of property rights for use of environmental resources, in conjunction with a market for the trading of such rights [Tietenberg (1985)l. In either case, efficient use of the public good is attainable. Although a first-best efficient price or quantity instrument may be possible theoretically, the complexities of the spatial and temporal variation in pollution transport and damage make efficiency difficult to achieve in practice. An efficient set of regulations may be complex and may require an extremely large amount of information. Furthermore, the regulations may have to be continually revised to reflect changing information and circumstances. For instance, with complex meteorology, efficient emission fees may have to vary in space as well as time [Nichols (1984)l. Thus, much current work is concerned with developing reasonably simple and thus workable economic incentive schemes that are fairly efficient, although simplicity is usually gained at the expense of efficiency [see Tietenberg (1980) and Kolstad (1987)l. Unfortunately, economic incentives, until recently, have not been common in the USA. In the early 1970s President Nixon proposed a sulfur tax, and the 1990 Clean Air Act Amendments include a marketable permit system for controlling acid deposition precursors. The pollution offset system currently in effect is a type of marketable permit. There are a few other examples [see Hahn (1989)l. Referring to model (I), it is straightforward to include both emission fees and a market in emission permits. An emission fee is represented by appending a term representing the cost of emissions of pollution to the objective function. Sulfur emissions in any region j are e,. Thus if the tax rate is T , then costs associated with an emission fee will be T El el.

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As Montgomery (1972) has shown, the operation of a market in rights to pollute can be represented in a dual fashion. If R rights to pollute are issued, then a market in these rights can be simulated by appending to model (1) the constraint e, R. If the shadow price on R is i?, then exactly the same activity levels will result from the application of an emission fee 7i as the use of marketable pollution rights.

0 is the elasticity of the marginal utility of consumption and indicates the 'curvature' of the utility function. Since consumption of a finite 'cake' eventually must decline to zero, it is not surprising that consumption decreases along the optimal path if the rate of discount is positive. A higher rate of discount implies a more rapid decline in consumption and shifts consumption from the future to the present. Dasgupta and Heal (1974), Garg and Sweeney (1978), Solow (1974) and Stiglitz (1974) examine a growth model that incorporates reproducible capital that serves as a substitute for the nonrenewable resource in the production technology. In certain cases, the accumulation of capital can overcome the effect of the depletion of the resource and consumption can increase over time. The economy chooses time paths for resource extraction and consumption that maximize eq. (14) subject to

the non-negativity conditions and the initial conditions. The first-order conditions include


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Again, we have the condition that the marginal value of consumption is equal to the shadow price of capital. In addition, thevalue of the marginal productivity of the resource must equal the price of the resource. The two dynamic conditions require equal rates of return to the asset and this implies that the rate of increase in the marginal productivity of the resource, FRIFR, must equal the marginal productivity of capital, F K . The rate of change in the level of consumption can be obtained by differentiating eq. (20) with respect to time and making the appropriate substitutions to obtain

The ability to substitute capital for the nonrenewable resource allows the possibility of increasing consumption. Indeed, without a nonrenewable resource in the model, the economy would accumulate capital until its marginal productivity was equal to the rate of discount, and then settle in to a steady-state level of consumption afforded by that capital stock. Since the extraction of the nonrenewable resource eventually must decrease to zero, the ultimate behavior of the consumption path is determined by what happens to the productivity of capital as the capital-resource input ratio increases without bound. This, in turn, is determined by the substitution opportunities allowed by the production technology. As we will see in the models below, the ultimate behavior of consumption is a key factor in determining the optimal level of environmental preservation. In the case of a production function with constant returns to scale and a constant elasticity of substitution, the productivity of capital declines to zero if the elasticity of substitution is less than unity. In this case, then, consumption eventually must decline to zero. If the elasticity of substitution is greater than unity, then the asymptotic productivity of capital is bounded away from zero and it is feasible to have continued growth in consumption. If the elasticity of substitution is equal to unity, then continued consumption growth is possible if and only if the elasticity of output with respect to capital is greater than the elasticity of output with respect to the resource input. Whether or not it is optimal to have continued consumption growth depends upon whether the asymptotic productivity of capital is greater than or less than the social rate of discount [Dasgupta and Heal (1974)l. A rate of technological progress that is greater than the rate of discount is another means by which a growth model can generate increasing consumption along the optimal path [Stiglitz (1974)l. Neither capital-resource substitution nor exogenous technological progress can sustain consumption growth unless the average and marginal productivity of the resource input becomes infinite. Hence, these models can be criticized on the grounds that they do not incorporate the restrictions imposed by the physical laws of


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nature, particularly the conservation of mass. If one pound of material production requires one pound of material input, then only a finite amount of output can be produced from a finite stock of the nonrenewable resource16. Of course, consumption also can be sustained if a renewable resource can be substituted for the nonrenewable resource. Krautkraemer (1985) incorporates preserved natural environments into a capital-resource growth model. Resource extraction disrupts the natural environment where the resource is found, resulting in the irreversible loss of environmental amenities. The irreversibility establishes a non-decreasing relationship between the remaining resource stock and the flow of amenity services from natural environments. This implies that the value of the environmental amenities can be captured by including the remaining resource stock as an argument of the utility function, and the model is reduced to two state variables. The formal description of the model is altered only by the presence of the resource stock in the utility function, which becomes U(C,Q)I7. This nonconsumptive value of the resource stock gives the resource stock a positive own rate of return so that eq. (23) becomes

XQ = 6XQ

- UQ(C,Q).

(23')

This equation demonstrates how the environmental impact of resource use affects the path of resource extraction. The amenity value of natural environments results in a less rapid increase in the price of the resource. This usually implies that the initial resource price is greater when environmental amenities are considered; otherwise the non-negativity constraint on the resource stock will be violated. Indeed, the resource price can be decomposed into two parts:

where X = lim,,, ec6' XQ gives the present-value user cost associated with the scarcity of the resource (and equals zero if the resource stock is not exhausted). The second term on the right-hand side of eq. (25) is the present value of the future marginal amenity value of preserved natural environments. The amenity value of the natural environments increases the conservation of the resource in that the rate See Anderson (1987) and Perrings (1986, 1987) for a more elaborate discussion of this issue. Vousden (1973) also includes the resource stock in the utility function of a cake-eating model to reflect a conservation motive, but does not indicate the source of the conservation motive. As in the discussion below, this conservation motive results in less rapid depletion of the resource. The optimality of exhausting the resource stock depends upon the marginal utility of consumption as the consumption of the resource goes to zero, the magnitude of the conservation motive, and the rate of discount. In particular, the resource stock is exhausted if U c > Up/G when R = Q = 0.

l6

l7


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of depletion of the resource stock is less rapid even if the resource stock is ultimately exhausted. Furthermore, the value of environmental amenities may imply that it is not optimal to exhaust the resource stock. Since the environmental amenities do not affect the production technology, they also do not affect the conditions for both feasibility and optimality of sustained consumption growth. If the marginal utility of consumption becomes infinite as consumption goes to zero, then the ability to prevent consumption from declining to zero is a necessary condition for permanent environmental preservation to be optimal. On the other hand, it may not be optimal to permanently preserve any natural environments containing the resource even if consumption is always increasing. This is because the ability to sustain consumption growth is based on increasing productivity of the resource as the capital stock accumulates. The value of the marginal productivity of the resource input can be increasing even though the marginal value of output is decreasing. A similar result occurs if the growth in consumption is based on technological progress that increases the productivity of the resource [Krautkraemer (1985)l. The case for permanent environmental preservation is enhanced by a backstop technology that provides a substitute for the nonrenewable resource since, in this case, the sustainability of consumption no longer depends upon increasing resource productivity [Krautkraemer (1986)l. The addition of a backstop technology to the model also illustrates the sensitivity of some results to basic qualitative features of the model. We usually would think that a lower rate of discount would result in greater conservation of the resource stock and would therefore preserve more natural environments for the future. This is the case in the one-state variable cakeeating model [Vousden (1973)l. However, in a capital-resource model with a backstop technology, the rate of discount also affects the mix of productive and environmental assets and there can be a positive relationship between the rate of discount and the level of environmental preservation. A lower rate of discount has the direct effect of increasing the demand for both the capital and resource assets. The indirect effect of the increased demand for capital is to increase the extraction of the resource. This indirect effect outweighs the direct effect if the elasticity of output with respect to capital is greater than the elasticity of output with respect to the resource input. Also, if the cost of the backstop technology is sufficiently high relative to the value of preserved environments, then a backstop technology may lead to more rapid depletion of the nonrenewable resource since the backstop reduces the future productive value of the nonrenewable resource but is too costly to warrant permanent preservation [Krautkraemer (1986)l. Pollution and environmental quality became a focus of growth models in the early 1970s [for example, Keeler, Spence and Zeckhauser (1973), Forster (1973), and Plourde (1972)l. Pollution can enter the model in a variety of ways. It can be treated as a stock variable such as the level of ambient quality or as a flow

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variable such as the rate of emission. It can be a by-product of consumption andior production and it can be an argument of either the production function, the utility function, or both. Pollution can be controlled by the choice of production processes or by allocating resources to cleaning up effluents. Because of the diversity of modeling possibilities, the literature has produced a wide variety of somewhat disparate results. An illustrative basic model is provided by Plourde (1972) and Forster (1973). The economy chooses a time path for consumption that maximizes the present value of utility, where utility U(C, P ) is a function of the level of consumption, C, and the current stock of pollution, P. The economy produces a fixed level of output from a fixed level of inputs and output is allocated to consumption or pollution control. Consumption activities generate pollution and the pollution stock decays at an exponential rate a. The level of pollution control is determined by the choice of the consumption level so that the net contribution to pollution, Z , can be written as a function of consumption only. The economy chooses a consumption path that maximizes

subject to

The first-order conditions include

where the shadow price of pollution is negative since pollution produces disutility. The optimal consumption path balances the marginal utility of consumption with the marginal disutility of the pollution caused by the consumption [eq. (28)l. In this model, environmental quality is a renewable resource. For an interior solution, the economy approaches a steady-state equilibrium defined by

A higher rate of discount results in greater consumption and pollution in the steady state. The steady-state level of consumption also increases with an increase in the exponential rate of decay of pollution. If the economy can accumulate productive capital as well as pollution, then there can be more than one steady-state equilibrium and the optimal steadystate levels of pollution and consumption depend upon the initial position of


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the economy [Heal (1982)l. That is, a capital-rich economy may move towards a relatively clean steady-state environment while a less well-endowed economy may find it desirable to pursue a lower level of abatement activity in order to allocate capital to the production of consumption goods. Recycling provides a means for reducing the amount of wastes emitted into the environment. Lusky (1976) examines a model in which productive resources can be allocated to a recycling activity that reclaims wastes. This reduces the level of pollution and provides an alternative source of commodity production. The social optimum calls for a decrease in consumption of the original good and an increase in production and consumption of the recycled good over the amounts that would occur in a market economy. The social optimum can be achieved in the marketplace through a tax on the original good and a subsidy for the recycled good. The potential for variation in models increases when both an exhaustible resource and an environmental asset are linked together in a model. As one might expect, a resource-environmental quality model generates pessimistic results about economic growth unless more attractive features, such as a backstop technology, recycling, or a capital or renewable resource substitute for the nonrenewable resource are also included in the model. The environmental impact of the consumption of the resource can alter the qualitative nature of the pattern of resource use. For example, if production depends upon a nonrenewable resource and pollution is a by-product of production activities, then the optimal extraction of the resource actually increases rather than decreases over time [Forster (1980), d'Arge and Kogiku (1973)l. This extreme form of increased conservation of the resource is necessary in order to balance the loss of utility for future generations that results as pollution accumulates. If there is a renewable, or 'non-depleting', resource substitute for the nonrenewable resource, that is more costly but does not pollute the environment, then the cumulative use of the nonrenewable resource is decreased [Forster (1980)l. Few dynamic models incorporate capital, resource, and environmental state variables. Maler (1974) examines such a model but the results are limited to a statement of the necessary conditions for efficiency. There is no qualitative analysis of the effect of the resource-environmental interactions or the asymptotic behavior of the model. Under standard neoclassical assumptions, there is a unique optimal path in such a general model, and effluent charges, environmental rental charges, lump sum transfers, and competitive prices will support the optimal path as a decentralized market equilibrium [Becker (1980)l. Dixit, Hammond and I-Ioel (1980) examine a general model that includes many capital assets that could be interpreted to include environmental assets and both renewable and nonrenewable natural resources. However, the intent is to demonstrate the general applicability of the rule that a constant consumption path can be maintained with zero net investment, and the dynamic features of resource-environmental interactions are not explicitly examined.

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Kamien and Schwartz (1982) simplify the analysis of the model presented at the beginning of this section by assuming that pollution grows in direct proportion to the rate of resource extraction, and this essentially reduces the model to having two state variables. In addition, the harmful effects of pollution are felt only in the productive sector, which eliminates the stock effect in the utility function. The utility function is assumed to be logarithmic and the production function is CobbDouglas. With these assumptions, the impact of environmental degradation can be summarized by one parameter. The analytical difficulties associated with these more complex models may preclude more than the most rudimentary analysis of the qualitative features of resource-environmental interactions in a dynamic setting. Because of these inherent difficulties, it may be necessary for models to focus on the most salient dynamic features of these interactions as economically as possible. It is extremely important that great care be taken to insure the robustness of qualitative results. Another important feature of resource-environmental interactions that has not yet entered the discussion is the large degree of uncertainty that surrounds some of the environmental impacts of resource use. This uncertainty raises additional issues when the environmental impacts occur over time. First, many of the environmental impacts of resource use are cumulative and essentially irreversible. For example, the atmospheric accumulation of carbon dioxide will not decline significantly if the combustion of fossil fuels ceases. If there is a substantial delay in identifying carbon dioxide as the source of a significant change in global mean temperature, then efforts to control carbon dioxide emissions should not depend upon conclusive evidence of the relationship between atmospheric carbon dioxide and climate [Smith (1981)l. The optimal timing of such regulation in the face of uncertainty is explored by Kolstad (1991). In general, uncertainty and irreversibility imply that it is not appropriate to use the expected values of future outcomes if society is risk averse or if the uncertainty about outcomes is resolved by the accumulation of information over time. That is, there is a premium associated both with risk aversion and with the intertemporal resolution of uncertainty. The premium associated with risk aversion is generally referred to as option value. The basic notion here is that individuals may be willing to pay some amount in order to achieve a more certain outcome. This could mean that individuals would forego some amount of current benefit from the combustion of fossil fuels in order to reduce the uncertainty about future climatic conditions. The premium associated with the resolution of uncertainty is generally referred to as quasi-option value. The basic notion here is that further information is not useful unless previous decisions are reversible. For example, the net benefits of the construction of a hydroelectric dam may depend upon the future cost of photovoltaic energy. If the dam is built and a natural environment is permanently lost (the irreversible action in this case), then the outcome is unaffected by any future information that reduces the uncertainty about the cost of solar energy.


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However, a decision not to build the dam can be reversed if new information indicates that the cost of solar energy is higher than expected. This is not to say that the dam should never be built, but only that there is a risk premium associated with the irreversible option. This risk premium is equivalent to the expected value of perfect information conditional on the decision not to develop [Conrad (1980)l. Because of the value of information, it can be desirable to devote resources to obtaining information that reduces the uncertainty about potential impacts I*. The risk associated with many dynamic resource-environmental interactions is such that there is a low probability of a high consequence or catastrophic outcome. Individuals may react differently to low probabilitylhigh consequence risks than they do to more usual risks. A large segment of the population is adamantly opposed to the risks posed by the potential environmental impact of the use of nuclear power even though scientific and technical experts have estimated that the expected loss of life from nuclear power generation and the storage of high-level radioactive waste is well within the bounds of commonly accepted risks [Cohen (1981)l. Possible explanations include evidence that individuals focus on consequences and ignore the probabilities, particularly when there is a threat to life [Burness (1981)], or they distrust the findings of technical experts, or they make a distinction between voluntary and involuntary risks. A final consideration regarding the uncertainty of resource-environmental interactions is the extent to which the risk can be spread or diversified. Society may be risk neutral even though the individual members of society are risk averse if the social risk premium becomes small as the risk is spread over many individuals [Arrow and Lind (1970)l. However, environmental risks are often 'public7 risks in that one individual's risk burden does not diminish the risk burden of any other individual and the risk cannot be spread [Fisher (1973)l. The risk premium associated with an uncertain event also depends upon its correlation with other uncertain events. It is possible for a risk premium to be negative if the outcome is negatively correlated with other risks - it pays to diversify. For example, there may be a negative risk premium associated with research and development expenditures on alternative energy sources that use the environment less intensively.

'' A thorough discussion of the literature on option value is given by Bishop (1982). Over the last two decades, the literature on option value has become quite voluminous and examines issues such as the ex ante nature of option price [Smith (1987)], how the dgn of option value depends on the type of uncertainty [Hartman and Plummer (1987)], the role of learning in quasi-option value [Miller and Lad (1984), Fisher and Hanemann (1987)], and how increasing uncertainty and a continuum of development levels affects quasi-option value [Hanemann (1989)l.

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4.2. Intertemporal eficiency and intergenerational equity Efficiency and equity are the standards by which an allocation of resources is evaluated. These standards apply to an intertemporal, as well as static, setting. The intertemporal efficiency and equity of an allocation of resources are examined more fully in other chapters of this Handbook. The discussion here focuses primarily on the effect of resource-environmental interactions on these issues. The discussion begins with a consideration of intertemporal efficiency followed by a look at intergenerational equity. 4.2.1. Intertemporal eficiency

The basic static conditions implied by Pareto efficiency can be extended to an intertemporal setting in a straightforward fashion through the dating of commodities. That is, final goods and productive factors are distinguished by time as well as by the type of good. For private goods, distributional efficiency requires that each pair of individuals has the same marginal rate of substitution between any pair of commodities, including the same good consumed at different points in time. The common marginal rate of substitution must be equal to the economy's marginal rate of transformation between the pair of commodities. The necessary conditions for a Pareto-efficient allocation of a public good are somewhat more complicated. In particular, efficiency obtains when the marginal rate of transformation is equal to the summation of individual marginal rates of substitution over both time and individuals [Sandler and Smith (1976)l. As demonstrated in the previous section, the efficiency conditions for the use of long-lived assets require that the marginal value of the flow of services from the asset is equal to the marginal value of the asset, and that the marginal rate of return to each asset is the same. The basic condition of equal returns to each asset is independent of any ethical criterion. That is, given any social welfare function, if the intertemporal condition is not satisfied, then there exists a better path for the economy to follow, where better is defined in terms of the chosen social welfare criterion. A market allocation will be intertemporally efficient given standard neoclassical conditions about the convexity of production and preference sets and a complete set of markets, including future markets for each dated commodity and a full set of contingent markets for each state of the world. Arbitrage activity by asset owners seeking to maximize the present value of their portfolio would ensure that the total return to each asset is equal. The future markets enable the economy to establish the proper initial price for each asset [Dasgupta and Heal (1979)l. In the absence of futures markets, it could be some time before an initial error is discovered and corrected. The absence of contingent markets would prevent the efficient allocation of risk. The exact impact on the pattern of natural resource


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use depends upon the source of uncertainty. For example, uncertainty about the timing of the development of a substitute for the resource can lead to more rapid depletion while uncertainty about the size of the resource stock can lead to less rapid depletion [Fisher (1981)l. The existence of a complete set of futures, risk, and capital markets is essential to the efficient allocation of any long-lived asset and is not specific to interactions between resource use and the environment. The open access to environmental assets and the public good characteristics of environmental amenities are important sources of intertemporal market inefficiencies derived from resource-environmental interactions. Because of the open-access and publicgood aspects of the environment, the environmental costs of resource use are not fully internalized in private decision making. This market failure results in both direct intertemporal inefficiencies and static misallocations with indirect implications for intertemporal allocation. In general, one would expect that environmental assets would be undervalued and, therefore, over-exploited. The static failure of the market to capture the current environmental costs of natural resource use induces greater extraction of natural resources than would occur if all costs were covered by the resource price. This static inefficiency also affects the entire time pattern of resource extraction. The intertemporal bias in the pattern of resource extraction created by market imperfections, including externalities, depends upon the rate of change in the market imperfection over time relative to the rate of discount [Sweeney 1977)l. A simple example is the case of a static environmental effect with a constant marginal cost so that the rate of change in the market imperfection is zero. In this case, if the rate of discount is positive and the environmental cost is external to the market, then the market depletes the resource more rapidly than socially desirable because the present value of the market imperfection is greater in the present than it is in the future. In addition to the dynamic implications of static inefficiencies, there are several direct sources of intertemporal inefficiency that are associated with the interaction between natural resource use and the environment. Many of the environmental effects of resource use are long-lived and cumulative in nature - the climatic impact of carbon dioxide emissions will be felt long after the consumption of fossil fuels has ended. In the case of cumulative effects, there is a dynamic cost of the externality that captures the present value of any future environmental damage caused by current emissions. For example, if D(P(t)) denotes the value of the environmental damage of an accumulation of pollutant P at time t, then the shadow price of the resource should include the term

which represents the present value of the present and future marginal environmental damage caused by the use of the resource [Schulze (1974)l.

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C.D. Kolstad and LA. Krautkraemer

This value is greater than the present value of the marginal damage of the current stock of pollution, D1(P(t))lS,whenever the marginal damage of pollution increases with the level of pollution and the level of pollution is increasing over time. In the models of the previous section, this cumulative effect of natural resource use is captured in the shadow price of the resource - note the equivalence of this term with the second term on the right-hand side of eq. (25) above. Note also that the correct valuation of the environmental damage depends upon the entire future path of pollution. The persistence of pollutants can imply that economic incentive policies do not have an informational advantage over direct controls since it is not possible to determine the optimal tax (or number of tradeable permits) without solving for the optimal path for environmental quality [Griffin (1987)l. The open access to the environment means that the benefits of the regenerative capacity of the environment are not appropriable. Consequently, there are no market incentives for investment in the assimilative capacity of the environment nor for the development of technologies that use the environment less intensively. Commoner (1972) presents evidence that changes in production processes were the most significant factor in the increase in environmental degradation in the postWorld War I1 period. For example, in the USA between 1949 and 1968, the use of fertilizer nitrogen increased by 648% while population increased by only 34% and per capita output increased by only 11%. Hence there has been a very significant increase in the use of nitrogen fertilizer per unit of output. Research and development efforts are guided by market forces and if environmental resources are undervalued, then R&D activities will be allocated inefficiently and technological progress will be oriented toward more extensive use of the environment and, in turn, the depletion of natural resources will be too rapid. Other intertemporal inefficiencies may arise because future generations do not participate in the market. The general nature of these problems is the inability to conduct trades across generations. Future generations may prefer a different mix of capital, resource, and environmental assets than the mix of assets bequeathed to them by the present generation. It is possible that they may desire to exchange material wealth for environmental amenities. The present generation might be willing to accept the trade but cannot because of the temporal barrier. Such a situation arises when development is irreversible and there is uncertainty about future preferences [Fisher and Krutilla (1974)l. The public-good nature of an environmental asset over time raises questions about the effect of discounting on the intertemporal allocative efficiency. Sandler and Smith (1976) have argued that discounting can result in Pareto inefficiency in the intertemporal allocation of long-lived public goods such as environmental assets. Cabe (1982) establishes that the proper rate of discount on future services is the marginal rate of transformation for the numeraire good between the current period and the period in which the services are provided. He argues that the result obtained by Sandler and Smith is due to their implicit assumption of a numeraire

Ch. 26: NaturalResource Use and the Environment

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with a marginal rate of transformation equal to unity and that this assumption is unrealistic in a growing economy. Sandler and Smith (1982) agree that the proper discount factor is the intertemporal marginal rate of transformation for the numeraire but argue that a value of unity is realistic for a commodity that serves as a standard of value. In any case, the market rate of discount is not necessarily the socially optimal rate of discount. In summary, because of the open-access and public-good characteristics of environmental assets, the interaction between resource use and the environment poses significant problems for achieving an efficient intertemporal allocation even in the presence of a complete set of futures, risk and capital markets for privately owned commodities. While a variety of outcomes is possible, it is generally expected that a market allocation would deplete natural resource stocks too rapidly and that environmental degradation would be too great.

4.2.2. Intergenerational equity Intergenerational equity is perhaps the most often discussed issue associated with the use of natural resource and environmental assets, and it has become increasingly important in recent years. Concerns about intergenerational equity quite naturally depend upon perceptions about future prospects. In a growing economy, the fair treatment of future generations seems to be a less critical issue precisely because the future will do better than the present. The depletion of reserves of nonrenewable resources and the deterioration of environmental quality have contributed to a growing perception that the historical trend of a steady improvement in human welfare is being reversed. The models in the previous section demonstrate that while capital accumulation, including technological knowledge embodied in human capital, can be seen as the engine of economic growth, the depletion of nonrenewable resources and environmental degradation are significant restraints on that growth. The environmental impacts of natural resource use, such as climatic change, have raised the question of whether or not future generations will receive a livable environment. Of course, equity has different meanings for different people and there is a variety of intergenerational equity criteria. The discussion here focuses on those criteria that can be interpreted to fall into one of two broad categories: the present-value, or utilitarian, criterion and a conservation criterion. The presentvalue criterion seeks to maximize the present value of utility while the conservation criterion requires the preservation of the economy's natural resource base. These two criteria are used to illustrate some of the basic intergenerational equity issues. Each of the optimal growth models in the previous section had a present-value objective functional. In these models, social rate of discount on utility plays a key role in determining the well-being of future generations. In the capital-resource growth model, capital accumulates and consumption increases until the marginal

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C.D.Kolstad and J.A. Krautkraemer

productivity of capital equals the rate of discount. If capital was the only productive input, then the economy would settle into a steady-state level of consumption, and a higher rate of discount reduces capital accumulation and consumption in the steady-state. The choice of the social rate of discount of utility is even more critical when the production requires an essential nonrenewable resource as an input. The discount rate now determines the asymptotic rate of growth of consumption and not just its steady-state level [Dasgupta and Heal (1974)l. It is possible that a high rate of discount will bring about exhaustion of the resource stock, deterioration of the environment, and the steady decline of consumption even when it is technologically feasible to sustain both the level of consumption and the quality of the environment [Krautkraemer (1985)]. The rate of discount also can affect the mix of assets left to future generations. Krutilla (1967) suggested that a lower discount rate could result in the accumulation of low-yield capital assets rather than increased preservation of natural environments. As discussed in the previous section, this effect is demonstrated by Krautkraemer (1986) in a capital-resource growth model with a backstop technology. Much of the discussion of intergenerational equity has centered on the role of the rate of discount in the intertemporal allocation of resources. Discounting future costs and benefits is usually justified on the basis of the productivity of capital and the time preference of individuals. Even if the social rate of time preference is zero, discounting may still be desirable because of capital productivity. Page (1988) argues that these two rationales for discounting can be thought of as occurring at different levels of the social choice problem. The productivity of capital affects the set of alternatives available to society so it warrants discounting at the level of the feasible set, while the social rate of time preference concerns the aggregation of the preferences of the different generations and so it represents discounting at the level of social choice from alternatives in the feasible set. To some degree, this distinction is similar to making a distinction between the discounting future consumption streams and discounting future utility. In this context, the discounting the dollar value of future costs and benefits (rather than utility) becomes a matter of intertemporal efficiency rather than intergenerational equity [Page (1977,1988)l 19. That is, discounting is useful in the identification of socially efficient paths and the choice among the efficient paths is determined by the ethical criteria of the society. The ethical criteria underlying a social choice rule may be too complex to be summarized in one parameter such as the social rate of discount on utility. For example, Sen (1982) has argued that the l9 Recall that intertemporal efficiency requires equal rates of return to each asset. In a capital-resource growth model, this requires that the rate of change in the marginal productivity of the resource be equal to the marginal productivity of capital, or FR/FR = F K .Setting both rates of return equal to the rate of discount on utility is one means of achieving this equality.


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utilitarian framework is inadequate for an analysis of social equity since it does not accommodate all of the fundamental rights of individuals. The conservation criterion requires that society seek to preserve the adequacy of the resource base, including its environmental assets. Essentially, this criterion argues that the future has a right to an environment in which it can do at least as well as the current generation. Of course, it then becomes important to determine what is necessary for this criterion to be met - that is, what is meant by preserving the natural resource base? After all, production and consumption activities inherently involve some use of natural and environmental resources. Some insight into this question is given by resource and environmental growth models that have used a 'Rawlsian', or maxi-min, criterion as the social welfare functional. The Rawlsian maxi-min criterion seeks to maximize the well-being of the least well-off individual member of society. Rawls (1971) argued that this criterion would be selected by individuals as the social rule of distribution if individuals were ignorant of which position in society they actually would occupy. This maxi-min criterion was intended as a distributional rule across individuals at any given point in time rather than as an intergenerational criterion. In an intergenerational setting, this criterion would not allow future generations to be made better off at the expense of the present generation, and this rules out economic growth even if it can be sustained forever. As such, the Rawlsian criterion is more restrictive than the conservation criterion. Solow (1974) examines a capital-resource growth model with a Cobb-Douglas production function and derives the maximum level of sustainable consumption as a function of the initial stocks of capital and the nonrenewable resource. This constant consumption path will be followed if and only if the share of the output from the natural resource is invested in the capital stock [Hartwick (1977)l. This zero net investment rule can be extended to a generalized setting of many assets which could include resource and environmental assets [Dixit, Hammond and Hoe1 (1980)l and it can be interpreted as the economy living off the interest on its wealth endowment, where that endowment includes natural and environmental resources [Solow (1986)l. This interpretation of the Hartwick rule seems compatible with suggestions that funds actually be set aside as allowance for compensation of future damages [Freeman (1977), Bromley (1989)l. Presumably, this would result in increased investment in other assets, including environmental enhancement. This would increase future productive capacity which is consistent, at least in spirit, with the Hartwick rule of zero net investment. In addition, this requirement would force greater consideration of the potential environmental impacts. The zero net investment rule also suggests that simply preserving the physical stock of natural capital is not necessarily in the best interest of future generations. A more efficient strategy could be to use some natural capital and invest in human and physical capital that future generations will find useful in improving the welfare that

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can be achieved from a finite flow of renewable resource inputs. Indeed, the initial endowment of physical capital can be an important determinant of the desirability of permanently preserving natural environments [Krautkraemer (1985)l. Of course, it should be noted that the translation of the zero net investment rule into practical policies is not straightforward, particularly when many of the key assets are difficult, if not impossible, to evaluate20.A zero net investment rule requires the ability to determine how much investment in capital (or compensation to future generations) is necessary to replace the loss of natural resource and environmental assets. In addition, the Solow result relies on the use of a CobbDouglas production function and therefore an elasticity of substitution equal to unity. As discussed in the previous section, a constant consumption path is not feasible if the elasticity of substitution is less than unity. This raises questions about the ability of the economy to substitute capital for the basic life support systems of the environment 21. Page (1982) suggests a possible means of reconciling the utilitarian and conservation criteria. If the future was endowed with the right to a livable environment, then resource and environmental policies would be constrained by that requirement. The social rate of discount would depend upon only the cost of capital. In this context, discounting would determine intertemporal efficiency but it would not raise issues of equity. This still leaves the practical problem of how to determine whether or not the future's right to a livable environment has been honored.

5. Conclusions

This chapter has concerned the overlap between the fields of resource economics and environmental concepts. Because each of these fields has been treated at length elsewhere in the Handbook, we have been concerned here with the unique theoretical, empirical and policy questions common to both resource and environmental economics. Consistent with the division of the chapter into statics and dynamics, empirical work is largely static in nature while theoretical work is largely dynamic. A real richness of empirical studies have developed, concentrating largely on energy development and the environment. The spatial nature of resource markets has been a major focus of much work. Because of the bulky nature of many resources, The literature on natural resource accounting attempts to get at these practical problems. See Harhvick (1990) for a discussion of the theoretical framework for natural resource accounting and some practical implications of the theory. 21 For example, sunscreen and hats may not be an acceptable substitute for the protection from ultraviolet radiation given by ozone in the upper atmosphere. 20


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they are costly to transport. Further, space plays a major role in transforming, and possibly rendering less harmful, many pollutants. Much analysis has involved the operation of environmental regulations within spatial resource markets. Other empirical studies have attempted to value the disbenefits associated with the externalities of resource use. Much of this work has been concerned with amenity values of clean air. While results are mixed, it appears that existence value for certain valuable resources such as the Grand Canyon, can be very large. A final set of empirical analyses seeks to balance costs and benefits, in an effort to determine efficient regulation of the environmental externalities that arise from energy use, principally electric power production from coal. In the area of dynamics, there are a large number of interesting issues common to resource and environmental economics. Some of the most thorny and interesting issues concern the interaction between resource depletion, irreversibility of environmental effects and intergenerational efficiency and equity, all within an atmosphere of considerable uncertainty. Treating all of these issues simultaneously in even the simplest of theoretical models leads to a very complex analysis. Much of the literature on dynamics has involved extension of classic optimal growth models. In our context, a dynamic model should incorporate capital accumulation, environmental quality and resource depletion. Most models have been concerned with two of these three components. The analytic difficulties associated with examining the interaction of all these variables has led to a dearth of such analyses as well as limited scope of the few analyses which have been performed. At a more philosophical level, very fundamental questions concern intergenerational efficiency and equity. In extracting a resource today, for current consumption, we are reducing the stock of that resource available for future generations. If, as depletion occurs, lower-grade ores are extracted, then in all likelihood, environmental damage per unit of resource used will consequently rise for future generations. Further, if irreversible environmental damage is associated with that resource use, future generations are also being asked to bear untold environmental costs. A very simple but deep question concerns the efficient and fair trade-off between present resource consumption and future environmental disbenefits. The intent of this chapter has been to provide a framework for viewing the ground common to resource and environmental economics. We have tried to view the large amount of past research within this framework so that it becomes clearer what progress has been made and where gaps in knowledge still exist.

References Ackerrnan, B.A., and W.T. Hassler, 1981, Clean CoalIDirtyAir (Yale University Press, New Haven, CT).

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Easterling 111, W.E., M.L. Parry and P.R. Crosson, 1989, "Adapting Future Agriculture to Changes in Climate", in: N.J. Rosenberg, W.E. Easterling 111, P.R. Crosson and J. Darmstader (eds.), Greenhouse Warming:Abatement and Adaptation (Resources for the Future, Washington, DC). Fisher, A.C., 1973, "Environmental Externalities and the Arrow-Lind Public Investment Theorem", American Economic Review 63 no. 4,722-725. Fisher, A.C., 1981, Resource and Environmental Economics (Cambridge University Press, Cambridge). Fisher, A.C., and W.M. Hanemann, 1987, "Quasi-Option Value: Some Misconceptions Dispelled, Journal of Environmental Economics and Management 14,183-190. Fisher, A.C., and J.V. Krutilla, 1974, "Valuing Long Run Ecological Consequences and Irreversibilities", Journal of Environmental Economics and Management 1,96-108. Forster, B., 1980, "Optimal Energy Use in a Polluted Environment", Journal of Environmental Economics and Management 7,321-333. Forster, B.A., 1973, "Optimal Consumption Planning in a Polluted Environment", The Economic Record 49,534-545. Frederick, K.D., and P.H. Gleick, 1989, "Water Resources and Climate Change", in: N.J. Rosenberg, W.E. Easterling 111, P.R. Crosson and J. Darmstader (eds.), Greenhouse Warming: Abatement and Adaptation (Resources for the Future, Washington, DC). Freeman 111, A.M., 1977, "Equity, Efficiency, and Discounting: The Reasons for Discounting Intergenerational Effects", Futures 9 no. 5,375-376. Garg, P.C., and J.L. Sweeney, 1978, "Optimal Growth with Depletable Resources", Resources and Energy 1,43-56. Graves, Philip E., 1991, "Aesthetics", in: J. Braden and C. Kolstad (eds.), Measuring the Demand for Environmental Quality (North-Holland, Amsterdam). Griffen, R.C., 1987, "Environmental Policy for Spatial and Persistent Pollutants", Journal of Environmental Economics and Management 14,41-53. Griffin, J.M., 1974a, "An Econometric Evaluation of Sulfur Taxes", Journal of Political Economy 82 no. 4,669-688. Griffin, J.M., 1974b, "Recent Sulfur Tax Proposals: An Econometric Evaluation of Welfare Gains", in: M.S. Macrakis (ed.), Energy: Demand, Conservation and Institutional Problems (MIT Press, Cambridge, MA). Hahn, Robert W., 1989, "Economic Prescriptions for Environmental Problems: How the Patient Followed the Doctor's Orders", Journal of Economic Perspectives 3,95-114. Hanemann, W.M., 1989, "Information and the Concept of Option Value", Journal of Environmental Economics and Management 16,23-37. Hanemann, W.M., 1991, "Willingness to Pay and Willingness to Accept: How Much Can They Differ?", American Economic Review 81,635-647. Hartman, R., and M.L. Plummer, 1987, "Option Value Under Income and Price Uncertainty", Journal of Environmental Economics and Management 14,212-225. Hartwick, J., 1990, "Natural Resources, National Accounting and Economic Depreciation", Journal of Public Economics 43,291-304. Hartwick, J.M., 1977, "Intergenerational Equity and the Investing of Rents From Exhaustible Resources", American Economic Review 67 no. 5,972-974. Heal, G.M., 1976, "The Relationship Between Price and Extraction Cost for a Resource with a Backstop Technology", Bell Journal of Economics 1 no. 2,371-378. Heal, G.M., 1982, "The Use of Common Property Resources", in: V.K. Smith and J.V. Krutilla, eds., Explorations in Natural Resource Economics (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future).

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Hekstra, G.P., 1989, "Sea-Level Rise: Regional Consequences and Responses", in: N.J. Rosenberg, W.E. Easterling 111, P.R. Crosson and J. Darmstader (eds.), Greenhouse Warming: Abatement and Adaptation (Resources for the Future, Washington, DC). Henderson, J.M., 1958, The Efjiciency of the Coal Industry (Harvard University Press, Cambridge, MA). Hotelling, H., 1931, "The Economics of Exhaustible Resources", Journal of Political Economy 39,137175. Howard, H.A., 1971, "A Measurement of the External Diseconomies Associated with Bituminous Coal Surface Mining, Eastern Kentucky, 1962-1967", Natural Resources Journal 11 no. 1,76-101. ICF, Inc., 1983, "Analysis of a Senate Emission Reduction Bill (S-3041)", unpublished report (Washington, DC, February). ICF, Inc., 1989, "Analysis of EDF's Acid Rain Control Proposal", memo to EPA dated May 19, 1989. Kamien, M., and N. Schwartz, 1981, Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management (North-Holland, Amsterdam). Kamien, M.I., and N.L. Schwartz, 1982, "The Role of Common Property Resources in Optimal Planning Models with Exhaustible Resources", in: V.K. Smith and J.V. Krutilla (eds.), Explorations in Natural Resource Economics (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Keeler, E., M. Spence and R. Zeckhauser, 1971, "The Optimal Control of Pollution", Journal of Economic Theory 4,19-34. Kneese, A,, R.U. Ayres and R. d'Arge, 1970, Economics and the Environment A Materials Balance Approach (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Kneese, A.V., 1976, "Natural Resources Policy 1975-1985", Journal of Environmental Economics and Management 3,253-288. Kneese, A.V., and B.T. Bower, 1968,Managing Water Quality: Economics, Technology, Institutions (Johns Hopkins University Press, Baltimore, MD). Kolstad, Charles D., 1986, "Empirical Properties of Economic Incentives and Command-and-Control Regulations fnr Air Pollution Controi", LL.LEconomics 62,250-263. Kolstad, Charles D., 1987, "Uniformity vs. Differentiation in Regulating Externalities", Journal of Environmental Economy and Management 14,386-399. Kolstad, Charles D., 1990a, "Acid Deposition and the U.S. Coal Industry", E n e r ~Policy 18,845-852. Kolstad, Charles D., 1990b, "Clean Air and Energy: Reform of the PSD Provisions of the Clean Air Act", Journal of the Air Pollution ControlAssociation 40, 177-184. Kolstad, Charles D., 1991, "Optimal Regulation of Stock Externalities with Learning", unpublished working paper (University of Illinois Department of Economics, Urbana-Champaign, IL). Koopmans, T.C., 1973, "Some Observations on 'Optimal' Economic Growth and Exhaustible Resources", in: H.C. Bos, H. Linemann and P. de Wolff (eds.), Economic Structure and Development (North-Holland, Amsterdam). Krautkraemer, J.A., 1985, "Optimal Growth, Resource Amenities, and the Preservation of Natural Environments", Review of Economic Studies 52, 153-170. Krautkraemer, J.A., 1986, "Optimal Depletion with Resource Amenities and a Backstop Technology", Resources and Energy 8,133-149. Krautkraemer, J.A., 1988, "The Rate of Discount and the Conservation of Natural Environments", Natural Resource Modeling 2 no. 3,421-437. Krutilla, J.V., 1967, "Conservation Reconsidered", American Economic Review 57,777-786. Krutilla, J.V., and A.C. Fisher, 1985, The Economics ofNatura1 Environments: Studies in the Valuationof Commodity and Amenity Resources, 2nd Ed. (Resources for the Future, Washington, DC). LeBlanc, M.R., R.J. Kalter and R.N. Boisvert, 1978, "Allocation~ofUnited States Coal Production to Meet Future Energy Needs", Land Economics 54 no. 3,316-336. Lin, W., R.L. Spore and E.A. Nephew, 1976, "Land Reclamation and Strip-Mined Coal Production in Appalachia", Journal of Environmental Economics and Management 3 no. 3,236-252.


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Lind, R.C., 1982, Discounting for Time and Risk in Energy Policy (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Lusky, R., 1976, "A Model of Recycling and Pollution Control", Canadian Journal of Economics 9,91101. Maler, K.G., 1974, Environmental Economics: A Theoretical Inquiry (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Mendelsohn, R., 1980, "An Economic Analysis of Air Pollution from Coal-Fired Power Plants", Journal of Environmental Economics and Management 7 no. 1,30-43. Michael Hanemann, W., 1991, "Willingness to Pay and Willingness to Accept: How Much Can They Differ?", American Economic Review, 81,635-647. Miller, J.R., and F. Lad, 1984, "Flexibility, Learning, and Irreversibility of Environmental Decision", Journal of Environmental Economics and Management 11, 161-172. Montgomery, W.D., 1972, "Markets in Licenses and Efficient Pollution Control Programs", Journal of Economic Theory 5,395-418. Morgan, M.G., W.R. Rish, S.C. Morris and A.K. Meier, 1978, "Sulfur Control in Coal Fired Power Plants: A Probabilistic Approach to Policy Analysis", Journal of the Air Pollution Control Association 23,993-997. Nichols, Albert L., 1984, Targeting Economic Incentives for Environmental Protection (MIT Press, Cambridge, MA). Nordhaus, W., 1980, "Thinking About Carbon Dioxide: Theoretical and Empirical Aspects of Optimal Control Strategies", Cowles Foundation Discussion Paper No. 565. Nordhaus, William D., 1990, "An Intertemporal General-Equilibrium Model of Economic Growth and Climate Change", Proceedings of MIT Workshop on Economic/Energy/EnvironmentalModeling for Climate Policy Analysis, Washington, DC, October 22-23. North, D.W., and M.W. Merkhofer, 1976, "A Methodology for Analyzing Emission Control Strategies", Computer and Operations Research 3, 185-207. O'Brien, B., A. Fuldner, M. Paull, T. Petersik and S. Kanhouwa, 1983, "Impacts of the Proposed Clean Air Act Amendments of 1982 on the Coal and Electric Utility Industries", Report DOEIEIA-0407 (US Department of Energy, Washington, DC, June). OECD, 1988, Environmental Impacts of Renewable Energy (Organization for Economic Cooperation and Development, Paris). Page, R.T., 1977, Conservation and Economic Eficiency: A n Approach to Materials Policy (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Page, R.T., 1982, "Approaches to the Choice of Discount Rates for Social Benefit-Cost Analysis: Comment", in: R.C. Lind (ed.), Discounting for Time and Risk in Energy Policy (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Page, T., 1988, "Intergenerational Equity and the Social Rate of Discount", in: V Kerry Smith (ed.), Environmental Resources and Applied Welfare Economics, Essays in Honor of John K Krutilla (Resources for the Future, Washington, DC). Perrings, C., 1986, "Conservation of Mass and Instability in a Dynamic Economy-Environment System", Journal of Environmental Economics and Management 13,199-21 1. Perrings, C., 1987, Economy and Environment (Cambridge University Press, Cambridge). Peterson, J.M., 1977, "Estimating An Effluent Charge: The Reserve Mining Case", Land Economics, 53 no. 3,328-341. Plourde, C.G., 1972, "A Model of Waste Accumulation and Disposal", Canadian Journal of Economics 5 no. 1,119-125. Portney, Paul, 1990, "Economics and the Clean Air Act", Journal i7fEconomic Perspectives 4,173-181. Ramsay, W., 1979, Unpaid Costs of Electrical Energy: Health and Environmental Impacts from Coal and Nuclear Power (The Johns Hopkins University Press, Baltimore, MD).

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Randall, A,, B. Ives and C. Eastman, 1974, "Bidding Games for Valuation of Aesthetic Environmental Improvements", Journal of Environmental Economics and Management 1 no. 2,132-149. Randall, A., 0.Grunewald, S. Johnson, R. Ausness and A. Pagoulatos, 1978, "Reclaiming Coal Surface Mines in Central Appalachia: A Case Study of the Benefits and Costs", Land Economics, 54 no. 4, 472-489. Rawls, J., 1971,A Theory of Justice (Clarendon Press, Oxford). Rosenberg, N.J., W.E. Easterling 111, P.R. Crosson and J. Darmstader, eds, 1989, Greenhouse Warning: Abatement and Adaptation (Resources for the Future, Washington, DC). Rowe, R.D., R.C. d'Arge and D.S. Brookshire, 1980, "An Experiment on the Economic Value of Visibility", Journal of Environmental Economics and Management 7 no. 1, 1-19. Samuelson, PA., 1952, "Spatial Price Equilibrium and Linear Programming", American Economic Review 42,283-303. Sandler, T., and VK. Smith, 1976, "Intertemporal and Intergenerational Pareto Efficiency", Journal of Environmental Economics and Management 2,151-159. Sandler, T., and VK. Smith, 1982, "Intertemporal and Intergenerational Pareto Efficiency: A Reconsideration of Recent Extensions", Journal of Environmental Economics and Management 8, 361-365. Schlottmann, A., 1976, "A Regional Analysis of Air Quality Standards, Coal Conversion, and the SteamElectric Coal Market", Journal of Regional Science 16 no. 3,375-387. Schlottmann, A,, and L. Abrams, 1977, "Sulfur Emissions Taxes and Coal Resources", Review of Economics and Statistics,59 no. 1, 50-55. Schlottmann, A., and R.L. Spore, 1976, "Economic Impacts of Surface Mine Reclamation", Land Economics 52 no. 3,265-277. Schneider, S.H., and N.J. Rosenberg, 1989, "The Greenhouse Effect: Its Causes, Possible Impacts and Associated Uncertainties", in: N.J. Rosenberg, W.E. Easterling 111, P.R. Crosson and J. Darmstader (eds.), Greenhouse Warning:Abatement andAdaptation (Resources for the Future, Washington, DC). Schulze, W.D., 1974, "The Optimal Use of Non-Renewable Resources: The Theory of Extraction", Journal of Environmental Economics 1,53-73. Schulze, W.D., R.C. d'Arge and D.S. Brookshire, 1981, "Valuing Environmental Commodities: Some Recent Experiments", Land Economics 57 no. 2,151-172. Schulze, W.D., D.S. Brookshire, E.G. Walter, K.K. MacFarland, M.A. Thayer, R.L. Whitworth, S. BenDavid, W. Malm and J. Molenar, 1983, "The Economic Benefits of Preserving Visibility in the National Parklands of the Southwestern", Natural Resources Journal 23, 149-173. Sedjo, R.A., and A.M. Solomon, 1989, "Climate and Forests", in: N.J. Rosenberg, W.E. Easterling 111, PR. Crosson and J. Darmstader (eds.), Greenhouse Warning:Abatement and Adaptation (Resources for the Future, Washington, DC). Sen, A.K., 1982, "Approaches to the Choice of Discount Rates for Social Benefit-Cost Analysis", in: R.C. Lind (ed.), Discounting for Time and Risk in Energy Policy (The Johns Hopkins University Press, Baltimore, MD: for Resources for the Future). Smith, V.K., 1981, "COz, Climate, and Statistical Inference: A Note on Asking the Right Questions", Journal of Environmental Economics and Management 8,391-394. Smith, V.K., 1987, "Uncertainty, Benefit-Cost Analysis, and the Treatment of Option Value", Journal of Environmental Economics and Management 14,283-292. Solow, R.M., 1974, "Intergenerational Equity and Exhaustible Resources", Review of Economic Studies, Symposium on the Economics of Exhaustible Resources, pp. 29-45. Solow, R.M., 1986, "On the Intergenerational Allocation of Natural Resources", Scandinavian Journal of Economics 88,141-149. Splash, C.L., and R.C. d'Arge, 1989, "The Greenhouse Effect and Intergenerational Transfers", E n e w Policy 17 no. 2,88-96.


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ENERGY, THE ENVIRONMENT, AND ECONOMIC GROWTH DALE W. JORGENSON Department of Economics, Haward University, Litauer Center 122, Cambridge, MA 02138, USA PETER J. WILCOXEN Department of Economics, University of Texas, Austin, TX 78712, USA

1. Introduction

Economic growth is a critical determinant of demands for energy. Utilization of energy, especially combustion of fossil fuels, is an important source of environmental pollution. Growth projections are essential for estimates of future demands and supplies of energy and future requirements for pollution controls to maintain environmental quality. The natural point of departure for modeling economic growth is the neo-classical theory of growth originated by Solow (1956, 1988). This theory has been developed in the form used in modeling the interrelationships among energy, the environment, and economic growth by Cass (1965) and Koopmans (1967) I . Maler (1974, 1975) and Uzawa (1975, 1988) have presented neo-classical theories of economic growth with pollution abatement and Solow (1974a, 1974b) has provided a theory that includes supply and demand for an exhaustible resource. These theories have generated an extensive literature, surveyed by Dasgupta and Heal (1979). In the neo-classical theory of growth, wage rates grow at the same rate as productivity in the long run, while rates of return depend on productivity growth and parameters that describe saving behavior. These long-run properties of economic growth are independent of energy and environmental policies. The neo-classical theory of economic growth also provides a framework for projecting intermediate-run growth trends. These trends depend on the same factors as long-run trends, but also depend on energy and environmental policies through their effects on capital accumulation and rates of productivity growth over shorter periods. In this context the intermediate run refers to the time needed for the

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The Cass-Koopmans theory of economic growth has been discussed by Lucas (1988) and Romer (1989). Handbook of Natural Resource and Energy Economics, vol. III, edited by A. K Kneese and J.L. Sweeney Q 1993 Elsevier Science Publishers B. K All rights reserved

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capital-output ratio to converge to a long-run stationary value. This often requires several decades, so that intermediate-run trends are critical for policy evaluation. A striking example of changes in growth trends is the sharp decline in rates of economic growth in the USA and other industrialized countries during the 1970s and 1980s. For example, Jorgenson (1990b) shows that US real output grew at an annual rate of 3.7% during the period 1947-1973, while the annual growth rate for the period 1973-1985 was only 2.5%. Englander and Mittelstadt (1988) have shown that the slowdown has been even more severe in other industrialized countries. Two events coinciding with the slowdown - the advent of more restrictive environmental controls and the increase in world petroleum prices - have led to a vast outpouring of research directed at a fuller understanding of the interactions among energy supplies and prices, environmental quality and its cost, and the sources of economic growth 2. The neo-classical theory of economic growth has provided the framework for a number of important modeling studies of energy and environmental policies. Nordhaus (1992) has presented a Dynamic Integrated Climate-Economy (DICE) model for analyzing the economics of global warming. This is a one-sector neoclassical growth model for the world economy that integrates a production model for world output, a model of intertemporal choice based on utility maximization by a representative consumer, and a model of the impact of climate change on productivity. Nordhaus's model of climate change links climate change to the level of world output through a series of dynamic relationships based on the well-known greenhouse effect '. Nordhaus considers the impact of a policy to control climate change by limiting the emissions of greenhouse gases, such as carbon dioxide. For this purpose he performs two simulations of world economic growth: one with no controls on greenhouse gas emissions, and the second with optimal controls on these emissions. The optimization criterion is the intertemporal utility function of the representative consumer in the DICE model. The difference between the two simulations is very small for half a century after 1990. The optimal reduction in greenhouse gas emissions begins around 9% and rises gradually to 14% by the year 2100. The optimal policy can be implemented by means of a world carbon tax, which rises from $5 per ton of carbon in the 1990s to $20 per ton by the end of the twenty-first century 4.

This literature has been surveyed by Christiansen, Gollop and Haveman (1980) and Christiansen and Tietenberg (1985). Overviews of the greenhouse warming problem are presented by Cline (1992), Manne and Richels (1992), ch. 1, Nordhaus (1991a), and Schelling (1992). We discuss the greenhouse effect and control of global climate change in Section 5, below. A carbon tax was first analyzed by Nordhaus (1979) and has been discussed by the Congressional Budget Office (1990). Alternative policy options for stabilizing the global climate are described in detail by EPA (1989).

Ch. 27: Energy, the Environment, and Economic Growth

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Nordhaus's model of world economic growth provides a dramatic illustration of the power of the neo-classical framework in analyzing the impact of energy and environmental policies. The parameters of this model are calibrated to extensive data on the growth of the world economy. Changes in the global climate are generated by economic activity, especially the combustion of fossil fuels. The physical model of climate change includes the principal features of simulation models for the global climate developed by climatologists. Climate change feeds back to economic activity by reducing productivity levels. These mechanisms provide the basis for the design of an optimal environmental policy by application of a sophisticated version of cost-benefit analysis 5 . A carbon tax like that considered by Nordhaus would internalize the externality associated with carbon dioxide emissions. However, this externality affects the whole planet, while carbon taxes are the responsibility of individual governments. The design of an appropriate policy must involve international coordination. An important limitation of Nordhaus's approach is that it fails to capture differences among regions of the world economy and gains from international cooperation on policies for emissions control. These limitations have motivated the development of a number of multi-region models of the world economy and global climate change. The GLOBAL 2100 model developed by Manne and Richels (1992) is the one most similar in spirit to Nordhaus's model. In the GLOBAL 2100 model the world economy is subdivided among five regions - the USA, other OECD, the former Soviet Union, China, and the Rest of the World. Each region is represented by a one-sector neo-classical growth model patterned after Manne's (1981) MACRO model. Output of the region is a function of capital, labor, and energy inputs, with exogenously given growth in productivity. Energy is allocated between electrical and non-electrical energy. Both forms of energy are supplied by a detailed energy technology assessment (ETA) model of the energy sector. The consumer sector in each region is modeled by means of a representative consumer who maximizes an intertemporal utility function. Environmental policy affects regional output through limitations on carbon dioxide emissions resulting from fossil fuel combustion. The model is employed by Manne and Richels for estimating costs of emissions controls 6 .

Optimal policies for controlling global climate change have also been analyzed by Peck and Teisberg (1990, 1992). Cline (1992) provides a detailed cost-benefit analysis of policies for climate control. Many estimates of costs of emissions controls on carbon dioxide are now available. Detailed surveys are given by Cline (1992), Hoeller, Dean, and Nicolaisen (1991) and Nordhaus (1991b). Dean (1992) presents a survey of estimates of costs of controlling carbon dioxide emissions from six multi-region models of the world economy, including the GLOBAL 2100 model of Manne and Richels (1992). These estimates are based on comparable assumptions about future world economic growth and world petroleum prices.

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Manne and Richels consider the impact of restrictions on carbon dioxide emissions for each of the five regions individually. For this purpose they perform alternative simulations of regional economic growth, first, with no controls on carbon dioxide emissions to estimate the consequences of 'Business-as-Usual' for energy utilization and emissions levels. The principal alternative simulation involves stabilizing these emissions at 1990 level through the year 2000, reducing them to twenty percent below this level by the year 2020, and stabilizing them at this level thereafter. The cost of this policy for the USA mounts to one percent of the gross domestic product (GDP) by the year 2000. These losses rise to two percent of the GDP by the year 2020 and eventually to 2.5%. This policy can be implemented by means of a carbon tax, which begins at $135 per ton in 1990 and rises sharply as emissions are reduced. The tax eventually reaches a level of $208 per ton. Manne and Richels consider the sensitivity of their results to alternative assumptions about the availability of energy supplies and technologies and alternative carbon dioxide limits. They consider the economic impact of reducing US emissions to fifty percent of 1990 levels by the year 2010 and stabilizing at that level thereafter. This produces much more substantial economic losses and requires considerably higher tax levels. Interaction among regions in the GLOBAL 2100 occurs through the world petroleum market and a hypothetical international market for emissions permits. Manne and Richels demonstrate that there would be sizable gains from international trade in these permits. For example, the USA would find it worthwhile to import permits from China and the Rest of the World regions; in the year 2020 these imports would be valued at around $50 billion. The costs of restrictions on emissions would be reduced substantially by introducing international coordination of global climate policy through tradeable permits. The GLOBAL 2100 model of Manne and Richels provides another excellent example of the potential of the neo-classical theory of economic growth for modeling the impact of energy and environmental policies. Their model is useful in assessing the costs of restrictions on carbon dioxide emissions and the potential benefits of international coordination. Through application of their energy technology assessment (ETA) model for each region, Manne and Richels also provide much valuable information on the potential pay-off from accelerated research and development on new energy sources and alternative energy technologies. However, the detail available for the individual regions is very limited, except for the energy sector. Their approach fails to capture important differences among industries and consumers that are critical to assessments of alternative energy and environmental policies at the national level. To overcome these limitations it is essential to employ an econometric approach for modeling the impacts of these policies. We next consider the


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application of this approach to the USA,the region that has been studied most intensively '. The framework for econometric analysis of the impact of energy and environmental policies is provided by intertemporal general equilibrium modeling8. The one-sector neo-classical growth models used by Nordhaus (1992) in modeling the world economy or Manne and Richels (1992) in modeling each region in their fiveregion model of the world economy provide illustrations of intertemporal general equilibrium models. The organizing mechanism of these models is an intertemporal price system balancing demand and supply for products and factors of production. In Nordhaus's DICE model there is only one product, world output, and two factors of production, capital and labor inputs. In the GLOBAL 2100 model of Manne and Richels there are three products in each region - regional output, electrical energy, and non-electrical energy - and two factors of production: capital and labor. In addition, the intertemporal price system links the prices of assets in every time period to the discounted value of future capital services. This fonvardlooking feature is combined with backward linkages among investment, capital stock, and capital services in modeling the dynamics of economic growth. Neither Nordhaus (1992) nor Manne and Richels (1992) have limited their considerations to characterization of economic growth in the long run. The alternative time paths of economic growth generated in their simulations depend on energy and environmental policies through their impact on capital accumulation. In Nordhaus's model productivity growth depends on these policies through the impact of greenhouse gas emissions on climate change and the effects of climate change on productivity. Productivity growth in the Manne-Richels model depends on the introduction of new sources of energy supplies and energy technologies in the ETA submodel of the energy sector. In disaggregating the economic impacts of energy and environmental policies for the USA,we preserve the key features of more highly aggregated intertemporal general equilibrium models. One important dimension for disaggregation is to introduce a distinction among industries and commodities in order to measure policy impacts for narrower segments of the economy. This also makes it possible to model differences among industries in responses to changes in energy prices and the imposition of pollution controls. A second dimension for disaggregation is to distinguish among households by level of wealth and demographic characteristics. This makes it possible to model differences in responses to price changes and environmental controls. It is also useful in examining the distributional effects

'

Beaver (1992) presents a detailed survey of models of the US economy that have been used in modeling the impacts of energy and environmental policies in EMF-12, aproject of the Energy Modeling Forum at Stanford University. The classic formulation of intertemporal general equilibrium theory is by Lindahl(1939). A detailed survey of intertemporal general equilibrium theory is presented by Stokey and Lucas (1989).

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of energy and environmental policies 9. We begin our discussion of intertemporal general equilibrium modeling by focusing on the econometric methodology that is required. At the outset of our discussion it is essential to recognize that the predominant tradition in general equilibrium modeling does not employ econometric methods. This tradition originated with the seminal work of Leontief (1951), beginning with implementations of the static input-output model over half a century ago. Leontief (1953) gave a further impetus to the development of general equilibrium modeling by introducing a dynamic input-output model. This model can be regarded as an important progenitor of the intertemporal general equilibrium models described below. Empirical work associated with input-output analysis is based on parametrizing technology and preferences from a single inter-industry transactions table. The usefulness of the 'fixed coefficients' assumption that underlies input-output analysis is hardly subject to dispute. By linearizing technology and preferences Leontief solved at one stroke the two fundamental problems that arise in practical implementation of general equilibrium models. First, the resulting general equilibrium model can be solved as a system of linear equations with constant coefficients. Second, the unknown parameters describing technology and preferences can be estimated from a single data point. The data required are now available for all countries that have implemented the United Nations (1968) System of National Accounts. The input-output approach was applied to modeling of environmental policy by Ayres and Kneese (1969) and Kneese, Ayres and d7Arge (1970). Their work was especially notable for introducing a 'materials balance' approach based on conservation of mass for all economic activities. Materials balances are useful in bringing out the fact that material not embodied in final products must be embodied in emissions of pollutants. These emissions accumulate as solid waste or enter the atmosphere or the hydrosphere and reduce air or water quality. In implementing the materials balance approach, the assumption that pollutants are generated in fixed proportions to output is a natural complement to the fixed coefficients assumption of Leontief's input-output model lo. The most detailed implementation of the input-output approach to modeling energy and environmental policy is the United Nations Study presented by Leontief, Carter and Petri (1977). In this study the world economy is divided among fifteen regions, including four regions representing industrialized countries - North America, Western Europe, Japan, and Oceania - and eleven regions We describe possible approaches to calculation of distributional effects in Section 6, below. Detailed surveys of fixed-coefficientinput-utput models applied to environmental policy, including those of Leontief (1970) and Leontief and Ford (1973), are presented by Forsund (1985) and James, Jansen and Opschoor (1978). The 'materials balance' approach is considered in the context of the Arrow-Debreu theory of general equilibrium by Maler (1974, 1985). lo


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representing countries at various stages of development. A fixed-coefficients inputoutput model with 45 industrial sectors and including resource requirements and pollution control activities is constructed for each region. The growth rate of GDP for each region is taken to be exogenously given. The regions are treated separately and also linked through international trade. One of the principal conclusions is that the availability of resources and requirements for pollution control do not pose insurmountable obstacles to growth of the developing countries. One perspective on the United Nations Study is that it provides a response to the Meadows (1972) Report, Limits to Growth, for the Club of Rome. This Report employs simulations based on systems dynamics to demonstrate the possibility of exhaustion of resources and inability to control pollution as barriers to growth of industrialized and developing countries. The viewpoint of the United Nations Study is reflected in the World Commission on Environment and Development (1987) Report, Our Common Future, also known as the Brundtland Report. This Report argues that economic development and maintenance of environmental quality are compatible through "sustainable development7'l ' . The obvious objection to the fixed-coefficients approach to modeling energy and environmental policies is that these policies induce changes in the input-output coefficients. In fact, the objective of pollution control regulations is to induce producers and consumers to substitute less polluting inputs for more polluting ones. A prime example is the substitution of low-sulfur coal for high-sulfur coal by electric utilities and manufacturing firms to comply with regulations on sulfur dioxide emissions. Another important example is the shift from leaded to unleaded motor fuels in order to clean up motor vehicle emissions. The first successful implementation of an applied general equilibrium model without the fixed-coefficients assumption of input-output analysis is due to Johansen (1960). Johansen retained the fixed-coefficients assumption in modeling demands for intermediate goods, but employed linear logarithmic or CobbDouglas production functions in modeling the substitution between capital and labor services and technical change. He replaced the fixed-coefficients assumption for household behavior by a system of demand functions originated by Frisch (1959). Finally, he developed a method for solving the resulting nonlinear general equilibrium model for growth rates of sectoral output levels and prices and implemented this model for Norway. Johansen's multi-sectoral growth (MSG) model is another important progenitor for the models of intertemporal general equilibrium we describe below. Linear logarithmic production functions have the obvious advantage that the capital and labor input coefficients respond to price changes. Furthermore, the relative shares of these inputs in the value of output are fixed, so that the unknown " The concept of sustainable development is discussed by the World Bank (1992). Meadows (1992) provides an update of the earlier Club of Rome Report.

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parameters characterizing substitution between capital and labor inputs can be estimated from a single data point. In describing producer behavior Johansen employed econometric methods only in estimating constant rates of technical change. Similarly, the unknown parameters of the demand system proposed by Frisch can be determined from a single data point, except for one parameter that must be determined econometrically. The essential features of Johansen's approach have been preserved in the applied general equilibrium models surveyed by Bergman (1985) and Fullerton, Henderson and Shoven (1984). The unknown parameters describing technology and preferences in these models are determined by 'calibration' to a single data point. Data from a single inter-industry transactions table are supplemented by a small number of parameters estimated econometrically. The obvious disadvantage of this approach is that highly restrictive assumptions on technology and preferences are required to make calibration feasible '2. Almost all general equilibrium models retain the fixed-coefficients assumption of Leontief and Johansen for modeling demand for intermediate goods. However, this assumption is directly contradicted by massive evidence of price-induced energy conservation in response to higher world energy prices beginning in 1973 13. Reductions in energy utilization induced by the successive energy crises of the 1970s and the higher level of energy prices prevailing in the 1980s has been documented in great detail by Schipper and Meyers (1992). This extensive survey covers nine OECD economies, including the USA, for the period 1970-1989, and describes energy conservation in residential, manufacturing, other industry, services, passenger transport, and freight transport sectors. Reductions in energyoutput ratios for these activities average 15-20% 14. Fixed coefficients for intermediate goods also rule out a very important response to environmental regulations by assumption. This is the introduction of special devices to treat wastes after they have been generated, substituting capital in the form of pollution control devices for other inputs such as energy or materials. This is commonly known as end-of-pipe abatement and is frequently the method of choice for retrofitting existing facilities to meet environmental standards. A typical example is the use of electrostatic precipitators to reduce the emissions of particulates from combustion. Regulations promulgated in the US by the

l 2 Johansen's approach has been used in modeling environmental policies for Norway by Forsund and Strom (1976). We discuss the calibration method for parametrization in more detail below. l 3 We describe reductions in energy utilization after 1973 for US industries in Section 4, below. Longrun trends in US energy utilization have been analyzed by Schurr and Netschert (1962) and Schurr, Burwell, Devine and Sonenblum (1990). l 4 Price-induced energy conservation in the USA has been analyzed in greater detail by Hogan and Jorgenson (1991), Jorgenson (1981, 1984b), Jorgenson and Fraumeni (1981), and Jorgenson and Stoker (1984).


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Environmental Protection Agency effectively encourage the use of this approach by setting standards for emissions on the basis of the 'best available technology'. Another important limitation of the Johansen approach is that changes in technology are taken to be exogenous. This rules out another important method for pollution abatement by assumption. This is the introduction of changes in technology by redesigning production methods to reduce emissions. An important example is the introduction of fluidized bed technology for combustion, which results in reduced emissions. Gollop and Roberts (1983, 1985) have constructed a detailed econometric model of electric utility firms based on a cost function that incorporates the impact of environmental regulations on the cost of producing electricity and the rate of productivity growth. They conclude that the annual productivity growth of electric utilities impacted by more restrictive emissions controls declined by 0.59 percentage points over the period 1974-1979. This resulted from switching technologies to meet new standards for air quality. To represent technologies and preferences that overcome the limitations of the Johansen approach, it is essential to employ econometric methods. A possible extension of Johansen's approach would be to estimate elasticities of substitution between capital and labor inputs along the lines suggested by Arrow, Chenery, Minhas and Solow (1961). Unfortunately, constant elasticity of substitution (CES) production functions cannot easily encompass substitution among capital, labor, energy, and materials inputs. As Uzawa (1962) and McFadden (1963) have shown, constant elasticities of substitution among more than two inputs imply, essentially, that elasticities of substitution among all inputs must be the same. An alternative approach to the implementation of econometric models of producer behavior is to generate complete systems of demand functions for inputs of capital, labor, energy, and materials inputs in each industrial sector. Each system gives quantities of inputs demanded as functions of prices and output. This approach to modeling producer behavior was originated by Berndt and Jorgenson (1973) and employed in modeling energy policy and US economic growth by Hudson and Jorgenson (1974). The approach was extended to incorporate endogenous technical change by Jorgenson and Fraumeni (1981) I s . A model combining substitution among capital, labor, energy and materials inputs and endogenous technical change is utilized in modeling environmental policy and US economic growth by Jorgenson and Wilcoxen (1990b). The econometric approach for modeling producer behavior has been implemented for Norway by Longva and Olsen (1983). The results are utilized in modeling energy policy and Norwegian economic growth by Longva, Lorentsen and Olsen (1983). An updated and revised version of this model has been Alternative models of endogenous productivity growth are surveyed by Jorgenson (1984a, 1990b). A comprehensive survey of models of producer behavior constructed along the lines of Berndt and Jorgenson (1973) is presented by Jorgenson (1986).

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employed in assessing the impact of restrictions on carbon dioxide emissions on Norwegian economic growth by Glomsrod, Vennemo and Johnsen (1992). Hazilla and Kopp (1986) have constructed an econometric model of producer behavior for the same thirty-five sectors of the US economy analyzed by Jorgenson and Fraumeni (1981). Hazilla and Kopp (1990) use this model in measuring the costs of US environmental regulationsI6. As in the descriptions of technology by Leontief and Johansen, production in the econometric approach is characterized by constant returns to scale in each sector. As a consequence, commodity prices can be expressed as a function of factar prices, using the non-substitution theorem of Samuelson (1951). This greatly facilitates the solution of the econometric general equilibrium models constructed by Hudson and Jorgenson (1974) and Jorgenson and Wilcoxen (1990b), since the non-substitution theorem permits a substantial reduction in dimensionality of the space of prices to be determined by the model. The corresponding feature of the Johansen approach has been exploited in applications of the 'fixed point7methods for solving nonlinear general equilibrium models pioneered by Scarf (1973,1984). Similarly, econometric models of consumer behavior can be used to overcome the limitations of the Frisch (1959) model employed by Johansen. Models stemming from the path-breaking contributions of Schultz (1938), Stone (1954), and Wold (1953) consist of complete systems of demand functions, giving quantities demanded as functions of prices and total expenditure. These models incorporate the restrictions implied by the theory of consumer behavior by introducing the notion of a representative consumer. Aggregate demand functions are treated as if they could be generated by a single utilizing maximizing individual. Per capita quantities demanded can be expressed as functions of prices and per capita expenditure. The obvious difficulty with the representative consumer approach is that aggregate demand functions can be expressed as the sum of individual demand functions. Aggregate demand functions depend on prices and total expenditures, as in the theory of individual consumer behavior. However, these demand functions depend on individual total expenditures rather than aggregate expenditure. If individual total expenditures are allowed to vary independently, models based on a representative consumer imply restrictions that severely limit the dependence of individual demand functions on individual expenditure. The simplest form of restrictions required for the representative-consumer approach is to require that preferences are identical and homothetic for all consumers. This set of restrictions is implicit in the linear logarithmic demand l 6 The same sectoral disaggregation has been used by the Congressional Budget Office (1990) in analyzing the effects of a carbon tax on US economic growth. Surveys of the literature on the econometric approach to general equilibrium modeling are given by Bergman (1990), Hazilla and Kopp (1990), and Jorgenson (1982). Bergman provides detailed comparisons with alternative approaches to general equilibrium modeling.


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systems employed by Stone (1954) and Wold (1953). Homothetic preferences are inconsistent with well-established empirical regularities in the behavior of individual consumers, such as Engel's Law, which states that the proportion of expenditure devoted to food is a declining proportion of total expenditure. Identical preferences for individual households are inconsistent with empirical findings that expenditure patterns depend on demographic characteristics of individual consumers 1 7 . A weaker set of restrictions for the existence of a representative consumer has been presented by Gorman (1953), requiring that quantities consumed are linear in total expenditure with slopes that are identical for all consumers. Muellbauer (1975) and Lewbel (1989) have presented generalizations of these conditions, requiring that preferences are identical for all consumers, but that quantities consumed are not necessarily linear functions of expenditure la. Econometric models of aggregate consumer behavior based on the theory of a representative consumer have been constructed by Berndt, Darrough and Diewert (1977) and Deaton and Muellbauer (1980a,b). The econometric general equilibrium models of Glomsrud, Vennemo and Johnsen (1992) and Hazilla and Kopp (1990) employ the representative consumer approach in modeling consumer behavior. An alternative approach to econometric modeling of aggregate consumer behavior is provided by Lau's (1982) theory of exact aggregation. This approach makes it possible to dispense with the notion of a representative consumer. Systems of aggregate demand functions depend on statistics of the joint distribution of individual total expenditures and attributes of individuals associated with differences in preferences. One of the most remarkable features of models based on exact aggregation is that systems of demand functions for individuals can be recovered uniquely from the system of aggregate demand functions. This makes it possible to exploit all the implications of the economic theory of the individual consumer in constructing an econometric model of aggregate consumer behavior. The implementation of an econometric model of aggregate consumer behavior based on the theory of exact aggregation has been carried out by Jorgenson, Lau and Stoker (1982). Their approach requires time-series data on prices and aggregate quantities consumed. This approach also requires cross section data on individual quantities consumed, individual total expenditures, and attributes of individual households, such as demographic characteristics 1 9 . By contrast, the nonReviews of the literature are presented by Deaton and Muellbauer (1980b) and Jorgenson (1990a). these restrictions have been discussed by Jorgenson (1984a, 1990a) and Kirman (1992). l 9 The theory of exact aggregation is discussed by Jorgenson, Lau and Stoker (1982) and Lau (1982). Econometric models based on the theory of exact aggregation are surveyed by Jorgenson (1990a) and Stoker (1993). l7

'* The implications of

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econometric approaches of Leontief and Johansen require only a single data point for prices, aggregate quantities consumed, and aggregate expenditure. We continue our presentation of econometric modeling of the impact of energy and environmental policies by considering the intertemporal general equilibrium model of the US economy constructed by Jorgenson and Wilcoxen (1990b). The general equilibrium model of production employed by Jorgenson and Wilcoxen is based on the model originated by Jorgenson and Fraumeni (1981). This model includes systems of demand functions for capital, labor, energy, and materials inputs and a model of endogenous productivity growth for each of thirty-five sectors of the US economy. The Jorgenson-Wilcoxen model incorporates a model of aggregate consumer behavior based on the exact aggregation approach of Jorgenson, Lau and Stoker (1982). This model dispenses with the notion of a representative consumer employed in previous econometric models of aggregate consumer behavior. The model includes a system of demand functions for five commodity groups - energy, food, nondurable goods, capital services, and other services. We outline the Jorgenson-Wilcoxen model in more detail in Section 2, below. Jorgenson and Wilcoxen (1990a) have presented a highly disaggregated model of the impact of environmental regulations on US economic growth. Detailed data on costs of compliance imposed on individual industries by these regulations are utilized in modeling the impact of environmental policy. Alternative regulatory policies generate different costs of production for these industries and different time paths of economic growth for the US economy. The industries most affected by environmental regulations are the motor vehicles and coal mining industries. These regulations have led to a substantial decline in the national product, amounting to a reduction of almost 2.6% in the long run. This reduction is produced by an even more severe decline in capital accumulation, illustrating the importance of the dynamics of adjustment of economic growth to its long-run trend. We outline the results of this study in Section 3, below. We have already summarized the studies of environmental policies for control of global warming by Nordhaus (1992) and Manne and Richels (1992). A very significant issue in modeling the impact of these policies is the price responsiveness of greenhouse gas emissions to changes in energy prices. In Section 4 we present an analysis of a 'natural experiment' provided by variations in energy prices during the 1970s and 1980s. Over the period 1972-1987 US emissions of carbon dioxide were stabilized by price-induced energy conservation. A major portion of the corresponding reduction in the growth rate of national output - almost two-thirds - can be attributed to oil price surges that took place in 1973-1975 and 1978-1980. The change in the oil price levels between 1972 and 1987 accounted for about one-third of the slowdown in the growth of output. A more detailed analysis of the stabilization of carbon dioxide emissions is given by Jorgenson and Wilcoxen (1992b).


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Finally, we turn our attention to the cost of controlling US carbon dioxide emissions. For this purpose we summarize the results of a study of these costs by Jorgenson and Wilcoxen (1992a) in Section 5. Jorgenson and Wilcoxen have considered three alternative sets of restrictions on carbon dioxide emissions stabilizing these emissions at 1990 levels, curtailing emissions by 20% of 1990 levels during the period 1990-2005 and stabilizing thereafter, and allowing emissions to increase through the year 2000 and stabilizing at that level. The costs of stabilization at 1990 levels amount to a loss in the national product of half a percentage point. However, these costs rise at an increasing rate as emissions targets are made more restrictive. In Section 6 we provide an overall evaluation of the econometric approach for modeling the impact of energy and environmental policies.

2. An overview of the model

Our analysis of the impact of energy and environmental policies is based on simulations of US economic growth, using an intertemporal general equilibrium model of the US economy. This model has been implemented econometrically by Jorgenson and Wilcoxen (1990b). In this section we outline the model, emphasizing features that are critical in assessing policy impacts. The starting point is a system of national accounts for the USA developed by Jorgenson (1980) and implemented by Fraumeni and Jorgenson (1980). This accounting system provides the time-series data needed for econometric modeling of producer and consumer behavior 20. The critical innovation in the accounting system implemented by Fraumeni and Jorgenson is the development of accounts for investment, capital stock, and capital services and the corresponding prices. These accounts incorporate a backwardlooking accumulation equation for capital, linking the current flow of capital services to all past investments. They also include a forward-looking equation for the price of capital services, linking the price of investment goods to all future prices of capital services. Equations of this type are essential for modeling the dynamics of economic growth. The capital accounts employed by Jorgenson and Wilcoxen are described in detail by Jorgenson (1990b).

Conventional systems of national accounts, such as the United Nations (1968) System of National Accounts and the US National Income and Product Accounts are unsatisfactory for modeling purposes, since they do not successfully integrate capital accounts with income and production accounts. The system of US national accounts presented by Fraumeni and Jorgenson (1980) disaggregates the accounts constructed by Christensen and Jorgenson (1973) to the industry level. The Christensen-Jorgenson system is used in modeling the US economy by Jorgenson and Yun (1990).

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D. W Jorgenson and l?J. Wilcoxen

2.1. Producer behavior We have constructed submodels for each of four sectors of the US economy: business, household, government, and the rest of the world. Since many of the most important features of our model are contained in our submodel of the business sector, we begin our presentation with this sector. Energy and environmental policies affect different industries in very different ways. For example, fossil fuel combustion results in emissions of pollutants, so that modeling the response to pollution control policies requires distinguishing among industries with different energy intensities. Accordingly, we have subdivided the business sector into the thirty-five industries shown in Table 2.1. Each of these corresponds, roughly, to a two-digit industry in the Standard Industrial Classification. This level of industrial disaggregation makes it possible to measure the impact of alternative policies on relatively narrow segments of the US economy. We have also divided the output of the business sector into thirty-five commodities, each one the primary product of one of the industries. Many industries produce secondary products as well, for example, the textile industry produces both textiles and apparel, so that we have allowed for joint production. Each commodity is allocated between deliveries to intermediate demands by other industries and deliveries to final demands by households, governments, and the rest of the world. We represent the technology of each industry by means of an econometric model of producer behavior. In order to estimate the unknown parameters of these production models we have constructed an annual time series of inter-industry transactions tables for the US economy for the period 1947 through 1985". The data for each year are divided between a use table and a make table. The use table shows the quantities of each commodity - intermediate inputs, primary factors of production, and noncompeting imports - used by each industry and final demand category22.The make table gives the amount of each commodity produced by each industry. In the absence of joint production this would be a diagonal array. The organization of the use and make tables is illustrated in Figures 2.1 and 2.2; Table 2.2 provides definitions of the variables appearing in these figures. The econometric method for parametrizing our model stands in sharp contrast to the calibration method used in previous general equilibrium modeling. Calibration Inter-industry transactions tables for the US are derived from those of the Bureau of Economic Analysis (1984). Income data are from the US national income and product accounts, also developed by the Bureau of Economic Analysis (1986). The data on capital and labor services are based on those of Jorgenson, Gollop and Fraumeni (1987). Our data integrate the capital accounts described by Jorgenson (1990b) with an accounting system based on the United Nations (1968) System of National Accounts. Details are given by Wilcoxen (1988), Appendix C. 22 Noncompeting imports are imported commodities that are not produced domestically. 21


Table 2.1 Industry classification Number

Description Agriculture, forestry and fisheries Metal mining Coal mining Crude petroleum and natural gas Nonmetallic mineral mining Construction Food and kindred products Tobacco manufactures Textile mill products Apparel and other textile products Lumber and wood products Furniture and fixtures Paper and allied products Printing and publishing Chemicals and allied products Petroleum refining Rubber and plastic products Leather and leather products Stone, clay and glass products Primary metals Fabricated metal products Machinery, except electrical Electrical machinery Motor vehicles Other transportation equipment Instruments Miscellaneous manufacturing Transportation and warehousing Communication Electric utilities Gas utilities Trade Finance, insurance and real estate Other services Government enterprises

involves choosing parameters to replicate the data for a particular year 23. Almost all general equilibrium models employ the assumption of fixed 'input-output' coefficients for intermediate goods, following Johansen (1960). This allows the See Mansur and Whalley (1984) for more detail on the calibration approach. An example of this approach is Borges and Goulder (1984), who present a model of energy policy calibrated to data for the year 1973. A more recent example is given by Whalley and Wigle (1991), who present a multi-region model of the world economy and analyze the consequences of imposing an international carbon tax.

23


USE

C

I

G

X

M

N

K L

B

T R

Fig. 2.1. Organization of the use table.

Fig. 2.2. Organization of the make table.

ratio of the input of each commodity to the output of an industry to be calculated from a single use table like the one presented in Figure 2.1; however, it rules out substitution among intermediate goods, such as energy and materials, by assumption. It also ignores the distinction between industries and commodities and rules out joint production.


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Table 2.2 Make and use table variables Variable

Description

Industry-commodity flows USE Commodities used by industries (use table) MAKE Commodities made by industries (make table) Final demand columns C Personal consumption I Gross private domestic investment Government spending Exports Imports Value added rows N K L T R

Noncompeting imports Capital Labor Net taxes Rest of the world

Commodity and industry output 0 Commodity output D Industry output Other variables B V F

Value added sold directly to final demand Total value added Total final demand

The econometric approach to parametrization has several advantages over the calibration approach. First, by using an extensive time series of data rather than a single data point, we can derive the response of production patterns to changes in prices from historical experience. This is particularly important for the analysis of energy and environmental policies, since energy prices have varied widely and environmental policies have changed substantially during our sample period. The calibration approach imposes responses to these changes through the choice of functional forms. For example, elasticities of substitution are set equal to zero by imposing the Leontief functional form used in input-output analysis, or to unity by imposing the Cobb-Douglas functional form employed by Johansen (1960). More generally, all elasticities of substitution are set equal to each other by imposing the constant elasticity of substitution functional form24. A second advantage of the econometric approach is that parameters estimated from time series are much less likely to be affected by the peculiarities of Surveys of functional forms employed in modeling producer behavior have been presented by Fuss, McFadden and Mundlak (1978), Jorgenson (1986), and Lau (1986).

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the data for a particular time period. By construction, parameters obtained by calibration are forced to absorb all the random errors present in the data for a single benchmark year. This poses a severe problem when the benchmark year is unusual in some respect. For example, parameters calibrated to the year 1973 would incorporate into the model all the distortions in energy markets that resulted from price controls and the rationing of energy during the first oil crisis. Econometric parametrization greatly mitigates this problem by reducing the influence of disturbances for a particular time period. Empirical evidence on substitutability among inputs is essential in analyzing the impact of environmental and energy policies. If it is easy for industries to substitute among inputs, the effects of these policies will be very different than if substitution were limited. Although calibration avoids the burden of data collection required by econometric estimation, it also specifies the substitutability among inputs by assumption rather than relying on empirical evidence. This can easily lead to substantial distortions in estimating the effects of energy and environmental policies. An important feature of our production submodel is that an industry's productivity growth can be biased toward some inputs and away from others. Biased productivity growth is a common feature of historical data but is often excluded from models of production. By allowing for biased productivity growth, our model provides a separation between price-induced reductions in energy utilization and those resulting from changes in technology 2 5 . In addition, the rate of productivity growth for each industry in our model is determined endogenously as a function of input prices. Other econometric models for analyzing energy and environmental policies, for example, Hazilla and Kopp (1990), Hudson and Jorgenson (1974), and Longva, Lorentsen and Olsen (1983), exclude biases in productivity growth and take the rate of productivity growth to be exogenous. Another important feature of our production submodel is that we allow for joint production. Accordingly, the price of an industry's output may differ from the price of its primary product. Recall our example that the textile industry produces both textiles and apparel, so that the price of the industry's output is a function of the prices of both the textile and apparel commodities. To capture this, we include a price function for each commodity, giving the price of that commodity as a function of the prices of the outputs of all industries that produce it. We parametrize these commodity price functions econometrically, using data from the make table shown in Figure 2.2. Our models of producer behavior are based on two-stage allocation. At the first stage the value of each industry's output is allocated among four commodity groups - capital, labor, energy, and materials. We take the price of output to be a Dean (1992) has drawn attention to the fact that this separation is the key to differences in estimates of the costs of reducing carbon dioxide emissions among alternative models of the world economy.

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homothetically separable function of the prices of commodities within each of these groups. This price function must be homogeneous of degree one, non-decreasing, and concave in the input prices. These restrictions are incorporated into the system of input demand functions that we construct for each industry 26. At the second stage of our production models the value of the energy and materials aggregates is allocated among individual commodities. The price of energy is a function of the prices of coal, crude petroleum, refined petroleum, electricity, and natural gas. In order to limit the number of estimated parameters in the materials aggregate, we employ a hierarchical tier structure of ten subaggregates *'. We derive demands for inputs of capital and labor services and the thirty-five intermediate goods into each industry from the price function for that industry. To present our production model more formally, we first require some notation. Let the thirty-five industries be indexed by i. We denote the quantity of output from industry i by Zi, and the quantities of inputs of capital, labor, energy and materials Similarly, we denote the price of output from industry i by qi, by Ki, Li, Eiand Mi. and the prices of the four inputs bypk,pt,pL andp&. Further, we define the shares of inputs in the value of output by:

We find it convenient to define the vector of input value shares for industry i as follows:

Similarly, we define the vector of logarithms of input prices faced by the industry as:

We assume that industry i allocates the value of its output among the four inputs in accord with the translog price function: lnqi =a6 + lnpf a;

+ i lnp[ B;,,

+ a: gi(t) lnpi + lnpi pjt gi(t) + i/5jtgi(t).

(2-1)

A more detailed discussion of our econometric methodology is presented by Jorgenson (1984a, 1986). Two-stage allocation in the context of producer behavior is discussed in more detail by Jorgenson (1986) and Blackorby, Primont and Russell (1978). The tier structure for our models of producer behavior is described by Wilcoxen (1988), Appendix A.

26

27


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The scalars a;, a;, P:,, the vectors a:, and the matrix Bip7 are unknown parameters that differ among industries, reflecting differences in technology. The function gi(t) contains additional unknown parameters and will be discussed in more detail below. We can derive the value shares of inputs to industry i by differentiating the price function (2.1) with respect to logarithms of the input prices to obtain

The elements of Bip can be interpreted as share elasticities and represent the degree of substitutability among inputs. These parameters capture the price are responsiveness of demands for energy and other inputs. The elements of biases of productivity growth and represent the impact of changes in productivity on the value shares of the inputs 28. These parameters incorporate 'autonomous' improvements in the efficiency of utilization of energy and other inputs. By fitting both sets of parameters to historical data we are able to separate price-induced changes in input coefficients from those that result from changes in technology. The limiting behavior of the functiongi(t) presents a potential problem for longrun simulations. In order for the price function to be homogeneous of degree one, must sum to zero. If any of the elements is nonzero, there the elements of will be at least one negative element. Unless gi(t) remains bounded as t becomes large, the value share of the corresponding input will eventually become negative 29. Accordingly, we take gi(t) to be logistic in form:

Pi,

Pi,

where the scalars pi and ~i are unknown parameters which differ among industries. In the limit each of these functions goes to unity. Although this specification does not guarantee that the input value shares remain positive since extremely large elements of pi, could still cause problems, we have found that it does so in practice. Equation (2.2) also solves a second potential problem in long-run simulations. If productivity grows indefinitely, the existence of a balanced growth equilibrium requires that the rates of growth must eventually become the same for all industries. Otherwise, the industry with the highest rate of productivity growth would eventually come to dominate the economy. In our model, productivity growth is limited. The translog price function was introduced by Christensen, Jbrgenson and Lau (1971, 1973). For further discussion of share elasticities and biases of productivity growth, see Jorgenson (1986). 29 This is often overlooked in modeling producer behavior, where it is customary to take these functions to be linear in time: gi(t) = t. See, for example, Jorgenson (1984a). 28


1287

To show this we differentiate eq. (2.1) with respect to time to obtain the endogenous rate of productivity growth in industry i, say vf :

From the logistic formulation (2.2) it is clear that gi(t) goes to zero in the limit, so that the level of productivity in each industry approaches a constant. This formulation has the advantages of representing productivity growth during the sample period in a flexible way, while producing long-run behavior of the economy consistent with balanced growth equilibrium. The demand side of our model can be divided between intermediate and final demands for the thirty-five commodity groups, capital and labor services, and noncompeting imports presented in the use table (Figure 2.1). Our models of producer behavior determine value shares for inputs of commodities, primary factors of production, and noncompeting imports into each industry. These value shares incorporate an income-expenditure identity for the industry, since the value of output must be equal to the value of all inputs. The value shares determine inputs per unit of output as functions of the input and output prices. The inputoutput coefficients are multiplied by the output of the industry to obtain the input quantities. These quantities are added over the thirty-five industries to obtain total intermediate demands for each commodity group, capital and labor services, and noncompeting imports. In summary, our model of producer behavior consists of two parts. The first is a set of thirty-five industry price functions and the second is a set of thirty-five commodity price functions. We have described how the industry price functions determine input demands and output prices in detail. The commodity price functions link output prices to commodity prices and determine the allocation of the output of each commodity among industries. The industry price functions account for the industry columns in the use table (Figure 2.1), and the commodity price functions for the commodity columns in the make table (Figure 2.2). We turn next to modeling the final demand categories. 2.2. Consumer behavior

Energy and environmental policies have different impacts on different households. For example, the imposition of a tax on energy would affect the relative prices faced by consumers. An increase in the price of energy resulting from the tax would adversely affect those consumers who devote a larger share of total expenditure to energy. To capture these differences among households, we have subdivided the household sector into demographic groups that differ by characteristics such as family size, age of head, region of residence, race, and urban versus rural location.


1288

We treat each household as a consuming unit, so that the household behaves like an individual maximizing a utility function. We represent the preferences of each household by means of an econometric model of consumer behavior. Our models of consumer behavior incorporate timeseries data on personal consumption expenditures from the annual inter-industry transactions tables for the US economy represented in Figure 2.1. The econometric approach for parametrization enables us to derive the response of household expenditure patterns to changes in prices from historical experience. Empirical evidence on substitutability among goods and services by households is essential in analyzing the impact of energy and environmental policies. If it is easy for households to substitute among commodities, the effects of these policies will be very different than if substitution were limited. The econometric approach to modeling consumer behavior has the same advantages over the calibration approach as those we have described for modeling producer behavior. An additional feature of our models of consumer behavior is that they incorporate detailed cross section data on the impact of demographic differences among households and levels of total expenditure on household expenditure patterns. We do not require that consumer demands are homothetic, so that patterns of individual expenditure change as total expenditure varies, even in the absence of price changes. This captures an important characteristic of cross section observations on household expenditure patterns that is usually ignored in general equilibrium modeling. Finally, we aggregate over individual demand functions to obtain a system of aggregate demand functions. This makes it possible to dispense with the notion of a representative consumer. Our econometric model of consumer behavior is based on two-stage allocation. We can summarize the representation of consumer behavior in terms of an indirect utility function for each household. At the first stage the household allocates total expenditure among five commodity groups - energy, food, nondurable goods, capital services, and other services. The indirect utility function must be homothetically separable in the prices of the commodities within each of these groups. This function must also be homogeneous of degree zero in prices faced by the household and total expenditure on all commodities. Finally, the function must be non-increasing in the prices, non-decreasing in total expenditure, and quasi-convex in prices and expenditure. These restrictions are incorporated into the system of demand functions that we construct for each household 30. At the second stage of our model of consumer behavior, expenditure on each of the five commodity groups is allocated among labor and capital services and the individual commodities included in our model according to a hierarchical tier structure of demands. In order to keep the number of estimated parameters --

--

The particular form of our model follows Jorgenson and Slesnick (1987). For further discussion of our econometric methodology, see Jorgenson (1984a, 1990a).

30


1289

small we break up these commodity groups into a total of fifteen subaggregates3'. As an example, the price of energy is a function of the prices of coal, refined petroleum, electricity, and natural gas. This results in a submodel of household energy consumption that is analogous to those employed in our econometric models of producer behavior. To present the consumption model more formally, we require some additional notation. First, let the number of households be J, and the individual households be indexed by j 3 2 . Next, let the five commodity groups be indexed by n. We denote the price of commodity group n by p,. Prices are assumed to be the same for all households. Similarly, we denote the quantity of commodity group n demanded by the household j byx,. In addition, if the total expenditure of consumer j is Y,, the following budget constraint must hold:

n=l

To allow for differences in preferences among households, we allow the indirect utility function to depend on a vector of attributes denoted Aj. Further, we define the expenditure share of consumer j on commodity n by:

We find it convenient to define the vector of expenditure shares for consumerj as follows:

Similarly, we define the vector of logarithms of prices faced by all consumers as:

Finally, we define the ratios of these prices to total expenditures for consumer j as: ln

yi

= (In P -,I ln P2 -,.

Y,

Y,

. . ,ln P5

-)I.

Yi

Two-stage allocation in the context of consumer behavior is discussed in more detail by Jorgenson, Slesnick and Stoker (1987,1988) and Blackorby, Primont and Rule11 (1978). The tier structure for our model of consumer behavior is described by Wilcoxen (1988), Appendix A. 32 The number of households varies over the sample period 1947 through 1985, but is approximately one hundred million at the end of the period. 31

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D. W Jorgenson and ELI. Wilcoxen

We assume that household j allocates its total expenditure among the five commodity groups in accord with the translog indirect utility function:

The vector q,and the matrices Bpp and BpA are unknown parameters that are the same for all households. The vector of attributes A, incorporates differences in preferences among households. The elements of this vector are one-zero dummy variables that classify households by the demographic characteristics - family size, age of head, region of residence, race, and urban versus rural location. Crossclassifying households by these characteristics, we distinguish among a total of 672 different household types 33. From the indirect utility function (2.3), we can derive the expenditure shares of household j using the logarithmic form of Roy's identity. This produces the following:

where the denominator Bj takes the form Bj = L ' U + ~ L ' B In~P ~ +L'B~~A,, Yj and L is a vector of ones. To derive a model of aggregate consumer behavior we assume that aggregate demand functions can be constructed from individual demand functions by exact aggregation. This requires that individual expenditure shares are linear in functions of the attributes Aj and total expenditure Y , that vary among households. These conditions will be satisfied if and only if the terms involving the attributes and expenditures do not appear in the denominators of the individual expenditure shares. Thus, we require that:

In addition, we find it convenient to employ the normalization

There are seven categories for family size, six categories for age of head, four categories for region of residence, two categories for race, and two categories for urbanversus rural location. For further details, see Jorgenson and Slesnick (1987). The translog indirect utility function was introduced by Christensen, Jorgenson and Lau (1975). Surveys of functional forms employed in modeling consumer behavior have been presented by Blundell(1988), Deaton (1986), and Lau (1986).

33


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The exact aggregation restrictions and the normalization given above imply that the denominators for individual households, Bj, each reduce to B = -1

+ L' Bpp lnp,

where the subscript j is no longer needed, since the denominator is the same for all households. Under these restrictions the individual expenditure shares can be written as W.

1

+ Bpp lnp - Bpp

- - (ap

'-B

L

In Yj + B p Aj) ~

The individual expenditure shares are linear in the logarithm of expenditure, In Yj, and the attributes Aj, so we have satisfied the conditions for exact aggregation. Aggregate expenditure shares, which we denote by w, are obtained by multiplying the individual expenditure shares by total expenditure for each household, Yj, adding over all households, and dividing by aggregate expenditure C Yj to give B

+

ap Bpp lnp - BppL

C Yj lnYj

c yj

The parameters of this system are precisely the same as those of the household demand equations. The parameters Bpp represent the degree of substitutability among commodity groups within the household sector, while the parameters B p ~ reflect the effect of changes in the demographic composition of the population and variations in relative expenditure levels for different demographic groups. Under homogeneity of degree zero, the vector Bpp L captures the impact of changes in the level of aggregate expenditure and its distribution among households. Unless preferences are homothetic, so that the elements of the vector Bpp L are all zero, the composition of personal consumption expenditures varies with the level of aggregate expenditure and its distribution. Potentially, this could lead to a problem for long-run simulations similar to the one we encountered in modeling production. If aggregate expenditure were to increase indefinitely, eventually one of the expenditure shares would become negative. In practice, however, two other features of the model limit the growth of total expenditure. First, industry productivity levels eventually become constant, so that per capita total expenditure converges to a stationary limit. Second, our projection of the future US population also converges to a stationary limit. This implies that aggregate expenditure eventually approaches a steady-state value 34. The system of expenditure shares shown in eq. (2.4) allocates total expenditure to five broad groups of consumer goods. Expenditure on each of these groups is then Projections of population and the long-run behavior of the economy are discussed in greater detail below.

34

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broken down to the level of individual commodities, using a nested tier structure similar to that we have used for production. Given prices and total expenditure, this system allows us to calculate the elements of personal consumption column in the make table of Figure 2.1. We employ the model to represent aggregate consumer behavior in simulations of the US economy under alternative energy and environmental policies. To determine the level of total expenditure we embed our model of personal consumption expenditures in a higher-level system that represents consumer preferences between goods and leisure and between saving and consumption. At the highest level each household allocatesfull wealth, defined as the sum of human and nonhuman wealth, across time periods. We formalize this decision by introducing a representative agent who maximizes an additive intertemporal utility function, subject to an intertemporal budget constraint. The allocation of full wealth is determined by the rate of time preference and the intertemporal elasticity of substitution. The allocation of full wealth to the current time period is full consumption, defined as an aggregate of goods and leisure. Given this allocation, each household proceeds to a second stage of the optimization process - choosing the mix of leisure and goods. We represent household preferences at this stage by means of a representative agent with an indirect utility function that depends on the prices of leisure and goods. We derive demands for leisure and goods as functions of these prices and the wealth allocated to the current period. This implies an allocation of the household's exogenously given time endowment between leisure time and the labor market, so that this stage of the optimization process determines labor supply. Our higher-level model of consumer behavior consists of two parts. At the highest level, we assume each household maximizes an additively separable intertemporal utility function:

whereF, is a per capita full consumption in period t,p is the rate of time preference, N o is the initial population, and n, is the population growth rate in periods. The household chooses the future path of full consumption F to maximize the intertemporal utility function U , subject to an intertemporal budget constraint. This requires that the present value of full consumption is no greater than household wealth. Wealth, in turn, is the present value of future earnings from the supply of capital and labor services, transfers from the government and the imputed value of leisure time. The conditions for optimality can be expressed in the form of an Euler equation. This equation gives the value of full consumption in one period

Ch. 27: Enew, the Environment, and Economic Growth

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in terms of the value of full consumption in the next period, the discount rate, and the rate of population growth 35. The Euler equation is forward-looking, so that the current level of full consumption incorporates expectations about all future prices and discount rates. The solution of our model includes this forward-looking relationship in every time period. The future prices and discount rates determined by the model enter full consumption for earlier periods through the assumption of perfect foresight or rational expectations. Under this assumption full consumption in every period is based on expectations about future prices and discount rates that are fulfilled by the solution of the model. Once each period's full consumption has been found, we proceed to the second part of the representative agent household model. In this stage, the household divides the value of full consumption between personal consumption expenditures and leisure time. This has three effects. First, by determining the value of personal consumption expenditures it completes our model for household sector final demand. Second, the difference between the quantity of leisure consumed and the household's total time endowment determines the quantity of labor supplied36. Third, saving is determined by the difference between current income from the supply of capital and labor services and personal consumption expenditures. Labor market time is allocated among the thirty-five industries represented in the model by equating labor supply with the sum of labor inputs demanded by these industries. In addition, labor services are included in demands for personal consumption expenditures and public consumption. We assume that labor is perfectly mobile among sectors, so that the price of labor services is proportional to a single wage rate for the economy as a whole. The supply price of labor is the numeraire for our price system. We model the household allocation decision by assuming that full consumption is an aggregate of goods and leisure. The share of each in full consumption depends on the price of consumption goods, the price of leisure, and the household's share elasticity between the two. We take the price of consumption goods to be the cost of living index generated from the first stage of our model of consumer behavior by Jorgenson and Slesnick (1990). We take the price of leisure time to be the wage rate less the marginal tax rate on labor income. Our model of consumer behavior allocates the value of full consumption between personal consumption expenditures and leisure time. Given aggregate expenditure on goods and services and its distribution among households, this model then The Euler equation approach to modeling intertemporal consumer behavior was originated by Hall (1978). Our application of this approach to full consumption follows Jorgenson and Yun (1990). 36 We assume the household has a single exogenous endowment of time which can be used for either labor or leisure. During the sample period, 1947 through 1985,we calculate the endowment by adjusting the population for educational attainment; for later periods, we employ the population projections of the Bureau of the Census and our own projections of future educational attainment. 35

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D.W Jorgenson and PJ. Wilcoxen

allocates personal consumption expenditures among commodity groups, including capital and labor services and noncompeting imports. Finally, the income of the household sector is the sum of incomes from the supply of capital and labor services, interest payments from governments and the rest of the world, all net of taxes, and transfers from the government. Savings are equal to the difference between income and consumption, less personal transfers to foreigners and non-tax payments to governments. This is the income-expenditure identity of the household sector. In summary, our model of household behavior consists of three stages. First, it includes a system of expenditure share equations derived from maximization of a household utility function and satisfying conditions for exact aggregation. Second, it includes a higher-level representative agent model that determines the intertemporal allocation of consumption through an Euler equation derived from maximization of an intertemporal utility function. Third, the representative-agent model also allocates full consumption between goods and leisure, determining personal consumption expenditures, labor supply, and saving.

2.3. Investment and capital formation

Our investment model, like our model of saving, is based on perfect foresight or rational expectations. Under this assumption the price of investment goods in every time period is based on expectations of future capital service prices and discount rates that are fulfilled by the solution of the model. In particular, we require that the price of new investment goods is always equal to the present value of future capital services37.The price of investment goods and the discounted value of future rental prices are brought into equilibrium by adjustments in future prices and rates of return. This incorporates the forward-looking dynamics of asset pricing into our model of intertemporal equilibrium. For tractability we assume there is a single capital stock in the economy which is perfectly malleable and mobile among sectors, so that it can be reallocated among industries and final demand categories at zero cost. Under this assumption changes in energy and environmental policy can affect the distribution of capital and labor supplies among sectors, even in the short run. However, the total supply of capital in our model in each time period is perfectly inelastic, since the available stock of capital is determined by past investments. An accumulation equation relates capital stock to investments in all past time periods and incorporates the backward-looking dynamics of capital formation into our model of intertemporal equilibrium. Since capital is perfectly malleable, the price of capital services in each sector is proportional to a single price of capital services for the economy as a whole. This The relationship between the price of investment goods and the rental price of capital services is discussed in greater detail by Jorgenson (1989).

37


1295

rental price balances each period's supply with the sum of demands by all thirty-five industrial sectors together with the demand for personal consumption. Our model gives the price of capital services in terms of the price of investment goods at the beginning and end of each period, the rate of return to capital for the economy as a whole, the rate of depreciation, and variables describing the tax structure for income from capital. The income from capital in each period is equal to the value of capital services. New capital goods are produced from the individual commodities included in our model. Each new unit of capital is an aggregate of commodities purchased for investment in producers' and consumers' durables, residential and nonresidential structures, and inventories. We have represented the technology for production of new capital goods by means of a price function for investment goods. We have estimated the unknown parameters of this investment submodel from time-series data on gross private domestic investment from the annual inter-industry tables for the US economy represented in the use table (Figure 2.1). As with our model of producer behavior, we use a nested tier structure of submodels to capture substitution among different inputs in the construction of new capital 38. The behavioral equations for our model include a system of demand functions for investment goods by business and household sectors. The business sector purchases goods for investments in producers' durables, residential and nonresidential structures, and inventories. The household sector purchases goods for investments in consumers' durables and residential structures. We generate value shares for all types of investment goods from the price function for new capital goods. We use these value shares to allocate the value of investment goods among commodity groups, resulting in the final demands for gross private domestic investment given in the use table (Figure 2.1). Finally, we determine the quantity of each commodity by dividing the value of investment in that commodity by the corresponding price. Our investment submodel allocates gross private domestic investment among commodity groups. The value of this investment must be equal to savings. The balance sheet identity of the household sector sets private wealth equal to the sum of the value of capital stock in the private sector, claims on governments, and claims on the rest of the world. The change in the value private wealth from period to period is the sum of private savings and the revaluation of wealth as the result of inflation. In summary, capital formation in our model is the outcome of intertemporal optimization by producers. Optimization by producers is forward-looking and incorporates expectations about future prices and rates of return. Optimization by consumers is also forward-looking and depends on these same expectations. Both types of optimization are very important for modeling the impact of future energy The tier structure for our model of production for new capital goods is presented by Wilcoxen (1988), Appendix A.

38

1296


and environmental policies. The effects of these policies will be anticipated by producers and consumers, so that future policies will have important consequences for current decisions. 2.4. Government and foreign trade

The two remaining final demand categories in our model are the government and rest of the world sectors. We determine final demands for government consumption from the income-expenditure identity for the government sector 39. The first step is to compute total tax revenue by applying exogenous tax rates to all taxable transactions in the economy. We then add the capital income of government enterprises, which is determined endogenously, and non-tax receipts, determined exogenously, to tax receipts to obtain total government revenue. The key assumption of our submodel of the government sector is that the government budget deficit can be specified exogenously. We add the deficit to total revenue to obtain total government spending. To arrive at government purchases of goods and services, we subtract interest paid to domestic and foreign holders of government bonds together with government transfer payments to domestic and foreign recipients. We allocate the remainder among commodity groups according to fixed shares constructed from historical data. Finally, we determine the quantity of each commodity by dividing the value of government spending on that commodity by its price. Foreign trade has two quite different components - imports and exports. We assume that imports are imperfect substitutes for similar domestic c o r n m ~ d i t i e s ~ ~ . The goods actually purchased by households and firms reflect substitutions between domestic and imported products. The price responsiveness of these purchases is estimated from historical data taken from the import and export columns of the use table (Figure 2.1) in our annual inter-industry transactions tables. In addition, the allocations of domestic supplies between domestic and imported commodities incorporate logistic time trends that capture determinants other than relative prices. The logistic functions approach unity in the limit, so that these trends eventually disappear. Since the prices of imports are given exogenously, the sum of intermediate and final demands implicitly determines quantities of imports of each commodity. Exports, on the other hand, are modeled by a set of explicit foreign demand equations, one for each commodity, that depend on exogenously given foreign Our treatment of government spending differs from the US national accounts in that we have assigned government enterprises to the corresponding indust j wherever possible. We include the remaining purchases by the government sector in final demands by governments. 40 This approach was originated by Armington (1969). See Wilcoxen (1988) and Ho (1989) for further details on our implementation of this approach. 39


1297

income and the foreign price of US exports. Foreign prices are computed from domestic prices by adjusting for subsidies and the exchange rate. The demand elasticities in these equations are estimated from historical data. Our model incorporates the income-expenditure identity of the rest of the world sector. The current account surplus is equal to the value of exports less the value of imports, plus interest received on domestic holdings of foreign bonds, less private and government transfers abroad, and less interest on government bonds paid to foreigners. The key assumption of our submodel of the rest of the world sector is that the current account is exogenous and the exchange rate is endogenous. In summary, final demands by governments are determined by first generating government revenues. Total expenditure is then determined from the incomeexpenditure identity of the government sector. The allocation of this expenditure among commodity groups is given exogenously. Final demands by the rest of the world are determined by modeling import demands and export supplies separately. The current account balance from the income-expenditure identity for the rest of the world sector is taken to be exogenous, so that the exchange rate is determined by the equilibrium of the model.

2.5. Constructing the base case

In order to analyze the impact of changes in energy and environmental policies, we simulate the growth of the US economy with and without changes in these policies41. Our first step is to generate a simulation with no changes in policy that we call the base case. The second step is to change the exogenous variables of the model to reflect a proposed policy change. We then produce a simulation that we refer to as the alternative case. Finally, we compare the two simulations to assess the effects of the change in policy. Obviously, the assumptions underlying the base case are of considerable importance in interpreting the results of our simulations. We conclude this overview by outlining the solution of our model. An intertemporal submodel incorporates backward-looking and forward-looking equations that determine the time paths of capital stock, full consumption, and the price of assets. Given the values of these variables in any time period, an intratemporal submodel determines prices that balance demands and supplies for the thirty-five commodity groups included in the model, capital and labor services, and noncompeting imports. These two submodels must be solved simultaneously to obtain a complete intertemporal equilibrium. To construct a simulation of US economic growth we first require the values of all exogenous variables in every time period. These variables are set equal to Our solution method is described in Wilcoxen (1988), Appendix E. Methods for solving intertemporal general equilibrium models are surveyed in detail by Wilcoxen (1992).

41

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D. W Jorgenson and PL Wilcoxen

their historical values for the sample period, 1947 through 1985. We project the values for all exogenous variables for the post-sample period 1986 through 2050. After 2050 we assume that these variables remain constant at their values in 2050, which allows the model to converge to a steady state by the year 2100. The most important exogenous variables are those associated with US population growth and the corresponding change in the time endowment of the US economy. We project population by age, sex and educational attainment through the year 2050, using demographic assumptions consistent with Bureau of the Census projection^^^. After 2050 we hold population constant, which is roughly consistent with Census Bureau projections. We project educational attainment by assuming that future demographic cohorts will have the same level of attainment as the cohort reaching age 35 in the year 1985. We then transform our population projection into a projection of the time endowment used in our model of the labor market by assuming that relative wages across all categories of workers are constant at 1985 levels. Since capital accumulation is endogenous, these population projections effectively determine the size of the economy in the more distant future. Next, we consider exogenous components of our submodels of the government and rest of the world sectors. We set all tax rates to their values in 1985, the last year in our sample period. We project a gradual decline in the government deficit through the year 2025, after which the deficit is held at four percent of the nominal value of the government debt. This has the effect of maintaining a constant ratio of the value of the government debt to the value of the national product when the inflation rate is four percent, as it is in our steady state. We assume that prices of imports in foreign currency and before tariffs remain constant in real terms at 1985 levels. Our projections of the current account deficit fall gradually to zero by the year 2000. After that we project a small current account surplus sufficient to produce a stock of net claims on foreigners by the year 2050 equal to the same proportion of national wealth as in 1982. Given projections of the exogenous variables of our model of the US economy, we can divide the simulation of US economic growth into two steps. The first step is to construct a stationary solution corresponding to constant values of all exogenous variables. In the stationary solution both full consumption and capital stock are constant. We determine the stationary rate of return from the Euler equation from our model of consumer behavior. Similarly, we determine the stationary level of investment from our accumulation equation for capital stock. We take this stationary solution to be our projection of the US economy for all years after 2100. Our second step in the generation of a simulation is to construct a transition path to the steady state of our model, beginning with the initial level of capital stock. Our breakdown of the US population by age, educational attainment and sex is based on the system of demographic accounts compiled by Jorgenson and Fraumeni (1989). The population projections are discussed in detail by Wilcoxen (1988), Appendix B.

42


1299

For this purpose we combine the solutions of our intertemporal and intratemporal models. Our intertemporal model determines time paths of full consumption, capital stock, and the price of new capital goods. These time paths are consistent with the forward-looking Euler equation from our model of consumer behavior and the asset-pricing equation from our model of investment behavior. The model also determines the time path of capital stock consistent with the backward-looking accumulation equation for capital stock. The solution of our intratemporal model determines prices for outputs of the thirty-five industries as functions of the prices of capital and labor senices and noncompeting imports. These output prices are determined from the industry price functions included in our submodel of the business sector. Given these prices, the domestic supply prices for the thirty-five commodities included in this submodel are determined from the commodity price functions. Finally, the domestic supply price for each commodity is combined with the price of imports to determine the total supply price for each commodity. These prices enter the determination of intermediate demands by all industries and final demands by business, household, government, and rest of the world sectors. The prices of competing and noncompeting imports are given exogenously in every time period. The prices of capital and labor services are determined by balancing demands and supplies for these services. The supply of capital services is determined by previous investments and is taken as given in each period. The supply of labor services is determined endogenously within our model of consumer behavior. This model allocates full consumption in each period between personal consumption expenditures and leisure time. The model also allocates the exogenously given time endowment between the labor market and leisure time. Our intratemporal model also guarantees that income-expenditure identities for all thirty-five industries and the household, government, and the rest of the world sectors are satisfied. These identities imply that gross private domestic investment is equal to private savings plus the current account deficit less the government budget deficit. Since we take the government and current account deficits to be exogenous, changes in gross private domestic investment are driven by changes in private savings. Thus, changes in the rate of capital accumulation depend on changes in private savings and the price of investment goods. It is interesting to contrast the behavior of our model with that of a onesector neo-classical growth model. In the short run the supply of capital in our model is perfectly inelastic since it is completely determined by past investment. In the long run, however, the supply of capital is perfectly elastic, since the rate of return depends only on productivity growth and parameters that describe the intertemporal preferences of the household sector. Thus, in the long run the rate of return in our model is independent of energy and environmental policy, just as in a one-sector neo-classical growth model. Since our model has many sectors, however,

1300


different policies result in different levels of capital intensity, all corresponding to the same rate of return. This is impossible in a one-sector model. In summary, we construct a simulation of US economic growth by solving our model for given values of all exogenous variables in all time periods. First, we solve an intertemporal submodel that contains forward-looking equations determining the time paths of asset prices and full consumption. This submodel also includes a backward-looking equation determining the time path of capital stock from past investments. Given the values of these variables, our intratemporal or oneperiod submodel determines prices that balance demand and supply for the thirtyfive commodity groups included in the model, capital and labor services, and noncompeting imports. We solve the two submodels simultaneously to obtain the full intertemporal equilibrium. 3. The impact of environmental regulation

Our next objective is to assess the impact of environmental regulations introduced in the 1970s and early 1980s. Our approach will be to use the model of Section 2 to simulate the growth of the US economy with and without regulation. We begin by observing that our base case implicitly includes environmental regulation since it is based on historical data. Thus, to determine the effect of regulation we conduct counterfactual simulations in which regulation is removed from the economy. In addition, we decompose the overall effect of regulation into components associated with both pollution control in industry and controls on motor vehicle emissions. We conclude by estimating the overall impact of environmental regulation by eliminating both types of pollution control. Removing environmental regulation produces simulations which differ from the base case at the steady state, at the initial (first-year) equilibrium, and along the transition path between the two. The difference between the new steady state and the base case shows the long-run impact of environmental regulation after the capital stock has adjusted. The difference between the new initial equilibrium and the base case gives the short-run impact of a change in policy before the capital stock can adjust at all. However, since agents in the model have perfect foresight, this initial equilibrium reflects changes along the entire time path of future regulatory policy. Finally, the transition path between the initial equilibrium and the steady state traces out the economy's adjustment to the new environmental policy. In presenting the results of our simulations we begin by quantifying the impact of pollution controls on production costs. We then incorporate these cost changes into the model and run counterfactual simulations. In interpreting the simulation results, we first consider the impact of environmental regulation on the steady state of the economy, concentrating our analysis on a few key variables. Next, we analyze


1301

the transition path of economy from the initial equilibrium to the new steady state. We focus particular attention on the path of capital stock, since it is the most important overall measure of the effect of the change in policy. We also discuss a number of other important variables, including the price of investment goods, the rental price of capital services and the level of the gross national product (GNP). 3.1. Operating costs

We employ data collected by the Bureau of the Census to estimate investment in pollution abatement equipment and operating costs of pollution control activities for manufacturing industries 4? The investment data give capital expenditures on pollution abatement equipment in current prices, while data on operating costs give current outlays attributable to pollution control. These are the actual costs reported by firms and do not include taxes levied as part of the Superfund program44. Figure 3.1 shows the share of pollution abatement in industry costs. For most industries, pollution control accounts for only a small part of total costs. The largest share is for the primary metals industry and it amounts to slightly more than two percent. Our first step in eliminating the operating costs of pollution control is to estimate the share of pollution abatement in the total costs of each industry. For years between 1973 and 1985, we have calculated the actual share from historical data. After 1983, we assume that the share remained constant at its 1983 value. Outside manufacturing, data were only available for electric utilities and wastewater treatment (wastewater treatment is part of the services industry). For both of these industries, data on operating costs and investment expenditures for pollution abatement are available from the Bureau of Economic Analysis 45. For electric utilities, the Bureau of Economic Analysis also estimates the extra cost of burning low-sulfur fuels to comply with sulfur dioxide regulations. The principal low-sulfur fuel used by utilities is low-sulfur coal. In terms of our model, switching from high-sulfur to low-sulfur coal changes the relative proportions of the two products in the output of the coal industry. Since low-sulfur coal is more expensive when transportation costs are included, this increases the price of coal. Eliminating regulations on sulfur emissions would lower the price of coal by permitting substitution toward high-sulfur grades. We model the impact of lifting 43 The Census data come from various issues of the annual publication, Pollution Abatement Costs and Expenditures. A detailed description of our data is given by Wilcoxen (1988), Appendix D. 44 Superfund taxes amounting to more than a billion dollars a year were placed on the petroleum refining and chemicals industries in 1981 and on the primary metals industry in 1986. These may have had a substantial impact on US economic growth, but we do not examine their consequences in this chapter. 45 Further details are given by Wilcoxen (1988), Appendix D.


Agriculture Metal Mining Coal Mining Crude Oil Other Mining Construction Food Products Tobacco Textiles Apparel Lumber, Wood Furniture Paper Printing Chemicals Refining Rubber. Plastic Leather Glass, etc. Primary Metals Fab. Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. Other Services Gov. Enterprises

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Fig. 3.1. Abatement costs by industry

these restrictions by subtracting the differential between high-cost and low-cost coal from the cost of coal p r o d ~ c t i o n ~ ~ . Twenty of the thirty-five industries in our model are subject to pollution abatement regulations. We use the share of abatement costs in total costs for each industry to compute the share of total costs excluding pollution abatement. Let the share for industry i be denoted Xi. Since our data set on pollution abatement ends in 1983,we assume the shares for later years are constant at their 1983values. To simulate the effect of eliminating the operating costs associated with pollution abatement we insert the cost shares Xi into the cost function for each industry. More precisely, we modify the translog price functions as follows: lnqi = In Xi

+

+ a; + lnpf a; + cytgi(t) lnpf B ; ~Inpi

+ lnpi P;, g i ( t ) + ;flit g i ( t ) -

Details of our methodology for estimating cost differentials between high-sulfur and low-sulfur coal are given by Wilcoxen (1988), Appendix D.

46

Ch. 27: Energy, the Environment, arzd Economic Growth

Table 3.1 The effects of removing environmental regulation Variable

Percentage change in steady state ENV

Capital stock Price of investment goods Full consumption Real GNP Rental price of capital Exchange rate

INV

MV

ALL

1.118 - 1.323 0.282 0.752 - 1.358 - 0.392

3.792 - 4.520 0.975 2.592 - 4.635 - 1.298

0.544

2.266

- 0.897

- 2.652

0.278 0.728 - 0.907 - 0.703

0.489 1.290 - 2.730 - 0.462

This has the effect of excluding operating costs associated with pollution control from total costs in each industry. The long-run impact of eliminating the operating costs of pollution abatement is summarized in the column labeled ENV in Table 3.1. The output of the economy, as measured by the gross national product, rises by 0.728%. Much of this comes from an increase in the capital stock which rises by savings in the long run, the rate of return is unaffected by regulation. However, the price of new investment goods falls by the price of capital services. Cheaper capital services lead to a fall in the prices of goods and services and a rise in full consumption by 0.278%. This increase is less than that of gross national product, since full consumption includes leisure time as well as personal consumption expenditures. Finally, the exchange rate, which gives the domestic cost of foreign goods, falls slightly, indicating an increase in the international competitiveness of the US economy 47. The long-run effects of eliminating operating costs associated with pollution abatement on the prices and outputs of individual industries are shown in Figure 3.2. Figure 3.2(a) shows the percentage change in the steady-state purchaser's price of each commodity while Figure 3.2(b) gives percentage changes in industry output levels. Not surprisingly, the principal beneficiaries of eliminating operating costs are the most heavily regulated industries. The greatest expansion of output occurs in coal production, since the fuel cost differential between low-sulfur and high-sulfur coal is large relative to the total costs of the coal industry. Turning to manufacturing industries, primary metals, paper, and chemicals have the largest gains in output from the elimination of operating costs for pollution abatement. Several other sectors benefit from the removal of operating costs of pollution abatement, but the impact is fairly modest. An alternative analysis of the impact of environmental regulation on US international competitiveness is given by Kalt (1988).

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Fig. 3.2a. Effect of ENV on prices.

We now turn from the long-run impact of eliminating operating costs to its dynamic effects. Figure 3.3 shows the effects of removing operating costs on the time paths of full consumption, the price of new capital goods, the capital stock and the level of gross national product. After 1973, the price of investment goods falls slowly, reflecting the gradual price decline brought about by the elimination of operating costs associated with increasingly stringent regulations. Lower costs of investment goods tend to increase the rate of return, stimulate savings, and produce more rapid capital accumulation. Additional capital eventually brings down the rental price of capital, lowering costs still further. This, in turn, raises the level of GNF! The transition from the short run to the steady state is relatively slow, requiring almost three decades for the capital stock to adjust to the change in environmental policy. Figure 3.3(c) shows that the adjustment process is not complete until the year 2000. In part this reflects the nature of the experiment: the actual regulations were imposed gradually, so their removal is also gradual. On the other hand, full consumption attains its final value fairly quickly as a consequence of intertemporal

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Agriculture Metal Mining Coal Minin Crude oil Other Mining Construction Food Products Tobacco Textiles Apparel Lumber, Wood Furniture PaDer printing Chemicals Refining Rubber, Plastic Leather Glass, etc. Primary Metals Fab. Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. other Services GOV. Enterprises

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Fig. 3.2b. Effect of ENV on output.

optimization by households. Since income is permanently higher in the future, consumption rises in anticipation. However, the rise of consumption is dampened by an increase in the rate of return that produces greater investment.

3.2. Investment in pollution control equipment

For some industries the most important impact of environmental regulation is through mandatory investment in costly pollution abatement equipment. Investment in pollution control devices crowds out investment for ordinary capital accumulation, reducing the rate of economic growth. Our second simulation is designed to assess the impact of this investment. The share of pollution control in total investment rose to a peak in the early 1970s and then declined substantially. This can be attributed to the fact that much of the early effort in pollution control was directed at reducing emissions from existing sources by retrofitting equipment already in place. Later, restrictions on emissions

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from new sources became more important. New source regulations increase the cost of new investments because producers are required to purchase pollution abatement equipment whenever they acquire new investment goods. The economic effects of retrofitting are quite different from investment in new source control, so we distinguish between the two in constructing our counterfactual simulation. We begin by assuming that investment in pollution control equipment provides no benefits to producers other than satisfying environmental regulations. Accordingly, we simulate mandated investment as an increase in the price of investment goods. Unfortunately, our data set does not distinguish between investments required for new and existing facilities. To separate the two, we assume the backlog of investment for retrofitting old sources was eliminated by 1983. This allows us to infer that the 1983 share of pollution abatement devices in total investment was due entirely to new investment. Thus, we can simulate the impact of removing environmental regulations on new investment by reducing the price of investment goods by that proportion. This captures the effect of requirements for pollution abatement on investment in new capital goods, but does not include the effect of windfall losses to owners of the capital associated with old sources of emissions. This approach has certain limitations that should be pointed out. First, it relies on the assumption that capital is completely malleable and mobile between sectors. An alternative technique would be to incorporate costs of adjustment into our models of producer behavior. However, this approach would lead to considerable additional complexity in modeling and simulating producer behavior. Moreover, the long-run impact of environmental regulations would be unaffected by costs of adjustment, since these costs would be zero in the steady state of our model. Column INV of Table 3.1 gives the steady-state effects of removing mandated investment in pollution control devices. The largest change is in the capital stock, which rises by 2.266% as a direct result of the drop in the price of investment goods. In the short run, this price decline pushes up the rate of return, raising the level of investment. Higher capital accumulation leads to a fall in the rental price of capital services, decreasing the overall price level. The long-run level of full consumption rises by 0.489%, almost double the increase resulting from eliminating operating costs of pollution abatement. The 1.290% rise in GNP is also nearly twice as large. The exchange rate appreciates by .462%, indicating an increase in the international competitiveness of the US economy. Figure 3.4 shows the long-run effect of eliminating pollution abatement investment on commodity prices and industry output. These effects stem from the drop in the rental price of capital services. The largest gains in output are for communications, electric utilities, and gas utilities, since these are the most capital-intensive industries. While most sectors gain from eliminating investment for pollution control, a few sectors are hurt by the change. Outputs of food, apparel, rubber and plastic, and leather, decline. These sectors are among the least capital intensive, so that the fall in the rental price of capital services has little

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Agriculture Metal Minina Coal in inCrude oi? Other Mining Food Products Tobacco Textiles Apparel Lumber. Wood ~urniture Paper Printing Chemicals Refining Rubber, Plastic Leather Glass. etc. Primary fietals Fab. Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. Other Services Gov. Enterprises

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Fig.3.4a. Effect of INV on prices.

effect on the prices of outputs. This leads both intermediate and final demand sectors to substitute away from those commodities. Moreover, nonhomotheticity in consumption leads to a relative drop in the output of less income-elastic goods such as food. The transition path of the US economy after investment requirements for pollution control have been eliminated is summarized in Figure 3.5. The process of adjustment is markedly different from that of the previous simulation. Capital stock grows immediately and rapidly to its new equilibrium value. This comes about as a consequence of the fall in the price of investment goods. As new capital goods become cheaper, beginning in 1973, the rate of return rises, driving up investment and producing a sharp increase in the capital stock. The initial surge in investment is financed by an increase in savings brought about by a temporary drop in consumption. Later, consumption rises as the capital stock grows.

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Agriculture Metal Mining Coal Minin Crude Oi? Other Mining Construction Food Products Tobacco Textiles Apparel Lumber. Wood ~urhiture Paper Printing Chemicals Refining Rubber, Plastic Leather Glass, etc. Primary Metals Fab. Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. Other Services Gov. Enterprises

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Fig. 3.4b. Effect of INV on output.

3.3. Motor vehicle emissions control Environmental regulation is not limited to controlling pollution by industries in the business sector. Restrictions on motor vehicle emissions affect both businesses and households. Like pollution control in industry, the reduction of motor vehicle exhaust emissions requires both capital expenditures and operating costs. A catalytic converter is a typical piece of pollution abatement equipment requiring capital expenditure, and the premium paid for unleaded gasoline is an example of an increase in operating costs. Kappler and Rutledge (1985) present data on the capital costs associated with motor vehicle regulation and three types of operating cost - increased fuel consumption, increased fuel prices, and increased vehicle maintenance. We first divide the total cost of pollution abatement equipment between imported and domestic vehicles in proportion to their shares in total supply. We then exclude the cost of this equipment from the total cost of domestic motor vehicle production, while reducing the price of imported motor vehicles in proportion to the cost of pollution control devices.


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Fig. 3.6a. Effect of MV on prices.

Given the industries in our model, the price premium for unleaded motor fuels can best be modeled as a change in the cost of output of the petroleum refining sector. This is similar to the treatment of the fuel cost differential between highsulfur and low-sulfur coal. Only the operating costs associated with higher fuel prices were removed in this simulation; fuel consumption and vehicle maintenance were held constant. Consequently, our results understate the overall impact of emission controls. As shown in column MV of Table 3.1, the long-run economic impact of imposing emissions controls on motor vehicles is similar in magnitude to the impact of pollution controls in industry (column ENV). The capital stock rises by 1.118%, full consumption increases by 0.282%, real GNP increases by 0.752%, and the exchange rate appreciates by 0.392%. Almost all of the impact is due to the drop in motor vehicle prices resulting from the elimination of required pollution control equipment. Motor vehicles are one of the principal inputs into the production of investment goods, so that changes in their price have a significant effect on the overall price of investment goods. As with our investment simulation, a drop in the


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Agriculture Metal Mining Coal Minin Crude oi? Other Mining Construction Food Products Tobacco Textiles Apparel Lumber, Wood Furniture Paoer ~rintlng Chemicals Refining Rubber, Plastic Leather Glass, etc. Primarv Metals ~ab: Metals Nonelec. Mach. E l m . Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. Other Services Gov. Enterprises

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Fig. 3.6b. Effect of MV on output.

price of investment goods raises the rate of return and leads to large changes in the capital stock. The long-run effects of eliminating motor vehicle emissions controls on commodity prices and industry outputs are shown in Figure 3.6. The principal beneficiary of the elimination of these regulations is the motor vehicles industry itself. This is due in part to the fact that the demand for motor vehicles is price elastic: a price change of seven percent produces an output change of fourteen percent. Thus, a small drop in price produces a large change in output. Two other industries also benefit significantly from the change in policy - petroleum refining and electric utilities. Both gain from the reduction in fuel prices associated with elimination of the fuel price premium. The dynamic response of the economy to an elimination of vehicle regulations is so similar to the response for the investment simulation that we omit the graphs. The differencescan be attributed to the fact that vehicle regulation began in earnest somewhat later and the imposed significantly smaller changes on the price of investment goods.

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Fig. 3.7a. Effect of ALL on prices.

3.4. The overall impact of environmental regulation

To measure the total impact of eliminating all three costs of environmental regulation - operating costs resulting from pollution abatement in industry, mandated investments to meet environmental standards in particular industries and cost of emission controls on motor vehicles -we performed a final simulation. However, this experiment was not a simple combination of the three components. Operating costs include capital costs, so combining the reductions in operating costs with the elimination of mandated investment would count the cost reductions associated with capital twice. To solve this problem, the capital component was removed from operating costs in the combined simulation. The results of removing all forms of environmental regulation are summarized in column ALL of Table 3.1. The long-run consequences of pollution control for different commodities and industries are presented in Figure 3.7. The sectors hit hardest by environmental regulations were the motor vehicles and coal mining industries. Primary metals and petroleum refining followed close behind. About half the remaining industries have increases in output of one to five percent after pollution controls are removed. The


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Agriculture Metal Mining Coal Minin Crude Oi? Other Minino ~onstruction Food Products Tobacco Textiles Apparel Lumber, Wood Furniture Paper Printing Chemicals Refining Rubber, Plastic Leather Glass, etc. Primarv Metals ~ab: Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. Other Services Gov. Enterprises

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Fig.3.7b. Effect of ALL on output.

rest are largely unaffected by environmental regulations. The economy follows the transition path to the new steady state shown in Figure 3.8. Driven by large changes in the price of investment goods, the capital stock rises sharply. The quantity of full consumption rises at a similar rate, as does real GNP. The adjustment process is dominated by the rapid accumulation of capital and is largely completed within two decades.

4. The impact of higher energy prices

The possibility that carbon dioxide emissions from fossil fuel use might lead to global warming has become a leading environmental concern. Many scientific and environmental organizations have called for immediate action to limit these emissions. To the extent that the emissions are a global externality, one possible policy would be to introduce a Pigouvian tax on fossil fuel use. In particular, it would be possible to introduce a tax on the carbon content of fossil fuels. A carbon


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Fig. 4.1. Real price of oil.

tax would reduce the use of fossil fuels by inducing substitution of energy sources such as solar, nuclear, and hydroelectric power for coal, petroleum, and natural gas. In addition, a carbon tax would raise the cost of using energy and induce the substitution of capital, labor, and materials inputs for energy. A carbon tax employs higher energy prices, especially higher prices of fossil fuels, to reduce carbon dioxide emissions. The past two decades of US historical experience have provided a natural experiment that is useful in assessing the economic impact of this strategy. Between 1973 and 1975 the price of imported petroleum increased by a factor of three as a consequence of supply disruptions associated with the Arab Oil Embargo. Between 1978.and1980 oil prices doubled as a result of disruptions in supply that followed the Iranian Revolution. The historical time path of petroleum prices between 1965 and 1990 in real terms is presented in Figure 4.1.


Year

Fig. 4.2. Total carbon emissions.

The dramatic increases in world petroleum prices during the 1970swere followed by a gradual decline in prices between 1980 and 1985 that gave way to a precipitous drop in 1986. By 1987 real petroleum prices had stabilized at levels that were more than double those prevailing in 1972. The increase in world petroleum prices raised the real cost of energy in the USA for all forms of energy. This increase in energy prices resulted in substantial energy conservation and stabilized carbon dioxide emissions for a period of fifteen years between 1972 and 1987. In Figure 4.2 we present historical data on carbon dioxide emissions for the period 19651987. In 1972, carbon dioxide emissions released 1224million tons of carbon into the atmosphere 48. Fifteen years later, in 1987, the emissions were identical. In order to analyze the natural experiment that resulted from higher world petroleum prices since 1973, we have simulated the growth of the US economy 48

Carbon dioxide emissions are conventionally measured by amount of carbon they contain.

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D. W. Jorgenson and IIJ. Wilcoxen

with and without these price increases. We take the actual path of world petroleum prices over the period 1973-1987 as our base case and extrapolate real petroleum prices forward from 1987 at the level of prices prevailing in 1987. As alternatives to the base case we have considered the following scenarios: OIL72: The real price of imported petroleum is held constant at its 1972 level. Thus, this scenario omits both the long-term increase in the level of world petroleum prices between 1972 and 1987 and the price shocks associated with supply disruptions in 1973-1975 and 1978-1980. OIL81: The real price of imported petroleum follows its historical path through the peak level in 1981, but after that it remains constant at the 1981 level. This scenario is the same as the base case through the year 1981, but omits the decline in world petroleum prices from 1981 to 1987. OILS7: The real price of imported petroleum rises linearly from its 1972 level to its level in 1987, after which it remains constant. This scenario omits the price shocks of 1973-1975 and 1978-1980, but captures the long-term rise in world petroleum prices over the fifteen-year period between 1972 and 1987. By comparing the results for each of these simulations to our base case (in which world oil prices follow their historical course) we can assess the cost of stabilizing carbon dioxide emissions through high oil prices. Moreover, by analyzing all three of the alternative scenarios we can decompose the impact of the increase in world petroleum prices into separate components associated with the sharp price increases of the 1970s and the overall rise in the price level between 1972 and 1987. 4.1. Effects on the steady state

Since the long-run price of petroleum is the same in the base case and the OIL87 scenario, there are only three distinct long-run equilibrium paths for our four scenarios. The base case associated with the historical path of oil prices and the revised OIL87 scenario result in the same long-run behavior of the economy. However, the OIL81 scenario is associated with higher oil prices while the OIL72 scenario captures the effects of lower oil prices. The aggregate impacts of these scenarios are presented in Table 4.1. Under OIL72, the price of imported oil is 61% lower than the base case while under OIL81 it is 183% higher. Apart from important differences in the magnitudes, the long-run impacts of OIL72 and OIL81 are close to mirror images of each other. With lower oil prices, real gross national product is 1.186% higher in the long run, while higher prices result in a 1.339% decrease in real GNP Also, it is clear that the level of world oil prices has an important long-run impact on the US economy. Lower prices increase GNP while higher prices decrease it. The real exchange rate, defined as the price of US imports relative to the price of US exports, is 1.098% lower under OIL72 than in the base case, and it is 1.254% higher under OIL81.


Table 4.1 Long-run oil simulation results Variable

Scenario

Price of imported oil Capital stock Price of investment goods Real GNP Full consumption Rental price of capital Exchange rate

More rapid economic growth under the OIL72 petroleum price scenario leads to a capital stock that is 0.790% above the base case level and a capital rental price that is 0.713% lower. This is brought about in part by a 0.886% fall in the price of investment goods. In the long run the rate of return in the US economy is the same under all three scenarios - the base case, OIL72, and OIL81. As before, OIL81 is close to a mirror image of OIL72, having a higher price of investment goods, a lower capital stock and a higher rental price of capital. The final indicator of aggregate US economic activity given in Table 4.1 is full consumption. This is an important indicator of the change in consumer welfare associated with variations in the world oil price. Since leisure time is closely tied to the exogenous time endowment of the US economy, we find that full consumption is only 0.432% higher with lower oil prices in the OIL72 scenario and 0.494% lower with higher oil prices in the OIL81 scenario. Finally, we present changes in industry output levels from the base case for OIL81 and OIL72 in Figure 4.3. Higher oil prices result in a drastic fall in the output of the petroleum refining sector illustrated graphically in Figure 4.3. The output of electric utilities is also substantially lower. The output of chemical manufacturing and gas utilities are also reduced by higher oil prices, while food and tobacco experience a modest increase in output as a consequence of substitution away from energy-intensive commodities by businesses and households. As before, the OIL72 scenario, corresponding to lower oil prices, is almost a mirror image of the high oil price scenario.

4.2. Dynamic effects

In Section 2 we showed that the dynamics of our model are determined by the backward-looking capital accumulation equation and the forward-looking


Agriculture Metal Minina Coal ini inCrude oi? Other Mining Construction Food Products Tobacco Textiles Apparel Lumber, Wood Furniture Paper Printina chemical; Refining Rubber, Plastic Leather Glass, etc. Primary Metals Fab. Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance, etc. Other Services Gov. Enterprises

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Fig. 4.3a. Effect of OIL81 on output.

asset pricing and Euler equations. We can illustrate these mechanisms by first considering the OIL87 scenario, which has the same long-run world petroleum price as the base case, but omits the price shocks of the 1970s. Figure 4.4 gives a comparison between this scenario and the base case. In Figure 4.4 we see that the long-run behavior of the US economy is identical in the base case and the OIL87 scenario. However, the transition path toward longrun equilibrium is very different in the two scenarios. Between 1973 and 1987, oil prices are higher in the base case than in OIL87. Thus, during that period real income is higher under OIL87. However, this increase in income is only temporary because prices become the same after 1987. Since households have perfect foresight, they know the change is temporary, so consumption increases very little and most of the extra income is saved. This leads to the pattern of capital accumulation shown in Figure 4.4(c). By the year 2005 differences between the base case and the OIL87 scenario are negligible. However, the impact of differences in world petroleum prices through 1987 is still substantial after ten years have elapsed. The model captures


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the effects of changes in world oil prices along the transition path toward long-run equilibrium of the US economy. However, the dynamics represented in the model are too highly simplified to capture the short-run impact of higher world oil prices. In the OIL81 scenario, world oil prices are above their historical values after 1981. A comparison between this scenario and the base case is given in Figure 4.5. Reflecting the long-run increase in oil prices, levels of full consumption decrease from the beginning of our simulations in 1973. This decrease facilitates the accumulation of capital in anticipation of future consumption needs. The sharp drop in the capital stock after 1987 reflects the permanent decline in real income after that time. In the OIL72 scenario, world petroleum prices are below those of the base case after 1972. We have already seen that the long-run impact of lower oil prices is a kind of mirror image of the effects of the higher oil prices in the OIL81 scenario. In Figure 4.6 we present the dynamics of the economy's adjustment to lower oil prices. In this case, the path of full consumption shown in Figure 4.6(a) is somewhat misleading. Figure 4.6(a) shows the value of full consumption falling during the


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Ch. 27: Erzergy, the Environment, and Economic Growth

Table 4.2 Decomposition of effects on average growth over 1974-1985 Description

Change in growth rate

Total change (OIL72) Change due to price surge (OIL87) Change due to price level (OIL72-OIL87)

early years of the simulation. During that period, however, the price of consumption falls by more than enough to compensate, so the quantity of full consumption actually rises. This reaches a peak in 1987, when world petroleum prices reach their long-run level under the base case. After that, it gradually subsides to a longrun level that is substantially above the base case. While this long-run level is the reverse of that in OIL81 (the high price scenario) the transition path followed by the economy is very different. Under OIL72, the economy undergoes a boom (relative to the base case) in both investment and consumption. Capital is accumulated very rapidly through 1987 and then declines slowly to a long-term equilibrium which sustains higher consumption after 1987. The difference between real GNP in the OIL72 scenario and the base case peaks in 1981, when the difference in petroleum prices is most pronounced; the long-run difference in real GNP is considerably lower.

By comparing the OIL72 and OIL87 simulations we can separate the impact of higher long-term world oil prices from the effects of the oil price surges that took place in 1973-1975 and 1978-1980. Recall that the OIL72 scenario corresponds to permanently lower oil prices at levels that prevailed before 1973, while OIL87 represents a gradual increase in world oil prices to the level of 1987. In Table 4.2 we summarize the impact of higher oil prices and decompose it into effects attributable to the long-run increase and those attributable to the price shocks of the 1970s. As shown in the table, the growth rate of real GNP was 0.216% per year lower over the period 1974-1985 in the base case than the OIL72 scenario. Thus, the rise in oil prices accounts for a substantial portion of the slowdown in US economic growth after 1973. The portion of the slowdown that can be attributed to the price shocks of the 1970s is captured by the OIL87 scenario. OIL87 has the same long-run price trend as the base case, but it omits the sharp rise and fall of oil prices during the 1970s and early 1980s. Under this scenario the growth of real gross national product over the period 1974-1985 was 0.136% per year higher than in the base case. Thus, the price shocks account for almost two-thirds of the overall 0.216% drop

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in growth. The remainder, given by the difference between OIL72 and OIL87, shows the effect of a gradual increase in oil prices. This difference accounts for a slowdown of 0.080% per year in the average annual growth rate of real GNP over the period 1974-1985.

5. The impact of carbon taxes In the preceding section we have calculated the implicit cost of stabilizing carbon dioxide emissions through high world oil prices. Clearly, however, this is not a policy that the US government would choose voluntarily. A more likely policy would be a broad-based tax on the carbon content of all fossil fuels. Such a tax could be applied to primary production of coal, oil and natural gas, and would have the advantage of taxing emissions directly. In this section we examine the carbon taxes that would be needed to attain various carbon dioxide emission targets, and discuss how those taxes would affect the economy.

5.1. Computing carbon emissions The first step in simulating different carbon tax policies is to calculate carbon dioxide emissions. For tractability, we have assumed that these emissions are proportional to fossil fuel use. This implies the carbon dioxide produced by a given combustion process cannot be reduced. In practice this is largely the case49.We then calculate the carbon content of each fossil fuel in the following way. From the US Department of Energy we obtain the average heat content of each fuel in millions of Btu per unit of quantity [US DOE (1990)) Next, we obtain data from the Environmental Protection Agency (EPA) on the amount of carbon emitted per million Btu produced from each fue150. Multiplying EPA's figures by the heating value of the different fuels gives the carbon content of each fuel. Carbon emissions can then be calculated from total fuel production. Table 5.1 gives the data for each fuel in 1987. Our simulation model is normalized so that all prices are equal to unity in 1982. The quantities do not correspond directly to physical units. Moreover, the model has a single aggregate sector for oil and gas. To convert the figures above into a form appropriate for the model's quantity units, we sum carbon production for oil and gas and divide by the model's base case output of oil and gas in 1987. This gives the carbon coefficient for the industry. Similarly, the coefficient for coal is Unlike ordinary pollutants, carbon dioxide is one of the natural products of combustion. Little can be done to change the amount of it produced when burning any particular fuel. 50 EPA (1990) internal memoranda. 49


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Table 5.1 Carbon emissions data for 1987 Item

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computed by dividing total carbon production from coal by the model's 1987 value for coal output. These coefficients are then used to compute carbon emissions in each simulation. 5.2. Carbon dioxide emissionspolicies We now turn to the consequences of using a carbon tax to achieve different carbon dioxide emissions levels. We have run three simulations in addition to the base case, one for each of the following policies: [I] Stabilizing carbon emissions at the 1990 base level beginning immediately. [2] Decreasing carbon emissions gradually over 1990-2005 until they are 20% below the 1990 base level. [3] Doing nothing until 2000, then gradually increasing the carbon tax over 20002010 to stabilize emissions at the year-2000 base level. These policies vary considerably in stringency. In 1990, base case fossil fuel use produced 1576million tons of carbon. Policy 1 would keep that level constant forever, even in the face of rapid GNP growth. Policy 2, however, is even more restrictive: it requires emissions to drop to 1261 million tons by 2005 and remain at that level forever. Policy 3, on the other hand, is the least restrictive: it allows emissions to rise to the base case year-2000 level of 1675 million tons. In each simulation, we constrain total carbon emissions and allow the level of the carbon tax to be determined endogenously. The tax is applied to primary fuels in proportion to carbon content. Since even the least stringent policy produces substantial tax revenue, it is necessary to make an assumption about how the revenue would be used. In these simulations, we hold the real value of government spending constant at its base case level. We then allow the average tax on labor

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to adjust to keep the difference between government spending and government revenue equal to the exogenous budget deficit. At the same time, we hold the marginal tax on labor constant, so that adjustments in the average rate reflect changes in the implicit zero-tax threshold.

5.3.Long-run effects The principal direct consequence of all three carbon control strategies is to increase purchasers' prices of coal and crude oil. This can be seen most clearly by examining the model's results for each simulation at a particular point in time, so in this section we present detailed results for the year 2020. We begin with results for the first experiment: holding emissions at 1990 levels. By the year 2020, maintaining 1990 emissions will require a tax of $16.96 per ton of carbon contained in primary fuels51. Using the data in Table 5.1, it can be shown that this amounts to a tax of about $11.01 per ton of coal, $2.32 per barrel of oil or $0.28 per thousand cubic feet of gas. The tax would generate revenue of $26.7 billion annually. The rising price of fossil fuels results in substitution toward other energy sources and away from energy in general. Total Btu consumption falls by 12% to about 68 quadrillion Btu (quads). This substitution away from energy, and hence toward more expensive production techniques, results in a drop of 0.7% in the capital stock and 0.5% in real GNP. These figures are fairly small because they measure, in a loose sense, the welfare losses from introducing a small distortionary tax. Since revenue from the tax is returned to households through lump-sum adjustments in the income tax, social welfare falls due to the inefficiency of the tax. At the commodity level the impact of the tax varies considerably. Figure 5.l(a) shows changes in the supply price of the 35 commodities measured as percentage changes relative to the base case. The largest change occurs in the price of coal, which rises by 40%. This, in turn, increases the price of electricity by about 5%. Electricity prices rise considerably less than coal prices because coal accounts for only about 13% of total utility costs. Other prices showing significant effects are those for crude and refined petroleum and gas utilities. These rise, directly or indirectly, because of the tax on oil. These changes in prices affect demands for the commodities, which in turn determine how industry outputs are affected. Figure 5.l(b) shows percentage changes in quantities produced by the 35 industries. Most of the sectors show only small changes in output. Coal mining is the exception; its output falls by 26%. Coal is affected strongly because the demand for it is somewhat elastic. Most coal is purchased by electric utilities, which in our model can substitute toward other 51

All dollar amounts are in 1989 prices.

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fuels when the price of coal rises. Moreover, the utilities also have some ability to substitute other inputs, such as labor and capital, for energy, further reducing the demand for coal. Since electric utilities play such an important role in determining how a carbon tax affects coal mining, we now digress briefly to discuss how the utilities are represented in the model. Electric utilities, like all other sectors, are represented by a nested translog unit cost function. The top tier of the function gives cost in terms of the prices of four inputs: capital, labor, an energy aggregate, and a materials aggregate. Substitution between energy and other inputs takes place at this level. The price of the energy aggregate itself is formed at a lower tier by translog aggregation of the prices of five inputs: coal, crude petroleum, refined petroleum, electricity, and natural gas from gas utilities. Substitution among fuels takes place at that level. Estimated parameters govern the ease of substitution at both the top tier and the energy tier of the cost function. At the top level, substitution between energy and capital is very inelastic (an elasticity of - 0.15), substitution between energy and labor is moderately inelastic ( - 0.64), and substitution between energy


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Fig. 5.lb. Effect of CONST on output.

and materials is slightly elastic ( - 1.16). Thus, increases in the relative price of energy will, for the most part, induce substitution toward materials. In addition, substitution possibilities exist at the energy tier. The elasticity of substitution between coal and refined petroleum is - 0.7, although between coal and natural gas it is only - 0.1. Thus, an increase in the relative price of coal will produce some substitution toward other fuels. Overall, the parameters appearing in the cost function for electric utilities imply that an increase in the relative price of coal will lead to substitution toward other fuels and toward non-energy inputs. The second policy we consider is a 20% reduction below 1990 emission rates, to be phased in gradually over 15 years. By 2020, this would amount to a drop of 32% below base case emissions, and would require a tax of $60.09 per ton of carbon. Using the data in Table 5.1, this is equivalent to a tax of $39.01 per ton of coal, $8.20 per barrel of oil, or $0.98 per thousand cubic feet of gas. The tax would produce $75.8 billion in revenues. Comparing these results to those for maintaining 1990 emissions shows that the tax would more than triple, from $17 to $60. At


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Fig. 5.2a. Effect of CUT20 on prices.

equilibrium, the tax gives the marginal cost of reducing emissions by an additional ton of carbon, so that further reductions are becoming significantly more difficult. Tighter carbon regulations also lead to a reduction in total fossil fuel Btu production to 57 quads, a drop of 27% from the base case. This, in turn, reduces the capital stock by 2.2% and real GNP by 1.6%. These figures are about triple the values obtained for holding emissions at 1990 levels. Although the changes in capital and GNP appear small, recall that they are measures of deadweight loss associated with fairly large marginal changes in the energy sector. At the commodity and industry level, results for this experiment are qualitatively similar to those for maintaining 1990 emissions, although they are numerically somewhat different. Figure 5.2(a) shows percentage changes in commodity prices relative to the base case. The price of coal more than doubles, rising by 137% from its base case value. The price of oil rises by 13%, while that of electricity rises by about 18%. The prices of refined petroleum and natural gas also rise, but by somewhat less. Comparing Figures 5.2(a) and 5.l(a) shows how this simulation compares with the previous one. In particular, commodity prices rise roughly in

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Agriculture Metal Mining Coal Mininq Crude Oil Other Minina constructio6 Food Products Tobacco Textiles Apparel Lumber, Wood Furniture Paoer Printing Chemicals Refining Rubber. Plastic Leather Glass, etc. Primary Metals Fab. Metals Nonelec. Mach. Elec. Mach. Motor Vehicles Other Trans. Eq. Instruments Misc. Manufac. Transportation Communication Elec. Utilities Gas Utilities Trade Finance. etc Other ~ e k v i c e s Gov. Enterprises

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Fig. 5.2b. Effect of CUT20 on output.

proportion to the increase in the carbon tax. The tax rises by a factor of 3.5, and so do most of the percentage changes in commodity prices. The quantity results, shown in Figure 5.2(b), display a similar pattern except that they scale up in proportion to the change in carbon reductions rather than the change in taxes. That is, reducing emissions to 20% below 1990 levels requires a cut of about twice the size needed to reach 1990 levels. Thus, percentage changes in quantities from the base case are about twice those of the previous experiment. The most important results are the 53% drop in coal production and the 15% drop in electricity produced. By contrast, the looser restrictions implied by maintaining emissions at year-2000 levels produce much smaller effects on the economy. The tax required is only $8.55 per ton of carbon, which implies charges of $5.55 per ton of coal, $1.17 per barrel of oil, or $0.14 per thousand cubic feet of gas. The tax would produce $14.4 billion annually in revenue. Aggregate effects are also considerably smaller than in the two previous scenarios. The capital stock falls by 0.4%, and GNP drops by 0.3%, about half the value obtained in the 1990 simulation. This is quite reasonable since

Ch. 27: Energy, the Environment, and Economic Growth Table 5.2 Summary of long-run carbon tax simulations Variable

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1990 level

80% of 1990 level

Carbon emissions Carbon tax Tax on coal Tax on oil Tax on gas Labor tax rate Tax revenue Btu production Capital stock Real GNP Price of coal Quantity of coal Price of electricity Quantity of electricity Price of oil

the cut in emissions is about half as deep. The industry results look qualitatively so similar to those of the previous experiments that we omit the graphs. The principal numerical result is that coal prices rise by 20% while coal output shrinks by about 16%. The results of all three carbon tax simulations are summarized in Table 5.2, in which the policies are listed in order of increasing stringency. From these results it appears that stabilizing emissions at the base-case level in the year 2000 can be accomplished with a very low carbon tax and a minimal disturbance of the economy. The strongest effect would be felt by the coal mining industry, which sees its demand fall as electric utilities substitute toward other fuels. More stringent regulations would lead to markedly higher energy prices and greater disruption of the economy. Coal mining would bear the brunt of the changes brought about by the tax under any scenario. Of the remaining sectors, electric utilities would be affected most strongly.

5.4. Intertemporal results Carbon restrictions adopted today will have effects far into the future. At the same time, anticipated future restrictions will have effects today. To assess the


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intertemporal consequences of carbon taxes, we now turn to the model's dynamic results. As with the long-run results, we begin by discussing a carbon tax designed to maintain emissions at 1990 levels. Following that, we examine the dynamic behavior of other experiments. The path of the carbon tax needed to maintain 1990 emissions is shown in Figure 5.3(a). Base case emissions increase over time, so the tax grows gradually, about $0.70 per year, over the next few decades. It reaches a peak around the year 2020, when our forecast of the US population crests52. The tax produces significant reductions in carbon emissions, which are shown in Figure 5.3(b) as As noted in Section 2, our population projections are based on those of the Bureau of the Census (1989).

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percentage changes from the base case. Emissions begin dropping immediately and by 2020 are about 14% below their unconstrained level. As suggested by the long-run results, the principal effect of the tax is to reduce coal mining. This is shown clearly in Figure 5.4(a), which gives percentage changes in coal output from the base case. Production gradually slows as the tax is introduced. It does not, however, fall all the way back to its 1990 level - some of the reduction in emissions comes about through reductions in oil consumption. This can be seen in Figure 5.4(b), which gives percentages changes in crude petroleum and natural gas extraction over time. The increasing price of energy raises costs and reduces household income. This, in turn, changes the rate of capital accumulation. The outcome is shown in


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Figure 5.5(a), which gives percentage changes in the capital stock from the base case. Unlike variables in the preceding graphs, the capital stock does not start declining immediately;instead, it tends to remain near its base case level for the first few years. This is the consequence of intertemporal optimization by households. From a household's point of view, the effect of the tax is to decrease its real income by an amount related to the tax's deadweight losss3.Thus, the household regards carbon taxes as reductions in future earnings, so it reacts by lowering consumption in all periods. In the early years, however, the carbon tax is minimal Since revenue earned by the tax is given back to households through a horizontal shift in the labor tax schedule, the simulation is essentially the replacement of a lump sum tax (the labor tax) by a distorting one (the carbon tax).

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and household income is largely unaffected. During that period, therefore, the drop in consumption leads to an increase in saving. This helps maintain investment -and thus the capital stock - in the early years of the simulation. Eventually, the income effect of the tax begins to be felt and the capital stock finally starts to decline relative to the base case. The decline in growth of the capital stock leads to a drop in GNP growth, as shown in Figure 5.5(b). Over time GNP gradually falls by about half a percent relative to the base case. The capital stock, however, is not the only factor contributing to the decline. In addition, higher energy prices reduce the rate of technical change in industries which are energy-using. This leads to slower income growth and helps keep GNP below its base case level. In fact, under the

D. l% Jorgmson and FJ. Wilcoxen

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carbon tax simulation average annual GNP growth over the period 1990-2020 is 0.02 percentage points lower than in the base casej4. About half of this is due to slowing productivity growth and half to slower capital accumulation. The two alternative carbon control targets we examined showed dynamic behavior qualitatively similar to that we have described above. These results can best be displayed by plotting each variable's values for all three simulations on a single graphsj. Figure 5.6(a), for example, shows the paths of the carbon tax The difference in two variables growing at rates differing by 0.02 percentage points is about 2% after a hundred years. j5 Recall that the targets were (1) maintaining 1990 emissions, (2) reducing emissions by 20% below 1990 levels, and (3) gradually introducing taxes to stabilize at year-2000 emissions.

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needed to achieve each of the targets. The highest path is the tax required to reduce emissions to 20% below their 1990 levels; the central path is that for maintaining 1990 emissions; and the lowest path is the tax needed to stabilize emissions at year2000 levels. Similarly, Figure 5.6(b) shows the carbon reductions achieved under each of the policies56.Plotting three curves on each figure makes it easy to compare different targets. For example, many of the figures show that as the target becomes more stringent, the variable of interest is pushed further away from the base case. Notice that target policies are drawn using the same line type in each graph. Maintaining 1990 emissions is always a solid line, reducing emissions to 20% below 1990 is always dashed, and maintaining emissions at year-2000 levels is dash-dotted. Also, variables are plotted on the same scale across different tax instruments for easier comparison.

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However, some of the figures show much more interesting behavior, and we will focus on these for the remainder of this section. The first feature apparent from Figure 5.6(b) is that the three targets require carbon reductions of roughly 8, 14 and 32%. Keeping these reductions in mind, Figure 5.7(a) shows that coal production does not fall in proportion to the drop in emissions. This occurs because it becomes increasingly costly to drive coal production. Coal users, notably electric utilities, find it increasingly difficult to substitute away from coal as the amount they use of it decreases. This is reflected in Figure 5.7(b), which shows that oil extraction increases more sharply as regulations become more stringent. One of the most interesting results of our study is shown in Figure 5.8(a), a graph of the capital stock under the three policies. Figure 5.8(a) is a very clear example of the effects of intertemporal optimization by households. For the policy which has least effect and occurs furthest in the future - maintaining emissions at year 2000 levels - the early reduction in consumption actually leads to a temporary increase in the capital stock. This comes about because households reduce consumption in anticipation of lower future earnings. Only under the most stringent policy reducing emissions by 20% from 1990 levels - does the capital stock begin to fall immediately. Finally, the results for GNP, shown in Figure 5.8(b), echo those for the capital stock. As mentioned above, GNP falls because of the drop in capital accumulation and the reduction in productivity growth resulting from higher energy prices. 6. Conclusion

The purpose of this section is to evaluate the usefulness of intertemporal general equilibrium modeling as a practical guide to assessment of the impacts of energy and environmental policies. The neo-classical theory of economic growth has been applied to the evaluation of policies to control global climate change by Nordhaus (1992), Manne and Richels (1992), and Jorgenson and Wilcoxen (1992a). Nordhaus's model of the world economy includes a physical model of climate change. This provides the basis for designing an optimal environmental policy that can be implemented by means of a carbon tax. The policy results from a sophisticated application of cost-benefit analysis. The GLOBAL 2100 model of Manne and Richels (1992) disaggregates the world economy into five regions - each represented by a one-sector neo-classical growth model. Environmental policy affects the output of each region through restrictions on carbon dioxide emissions resulting from fossil fuel combustion. This approach is useful in assessing the costs of these restrictions and the benefits from international cooperation in controlling global climate change through tradeable permits. Finally, the energy technology assessment (ETA) submodel provides


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valuable information on the pay-off from accelerated research and development on new energy sources and alternative energy technologies. The framework for the econometric approach to modeling the impact of energy and environmental policies is also provided by intertemporal general equilibrium theory. This makes it possible to preserve the features of the aggregate growth models employed by Nordhaus (1992) and Manne and Richels (1992), while disaggregating the impacts of these policies. We have distinguished among thirtyfive industrial sectors of the US economy and have also identified thirty-five commodity groups, each one the primary product of one of the industries. In modeling consumer behavior we have distinguished among 672 different household types, broken down by demographic characteristics. Aggregate demand functions for components of consumer expenditure are constructed by summing over individual demand functions. The econometric method for parametrization used in modeling technology and preferences can be contrasted with the calibration approach employed in earlier general equilibrium models. The main advantage of the econometric approach is that the responses of production and consumption patterns to changes in energy prices and environmental controls can be derived from historical experience. The implementation of the econometric approach requires a system of national accounts that successfully integrates capital with the income and production. The new accounting system incorporates an accumulation equation relating capital to past investments and an asset-pricing equation linking the price of assets to future prices and rates of return. Jorgenson and Wilcoxen (1990b) have provided a highly disaggregated model of the impact of environmental regulations on US economic growth. This model incorporates detailed data on costs of compliance with environmental regulations by individual industries. An important mechanism for adjusting to changes in environmental policy is altering rates of capital formation. A second mechanism is the pricing of capital assets through forward-looking expectations of future prices and discount rates. This illustrates the significance of intertemporal general equilibrium modeling for obtaining insights into dynamic effects of energy and environmental policies on US economic growth. Jorgenson and Wilcoxen (1992a) have analyzed a 'natural experiment' in stabilization of carbon dioxide emissions for the USA during the period 1972-1987. This is the result of price-induced energy conservation that has important feedbacks to the rate of economic growth through capital asset pricing and capital formation. By combining forward-looking features of the model with the backward-looking capital accumulation equation, the decline in economic growth can be separated into two components. The first is the impact of the rise in energy prices from 1972 to 1987. The second is the effect of the energy price shocks of 1973-1975 and 19781980. The slowdown in economic growth during the period is largely attributable to the price shocks.

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Finally, Jorgenson and Wilcoxen (1992b) have modeled the impact on US economic growth of a carbon tax that would stabilize emissions of carbon dioxide at 1990 levels. Since the tax would be phased in gradually, this has a relatively modest impact on growth. Both consumers and producers anticipate the steady increase in carbon tax rates and plan accordingly. This brings about a gradual re-orientation of the economy to reduce dependence on coal, the most carbon-intensive fuel, and conserve energy more generally. An important qualification is that the cost of controlling carbon dioxide emissions rises at an increasing rate as restrictions on these emissions become more stringent. Although the intertemporal general equilibrium approach has proved to be useful in modeling the impact of energy and environmental policies, much remains to be done to exploit the full potential of this approach. As an illustration, the model of consumer behavior employed by Jorgenson and Wilcoxen (1990b) successfully dispenses with the notion of a representative consumer. An important feature of this model is that systems of individual demand functions can be recovered from the system of aggregate demand functions. The consumer preferences underlying these individual demand systems can be used to generate measures of individual welfare that are useful in evaluating the distributional consequences of energy and environmental policies. For example, Jorgenson and Slesnick (1985) have separated the impacts of changes in US petroleum taxes into equity and efficiency components. Similarly, Jorgenson and Slesnick (1987b) have considered the equity and efficiency impacts of natural gas price deregulation in the US. Finally, Jorgenson, Slesnick and Wilcoxen (1992) have analyzed the progressiveness or regressiveness of carbon taxes that would stabilize emissions of carbon dioxide at 1990 levels. Although the size of the equity impact depends on normative considerations, the efficiency impact greatly dominates in all three applications. Our conclusion is that intertemporal general equilibrium modeling provides a very worthwhile addition to methodologies for modeling the economic impact of energy and environmental policies. The neo-classical theory of economic growth is essential for understanding the dynamic mechanisms that underly long-run and intermediate-run growth trends. The econometric implementation of this theory is critical for capitalizing on the drastic changes in energy prices and substantial alterations in environmental policies of the past two decades. This wealth of historical experience, interpreted within an intertemporal framework, can provide valuable guidance in future policy formulation. References Armington, P.S., 1969, "The Geographic Pattern of Trade and the Effects of Price Changes", IMF Staff Papers 16 no. 2 (July) 176-199.


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INDEX

Absorptive capacity, 1138, 1149 Acid rain, 1220 Ad valorem tariff, 902 Adaptive Expectations Hypothesis, 971, 1102 Adjustment costs, 968,1102,1167,1194 Adjustment speeds, 760 Age of substitutability, 1111, 1124, 1128 Aggregate resource base, 818 Aggregation, 944,949, 1277 Alaoglu's theorem, 871 Allen-Uzawa-partial elasticities of substitution. 955 Alternative energy sources, 1202 American Gas Association, 1099 Appliance stocks, 953 Arab Oil Embargo, 1171, 1316 Arbitrage rule, 1133 Arizona appraisal system, 1068, 1070 Arps-Roberts, 1059 Arrow-Debreu model, 860,1143 Asset pricing, 1320 Asymmetric information, 1139 Backstop technology, 819,855,864,866,1088, 1122, 1134, 1247 Backward-bending supply curve, 1090, 1138, 1178 Balanced growth equilibrium, 1286 Banach-Sachs theorem, 871 Bauxite, 1097 Bellman Principle of Optimality, 889 Benchmark year, 1284 Biased productivity growth, 1284 Bidding-games, I236 Biological resources, 759 Block consignment rule, 1162 Block pricing, 978, 980 Brouwer fixed point theorem, 820 Brundtland Report, 1273 CAFE standards, 846 Cake-eating problem, 870,871, 1243 Calculus of variations, 777

Calibration, 1274, 1280 Capacity constraint, 892 Capital-energy substitutability, 956 Capital formation, 862, 864, 1267, 1294, 1319 Capital gains, 780,882,1118 Capital market, 917 Capital stock, 862 Carbon dioxide, 1220, 1223, 1270, 1279,1314 Carbon tax, 1316,1326,1333,1342 Cartels cheating, 887, 1094, 1131 competitive fringe, 908, 909, 1091, 1135 core, 1146 instability, 1094, 1132 models, 1092, 1131,1144 welfare implications, 1142 Certainty equivalent, 873 Choke price, 818,820 Classical period, 936 Clean Air Act, 1235, 1239 Climatic change, 1220 Closed-loop feedback control, 799 Closed-loop strategies, 885 Club of Rome, 1273 Coal, 987, 1225,1229, 1328 Coase Conjecture, 924 Cobalt, 952 Coefficient of mineralization, 1027 Collusion, 1131 Command-and-control regulations, 1232 Commitment, 928 Commodity-price stabilization, 982 Common property resources, 1254 Comparative dynamics, 782,800,803 Competitive equilibrium, 817 Competitive fringe, 908, 909, 1091, 1135 Computational models, 1077 Congressional Budget Office, 1233,1276 Conservation, 937 Conservation of mass, 1221, 1272 Consistent aggregation, 949 Consistent equilibria, 883 Constraint qualification, 772,774

Index Consumption discounting, 869 Consumption rate of discount, 869,873 Consumptive use, 760, 762 Continental crust, 1025 Contingent valuation methods, 1236 Continuation of strategy, 884 Continuous time, 764,767 Continuous-time representation, 767 Control theory, 883 Convergent trajectory, 799 Cooperative behavior, 1132 Copper, 952,1056, 1093 Cost function, 767,940, 1078 Costbenefit analysis, 1238 Credibility, 928 Credible Commitment, 883 Credible threat, 887 Critical credible stock, 919 Cross-section studies, 957 Crustal abundance, 1025-1027,1031, 1124 Cumulative cost functions, 1081,1089 Data contamination, 1043 De Beers Consolidated Mines, 1160 Decentralization of decisionmaking, 837 Decision analysis, 1057, 1201 Declining-block structure, 981 Deindustrialization, 856 Demand functions Almon lag, 970 compensated, 943 constant-elasticity, 838, 845 consumer, 939 derived, 939, 940, 1114 distributed lags, 970 elasticity, 837, 838, 1134 electricity, 965 general, 817,935 Hicksian, 943 linear, 840,845,904 Marshallian, 943 speculative, 991, 999 uncompensated, 943 Depletability concept, 760 Depletability condition, 763 Deposit models, 1040 Detection, 1140 Diamond, 1160 Diamond Producers' Association of London, 1160 Diminishing marginal productivity, 937

Diminishing marginal utility, 937 Disadvantageous market power, 927 Discounting, 856,859,863,868,869,873,876, 974, 1256 Discoverability, 1053 Discoveries, 833 Discovery process, 1120 Discovery process models, 1082 Discrete choice, 974 Discrete-time, 764 Disequilibrium, 972 Disruption premium, 1191 Distributional issues, 1226 Divisia index, 946 Dominance of extraction rate on marginal cost, 770 Dominant firm, 892,898,909, 1091 Dual variable, 774 Duality, 940 Durability, 975 Durability of cartels, 1138 Durable goods, 908,925,970, 1093 Dutch disease, 856, 1168 Dynamic consistency, 881, 882, 1137 inconsistency, 882,883,891,926, 1136 Dynamic games, 883 Dynamic Integrated Climate-Economy model, 1268 Dynamic supply, 1015 Econometric supply models, 1098 Economic growth, 1267, 1278 Economic incentives for environmental protection, 1231 Economic performance, 1168 Economic shutdown of extraction, 794,796 Economic truncation, 1045 Efficient-market hypothesis, 993 Elasticity of marginal utility, 856,858,859,863, 1244 Elasticity of substitution, 863, 946, 1115, 1245 Electricity, 952,978, 1229, 1328 Endowment, 1017 Energy Modeling Forum, 999,1181, 1195,1198, 1271 Energy price instability, 1167, 1168 Energy resources, 1127 Energy security, 1167 Energy use, 1219 Engel curves, 947

Index Engel's law, 1277 Environment, 1219 Environmental amenities, 1221 economics, 1219 effects, 796, 1219, 1220 externalities, 786 pollution, 1267 regulation, 1268, 1278, 1300 resources, 759 Essential commodities, 819 Estimation, 951, 1020 ETA model, 1269 Euler equation, 1293, 1320 Exact aggregation, 949, 1277 Exchange rate, 1189 Excise taxes, 785, 842 Exhaustion condition, 902 Exhaustion principle, 912 Existence of competitive equilibrium, 819 Existence of optimal policies, 870 Existence value, 1237 Expansion paths, 949 Expectations, 783,882, 970, 997 Expected utility, 861 Expendable resources, 759 Expenditure function, 942 Expenditure shares, 1289 Exploration, 764, 855, 1011, 1057, 1101 Exploration cost function, 1082 Exploration models, 1037, 1052, 1059 Externalities, 815,888, 1219, 1220, 1269 Extraction costs, 1102 Extraction order, 824,830 Feedback solutions, 889 First-order necessary conditions, 774,790,836, 859,861,865,1242,1244 'Fixed coefficients' assumption, 1272 Fixed initial state problem, 889 Fixed point, 819,821 Fixed-weighted quantity aggregate, 945 Flexible Fourier, 954 Flow-adjustment models, 965 Flow-related externalities, 816 Folk Theorem, 887,891,927,1132 Foreign trade, 1296 Forward markets, 1182 Forward trading, 901 Fossil fuels, 1124, 1126 Free disposal, 1221

Fringe buyers, 898 Full wealth, 1292 Futures markets, 1182 Game theory, 881,1096,1132 Gasoline, 952 General equilibrium modeling, 1271 Geologic endowment models, 1062 Gibbs free energy, 1028 GLOBAL 2100 model, 1269,1340 Greenhouse effect, 1223 Ground rent, 1118 Growth models, 1247 Hartwick rule, 1257 Hedging, 983, 991 Hedonic index, 945 Hessian matrix, 771 Heuristic bias, 1067 Hicks neutral technical progress, 960 Hnyilicza-Pindyck model, 1093 Homogeneous functions, 941 Homothetic preferences, 1276 separable functions, 946, 1285 technology, 963 Hotelling models, 771, 779, 780, 823, 845, 860, 875,912,1083, 1086,1088,1100,1118, 1133 Hunt, Nelson Bunker, 990 Hypothetical bias, 1237 IEA, 1209 Imperfect competition, 976 Import dependence, 1167 Import quotas, 1202 Incomplete information, 1139 Index of discoverability, 1053 Indicative planning, 1144 Indirect utility, 954 Indirect-utility function, 942 Industrial Revolution, 1113 Infinitely repeated non-cooperative games, 927 Information bias, 1237 Information exchange, 1143 Information set, 886,888 Informational inefficiency, 994, 1182 Innovation, 1114 Input-output model, 1272 Instability, 1167 Instrument bias, 1237

Intensity of use analysis, 950 Inter-industry transactions table, 1272, 1280 Interest rate, 766,787,813, 1088 Interfuel substitution, 954 Intergenerational balance, 856 Intergenerational equity, 1252, 1255 Internalization of externalities, 786,815 International commodity agreements, 1144 International Energy Agency, 1209 International policy coordination, 1200, 1208 Intertemporal arbitrage, 893 bias, 842, 844,848, 1253 efficiency, 1252 general equilibrium models, 1272, 1278 linkage, 817 welfare economics, 869 Inventories, 1203 Inventory theory, 997 Investment, 1294 Involuntary risks, 1251 Iranian Revolution, 986,1171, 1172 Iraqi invasion, 1174 Irreversibilities, 1220, 1250 Jump state, 890,891,894, 909 Kuhn-Tucker conditions, 772-774,790 Kuwait, 1174 Lagrange multipliers, 773 Land management, 1013 Land reclamation, 1236 Leakage, 763 Learning-by-doing, 770,789,1116, 1123 Learning-by-using, 1116 Limit pricing, 1131, 1146 Limits to Growth, 1273 Linear expenditure system, 979 Linear stock dynamics, 763 Linear utility function, 874 Lithosphere, 1025 Load forecasting, 980 Lognormal distribution, 1031 London Coal Exchange, 984 Long-term contracts, 922 MACRO model, 1269 Macroeconomic policies, 1169 Make table, 1280 Manganese, 1126

Marginal efficiency of investment schedule, 1138 Marginal product of capital, 875 Market clearing, 817 Market disturbances, 1170 Market failure, 1168 Market imperfection function, 839,842-844, 848 Market power, 835,881,891,998, 1091, 1117 Market structure, 922 Market supply, 817 Marketable permit system, 1231 Markov equilibrium, 887,925, 927 Markov strategies, 891 Martingales, 993 Materials balance analysis, 1221, 1272 Mercurio Europeo, 1154 Mercury, 1152 Metal exchanges, 989 Metal markets, 988 Method of moments, 1102 Mineral demand, 935 Mineral endowment, 1018 Mineral potential, 1013 Mineral resource stocks, 1011 Mineralizability, 1027 Minerals Availability System, 1020 Model validation, 999 Molybdenum, 976 Monopoly, 834,835,837,844, 1091, 1133 Monopsonist, 892 Monopsony wedge, 1168, 1185 Morishima elasticity of substitution, 955 Motivational bias, 1068 Motor vehicle emission, 1300 Motor vehicle emissions control, 1309 Multicommodity models, 953 Myopic pricing model, 1100 Nash-Cournot equilibrium, 884,908,920,1092 National security externalities, 787 National Uranium Resource Evaluation, 1012, 1064 Natural endowment, 765,818 Natural gas, 953,987, 1101 Necessary conditions, 861, 862 Neo-classical growth theory, 1267 Neoclassical period, 936 'Netback' pricing, 1174 New deposits, 833 Nickel, 1100

Non-cooperative game, 884,887 Non-essential commodities, 819 Non-existence of competitive equilibrium, 821 Non-perfectly competitive markets, 835 Non-strategic agents, 908 Nonlinear prices, 980 Nuclear power, 1225 NURE, 1012, 1021,1064 Obsolescing bargain, 928 Oceanic crust, 1025 Oil, 1145, 1167, 1316,1328 embargo, 1171,1316 futures market, 1176 import constraints, 1201 import dependence, 1187, 1201 imports, 1167 prices, 1325 sharing agreements, 1209 shocks, 1167,1192 spills, 1224 stockpiles, 1169 Oligopoly, 901 OPEC, 835,908,917,938,1090,1091,1093, 1112,1138, 1145, 1170, 1176 Open access, 1254 Open-loop equilibria, 886 Open-loop policy, 897,909 Open-loop strategy, 885 Opportunity cost, 775, 777,778,780,791, 792, 881,896, 1133 Opportunity cost-constant locus, 797 Optimal natural resource use, 855 Optimal rate of depletion, 856 Option value, 1237, 1250, 1251 Options, 1207 Our Common Future, 1273 Out-of-equilibrium behavior, 891 Paley Commission, 1012 Pareto efficiency, 860 Perfect equilibrium, 884, 891, 926 Perfect foresight, 1294 Perfect import tariff, 920 Perfect substitute, 867 Period of commitment, 922,923 Permanent environmental preservation, 1247 Persistence of pollutants, 1254 Petroleum, 1316 Phase diagram, 796 Phosphates, 1126

Phosphorus, 1126 Pigouvian fees, 1231 Plate tectonics, 1033 Pollution control equipment, 1305 Pollution control in industry, 1300 Population growth, 936 Positive semidefinite matrix, 771 Posted-price system, 985 Potential GNP, 1193 Potential supply, 1014, 1017, 1053 Preference ordering, 942 Present value opportunity cost, 774 Preserved natural environments, 1220 Price, 806 aggregator, 945 determination, 816 expectations, 783,809 reaction curve, 1180 stabilization, 1144 trajectory, 811 Primary-metals industries, 962 Principle of Optimality, 888, 891 Production function, 862, 940 Cobb-Douglas, 1283 constant elasticity of substitution, 1275, 1283 Leontief, 1283 linear logarithmic, 1273 Productivity growth, 1267, 1284 Promises, 882 Property rights, 1231 Property-rights hypothesis, 1090, 1094, 1148, 1179 Psychology, 886 Public goods, 1254 Pure depletion, 858 Purely competitive markets, 817 Quadratic extraction costs, 781, 800 Quantity aggregator, 944 Quasi-option value, 1250 Rate-of-return regulation, 964 Rational expectations, 882, 1101, 1102, 1184, 1294 Rational-expectations hypothesis, 971 Rationing, 972,998 Rawlsian criterion, 868, 1257 Recycling, 975, 1112, 1249 Reduced-form cost function, 1079 Reference path, 884 Reference strategy, 884

Index Regulatory response, 1230 Renege, 884 Renewable resources, 855 Rent, 881 Representative consumer approach, 1276 Reproducible capital, 863 Reputation models, 1132 Research and development, 864, 1114, 1123 Reserve, 1016 Reserves discoveries, 1082 Resource, 1016 adequacy, 1012 base, 1017,1026, 1124 economics, 1219 grades, 1088,1115, 1120 scarcity, 1121 stocks, 1011 supply, 1077 taxation, 928 use, 1219 Restricted-cost function, 941 Risk analysis, 1201 Risk-bearing, 1199 Risk premium, 1199,1251 Royalty, 1118 Roy's identity, 943, 1290 Saddam Hussein, 1175 Saudi Arabia, 1145, 1172 Scale effects, 963 Scarcity, 881, 1112 Scarcity value, 856, 881 Scenic resources, 1236 Scrap metal, 975 Second Law of Thermodynamics, 1112 Secondary markets, 975 Separability, 944 Separable cost function, 804 Shadow price, 896, 1080 Shephard's lemma, 941 Shutdown cost, 796 Side payments, 1139 Size bias effect, 1045 Social costs of oil import, 1170 Social Darwinism, 937 Social rate of discount, 787, 1245, 1255 Soil erosion, 1124 Spatial equilibrium, 1229 Spatial models, 1229 Speculators, 983 Spencer, Herbert, 937

Spot market, 1182 Stackelberg game, 908,917, 1135 State contingent consumption rules, 925 State-contingent control, 889 State valuation function, 865 Stationary equilibrium, 882 Steady state, 794,798, 1248 Stock-adjustment models, 965 Stock-constant locus, 797 Stock-dependent cost, 796 Stock effects, 770,772,789,832,841,892, 1083, 1097 Stock of knowledge, 864 Stock-related externalities, 816 Stockpiling, 982 Storage, 901 Strategic agent, 884 Strategic bias, 1237 Strategic petroleum stocks, 1168, 1176, 1203 Strip mining, 1225 Subsidence of land, 771 Substitute, 864, 1112 Substitution, 1111, 1115, 1122 Sulfur dioxide, 1220, 1225 Supergames, 887 Supply, 1077 Supply functions, 780 Swing producer, 1145 Systems dynamics, 1273 Target revenue model, 1090, 1094,1138, 1149, 1178 Tariffs, 1202 Taxes, 883 Technical change, 864,959 Technological forecasting, 997 Technological progress, 783,827,864, 1115, 1117,1245 Temporary equilibrium, 998 Terms-of-trade effects, 1188 Theorem of the maximum, 822 Threats, 888 Time-consistent equilibrium, 884,891, 926 Time horizon, 794 Time-inconsistency, 1094 Time invariance, 782,794,803 Time of use pricing, 978 Time-series data, 957 Tin, 952 Top soil, 762 Tornqvist index, 945

Translog function, 945,954, 1285 Trigger price, 1140 Truncation effect, 1043 Two-part tariff, 895 Uncertainty, 861,864, 872,982,997, 1096, 1120 Underlying continuous-time representation, 767,768 Undiscovered deposits, 1011 United Nations System of National Accounts, 1279 Uranium, 1054, 1155 Uranium cartel, 1155 US Bureau of Mines, 1020, 1050 US General Services Administration, 952 US Geological Survey, 1012, 1042, 1050 Use table, 1280

Utilitarian framework, 856, 869 Utility function, 936, 942 Utility rate of discount, 869 Valuing environmental externalities, 1236 Volatility of prices, 995 Voluntary risks, 1251 Waste products, 1222 Weak convexity, 771 Westinghouse Electric, 1159 Yom Kippur War, 1171 Zero net investment rule, 1257 Zinc, 952


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