The Theory of Natural Monopoly

The theory of natural monopoly

The theory of natural monopoly WILLIAM W. SHARKEY Bell Laboratories Murray Hill, New Jersey

The right of the University of Cambridge to print and sell all manner of books was granted by Henry VIII in 1534. The University has printed and published continuously since 1584.

CAMBRIDGE UNIVERSITY PRESS Cambridge New York New Rochelle Melbourne Sidney

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521243940 Copyright © 1982 Bell Telephone Laboratories, Incorporated This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1982 Reprinted 1984, 1986, 1989 Re-issued in this digitally printed version 2008 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Sharkey, William W. The theory of natural monopoly. Bibliography: p. Includes index. 1. Monopolies. I. Title. II. Title: Natural monopoly. HD2757.2.S47 338.8'2'01 82-1136 AACR2 ISBN 978-0-521-24394-0 hardback ISBN 978-0-521-27194-3 paperback

Contents

Preface 1 Introduction and overview 2 Historical survey of natural monopoly 2.1 Evolution of the theory of natural monopoly 2.2 Natural monopoly and economies of scale 2.3 Natural monopoly and destructive competition 2.4 Concluding comments Natural monopoly and economic theory: some basic results 3.1 Competitive equilibrium and monopoly equilibrium 3.2 General competitive equilibrium 3.3 The theory of joint production 3.4 Fixed costs and the theory of cross-subsidization 3.5 The theory of the firm and increasing returns 3.6 Public goods and collective choice 3.7 Public enterprise pricing and the theory of the second best 3.8 Concluding comments Natural monopoly and subadditivity of costs 4.1 Natural monopoly in a single output market 4.2 Multiple output natural monopoly: basic results 4.3 Sufficient conditions for subadditivity in multiple output production 4.4 Plant subadditivity and firm subadditivity 4.5 Transactions costs and firm subadditivity 4.6 Concluding comments

page vii 1 12 13 21 24 28 29 29 33 35 37 42 45 48 52 54 57 62 67 73 80 83

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Contents

5 Sustainability of natural monopoly 5.1 Sustainability of single output natural monopoly 5.2 Sustainability of multiple output natural monopoly 5.3 A game theoretic approach to crosssubsidization and the stability of natural monopoly 5.4 Concluding comments 6 A game theoretic analysis of destructive competition 6.1 Game theoretic preliminaries 6.2 Sufficient conditions for a stable market 6.3 Destructive competition: examples of unstable markets 6.4 Concluding comments 7 Competition in natural monopoly and natural oligopoly markets 7.1 The rationale for regulation 7.2 Contestable markets and barriers to entry 7.3 Some complications in a dynamic natural monopoly market 7.4 Limit and predatory pricing 7.5 Concluding comments 8 Noncooperative equilibria in a contestable market 8.1 Preliminary results 8.2 A Bertrand-Nash model of competition 8.3 Concluding comments

84 86 90 102 109 111 113 123 134 143 145 147 151 157 159 164 165 166 170 179

9 Natural monopoly and the telecommunications industry 181 9.1 The nature of demand in telecommunications 182 9.2 Characteristics of telecommunications technology 189 9.3 Econometric studies of the telecommunications industry 197 9.4 Competition in telecommunications and the changing structure of the industry 205 9.5 Concluding comments 213 References

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Index

223

Preface

This study was begun in the fall of 1978 following the publication in several major economics journals of results that cast the "theory of natural monopoly" in a new light. The traditional viewpoint had generally been that certain industries, primarily the regulated public utilities, might by nature be monopolies but that assuredly no theory was required to account for the natural monopoly status of any given industry. Recently this viewpoint has been questioned by a number of sources. From a policy-making perspective the last decade has witnessed the transformation of many industries from a regime of pervasive regulation to one of substantial competition. From a theoretical perspective it has been observed that the proper definition of natural monopoly depends on the more elusive property known as subadditivity of costs, rather than on the simple and easily measured condition of economies of scale. Therefore it is no longer obvious, or self-evident, whether or not a given industry satisfies the conditions of natural monopoly. The purpose of this book is to provide a comprehensive theory that will help those who wish to investigate natural monopoly from either a theoretical or a policy-making perspective. The mathematical level of presentation varies greatly from chapter to chapter, depending on the subject matter. However, at no point is the technical exposition more advanced than is necessary to convey the essential aspects of the theory. Thus, although the potential audience for this study is primarily the professional economist and the student of industrial organization, hopefully other sufficiently interested and motivated individuals, with some mathematical background, can gain a basic understanding of the essential ideas that are developed in this volume. It is a pleasure to acknowledge the substantial support that an organization within AT&T, managed by Tim Stewart, provided during the preparation of an early draft of this book, consisting of Chapters 2, 3, 4, and 9. Michael Kennedy and Carl Inouye were particularly helpful during this phase of the research. A number of individuals from Bell Laboratories have also contributed greatly to the development of this study. In particular,

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Preface

John Panzar, whose own work is frequently cited in the following pages, and Ed Zajac have read the entire manuscript and offered valuable suggestions. In addition, Richard Spady was most helpful in instructing me on some of the material described in Chapter 2; Don Topkis contributed an example discussed in Chapter 6; and Asher Wolinsky offered useful suggestions on Chapter 8. In discussing the cost characteristics of telecommunications networks in Chapter 9, I was able to draw on the considerable expertise of Ron Skoog and others in his organization at Bell Laboratories. In addition to Bell Laboratories staff, I am indebted to Gerry Faulhaber, Richard Gilbert, Carl Inouye, Michael Kennedy, Charlotte Kuh, Robert Rohr, Lester Telser, and Bobby Willig for their helpful suggestions and comments on various portions of the book. I am especially grateful to Carmela Patuto, Geraldine Moore, Donna Manganelli and other members of the Text Processing Department of Bell Laboratories for the speed, accuracy, and good humor that they displayed while typing this manuscript. Finally, I wish to express a sincere debt of gratitude to my wife, Rose, whose constant support and encouragement made The Theory of Natural Monopoly possible. W. W. S.

CHAPTER 1

Introduction and overview

The purpose of this study is to define in substantial detail the conditions under which monopoly — production by a single firm — is a desirable form of market organization. In this chapter I will briefly describe many of the results that will be discussed at greater length later in the book. The "theory of natural monopoly," which will be developed in the following chapters, should be considered as a part of a larger theory of "market organization" or "industrial organization." In the theory of industrial organization the concept of a "market" and of a "firm" in a market are fundamental. Although it will be assumed that the reader is familiar with the way in which these terms are used in economic theory, a brief discussion of each will help to lay the groundwork for the results that follow.1 Throughout this book the term "market" will refer to any collection of buyers and sellers and to the outputs that are produced and sold. A market is a competitive market if there are a large number of sellers and no seller is able to influence the market price by a unilateral change in output. Consequently, in a competitive market there is no strategic interaction among sellers. None of them can increase their profits by taking account of the behavior of other sellers. A market is an "oligopoly" if the number of sellers is small, but greater than one, and if strategic interactions among sellers are important. The profit of any one seller in an oligopoly market depends on his or her own price and quantity decision, as well as on the price-quantity choices of other individual sellers in the market. Furthermore, a change in the strategy of any one seller is likely to induce a change in the strategy of every other seller. Chapter 3 will contain a more extensive review of these and other concepts used in the book.

2

1 Introduction and overview

Finally, a market is a "monopoly" if there is only one active seller in the market, although there may or may not be other potential sellers who are ready and willing to take the place of the monopolist. If there are no inactive sellers in a monopoly market, then a monopolist, unless he or she is regulated, is free to make price and output choices so as to obtain the maximum profit. However, if there are inactive sellers, then a monopolist must take their behavior into account, just as a seller in an oligopoly market must consider the behavior of other active or inactive sellers. Having described a market in terms of buyers, sellers, and outputs, I will now discuss somewhat more fully a seller, or firm in the market. A "firm" is an organizational structure in which a centralized planning authority replaces the decentralized, impersonal forces of a market. Fundamentally, this book is about the "theory of the firm." I do not intend, however, to develop a theory of the internal organization of firms.2 Instead, I will use the concept of a cost of output function for a single firm in a market. Then if q = (QwAn) represents a vector of outputs in a particular market, I let C(q) represent the monetary value of both physical and organization inputs that are required if q is to be produced by a single firm. In this book the trade-off between a centralized firm and a decentralized market will be expressed in terms of the relative cost of producing an output q with a single firm or with many firms. Thus if q\",qk are output vectors that sum to q, then a single firm is more efficient than a multifirm market if C(q)