Economics of Rivalry, Conflict and Cooperation

World Scientific Gangopadhyay This book offers an extensive and original study of the dynamics of rivalry, evolution o...

Author: Partha Gangopadhyay

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World Scientific

Gangopadhyay

This book offers an extensive and original study of the dynamics of rivalry, evolution of costly and violent conflicts, and potential cooperation among powerful players. It unravels the special features of the global socio-economic system that can make it extremely fragile and vulnerable. It serves as a good reference source for anyone interested in some of the pressing and emerging problems of the global system, such as intra-national and interethnic conflicts, climate change challenges, poverty and terrorism, and provides useful and rigorous insights into the collective bid to resolve some of these problems. Written in a simple and accessible manner, this book will help researchers and policy makers in understanding and abetting costly conflicts.

ECONOMICS OF RIVALRY, CONFLICT AND COOPERATION



Partha Gangopadhyay

World Scientific

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ISBN-13 978-981-4289-83-2 ISBN-10 981-4289-83-3

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Partha Gangopadhyay University of Western Sydney, Australia

World Scientific NEW JERSEY

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LONDON

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SINGAPORE

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BEIJING

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SHANGHAI

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HONG KONG

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TA I P E I

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CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

ECONOMICS OF RIVALRY, CONFLICT AND COOPERATION Copyright © 2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN-13 978-981-4289-83-2 ISBN-10 981-4289-83-3

Typeset by Stallion Press Email: [email protected]

Printed in Singapore.

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The book is dedicated to three women of my life — Uma, Renu and Ishani


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Foreword

The global community needs to urgently and effectively address multiple economic, social and environmental challenges. On the development front, we already face formidable problems like poverty, resource scarcities (food, energy and energy), and sicknesses. Furthermore, climate change is an emerging threat that will exacerbate these existing problems. The scarcity of resources has been a major driver of human actions since the dawn of history. While basic human needs can be met, seemingly limitless human greed is now exceeding the capacity of the limited global resource base. The ever-growing needs of economic agents for scarce natural resources is one of the fundamental sources of conflict and social disharmony. The sustainomics framework provides a practical approach to address the broader challenge of making development more sustainable and to balance the economic, social and environmental dimensions of sustainability. On the more specific issue of resource scarcity, economists have spent some time trying to study the fierce competition for productive resources. Mechanisms to limit the demand for scarce resources or share them are essential, because merely searching for new resources and technologies to exploit resources more efficiently cannot keep pace with demand growth. John Nash proposed an ideal theoretical solution (called the Nash equilibrium) that would help to amicably allocate scarce resources and resolve conflicts — but assuming there are rational expectations, perfect foresight and being aided by market mechanisms and other relevant institutions. vii

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Economics of Rivalry, Conflict and Cooperation

However, in the real world, intense rivalry can lead to serious and costly conflicts due to human failings (like envy, jealousy, and emotions of relative deprivation), as well as economic imperfections (like policy and market failures, and missing institutions and information). Once a socio-economic system experiences conflicts, severe rivalries and damaging conflicts need to be managed through social mechanisms that promote sustained cooperation. This book provides a comprehensive and excellent study of the dynamics of rivalry, costly disputes, and cooperation, starting from the Nash equilibrium. The author explains clearly, concisely and authoritatively, the manner in which simple business rivalries may be resolved, and how that process could shed useful light on managing more complex, costly and violent social conflicts. Three important observations shape the analysis in this volume. First and foremost, the economic foundation of rivalry and violent conflicts relies on a mechanism that is akin to the proverbial industry/ business that generates excess rents and thereby perpetuates rivalry and conflicts as an equilibrium phenomenon. Second, the apparatus of globalization has resulted in gradual dissemination of ethics and market-based principles worldwide. With the firm rooting of market principles, there is a tendency towards homogenization of economic and commercial practices across the globe. Peace through cooperation among rivals is possible if unrestrained market forces and greed could be better managed through the spread of more ethical principles also implicit in modern economics. Third, and finally, there appears to be an unfortunate concentration of rivalry and violent conflicts in poorer regions of our globe, and the initial phase of globalization has intensified these conflicts. The pathway from conflicts to peace will need to be built on cooperation — for which the economics of cooperation can work as an important guidepost. This book is a valuable contribution towards resolving damaging social conflicts, using the experience of the business world that usually relies on cooperation to limit conflict and rivalry within reasonable bounds. Other sources of rivalry and conflict that interact with market mechanisms to perpetuate conflicts in our modern societies, are also examined.

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This book is recommended reading for students, researchers, policy analysts and practitioners in the field. Mohan Munasinghe Chairman Munasinghe Institute for Development (MIND) Sri Lanka Professor of Sustainable Development University of Manchester, UK Shared the 2007 Nobel Prize for Peace (Vice Chair, IPCC-AR4)


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Contents

Foreword

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Introduction Economics of Rivalry, Conflict and Cooperation

1

Section A

Rivalry, Conflict and Cooperation: Lessons from the Business World

13

Chapter 1

Endogenous Collusion and Rivalry: Theoretical Models and Conjectures

15

Chapter 2

Politics of Campaign Contributions, Economics of Rivalry and Endogenous Market Structures

87

Chapter 3

Rivalry in Formation of Social Capital in Networks and Endogenous Social Norms

Chapter 4

Economics of Cooperation in Successive Markets 127

Chapter 5

Secret Price Discounts and Chaotic Discrimination and Industrial Conflicts

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107

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Chapter 6

Globalization, Market Hostility and Endogenous 169 Mergers among Rivals

Chapter 7

Endogenous Rivalry, Conflicts and Cooperation in Vertical Markets

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Section B

Rivalry, Conflict and Cooperation: Goliath against Goliath

213

Chapter 8

The Art of Central Banking and Policy Conflicts

215

Chapter 9

Intellectual Property Rights and SIDS: Vertical Foreclosure and the Role of Ethics in Cooperation

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Chapter 10

Local Governance: Fiscal Decentralization and Conflicts in LDCs

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Chapter 11

Multinationals and Labor Unions in LDCS: Cooperation vis-à-vis Conflicts

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Chapter 12

Globalization, Democratization and Urban Crises in Developing Nations

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Concluding Comments: Whither Rivalry, Conflicts and Cooperation?

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Bibliography

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Index

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Introduction


The availability of economic resources relative to their demands is limited, which often gives rise to intense competition and continuing rivalry among economic agents. Economic agents, driven by their rational expectations, perfect foresight and aided by market mechanisms and other relevant institutions, are capable of resolving the tyranny of relative scarcity by achieving an outcome commonly known as the Nash equilibrium. The Nash equilibrium implies an economic outcome that is a collection of mutual best responses such that no agent can make an improvement in one’s well-being by a unilateral deviation from the Nash outcome. On the theoretical plane, though the competition for resources can be settled in the Nash equilibrium in an amicable fashion, the rivalry can engender serious and costly conflicts in the real world. Once a social system has conflicts, severe rivalry and costly conflicts can be kept at bay only through lasting cooperation. This book offers an extensive study of the dynamics of rivalry, costly and violent conflicts, and cooperation. There are three important observations that propel our analysis: First and foremost, we argue that the economic foundation of rivalry and violent and excessive conflict relies on a mechanism that is akin to the proverbial industry/business that generates excess rents, or supernormal profits, and thereby perpetuates rivalry and conflict as an equilibrium phenomenon. Second, we posit that the turning wheels of globalization have resulted in a dissemination of market principles all across the 1


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globe. With the market principles, we also note a homogenization of economic cultures. Finally, the above developments along with the demise of the Cold War resulted in a concentration of rivalry and violent conflict in poorer regions of the world. The economics of rivalry and conflict as a profiteering business offers us an avenue to examine the genesis of violent conflicts from the perspective of a simple business rivalry. We then turn to the question of resolving costly conflicts in the light of the experience of the business world that usually relies on cooperation to retain conflict and rivalry within a reasonable bound. We also highlight various other sources of rivalry and conflict that intermingle with the market apparatus to perpetuate violent and costly conflicts in our modern societies. Let us have a cursory look at some of the critical issues of our thesis. Violent Conflict as a Profiteering Industry/Business Conflict models are usually cast as general equilibrium models with presumed perfectly competitive markets that involve a trade-off between economic, or productive activity, vis-à-vis unproductive activity entailing conflicts. This is the much-famed trade-off involving the “guns and butter” of economics. Hirshleifer (1988, 1989, 1995, 2000) put forward several models to explain conflicts in terms of three economic variables: (1) preferences, (2) opportunities within constraints, and (3) prevailing perceptions. Hirshleifer in his work introduced a contest to explain conflict as a means to economic gains. One of his many contributions to the field was to introduce a Tullocktype contest success function that came to be called “conflict technology” in the relevant literature. In light of the conflict technology and the economic prize to be won in conflicts, akin to that of a contest, Hirshleifer offered an equilibrium conflict as a Nash equilibrium of the proposed contest such that efforts (guns) are chosen as the mutual best responses of the micro agents. The Hirshleifer model thereby explains feasible equilibrium defense expenditures/ spending of a group of competing nations. The prototype model was further finessed to explain various interesting results related to the


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Introduction

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incentives for nations to arm themselves and explore the well-known paradox of power. Several important papers developed along the line of the Hirshleifer-style model, which focused on the optimal choice on defense spending for a nation in the context of a general equilibrium setting. The important work of Grossman (1991, 1998, 2004) also shares the similar notion of conflict, though in a richer setting. Grossman reduces a society into three groups: First, there is a group of peasants who decides to choose between two activities — to fight or to produce an agricultural product. The second group represents a government agency that taxes the peasants and thereby collects booty and raises an army to protect the booty. The third group is a rebel group who recruits and raises a rebel army from the peasants to fight the government for securing the booty. The rebel group funds its activities by raising an army and looting peasants. It is the treatment of rebellion as business that is one of the most distinguishing features of conflict — insurgents are similar to bandits or pirates who engage in rebellion and conflict to make profit. Thus, the new model of Grossman is more intricate than the models of Hirshleifer; however, the fundamental notion is that conflict is akin to a contest for acquiring resources, as opposed to peaceful participation in a market exchange that involves mutually beneficial trade. Conflict is a zerosum game — there is only one winner in the contest who takes the whole prize, or stake. Conflict is a product of rebellion that is akin to an industry that creates profit-making opportunities from an act of piracy or looting. The rebel group has an increasing marginal cost of recruiting soldiers/fighters from the peasantry and also a declining marginal benefit in terms of the increased probability of winning the contest and prize with the increasing size of the armed force under the control of the rebel group. The economic equilibrium is struck where the marginal cost of employing one more soldier is balanced by the marginal benefit of so doing by the rebel group. Skaperdas (1992) introduced the possibility of cooperation, as opposed to conflict, in a game that repeats over time. In the proposed model, Skaperdas confirmed the existence of multiple Nash equilibria: The first Nash equilibrium involves a full cooperation equilibrium


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in which contesting parties share the available prize without arming themselves, under a set of restrictive assumptions. Thus, one may call the first equilibrium, a complete peaceful equilibrium in which nations invest zero dollars in defense spending, a Nash equilibrium. In the second equilibrium, only one nation invests in defense spending and the equilibrium has come to be termed as a partially cooperative equilibrium. Finally, he established the existence of a conflict equilibrium in which each nation spends adequate resources to create effective conflict technology. Garfinkel (1994) extended the analysis to the international arena by introducing domestic politics as a determinant of defense spending by a nation. Her famous result in a two-period model shows that electoral uncertainty in democracies can reduce the severity of international conflicts by inducing competing nations to reduce their defense spending as an equilibrium phenomenon. The negative impact of democracies on defense spending is derived from the probability that the incumbent government will not be re-elected, which induces the incumbent governments to commit less to military spending. Against the backdrop of this strand of economic theory, political scientists traditionally argue that conflicts and rebellions are actuated by political protests that are driven by deep-rooted grievances of people. The grievances are precipitated by a host of social banes like inequality, racial, ethnic or religious intolerances, and oppression of one group by another. The exploitation of one group by another has also received serious attention from Hirshleifer (2000) who calls this proclivity of human beings to form a gang against others Machiavelli’s Theorem, which can shape preferences and stir up grievances and exaggerate opportunities from conflicts. The political science literature has highlighted two elements in exacerbating conflicts: First, the type of political regime has been isolated as a determinant of conflicts (see Hegre et al., 2001). There is some evidence to believe that more democratic countries have a lower risk of war (see Collier and Hoeffler, 1998, 2002). Second, economic inequality is believed to be an important determinant of conflicts, though recent economic studies have not found any systematic relationship between inequality and conflicts (see Collier and Hoeffler, 2002). In their study, Collier and


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Introduction

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Hoeffler noted that low per capita income and low growth rates are contributing factors to conflicts. Our principal goal is to develop a simple model to show how democracies can endogenously drive inequality that may play an important role in determining equilibrium levels of conflict in a society. Globalization and Diffusion of Market Principles and Homogenization of Economic Cultures Globalization is a multidimensional concept, having various important facets that involve economic, financial, technological, social and political processes, which continually transform the global economy, society and politics. In recent years, social scientists have highlighted several important facets that accompany globalization: trans-border trade, trans-border movement of capital, emergence of a new international order, diffusion and homogenization of economic cultures and institutions, labor market consequences, governance issues; and finally, prospects and problems of our global economy and society. It is widely recognized that the process of globalization has been significantly aided by the fall in the cost of communication and transportation, leading to an inevitable shrinkage of our globe into a quasi “global village” — characterized by an integration typically observed in traditional village communes. We therefore view globalization as a complex process that gradually unleashes a series of transitions: the process starts off with an increased integration of the world economy through trade and investment networks. It is well understood that the harbinger of this stage of increased integration turns on the pivot of decreasing transaction costs of trans-border trade and investment. Declining transaction costs are explained in terms of technical progress that reduces the cost of communication and transport costs. Declining transaction costs have a direct and positive impact on crossborder trade and portfolio and direct investment. The economic consequence of this increased integration is two-fold: First, nations become more interdependent in economic terms. Second, there arises a perception that trans-border trade and investment offer tremendous and often unprecedented economic opportunities for a nation.


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The first transition thus results in an increased integration of the world economy — through a mesh of multinational investment, trade flows and flows of financial capital — with an equally important transition in the perception about the importance of trans-border trade and investment as a vehicle of economic progress and prosperity for a nation. The second transition impacts on the realm of national management as national governments actively respond to this new perception that trans-border trade and investment offer great benefits to those nations that entertain relevant openness to foreign trade and investment. As a number of nations vie and compete against each other to take home the spoils of the world economy, policy makers come to agree that the main barrier to the access of these spoils lies in the domestic economic structure characterized by the labyrinth of controls that has been a by-product of the Keynesian era of de-globalization. This leads to the third transition that paves the way for the homogenization of economic ideologies, convergence of macroeconomic and trade policies, and the consequent adoption of measures of domestic liberalization. For any national government, options are pretty limited — either it chugs along with the pre-existing regime of economic control with limited global trade as pursued by China and India or, alternatively, the nation must ditch the olden economy and substitute it with a functional market mechanism, openness to transborder trade, liberalization of domestic and external sectors and exchange rates, and privatization of state-owned enterprises. The hard fact is that the majority of nations went for the second option that represents an unprecedented convergence of economic ideologies during the 1980s and 1990s. This common act of nations, as though to the dictate of a common script, has further consolidated the process of the integration of the global economy. The final transition typically takes place in the social and economic spheres of our globe as a direct consequence of these previous transitions. The process of globalization can thus be reduced to this simple and uncomplicated fable. Within this simple fable highlighting various, possibly virtuous, transitions lies a plethora of terribly complicated subplots without which it is impossible


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Introduction

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to understand the process, consequences and ramifications of globalization. The Dynamics of Violent Conflict Violent conflict and peace are the flip sides of the same coin of our societies. In many societies, conflicts of violent nature regularly spring up, usually causing the destruction of economic and social assets, and leading to the needless loss of human lives. In similar societies, on the contrary, a peaceful resolution of serious conflict often takes place. Many societies even seem to traverse from conflict to peace and to costly conflict again. It is also important to note that some societies do seem to enjoy lasting peace. The literature on the economics and politics of peace and conflict has been with us now for several decades. An abundant crop of excellent work has appeared, supporting, critiquing and complementing the original idea that economic development is a precursor to effective resolution of conflicts and, hence, to sustainable and lasting peace. The frequency of international and civil wars, as well as their lethality and indirect costs, declined substantially from the end of the 1980s until 2003. A few important observations are in order: • • • • • • • •

the frequency of armed conflicts fell by about 40% in the 1990s except in Sub-Saharan Africa where the incidence remains high; genocides and politicides declined by 80%; international arms transfers went down by 33% in value; forced migration of refugees fell by about 45%; battle deaths declined by about 80%; war mortality rates came down by about 35%; military spending as a percent of GDP declined in most countries and globally by almost 50%; the number of soldiers per 1000 people went down by 35%.

The picture painted by the above statistics suggests that the forces supporting peaceful settlements of conflicts and violent disputes have been gaining significant momentum in our modern world. There are


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many apparent factors that have led to significant improvements in the global picture of conflict. •

•

• •

First and foremost, the period witnessed a gradual withering of colonial states in the less developed world. Violent conflicts of liberation against European colonial powers in developing countries gradually achieved independence for these nations by the early 1980s. Second, with the conclusion of the Cold War, the USA and the Soviet Union scaled down their military support for their allies in developing countries. As a result, the war fields of the Cold War were drastically changed into spheres of economic progress and development. Third, the United Nations and other international agencies started to play a more significant role in peace-keeping and peace-making. Fourth, the 1990s also experienced unprecedented times of global growth from which many, but not all, previously conflicted regions benefited, resulting in a further decline in violent conflicts.

Now let us have a cursory look at the regions of violent conflict in our contemporary world: According to the 2006 Global Hunger Index of the International Food Policy Research Institute (IFPRI), of the 12 countries with the highest levels of hunger, 9 were affected by civil wars and costly and violent conflicts. The 10 countries that scored the worst are all in Sub-Saharan Africa, but South Asia was also a hotspot of conflicts and malnutrition. The three indicators are: child malnutrition, child mortality, and estimates of the proportion of people who are calorie-deficient. Doris Wiesmann, the IFPRI researcher who developed the Global Hunger Index, states: “This index provides a particularly comprehensive measure of global hunger because it ranks countries on three leading indicators and combines them into one.” The researcher continues, “Alone, each indicator has limitations, but put together, they give us a much more complete picture of the state of hunger around the world.” The latest index ranks 97 developing countries and 22 countries in transition; the data is not available for three nations (Afghanistan,


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Introduction

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Iraq and Somalia) where violent conflicts have taken unprecedented states. The index indicates that scores have improved in South Asia and in most other parts of Asia since 1981, though many countries in this region suffer from high levels of hunger. Several countries, such as Botswana and Namibia, do worse than expected on the index, relative to their level of development, or gross national income per capita. High income inequality is one of the major factors that push these countries towards high levels of hunger and malnutrition. With the adoption of the Millennium Development Goals, hunger and poverty have become the prime targets of the global development agenda, with the goal of reducing hunger by half by 2015. As a result, the major exception and continuing source of conflicts has been Sub-Saharan Africa whose growth of real GDP per capita adjusted for PPP halved from the 1980s to the 1990s. A recovery has started since 2000, which may reverse the trend in violent conflicts. However, there are a host of problems in the region: •

• • •

•

•

According to the World Bank’s World Development Indicators of 2005, the number of people living in extreme poverty (at less than $1 a day) doubled in Sub-Saharan Africa from 1981 to 2001. Since the end of the 1980s, 80% of the world’s 20 poorest countries (many in the Sub-Saharan region) have suffered a major war. Military expenditure as a proportion of GDP and the number of soldiers per 1000 people changed little. Battle-deaths actually fell in Sub-Saharan Africa through the 1990s (apart from an all-time high spike from 1998 to 2000 due to the Eritrean war). However, war-deaths in this region have vastly exceeded battle-deaths due to indirect deaths. Compared to the wars from the 1950s to the 1970s, most of the recent conflicts are between badly equipped government troops and lightly armed, untrained rebel forces in poor countries. Most of these violent conflicts have been set in remote rural areas, where national governments have limited presence and where insurgent groups can find easier hide-outs. On one hand, conflict caused increased vulnerability of the population, often spreading epidemics and intensifying famines in the


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•

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region. On the other hand, diseases and famines are likely to have a feedback effect on the incentives for war. Thus, one expects a positive correlation between the incidence of conflict and disease or famine, which has been evident in Sub-Saharan Africa. The aim to control valuable natural resources such as timber, diamonds, oil and minerals has precipitated some of these violent conflicts. Governments and insurgent forces usually utilize the revenues from these products to finance military activities. Disputes over natural resources triggered some of the region’s long-standing ethnic tensions that have contributed to violent conflict as well. The trade of “conflict timber” has been a source of conflict in many countries with tropical forests, as it has been the direct cause of violent conflicts and is also used to finance them. Either the timber benefits some groups under conditions of violent conflict, or it is produced and traded in the wake of recent violent conflict. The World Health Report 2004 from the World Health Organization stated that the HIV/AIDS epidemic had its “most explosive growth” in the mid-1990s in Africa, and that by 2003, it was “home to two-thirds of the world’s population living with HIV/AIDS.” Malnutrition, HIV/AIDS, the onslaught of and perpetuation of human hunger, and personal insecurities can turn some of the backward regions into veritable minefields wherefrom one can only expect holocaust. The persistent famine in the Horn of Africa coincided with violent conflicts within and between Ethiopia, Eritrea and Somalia in the last 15 years.

Managing Conflicts and Promoting Peace Through Cooperation There are two critically important ideas that propel the economics of peace: •

First and foremost, it is John Maynard Keynes who introduced the important idea of the mutual dependence of peace and the


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•

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economy. According to this view, on the one hand, it is usually held that economic development is a necessary precondition for achieving peace. On the other hand, peace is ultimately a precondition for economic development. Thus a lasting peace is feasible if and only if peace treaties are economically sustainable and fair. Otherwise, temporary peace will be replaced by renewed and armed conflicts. Secondly, peace is feasible only when agents with diverse and nonmutual interests collaborate with each other to create a peace dividend that is relied upon to propel the peace dynamics forward. In the context of achieving peace, cooperation is warranted on two fronts: First, cooperation is necessary to create an economic incentive — what is known as a peace dividend. Second, cooperation and coordination are necessary to share the peace dividend in an equitable manner so that the allocation is considered “fair.” In the absence of an economic incentive and fairness, lasting peace would be a fading mirage.

In our current work the focus is also on the question of cooperation that seems to play a critical role in the resolution of rivalry and violent conflict. Where are we going to get our lessons from? It is the business world that regularly confronts similar situations, as described above, and which calls forth active cooperation to resolve a conflict of interests among business partners.


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Section A

Rivalry, Conflict and Cooperation: Lessons from the Business World


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Chapter 1

Endogenous Collusion and Rivalry: Theoretical Models and Conjectures

1.1 Competition and Collusion in a Segmented Industry: Introduction The primary intuition of this work is that market segmentation creates an opportunity of entry for a business firm into other markets that can have serious impacts on the equilibrium configuration through the effects of the potential entry on the incentives of and constraints on incumbent firms. On a similar note, market segmentation offers new scope for cooperation among incumbents to forestall entry. There is little literature on this important issue that this work intends to address. Entries and exits, through their effects on the cost, or efficiency, asymmetry in a segmented market, can trigger a series of endogenously driven changes in a market. One of the major key endogenous changes is the endogenous partnership formation, or collusion, of business alliances that is driven by these changes in the efficiency/cost asymmetry. We offer a model of endogenous alliance formation, which we believe to be the first of its kind to shed light on the incentives for firms to form coalitions and alliances endogenously in the context of threatened entry in a segmented market. The caveat is that it is a restrictive form of alliance that we consider in this work. Upon the formation of an alliance between two firms, the new entity sells off the assets of the less efficient business in the relevant segment and offers appropriate compensation to all old shareholders and workers

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of this less efficient organization. The implicit assumption is that the value of the less efficient firm is less than the competing claims of its owners and workers. Formation of alliances and group behavior have offered timehonored challenges and facile opportunities to economists for a long time. There are two distinct approaches to the formation of alliances, or groups, in economics. First, considerable attention has been accorded to the problem of alliance formation from the perspective of cooperative games (Aumann, 1989; Aumann and Peleg, 1960; Gillies, 1959; von Neumann and Morgenstern, 1944, pp. 583–584; Shapley and Shubik, 1969). In these models, potential members decide whether to join an alliance or group. Once they join and the alliance is formed, the actions of all these members are constrained by the dictate of a mutually agreed contract. The focus is on the collection of joint actions that the alliance can take independent of the actions of non-alliance members. In order to highlight alliance formation, these models typically examine the terms of the contract that is mutually acceptable. These models also examine the joint action of the alliance and also the related issue of limits to group size. More complex models examine the possibility of simultaneous formation of multiple alliances. The crux of the analysis is to home in on the formation of an alliance and the joint action it broaches on itself. The natural extension of this line of reasoning is to attribute some kind of stability to such alliances: the major requirement is to have alliances and their joint actions immune to deviations either by a member or by a sub-alliance of members (see Gangopadhyay, 2000; Harsanyi, 1974). On the other hand, the non-cooperative approach highlights the formation of an alliance in light of the internal functioning of the alliance. To put it baldly, in non-cooperative games, the focus of research is on how members choose their joint actions (see Gangopadhyay, 2000, 2002; Harsanyi, 1974; Chatterji et al., 1993). Outcomes of cooperative games, or coalitional games, do not depend on the details of individual actions. Our focus is on the

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Endogenous Collusion and Rivalry

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non-cooperative aspect of the formation of equilibrium alliances. But once the alliance is formed, it behaves like a single entity in choosing the alliance activity and, in this regard, our model belongs to the former class of models. Possibilities of cooperative ventures in oligopolies have been examined in Katz and Shapiro (1985); Kamien et al. (1992); Matutes and Padilla (1994); and Yi (2000). Katz and Shapiro (1985) examine incentives for firms to reach perfect compatibility with all the products in the industry. Kamien et al. (1992) highlight joint research ventures in the context of industry-wide agreements. Matutes and Padilla (1994) consider formation of alliances as a simultaneous game (like ours) and consider the coalition-proof Nash equilibrium as their solution concept (as opposed to the Cournot–Nash equilibrium in this chapter). Yi (2000) develops non-cooperative games of coalition formation to compare equilibria of different alliance-formation games. In this work, we examine a model of endogenous alliance formation in the highly simplified context of oligopoly with a linear demand function. In this model, firms form alliances in order to reduce their marginal cost of production, or improve efficiency. They also form alliances to capture the largest possible market spoils by acting as a single entity to enhance their market power in the relevant market segment. We start off with a simple duopoly and examine the exogenous possibilities of a potential merger between these incumbents. We then consider entry by a firm into this duopoly that opens up the possibility of endogenous mergers/collusion/cooperation, or alliance formation. Based on the (marginal) cost differences/asymmetry in efficiency we are able to determine the driving forces behind alliance formation in this triopoly. Bloch (1995) and Belleflamme (2000) consider cases where firms form alliances in order to decrease costs. The existing theory of partnerships highlights that partners get together to exploit economies of scale wherefrom alliances form (Farrell and Scotchmer, 1988). Yi (1997) shows in the context of coalitional games that the

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alliance/coalition contains too many members in equilibrium. Our work bears some apparent similarities to Bloch’s paper. But there are major differences: Bloch considers the alliance formation in a sequential setting in which one alliance acts as a Stackleberg leader and thereby captures more than three-quarters of a market by forming an alliance with roughly three-quarters of firms in an industry. The followers are forced to accept a lower share by the formation of a smaller alliance. We, on the other hand, postulate simultaneous moves for endogenous alliances, which respond to each other when forming the alliance. Bloch’s findings are driven by a very restrictive assumption about alliance formation: he posits a two-stage model such that firms form an irrevocable alliance in the first stage in a sequential fashion as described above. In the second stage, they compete against each other for market shares in order to maximize their individual market spoils.1 The formation of an alliance is thus limited to the first stage. In the second stage, these firms do not take any joint action. Such a setting may be appealing in some scenarios such as common R&D projects, common use of facilities, and network externalities as stressed by Bloch. But there are important cases when the alliance or alliance formation takes place for the simple motive of seizing larger market shares and thereby capturing larger profits. A common example is mergers and acquisitions. Our model considers the formation of alliances in a scenario in which once alliances are formed, they take joint actions to vie against each other as unified entities.

1

The equilibrium in Bloch’s papers is derived from this assumption: since these firms still compete in the product market as oligopolists, the formation of an alliance has dual effects. First, the reduction in a firm’s own marginal cost increases its profit. Second, the cost reduction of its competitors induces more aggressive behavior on their part and causes a decline in its profit. The implicit assumption is that as a new firm enters an alliance, it enjoys a decline in its cost which increases its the alliance size. Thus, as the alliance size increases, the incentive to admit one more member into the alliance decreases wherefrom the critical size is arrived at. Beyond the critical size, the admission of a new member lowers the profit of each member.

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1.2 Baseline Model 1.2.1 The model of a segmented banking industry in Australia In order to drive our main message home, let us consider two geographical locations in Australia, namely New South Wales (NSW) and Victoria, and focus on two dominant banks, Westpac and ANZ, and a small player in the Australian banking industry, say Bendigo Bank. The intuition of market segmentation highlights the possibility that each of the dominant banks, due to historical and strategic reasons, has a stronger economic presence in one of the regions, or segments. Alternatively, one may like to argue that they have different efficiencies in different market segments. For the sake of simplification and tractability, we assume that the NSW market is a duopoly between Westpac and Bendigo Bank as an extreme form of segmentation and ANZ does not have any presence in NSW at the outset. This is an extreme assumption that will be dropped in due course. In a similar fashion, we assume that the Victoria market is a duopoly between ANZ and Bendigo Bank, and Westpac has yet to enter the Victoria market. In order to carry out the basic analysis, we further posit that these two duopolies are mirror images in terms of relative efficiency and demand parameters so that we can focus our analysis, on one market. This assumption will be relaxed later on to introduce market differences. We start off with a simple duopoly in which two banks engage in quantity competition. For the sake of tractability, the demand function is postulated as q = [1 − (p/9)]. It is further assumed that these banks have constant marginal costs Ci for firm i, i = 1, 2. In our model, efficiency is represented by a ranking of marginal costs. We assume that C1 < C2. We label the cost difference as ∆, hence ∆ = C2 − C1. This cost difference/asymmetry in efficiency determines the market share and profits of each incumbent in a duopoly. The profits of these incumbents from the Cournot–Nash equilibrium are: Π1* = (1 − c1 + ∆)2, 2 Π* 2 = (1 − c2 − ∆) . Since, by construction, Bank 1 is more efficient, Π1* > Π * 2.

(1a) (1b)

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We now consider possible entry by Bank 3 which has a constant marginal cost of production C3. We examine exogenous alliance possibilities between Banks 1 and 2 as Bank 3 makes an entry — assuming that the alliance does not attract flak from the regulatory authority. As Banks 1 and 2 merge/collude into a single entity, the merged entity with the marginal cost C1 engages in Cournot competition with Bank 3. We represent the cost difference as C3 − C1 = ∆1. The profits from the Cournot–Nash equilibrium of the newly emerged duopoly are the following: * = (1 − c1 + ∆1)2, Π1,2 2 Π* 3 = (1 − c3 − ∆1) .

(1c) (1d)

Equation (1c) gives the profits of the merged/colluded bank. We examine the incentives for Banks 1 and 2 to form an alliance. It is a very restrictive form of alliance that we consider in this work. Upon the formation of an alliance, the new entity sells off the assets of the less efficient bank and offers appropriate compensation to all shareholders and workers of the less efficient bank. The implicit assumption is that its value is less than the competing claims of its owners and workers. It is also recognized that the compensation to the less efficient bank is larger the greater the profits of the newly merged bank are. This assumption is for the tractability of the proposed model. We first consider the possibility that C3 > C2. Suppose there is no alliance, then the duopoly is turned into a triopoly as Bank 3 enters. We label the cost difference between Banks 2 and 3 as ∆2, ∆2 = C3 − C2. The profits of these three banks from the Cournot–Nash equilibrium are: Π1 = 9(1 − c1 + ∆ + ∆1)2/16,

(2a)

Π2 = 9(1 − c2 − ∆ + ∆2) /16,

(2b)

Π3 = 9(1 − c3 − ∆ − ∆2) /16.

(2c)

2

2

A simple comparison will give us the incentives for exogenous alliance formation between Banks 1 and 2.

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Observation 1. The incumbents — following the entry of Bank 3 — have an incentive to form an alliance if C3 > 2C1 + 3∆ − 1. Proof. Banks 1 and 2 have incentives to merge if Eqs. (1c) > (2a). That is, (1 − c1 + ∆1)2 > 9(1 − c1 + ∆ + ∆1)2/16. Simplification of Eq. (2d) yields the result.

(2d)

1.2.2 Endogenous alliance formation/merger The entry of Bank 3 leads to the possibility of three distinct mergers, or alliance formation — Banks 1 and 2, Banks 1 and 3, Banks 2 and 3. Assuming C1 < C2 < C3 and retaining the previous symbols, we label the post-merger profits of Bank i and j with Πi,j*: * = (1 − c1 + ∆1)2, Π1,2 2 Π* 1,3 = (1 − c1 + ∆) ,

(3b)

Π* 2,3 = (1 − c2 − ∆) .

(3c)

2

(3a)

* > Π1,3 * > Π2,3 *. Thus, both Banks 2 From these values, we know Π1,2 and 3 have an incentive to form an alliance with Bank 1, whilst Bank 1 has an incentive to merge with Bank 2. Observation 2. Banks 2 and 3 have an incentive to merge if C3 < (1 + 2C2 − ∆)/3. * > Π2: Proof. Banks 1 and 2 have an incentive to merge if Π1,3 substituting Eqs. (3b) and (2b) yields the result. From Observations 1 and 2, we offer the first result on endogenous alliance formation. Proposition 1. Assuming C1 < C2 < C3, Banks 1 and 2 will form an alliance if C3 > (1 + 2C2 − ∆)/3 > 2C1 + 3∆−1.

(4a)

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Banks 2 and 3 will form an alliance if C3 < 2C1 + 3∆ − 1 < (1 + 2C2 − ∆)/3.

(4b)

There will be no alliance formation if (1 + 2C2 − ∆)/3 < C3 < 2C1 + 3∆ − 1.

(4c)

Banks 1 and 2 will form an alliance if 2C1 + 3∆ − 1 < C3 < (1 + 2C2 − ∆)/3,

(4d)

* > Π* * since Π1,2 1,3 > Π2,3 . Proof. Comparisons of Eqs. (2a)–(2c) with Eqs. (3a)–(3c), respectively, will yield the result. We now consider the case in which C1 < C3 < C2. That is, Bank 3 is more efficient than Bank 2. Let us label the cost difference as: C3 − C1 = d, C2 − C1 = d1, C2 − C3 = d3. The profits of these three banks from the Cournot–Nash equilibrium are Π1 = 9(1 − c1¨+ d + d1)2/16,

(5a)

Π3 = 9(1 − c3¨− d + d2)2/16,

(5b)

Π3 = 9(1 − c2 − d1 − d2) /16.

(5c)

2

The post-merger outcomes are * = (1 − c1 + d1)2, Π1,3 * = (1 − c1 + d)2, Π1,2

(6b)

Π* 2,3 = (1 − c3 − d) ,

(6c)

2

(6a)

* > Π1,2 * > Π2,3 * . We now offer the result for endogenous while Π1,3 alliance formation.

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Proposition 2. Assuming C1 < C3 < C2, Banks 1 and 3 will form an alliance if d < C1 + [(1 − C1 + d1)/3],

(7a)

C3 < (1 + C1 + C2)/3.

(7a′)

that is,

Banks 2 and 3 will form an alliance if C3 > (3C2 − C1 − 1).

(7b)

Banks 1 and 2 will form an alliance if C3 > (3C2 − C1).

(7c)

There will be no alliance at all if (1 + C1 + C2)/3 < C3,

(7d)

(3C2 − C1) < C3.

(7e)

and

Proof. These results are derived from the above profit functions. 1.3 Mimicking as a Low-Cost Entrant: An Extension of the Model In order to introduce signaling and possible mimicking, we consider two periods and three banks. At date 1, Banks 1 and 2 form a duopoly and Bank 3 is an entrant. At date 1, as Bank 3 enters, there are

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three banks which engage in quantity competition in this market. At date 2, this entry can trigger an endogenous merger that depends on the cost of production of Bank 3 as articulated in Section 1.2. The entrant (Bank 3) knows its cost from the start while the incumbents do not know Bank 3’s cost. Because Bank 3 prefers to merge with Bank 1, Bank 3 intends to convey the information that it has low cost such that C1 < C3 < C2, and C3 > (1 + 2C2 − ∆)/ 3 > 2C1 + 3∆ − 1. The problem is that it does not have the direct means to do that, even if the above inequalities are true. The indirect way is to signal by increasing its output. The knotty problem is that Bank 3 may want to increase its output at date 1 even if it has a high cost and the above inequalities do not hold. The loss in the first-period profit may be offset by the gain in the second-period gain from a merger with Bank 1. Does this mean that Bank 1 will merge with Bank 3 after observing a high output from Bank 3? It is not straightforward. A rational incumbent, Bank 1, knowing that it is in the entrant’s self-interest to “lie” in this manner, will not necessarily believe that the entrant has a low cost bounded within the above inequalities. In turn, the entrant knows about this incentive. We look at the much-famed separating equilibrium in which the entrant does not pick the same first-period price when his cost is low as opposed to the case when it is high. The first-period equilibrium then fully reveals the cost of Bank 3 to Bank 1. It is well-known that there are two necessary conditions for the existence of an equilibrium. First, the low-cost type does not want to pick the high-cost type’s equilibrium output, and vice versa. In the separating equilibrium, the low-cost entrant’s output will induce the merger of Bank 1 with the entrant, Bank 3. In the separating equilibrium, the high-cost entrant’s output will not induce any merger. In order to derive the result, we assume the possibility of a subsequent de-merger if Bank 3 has “lied” about its cost in the earlier stage. The cost of a de-merger to the entrant is labeled as D. On the basis of this de-merger cost and the previous results, we offer the following findings.

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Proposition 3. An entrant, Bank 3, with cost C 3 such that C 1 < C 2 < C 3, does not mimic a low-cost bank and the entry does not induce endogenous mergers if: (1 + 2C2 − ∆)/3 < C3 < 2C1 + 3∆ − 1,

(8a)

2C2 − C1 > 1/2,

(8b)

C3 > C2 − C1 + 2.

(8c)

Proof. Details are available from the author.

Proposition 4. An entrant, Bank 3, with cost C3 such that C3 > C2 > C1, does not mimic a low-cost bank and the entry triggers an endogenous merger between incumbents if: 2C2 − C1 > 1/2,

(8b)

C3 > C2 − C1 + 2,

(8c)

C3 > 2C1 + 3∆ − 1.

(8d)


Proposition 5. An entrant, with cost C3 such that C3 > C2 > C1, does not mimic a low-cost bank and the entry induces an endogenous merger between the entrant and the less efficient incumbent, Bank 2, if: C3 < (1 + 2C2 − ∆)/3. Proof. Details are available from the author.

(9a)

Proposition 6. An entrant, with cost C3 such that C3 > C2 > C1 mimics a low-cost bank with cost C** and the entry induces an endogenous merger and subsequent de-merger between the entrant and the more efficient incumbent, Bank 1, if: C3 < C2 − C1 + 2, C 3** > 2C1 + 3∆ −1,

(9b) (9c)

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2C2 − C1 > 1/2,

(8b)

D > 0.

(9d)


Proposition 7. An entrant, with cost C3 such that C3 > C2 > C1, mimics a low-cost bank with cost C** and the entry induces an endogenous merger and subsequent de-merger between the entrant and the less efficient incumbent, Bank 2, if: C3 < C2 − C1 + 2, C3** < 2C1 + 3∆ −1.

(9b) (9c′)

Proposition 8. An entrant, with cost C3 such that C3 < C 2 < C1, mimics a low-cost bank with cost C** and the entry does not trigger an endogenous merger if: C3 < C2 − C1 + 2, (1 + 2C2 − ∆)/3 < C ** 3 < 2C1 + 3∆ − 1. Proof. Details are available from the author.

(9b) (10a)

The above are all pooling-strategy equilibria. Let us now consider the possibility of a signaling equilibrium. Proposition 9. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2) and the entry triggers an endogenous merger between the entrant and the more efficient incumbent if: C*** < (1 + C1 + C2)/3.

(10b)

C2 < 2C1 − 3.

(10c)

This is possible if


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Proposition 10. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2) and the entry triggers an endogenous merger between the entrant and the less efficient incumbent if: C2 > 3/2. Proof. Details are available from the author.

(10d)

Proposition 11. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2) and the entry does not trigger an endogenous merger if: C2 > 2C1 − 3. Proof. Details are available from the author.

(11a)

Proposition 12. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2) and the entry triggers an endogenous merger between incumbents if: C2 < 1. Proof. Details are available from the author.

(11b)

1.3.1 Discussion We observed two distinct sets of results in the context of endogenous alliance formation induced by entry into a very stylized case of market segmentation. First, we note that an innocuous entry by a profit-seeking firm into an oligopoly can have far-reaching consequences. Entry can result in a change in the cost-asymmetry of oligopolists, which in turn offers incentives to these oligopolists to seek alliances in order to enhance their market shares and profits. Secondly, we are able to derive the precise cost/efficiency asymmetries that induce the specific formation of alliances. We now can tell which firms will form/seek alliance with which firms simply on the basis of the observed cost asymmetry in an oligopolistic market. We now see how a simple exogenous change (entry in our case) triggers serious changes in the

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endogenous behavior of firms that can have profound impacts on the market structure and performance. A proper understanding of these endogenous changes is an important step forward to the study of modern businesses in the current conjuncture (see Gangopadhyay, 2004). In the next section, we offer evidence for endogenous collusion in the banking industry of Australia. 1.4 Measuring Endogenous Collusion: The Traditional Approach 1.4.1 Traditional measures of competition in the Australian banking sector Traditionally, collusion is an integral component of competition analysis which entails some measures of concentration. The two most prominent methods of concentration measurement are the Herfindahl–Hirschman index (HHI) and concentration ratios. Figure 1.1 plots the concentration of Australian banking assets and profits as measured by HHI. This index is defined as: n

HHI = Â si2

(12a)

i =1

where si is the share of each bank in the market (in terms of assets and profits). HHI can be interpreted as follows; if HHI is below 1000, the market is considered “unconcentrated”; if between 1000 and 1800, it is “moderately concentrated”; and if above 1800, it is “highly concentrated.” Figure 1.1 shows that HHI has generally decreased over time for both Australian bank assets and profits. It is clear that this decrease has been smoother and subtler under the assets analysis, whereas, under the profit analysis, it is much more volatile and erratic. Furthermore, although HHI has fallen over time, it has been maintained at over 1800 throughout the period. Hence, while some improvements in concentration have been made, the Australian banking sector continues to be highly concentrated.

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2800 2600 2400 2200 2000 1800 1600 1400 1995

1996

1997

1998

1999

2000

Assets

Figure 1.1.

2001

2002

2003

2004

2005

Profits

Herfindahl–Hirschman index — assets and profits of Australian banks.

100 95 90 85 80 75 70 1995

1996

1997

1998

1999

2000

Assets

Figure 1.2.

2001

2002

2003

2004

2005

Profits

Concentration ratios — assets and profits of Australian banks.

An alternative to HHI is the use of concentration ratios. Figure 1.2 plots the concentration of Australian banking assets and profits as measured by concentration ratios. Concentration ratios are defined as the market shares (si) of the top n firms in an

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industry. The most widely used is the four-firm concentration ratio (CR4): n

CR4 =

Â s 4.

(12b)

i =4

The findings in Fig. 1.2 are in line with those found under HHI. That is, there has been a decrease in concentration over time, although the Australian banking sector still remains highly concentrated. Again, the decrease under the profits analysis is found to be slightly more volatile, but not to the extent demonstrated using HHI. The fall in concentration under both methods demonstrates that there has been an increase in competition within the Australian banking sector. This may be attributed to the deregulatory reforms which took place in the 1980s and early 1990s. These reforms included the opening up of the Australian banking and financial system by floating the Australian dollar and allowing foreign banks to operate in Australia. More recently, technological innovation has allowed banks to operate in markets they never had access to. For instance, small regional banks now offer their services in major capital cities all around Australia without the need to operate branches in these areas. Hence, they now compete directly with their larger competitors. Nevertheless, the results from HHI and concentration ratios indicate that the Australian banking sector is still highly concentrated. Although HHI and concentration ratios allow us to measure competitiveness through concentration, these methods are somewhat flawed as they fail to take into account the behavior of the firms (Australian banks in the present analysis) under consideration. This point is well-known among economists working in the field of industrial economics, yet it does not seem to be recognized in the prior literature on the Australian banking sector. 1.4.2 Degree of competition: Background of the conjectural variations approach In contrast to HHI and the concentration ratio, the conjectural variations approach takes into account the behavior of firms in estimating

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the degree of competition within an industry. The earliest models of oligopolistic behavior such as Cournot, Bertrand and Stackelberg can be interpreted as conjectural variations models rather than as game theory models. In each model, firms control either quantity or price. In the Cournot and Stackelberg models, firms choose their output levels, and the demand curve determines the price; in the Bertrand model, firms choose the price and let demand determine output. As introduced by Bowley (1924), the idea began to spread that the duopolists’ Cournot-style reaction functions had to be given a conjectural interpretation. One of the issues was that of integrating the reaction function, which is a dynamic concept, with the static set-up of the standard Cournot model. The standard Cournot model mixed a static formalization of a one-shot simultaneous game with a dynamic story in terms of firms’ actions, reactions and counter-reactions. Each of the Cournot’s reaction functions was formulated as a static equilibrium notion but featured as an argument the actual output produced by the other firm — the kind of information that each firm could obtain only in a sequential game. However, the feature of the Cournot model that raised the most objections was the assumption that each firm behaved as if its rival would not react to its own move. This assumption was really puzzling because in Cournot’s story, each firm would inevitably realize that its rival was not passive at all and had reacted to its moves. Bowley (1924) offered a chance to overcome both these problems with his new notion of conjectural variations which generalized the Cournot assumption and, at the same time, emphasized the conjectural nature of the reaction functions. Bowley’s approach gained further support when, a few years later, another key model of oligopolistic competition — the Stackelberg model — originally formulated in terms of tangible reactions to firm’s actual output choices, underwent a similar process of conjecturalization (Giocoli, 2005, pp. 602–603). Bowley (1924, p. 38) argued that in order to solve the first-order conditions of a standard duopoly problem with quantity competition: “We should need to know q2 as a function of q1, and this depends on what each producer thinks the other is likely to do. There is then

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likely to be an oscillation in the neighbourhood of the price given by the equation marginal price = selling price, unless they combine and arrange what each shall produce so as to maximise their combined profit.”

In order for firms’ choices to constitute equilibrium, two conditions need to be satisfied (Giocoli, 2005, p. 605). First, no firm, on the basis of its own beliefs, must desire to modify its choice. Second, the equilibrium actions of the firms are consistent with the beliefs upon which they act. Thus, in the duopoly model, equilibrium is given by every pair of output levels (q 1, q2) such that: • •

each firm chooses its profit-maximizing output given the beliefs about the other firm’s choice; and each firm’s beliefs are correct at equilibrium.

Although the duopolists’ reaction functions are characterized in terms of each firm’s beliefs about its rival’s choice, before Bowley’s innovation the standard interpretation saw the interaction between the duopolists as taking place sequentially, so that each reaction function was a relation determining a firm’s action in a given period in terms of the other firms’ action during the preceding period (Giocoli, 2005, p. 605). Accordingly, the reaction function of Firm 1 depicts how it will modify its output choice according to its rival’s choice q2. The reaction functions were therefore static equilibrium notions applied to a sequential setup. Bowley’s idea was specifically to solve the tension between the statics and the dynamics of duopolistic competition by giving a conjectural interpretation of the reaction functions. This entailed the possibility of considering the duopolists’ interaction as a one-shot, simultaneous choice setup.2 Bowley’s introduction of the conjectural variations term in the first-order conditions was an innovation with respect to the usual representation of the duopoly problem. This term meant that the model’s solution depended on the exact value of each firm’s conjecture 2

See Friedman (1997, p. 149).

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about its rival’s reaction. The conjectural variations approach could capture, in a single parameter, the intensity of firms’ rivalry and encompass as special cases the classic duopoly models entailed (demonstrated in the following section). In the absence of any a priori constraint upon the firms’ conjectures, the duopoly equilibrium was actually undetermined. This feature gave economists the freedom to devise values for the conjectural variation terms that warranted the desired solution. In short, Bowley’s proposal showed that indeterminacy still hung over the duopoly model, but only up to a proper assignment of values to the conjectural variation terms (Giocoli, 2005, p. 606).3 Unfortunately, the conjectural variations approach is not without criticisms. For instance, it is now known that conjectural variations cannot constitute a satisfactory method for tackling a firm’s behavior, the reason being they fall short of eliminating the confusion between statics and dynamics. Each conjectural variation term indicates that one of the firms expects the other to react in some specific way to its own choice. If the interaction takes place just once and simultaneously, either we have an explicitly sequential setup or one must admit that the only reasonable conjectural variation is the Cournot one — the rival is expected not to react because the game ends with the simultaneous moves. This is particularly questionable with respect to multi-period interpretations of conjectural variation models. For instance, there are two criticisms that stand out with regard to multi-period Cournot models. Firstly, the firms’ myopia over time is unreasonable. A firm can observe the response of its rivals to changes in its output during the last period and can verify that those changes do affect what its rivals do. In other words, although a firm sees that its Cournot conjecture of no response by its rival is 3

As for Bowley himself, he was probably more inclined to highlight the indeterminacy of the result. This at least is what can be argued as he seemed to claim that the dependence of the solution upon the conjectures entailed that the system would “oscillate,” unless an explicit collusive agreement was reached. Hence, collusion represented for Bowley the way out from the indeterminacy caused by the conjectural term.

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wrong, it continues to rely on this false conjecture. That is, it continues to use its one-period best-response function. Alternatively stated, the Cournot equilibrium is not robust with respect to experimentation. At the equilibrium, if one firm varies its output slightly as an experiment and observes how the other firm behaves, it will learn that its Cournot assumption of no reaction is false. Second, in a multiperiod model, it does not make sense for a firm to maximize its profits in the current period alone, as these models imply. Rather, the firm should maximize the present discounted value of its future stream of profits. A firm may be willing to trade large profits in the future for smaller profits today. Indeed, firms can increase profits by varying their behavior over time. Interestingly, these criticisms arose as early as the 1930s. Yet, as Cournot (1971, p. 83) himself had anticipated, the most immediate effect of letting the mental variables in was that of enhancing the plausibility of the joint monopoly solution. Young (1925, p. 134) argued that if we allowed the conjectural element to enter the analysis, we also had to concede that each firm could anticipate the ultimate consequences of its rival’s chain of adjustments and thus discover that they were less profitable than the joint monopoly outcome. Collusion would then turn out to be the stable solution for the duopoly model because each perfectly rational duopolist would understand that deviating from it would cause losses to both firms. Similarly, Schumpeter (1928) argued that intelligent duopolists could not fail to realize all the implications of their situation, so that “they will hit upon, and adhere to, the price which maximizes monopoly revenue for both taken together… The case will not differ from the case of conscious combination — in principle — and be just as determinate” (Schumpeter, 1928, p. 134). Hicks (1935) noted the conjectural variations approach was becoming increasingly more popular in the literature. After a review of the approach, he stated that there was no need to impose any particular consistency condition upon the firms’ conjectures in the short period. In contrast, in a footnote added before the 1953 reprint of the paper, Hicks claimed that the most important work in duopoly theory since 1935 had dealt precisely

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with the imposition of a consistency postulate on the conjectural variation terms. Harrod (1934) had proposed the idea of imposing a consistency condition before Hicks’ (1935) survey. Harrod had argued that in order to obtain a determinate duopoly equilibrium all we had to do was to equalize, for both firms the rival’s conjectured reaction to its actual reaction. This reduced the duopoly model to a system of two equations with two unknowns, so that the equilibrium was necessarily determined. Thus, he concluded that “there does not appear to be any reason of economic principle for supposing that the equilibrium of duopoly would on normal assumptions be any less determinate” (Harrod, 1934, p. 335). Simply, Harrod believed that to achieve a determinate equilibrium, it was required that the duopolists’ beliefs be mutually consistent. The equilibrium output (or price) could then be anything, provided the consistency condition was met. In modern terms, the consistency restriction that needs to be imposed upon firms’ conjectures is that the conjectural variations must be correct in equilibrium (Giocoli, 2005, p. 610). A consistent conjectural equilibrium is one in which firm i’s conjecture as to how firm j will react to a small variation of i’s output is correct (i, j = 1, 2). Later, the use of a consistency condition was very much criticized. The criticisms drew on the fact that the new solution to duopolistic interaction envisaged economics as a mathematical discipline only dealing with equilibrium relations, rather than with the dynamics of market processes. The condition of correct conjectures placed an excessive and unrealistic requirement upon the duopolists’ forecasting ability. As Giocoli (2005, p. 613) states, “this clashed with the trend in contemporary economic theory to delimit carefully, if not altogether abandon, the assumption of perfect foresight and showed the descriptive weakness of focusing too much on equilibrium conditions. Indeed, for those economists who in the 1930s and 1940s still believed that the goal of economics was to investigate the actual working of market forces, and not just formal equilibrium relations, there was little doubt that in the case

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of a contradiction between the necessary assumptions to establish equilibrium and the observations taken from real market interaction, something had to be conceded with respect to the former more than to the latter.”

A further criticism was that if firms were endowed with perfect foresight, the outcome of their interaction would more than likely be the most profitable one — the joint monopoly outcome — and this is not only in the duopoly case, but even with n firms. The criticisms primarily stem from Stigler (1940), Kahn (1937) and Fellner (1949). Stigler (1940) argued that the problem of duopoly theory was how much additional knowledge should be attributed to each firm in addition to the full knowledge of the demand function and of its own cost function (Stigler, 1940, p. 524). He noted that when firms are endowed with perfect knowledge, a curious result arises. Two such firms would inevitably form a joint monopoly, but the argument could be extended to any number of firms.4 However, if all firms in all industries behaved like that, none of them would benefit from the collusive behavior, since while it would sell its output at the monopoly price, it would also pay the monopoly price for its inputs. Anticipating this, no firm would want to collude in the first place, and so on ad infinitum (Stigler, 1940, p. 525).5 To avoid this problem, Stigler (1940, p. 525) proposed that the perfect knowledge hypothesis be discarded. That is, each duopolist should be endowed with all the relevant information, except the knowledge of what its rival would do. This emphasized that the crucial issue of duopoly theory was precisely that of anticipating the rival’s behavior; yet it also entailed that no general results could be reached in this respect: all economists could do was to deal with

4

For instance, even a million firms, if endowed with perfect knowledge, would not fail to realize that the joint monopoly situation was the best for them. 5 For a similar argument, see Morgenstern (1935, pp. 181–182), who added that, since in a world of universal monopoly the whole price system would become indeterminate, the question would be raised of how firms could perfectly foresee the prices in the first place.

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special cases, each characterized by an ad hoc assumption as to each firm’s beliefs about its rival’s reaction. This also included the case in which such beliefs were indeed correct, though Stigler (1940) remarked that the correct conjectures solution to duopolistic indeterminacy should not be credited with general validity, but at most with a benchmark role. The attribution of such a role to the correctness condition entailed that the generic conjectural variation terms introduced by Bowley (1924) had little, if any, relevance for the analysis. In fact, whenever firms’ conjectural variations were mutually incompatible or inconsistent with their rival’s actual behavior, their usefulness as a guide to explain market interaction was nil (Stigler, 1940, p. 528). Kahn (1937) suggested a stronger rejection of the correct conjectures condition. He claimed that there was no unique solution to the duopoly problem because every position of equilibrium depended on the nature of the two competitors’ mental processes (Kahn, 1937, p. 2). He recognized that there was a possible hypothesis for such processes which warranted the attainment of a unique position of equilibrium, namely, Harrod’s (1934) assumption of “sensible thinking”, where each firm was said to be capable of formulating a correct conjecture about its rival’s behavior, and thus, of following a demand curve that made full and correct allowance for such behavior (Kahn, 1937, pp. 2–3). However, he believed that the correct conjectures approach was hopelessly flawed, the fault lying in the interdependence between the duopolists’ demand curves and reactions. Accordingly, Kahn argued the following. Each point on Firm 2’s demand curve corresponds to a certain equilibrium behavior of Firm 1. Harrod’s suggestion was based on the shift in Firm 2’s demand caused by a change in Firm 1’s offer, that is, on the size of the slope of Firm 2’s reaction function. However, whenever Firm 1 modifies its own offer, this is not a change in Firm 1’s position of equilibrium, rather, it is a movement out of equilibrium. As Firm 2’s demand curve is drawn on the assumption that for every point on it Firm 1 is in equilibrium, any such movement by Firm 1 implies that Firm 2’s demand ceases to have any significance. With regards to the basic duopoly model, the problem in Harrod’s argument is that

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it is meaningless to impose the equality between a firm’s conjectural variation and the actual slope of its rival’s reaction function since the latter ceases to exist as soon as the variation featuring in the denominator in the former takes place. In short, Firm 2’s reaction depends on Firm 1’s equilibrium behavior, but Firm 1’s deviation is not equilibrium behavior. Kahn (1937) was aware that the real issue resided in the troublesome combination of statics and dynamics in duopoly theory in general, and in Bowley’s (1924) approach in particular: any conjectural variation term based on a belief about the rival’s adjustment policy was a pseudo-dynamic notion which clashed with the static character of the other elements of the basic duopoly model, as for instance, the reaction functions. Alternatively, Kahn (1937, pp. 15–16) proposed a mechanical, trial and error process leading to a short-run equilibrium based on the knowledge of, rather than the belief about, the rival’s reaction6 — that is, a kind of “objective” equilibrium, independent of the firms’ expectations and conjectures. Fellner (1949) also criticized Bowley’s (1924) approach. This criticism may partly stem from his objections of the Cournot model. According to Fellner (1949, p. 57), the peculiarity of the Cournot solution was that duopolists’ beliefs proved correct only at equilibrium, while they were always mistaken during the convergence process. As he stated, the beliefs were “right” for the wrong reason. At equilibrium, it was true that the rival went on producing a fixed output; however, the reason for this behavior was not that it behaved a la Cournot (i.e., neglected the other firm’s choice) but rather that, this was what was dictated to him by his policy of profit maximization via quantity adjustment (Fellner, 1949, p. 57). From this, Fellner inferred that the intersection of the two reaction functions, that is, the Cournot solution, did not represent a real equilibrium. It would if the firms were to really follow the reaction functions, but,

6

The “reaction” being, in the short run, that of not reacting at all, i.e., in the Cournot case, that of keeping the output unchanged (see Kahn, 1937, p. 5).

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like Kahn, he too argued that this was not the case, as it was unreasonable for both firms to do so when its rival deviated.7 Part of Fellner’s reasoning was the idea that duopolistic competition involved a real dynamic process towards equilibrium. The reaction functions could not hold during such a process because the latter took place in disequilibrium, while the former were static equilibrium notions. The dismissal of the reaction functions entailed that the Cournot solution itself was useless, since it was an equilibrium concept for which there was no available explanation of “how and why” it could be reached.8 Fellner (1949, p. 67) argued that economists could never separate the equilibrium problem from the analysis of the disequilibrium mechanism. With regard to the duopoly case, it was pointless to isolate the intersection point of the reaction functions and study it as a static equilibrium in “pure” theory, while leaving to “impure” dynamic analysis the investigation of what happened when the system was out of equilibrium because, say, firms did not believe that their rival behaved a la Cournot. Hence, Fellner (1949) rejected the idea that would become so common among neo-classical economists of viewing the defining conditions of a static equilibrium as a separate and privileged issue with respect to disequilibrium analysis. For Fellner (1949), equilibrium was a useful notion only as long as it represented the end point of a dynamic process.9 Given the above, Fellner also rejected the conjectural variations approach. The conjectural variations approach was an extension of the 7

Even if both the firms did believe that its rival reacted along its own reaction function, they would immediately realize that the belief was incorrect, thereby destroying the reaction functions themselves. Thus, the system was unstable with respect to the firms’ doubts about their own beliefs about their rival’s behavior (Fellner, 1949, pp. 65–66). 8 Fellner (1949, p. 66) noted that the stability property of the Cournot solution was of no help as it was a property that referred to the movements away from equilibrium, not to the reaction functions or the actual convergence process. 9 This was even more true in the case of imperfect competition, where mental variables featured so prominently as to make a dynamic analysis capable of explaining the “how and why” of equilibrium in terms of firms’ ever-changing conjectures, the only kind of investigation that deserved to be undertaken (Fellner, 1949, p. 94).

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Cournot model in which the reaction functions were given a more general form. As such, some of the criticisms of the Cournot model extended also to the conjectural variations approach. According to Fellner (1949, p. 73), the conjectural variations were incorrect outside the equilibrium so that equilibrium itself could not be reached for the reasons already mentioned; whatever the original beliefs, they would be changed as soon as they turned out to be wrong, thereby making the conjectural variations approach useless. Furthermore, as in the Cournot case, the conjectures were “quasicorrect” at equilibrium, that is, right for the wrong reason. The pair of equilibrium outputs were justified on the basis of entirely arbitrary beliefs on each firm’s reaction. Such beliefs were indeed correct at equilibrium — in the limited sense that each firm actually produced what the rival expected it to produce — but their correctness rested upon a mistaken idea of the rival’s behavior. Doubt concerning these beliefs would destroy the validity of the reaction functions. It followed that the conjectural variations model could maintain no claim of superiority with respect to the Cournot one (Fellner, 1949, p. 74). Fellner (1949) had therefore acknowledged that even if the conjectural variations had happened to match the slope of the reaction functions, this did not suffice for the stability of equilibrium, because in the case of a deviation by any of the firms, the system would not go back to equilibrium since the reaction functions would be destroyed by the deviation. This proved once more that a static equilibrium could not be used to support a dynamic process. As Giocoli (2005) explained, “any movement away from equilibrium, say, along one of the reaction functions, revealed to the firms the mistaken nature of the hypotheses upon which the reaction functions were based. The hypotheses would then be modified and new reaction functions would arise, but this would simply show the analytical usefulness of a tool that did not stay unchanged whenever its independent variable was modified.”

Fellner (1949, p. 94) concluded that the traditional idea that the intersection of two independent reaction functions determined the

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equilibrium of the duopoly model could never constitute a fruitful foundation for oligopoly theory. This marked for a long time the end of the conjectural variations approach as a legitimate research technique and relegated it to the role of a mere didactic device. The conjectural variations approach regained momentum only in the 1980s thanks to the interpretation of the conjectural variation terms as reduced form parameters summarizing the unspecified, and possibly very complex, patterns of behavior followed by competing firms (Schmalensee, 1989, p. 650). Today, the conjectural variations approach is considered to be a more useful tool for empirical research in industrial economics than most game theory models (Martin, 1993a, b, p. 30). 1.4.3 Degree of competition and conjectural variations model As outlined above, the conjectural variations approach, as proposed by Bowley (1924), takes into account the behavior of firms in estimating the degree of competition (or non-competitiveness) within an industry. To understand Bowley’s idea, consider two firms that produce a homogeneous product with output levels q1 and q2, and an aggregate output of Q = q1 + q2. Provided that the invertibility conditions are met, the market price associated with this output may be expressed in terms of the inverse demand function: P (Q) = p (q1 + q2). Each firm i is supposed to have a cost function ci (qi), i = 1, 2. Assuming that the strategic variable for both firms is the output level, Firm 1’s maximization problem is: maxq1 π1 (q1 + q2) = p (q1 + q2) q1 − c1(q2).

(12c)

This demonstrates that Firm 1’s profit depends on the output choice of Firm 2. In order to make an informed decision, Firm 1 must therefore forecast Firm 2’s choice. A similar problem can be formulated for Firm 2. According to the standard version of the Cournot assumption, each firm expects the other not to modify its behavior as

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the market price changes. The first-order conditions of the firms’ maximization problems are: ∂pi (q1 , q 2 ) = p (Q ) = p ¢(Q )qi - ci¢(qi ) = 0, i = 1, 2. ∂qi

(12d)

Given that each first-order condition determines the optimal choice as a function of the rivals output, Firm 1’s reaction function f1(q2) is implicitly defined by the first-order condition: ∂p 1 ( f 1 (q 2 ) - q 2) = 0. ∂q1

(13a)

A similar equation holds for Firm 2’s reaction function, f2(q1). ∂q

j The conjectural variation vij = ∂q represents Firm i’s conjecture i about how j will respond to a small variation of i ’s output. Call ν12 the arbitrary conjecture that Firm 1 formulates over Firm 2’s conduct. Firm 1’s first-order condition becomes:

∂p (q1 , q 2 ) = p (Q ) + p ¢(Q )[1 + v12 ]q1 - c1¢ (q1) = 0. ∂q1

(13b)

The same reasoning can be repeated for Firm 2, whose conjectural parameter is ν21. Several cases can be derived: •

•

If ν12 = ν21 = 0, we obtain the first-order conditions of the Cournot model, where each firm believes that its rival will not react to one’s own choice. That is, a firm conjectures that the other firm will not change its output response to a change in its own output level. If ν12 = ν21 = −1, we have the competitive model or Bertrand competitive conjecture (Telser, 1972), where the first-order condition is nothing but the standard marginal cost-pricing rule. This is where a firm believes that any increase in its output is

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•

43

exactly offset by a decrease of its rivals’ output, so that the market price remains unchanged. If there are n identical firms, the Bertrand conjecture is ν = −1/(n − 1). Substituting ν = −1 into Eq. (4) gives the equilibrium condition p = C ′ (price equals marginal cost), which is the Bertrand or competitive equilibrium. If νij = qi/qj , where i, j = 1,2, we get the joint monopoly outcome. The firm holds a conjecture that leads to a collusive equilibrium if the firms behave symmetrically (q1= q2). In such a case, νij = 1 as the firm believes that its rival will change its output by the same amount as it does. Thus, the firm can affect total industry output, but not its market share by varying its output. The firm cannot increase its profits at the expense of the other firm, so it produces the cartel output.

1.4.4 The data The sample used for the study comprises 10 domestic Australian banks. The study covers the time period between 1995 and 2005 in order to capture the changes within the Australian banking industry that occurred following the Wallis Inquiry. Hence, the base year of 1995 represents the year before the announcement of the Wallis Inquiry in 1996 while the post-Wallis period commences after the publication of the inquiry’s Final Report in 1997. The sample size was dictated by two factors. First, foreign banks operating in Australia were omitted. This is due to the fact that there are no data available on the branches of foreign banks operating in Australia and the data on foreign bank are difficult to collect. This difficulty is attributed to the fact that they are subsidiaries of foreign banks. Due to their status, they have lower levels of disclosure. This is attributed to the fact that they are not listed on the Australian Stock Exchange and so are subject to less onerous public disclosure requirements. Second, through the 1980s, 24 domestic Australian banks were in operation; however, today there are only 14.10 The number of 10

In the current study, four banks have been excluded as only consistent and suitable data were available on 10 Australian banks.

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domestic banks has fallen due to bank closures, takeovers, and mergers across the Australian banking sector. In particular, the beginning of the 1990s saw the decline of a number of smaller banks. Many stateowned banks were taken over by larger banks, for example, State Bank of Victoria by Commonwealth Bank, Bank of South Australia by St George Bank, and the Bank of Melbourne by Westpac Bank. To ensure the reliability and consistency of the results, the data were obtained from the individual bank’s audited annual reports produced in accordance with company reporting standards in Australia. These annual reports are publicly disclosed as part of the Australian Stock Exchange listing requirements (all of the sampled banks are listed on the Australian Stock Exchange). The BankScope database which is used in many international studies did not contain the required data. In fact, it should be noted that data obtained from BankScope actually suffer from a number of problems and their use in banking studies is questionable. This is for two reasons. First, BankScope does not disclose anything about its data selection and inclusion policy. Second, the samples compiled by BankScope suffer from an implicit selectivity bias in favor of large banks and are not representative of the actual banking industry and thus may yield biased and inaccurate results.11 Ehrmann et al. (2001) noted that this appears to be stronger between 1992 and 1999 since the coverage of BankScope was relatively poor during its earlier years of data compilation. Bhattacharya (2003) and Ehrmann et al. (2001) recommended the use of databases, such as those maintained by central banks, because they usually have more complete data and therefore produce more consistent, robust, and stable results. Unfortunately, in the Australian context, although the RBA and APRA maintain data on Australian banks, their data are primarily statistical. Hence, the required data for this study were not available from any database or data collection service.

11

Bhattacharya (2003), Ehrmann et al. (2001), De Brandt and Davis (1995), and Corvorseir and Gropp (2001) all questioned the usefulness of Bankscope for the purposes of examining the financial statements of individual banks across several years and the comparison of these figures with peers and competitors.

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Endogenous Collusion and Rivalry Table 1.1. Bank Type Large-sized banks (Big four banks)

Medium-sized banks

Small-sized banks (regional banks)

45

Sampled Australian banks.

Name of Bank

Abbreviation Used

1. National Australia Bank 2. Commonwealth Bank of Australia 3. Westpac Banking Corporation 4. ANZ Banking Group 5. St George Bank 6. Suncorp Metway 7. Macquarie Bank 8. Bendigo Bank 9. Adelaide Bank 10. Bank of Queensland

NAB CBA WBC ANZ SGB SUN MAQ BEN ADB BOQ

Source: Axiss Australia (2004).

The only alternative available was to collect the data from the bank’s individual annual reports. A total of 110 annual reports were collected and analyzed. This was a difficult and time consuming process, particularly as most of the banks did not maintain copies of their annual reports which were more than seven years old. Without a doubt, the lack of data availability has restricted greater research into the Australian banking sector (Table 1.1). The variable collected for the analysis is the value of total banks loans produced (change in value). 1.5 Collusion in the Australian Banking Industry 1.5.1 Evidence of collusion in the Australian banking industry: A simple analysis Let us consider the output of a bank i and call it qi. In the following, we calculate the conjectural variations (λi) from the year 1996 to 2005, that is, li = vij =

∂q j ∂qi

.

Note that ∂qi is the change in output of bank, for all i.

(14a)

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Formula B is used to calculate the index for the above years. As an example, for the year 1996, the value of index of collusion is about −3.36, which shows a strong element of collusion. The result is based on the following variables as defined below: qi = output of bank i, λi = conjectural variations in output of the rest of the firms as firm i changes its output. I = Index of collusion for a year = Â (qi2 l j ) / Â qi2 .

(14b) ∂q

j Table 1.2 gives the measures of conjectural variations li = vij = ∂q of i the major banks of Australia from 1996 to 2005. We calculate the collusion index on the basis of the conjectural variations and the output of banks in Table 1.3. The time profile of the above collusion index is presented in Fig. 1.3 that clearly depicts two critical issues:

1. The collusion index is significantly different from the value of one (1), which implies significant collusive arrangement in the banking industry. 2. Second, the value of the index is not stable and rather fluctuating overtime. It is also important to note that the value of the index has gradually stabilized towards the expected value of −1, which is a reflection of increasing rivalry and decreasing degree of collusion since the year 2000. The presented evidence alludes to a possibility of significant collusive arrangements in the Australian banking industry. In Section 5.8, we offer the model that can explain how and why significant collusion can characterize the Australian banking industry. 1.5.2 An extension: Chaotic discrimination as a colluding strategy in the banking industry The goal of this section is to offer a constructive model to explain how banks can adopt a collusive strategy to significantly limit

b910_Chapter-01.qxd

λi

Conjectural variation of individual banks 1996–2005.

1998

1999

2000

2001

2002

2003

2004

2005

−1.446 −1.275 −1.633 −9.9 −0.844 3.26 4.232 −12.63 0.35 0.038

9.066 5.79 1.594 −15.169 9.303 4.405 −98.98 159.06 42.34 167.4

−18.45 −15.72 4.76 3.56 0.174 −8.087 78.34 271.75 175.79 8133.5

7.07 −9.47 2.1 −30.3 0.393 31.76 −59.98 −81.79 −73.14 1386.82

0.85 −7.63 6.15 1.48 5.32 −8.76 35.14 52.95 −47.1 59.8

−14.1 −0.39 0.47 −1.79 −4.3 4.14 7.82 −24.47 22.47 210.24

0.187 1.4 0.44 1.089 1.29 −17.02 −8.85 4.12 −9.27 15.07

−0.74 −2.99 −5.63 −1.64 −3.01 25.86 3.715 14.37 −1.91 −11.81

0.92 0.98 −7.13 8.02 −36.22 9.75 −39.57 −399.77 43.7 57.38

−0.5 −2.367 −2.03 1.62 −3.64 −4.11 −13.57 −13.71 −11.1 −4.41

Note: li = vij =

∂q j ∂q i

is computed as change in output of j over change in output of i at a date t.

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1997

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1996


NAB CBA WBC ANZ SGB SUN MAQ BEN ADB BOQ

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Table 1.2.

47

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Table 1.3. Summary measures of collusion index (I) in the banking industry, 1996–2004.

I

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

−3.44

3.97

−2.03

−10.36

0.98

−3.73

0.39

−4.14

−1.07 −1.008

Index of Coolusion

Note: Computed from the banking data applying Formulas 14(a) and 14(b).

6 4 2 0 -2 -4 -6 -8 -10 -12 1994

Series1

1996

Figure 1.3.

1998

2000 Years

2002

2004

2006

Temporal movement of the collusion index, 1995–2005.

potential competition. In our model, we explain the colluding strategy as chaotic discrimination. Bain (1952) identified two principal forms of price discrimination as chaotic discrimination. The fundamental characteristic of such discrimination, he argued, embodies an element of irrationality in pricing decision. As a result, such prices are believed to be “arbitrary and non-profit maximizing” (Bain, 1952, p. 431). The first form is popular as the basing-point pricing. Many goods are sold at delivered prices which are the factory prices plus shipping mark-ups while sellers are “disparately located.” Every seller quotes a delivered price at a delivery point which equals the base price of the nearest seller plus the shipping mark-up from the nearest 12

Bain (1952) elucidates: “Thus, if sellers were located at New York and Chicago, buyers at the vicinity of Chicago would be quoted a delivered price equal to a Chicago base factory price (before freight) plus freight from Chicago, and they would have this same price quoted to them by both the Chicago and the New York seller, regardless of whether the goods were shipped at low cost from Chicago or at a high cost from New York” (p. 430).

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seller.12 As a result, price discrimination may emerge if buyers do not buy from the nearest seller. Such a form of discrimination is labeled as “chaotic” since the delivered prices do not derive either from individual or collective profit maximization. Such a scheme of pricing evolved between 1880s and 1949 in cement, steel, and certain other industries but after 1949, it gradually disappeared (see Shepherd, 1985, p. 249). The second type of chaotic discrimination emerges when sellers quote a common price but secretly engage in “arbitrary” price discounts. As a result, different buyers pay different prices. Such price discrimination, Bain (1952) argued, does not conform to a pattern of joint profit maximization and hence is “arbitrary and non-profit maximizing.” Bain (1952) rationalized such discrimination as an effort by oligopolists to avoid an open price war.13 In his opinion, there may exist a uniform pricing rule that may engender a higher individual as well as joint profits. Therefore, such a discrimination may not be underpinned by instrumental rationality of sellers. Such a scheme of pricing, hence, came to be termed as chaotic discrimination. This form of chaotic discrimination is an important element of modern markets, but what causes it remains unclear. The explanation of Bain is inadequate for two reasons: First, we do not understand why sellers choose a common posted price in such markets. Second, we know very little about the forces that bind sellers from secretly making Pareto-improving price discounts. The main purpose of this chapter is to address the second form of chaotic discrimination. We consider a stylized case of chaotic discrimination: the incumbent sellers in a market choose the same posted price, but they engage in “secret” and “arbitrary” price discounts from the posted price. We provide a model to show that such discrimination may derive from the hyper-rationality of sellers. If there is effective 13

Bain (1952) articulated, “This type of discrimination is quite common in oligopolistic markets, and it results from the fact that destructive price rivalry is more easily avoided by sellers if they make special and secret concessions to particular buyers rather than openly announced price cuts available to all buyers” (p. 431).

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collusion, all the sellers would charge the joint profit-maximizing price, otherwise the Nash–Cournot price if the incumbent sellers engage in quantity competition. No seller would have any incentive to deviate post hoc from the optimal price. So it remains a moot point why sellers in reality deviate from this optimal price. One plausible explanation, following Bain (1952), is that sellers act irrationally and choose the posted price above profit-maximizing price and, hence, each seller has an incentive to secretly discount his price. An overt discount is avoided since it may cause instability due to price competition among incumbent sellers. This work, on the contrary, seeks a rational basis of such discrimination. The contribution of this work is twofold: First, we provide a strong theoretical justification for chaotic discrimination as an optimal pricing strategy. This work establishes that chaotic discrimination is a subgame perfect Nash equilibrium (PNE) in a segmented banking oligopoly, or duopoly. Second, we focus on the “arbitrary,” “non-profit maximizing,” and “inconsistent” nature of price discounts. We attempt to provide an answer to the following question: why are price, or interest and fees discounts “chaotic” in the sense that sellers fail to adopt profit-maximizing price discounts? It is constructively argued that sellers may fail to coordinate price discounts due to multiple equilibria. Since there is no explicit coordination device, price discounts will be uncoordinated and, hence, erratic and chaotic. In the following section, we provide the bare essentials of the model that presents a signaling game to link the pre-entry price to the post-entry profit of a potential entrant. It is assumed that there exists a specific type of informational asymmetry: the incumbents have full knowledge of the cost functions whereas the potential entrants do not possess this information. If the cost functions of the incumbents and that of the potential entrants are positively correlated (see Harrington, 1986, 1987), then the incumbents have an incentive to distort the price upward. This is so since higher prices indicate higher costs of production and hence lower post-entry profits. The incumbents, thereby, sacrifice market shares and shortrun profits in their pursuits to maintain their long-run market shares

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and profits.14 Our model demonstrates that one means of reducing such sacrifices is the second type of chaotic discrimination that would effectively forestall entry. We will subsequently examine the internal consistency of the chaotic pricing rule when the market is characterized by multiple, uncoordinated incumbents. Our analysis will determine optimal price discount rules and demonstrate how such a market is beset with multiple equilibria and coordination failure that may engender “chaotic” nature of these price discounts. 1.5.3 “Chaotic discrimination” as an optimal colluding strategy: The basic model We consider a stylized market in which there are two incumbent sellers who engage in quantity competition. Suppose there is a single entrant. These sellers interact in a two-period market. There are two periods, t and t + 1. In order to keep our analysis tractable, we envisage a twoperiod optimization exercise. At the beginning of each period, each incumbent seller decides anew about his output. As a result, there is no loss of analytical rigor associated with such a two-period optimization scheme. At the beginning of period t + 1, the entrant decides whether to enter the market, or not. And, hence, at period t + 1, there are either two or three sellers. The potential entrant does not know the cost function and infers the cost function from the price at period t. The game unwinds in a market in which demand function and cost function remain invariant through time. The inverse demand function is assumed to be linear for both periods, t and t + 1, which for period t, is as follows: P t = a − bX t 14

(15a)

This issue concerning a conflict between short-run and long-run profits has a rare vintage. Harrod (1952) initiated this point while Hicks (1954) attempted to formalize this point as follows: a typical seller seeks to maximize a weighted sum of short-run and long-run profits (see also Kamien and Schwartz, 1971).

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where Xt = x 1t + x 2t

(15b)

where X t is the market output and xi is the individual output. The cost function for seller i at period t is as follows: C ti = cxit.

(15c)

The same demand and cost conditions will persist in period t + 1. The profit function of seller i at period t is as follows: Π ti = (a − c)xit − b(xit)2 − bxitxjt

(15d)

for i, j. The Nash–Cournot equilibrium is presented in Table 1.4. The profits corresponding to the Nash–Cournot strategy are as follows: Π1t ** = Π2t ** = (a − c)2/9b.

(16a)

Now suppose the entrant enters the market in period t + 1 being attracted by the supernormal profits made by incumbent sellers. As he enters, the market is shared among three Cournot sellers. The resultant Nash–Cournot equilibrium is presented in Table 1.5. The profits in period (t + 1) are as follows: 2 Π1t+1** = Π2t+1** = Πt+1 3 ** = (a − c) /16b.

(16b)

If incumbents choose their Nash–Cournot strategies at period t, then the new seller will enter the market to reduce their profits at period t + 1. Table 1.4.

Seller 1 Seller 2

The Nash–Cournot equilibrium. x t**

P t**

(a − c)/3b (a − c)/3b

(a + 2c)/3 (a + 2c)/3

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Endogenous Collusion and Rivalry Table 1.5.

Seller 1 Seller 2 Seller 3

53

The Nash–Cournot equilibrium. x t+1**

P t+1**

(a − c)/4b (a − c)/4b (a − c)/4b

(a + 3c)/4 (a + 3c)/4 (a + 3c)/4

If the potential entrant has sketchy information about cost conditions, then incumbents can forestall entry by an upward distortion of prices at period t. This result is outlined in Lemma 1. Lemma 1. If ρ is the total profit, associated with the normal profit rate R, then the distorted price signal, PD, which forestalls entry, is given by: P D = a − 8/3(b ρ)1/2 = a − 8/3 m

(16c)

where m2 = bρ . Proof. The potential entrant would stay out of the market if Π3t+1 is less than or equal to ρ. The maximum profit which would not attract entry is as follows: Π1t+1 = Π 2t+1 = Πt+1 3 = ρ.

(16d)

The cost c*, as signaled by the distorted price P D, would set Π t+1 3 equal to ρ . This upward price distortion would signal lower post-entry profit to the entrant and, hence, he would stay out of the market. Hence, from Eqs. (16b) and (16c), we know the following: (a − c*)2/16b = ρ,

(16e)

c* = a − 4(bρ)1/2.

(16f)

hence,

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From Table 1.5, we know the following: P t = (a + 2c)/3,

(17a)

hence the distorted price signal at period t, P D, is given by P D = (a + 2c*)/3.

(17b)

Substitution of Eq. (3a) into Eq. (3c) yields the following: P D = a − 8/3(bρ)1/2,

(17c)

= a − 8/3m.

(17d)

Lemma 2. The profit to each incumbent seller, Π t* (ignoring subscript), from price distortion in period t, PD, is as follows: Πt* = 4/3m(a − c − 8/3m) = 4/3mK

(18a) (18a′)

where K = (a − c − 8/3m).

(18a′′)

Proof. From the inverse demand function (13a), we know that the quantity sold, X t*, corresponding to P D, is 8/3m. Each seller, therefore, sells the following quantity: x 1t = x t2 = 4/3m, Π it = (P D − c)x it.

(18b) (18b′)

Substituting Eqs. (17d) and (18b) in Eq. (18b′) would yield Eq. (18a′).

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1.5.4 Definitions and preliminary results Definition 1. We define the “quasi chaotic discrimination” as follows: an incumbent seller quotes and adopts the distorted price signal P D at period t and undertakes secret price discounts in period t + 1. Definition 2. Chaotic discrimination is defined as follows: an incumbent seller chooses P D as the posted price, but undertake price discounts both in periods t and t + 1. The colluding incumbent sellers quote the entry-preventing price P D at period t and each seller makes profit Π t* at period t. In period t + 1, these sellers undertake a secret price discount ∆P. What is to be shown is that the overall profit of each seller from price distortion strategy is greater than the overall profit from the Nash–Cournot strategies in periods t and t + 1. The following results are crucial in demonstrating the optimality of the chaotic price discrimination. The following notations are used to derive the results (Table 1.6): Result 1. Quasi chaotic discrimination yields higher profit than the strategy profile (PD, N–C) if the following condition is satisfied: ∆P > [2(a − c)2/9b] − 8/3m.

(19a)

Proof. See Appendix. Table 1.6.

Major notations.

1. Quasi chaotic discrimination = (PD, ∆P): Strategy profile involving upward price distortion PD in period t and secret price discount ∆P in period t + 1. 2. N–C: Nash–Cournot quantity strategy. 3. (PD, N–C): Strategy profile involving upward price distortion in period t and N–C in period t + 1. 4. (N–C, N–C): Strategy profile involving N–C strategies in both period t and period t + 1. 5. ∆P : Secret price discount.

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Result 2. Quasi chaotic discrimination yields lower profits than chaotic discrimination if the following condition is satisfied: ∆P < a − c − 16/3m.

(19b)

Proof. See Appendix. Result 3. The strategy profile (N–C, N–C) yields higher profit than the strategy profile (N–C, ∆P).

Proof. See Appendix.

Result 4. Quasi chaotic discrimination yields higher profit than the strategy profile (N–C, N–C) if the following condition holds: (a − c − 8/3m) > 2.6.

(19c)

Observation 1. If sellers choose PD in period t, then from Result 1, we know that secret price discounts ∆P would yield higher profits than from the N–C strategy in period t + 1. Hence once P D is committed in period t, ∆P would be the Nash equilibrium in the subgame. Similarly, Result 3 establishes that once sellers choose N–C at period t, N–C would be the Nash equilibrium in the other subgame. Result 4 establishes that quasi chaotic discrimination is the subgame PNE of the extensive form game since the strategy profile (P D, ∆P) constitutes a Nash equilibrium in each subgame. Since chaotic discrimination Pareto-dominates quasi chaotic discrimination (Result 2), chaotic discrimination is the subgame PNE. 1.5.5 Discussion If the price discount is contained within these suitable bounds, then the Pareto optimal pricing strategy under threatened entry embodies chaotic price discrimination. That is each incumbent sends the posted price P D and engages in secret price discounts ∆P that are contained within suitable bounds. The explanation of chaotic discrimination by Bain (1952) is hinged on a static analysis of oligopoly in which oligopoly is viewed as a stable market form. In such an analysis, economists attempt to explain

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an (efficient, or otherwise) allocation of profit among the fixed number of interacting members (see Rothschild, 1993, p. 155). In this framework, price discrimination of the above type can only be explained in terms of a departure from rationality. On the other hand, the dynamic analysis posits an oligopoly as “precarious formations whose privileges (if any) are constantly threatened by potential entrants” (Rothschild, 1993, p. 155). As a result, the central problem turns on the issues concerning the maintenance of status quo in a quasi competitive set-up. Bain (1956) and Labini (1956) independently advanced the limit price theory as a model of such dynamic issues. These early works relied on a commitment linkage to explain how the incumbents may ward off entry (see Bagwell and Ramey, 1991). The main problem of applying this traditional limit price theory in the context of chaotic discrimination is that the limit price is always less than the short-run, joint profit-maximizing price. The limit price, thereby, signals a lower post-entry profitability. The main intuition of the limit price theory is that the current price is believed to signal the probable nature of the rival policy if the entrant decides to enter. The incumbent firm indicates its commitment/threat to maintain output consistent with the low limit price (see Bain, 1949, 1956; Modigliani, 1958). If the threat is credible, then the potential entrant is deterred by the low price and high output.15 15

Such a threat may not be credible since the incumbent has an incentive to deviate from the committed output once entry occurs. As a result, such a commitment cannot be sustained in a perfect Nash equilibrium (see Friedman, 1979). Most of the earlier studies, however, side-stepped the credibility problem (see Kamien and Schwartz, 1971 and 1975; Gaskins, 1971; Pyatt, 1971). Subsequently, the commitment to maintain the low price is justified in terms of an irreversible decision, such as plant investment; advertising (see Flaherty, 1980; Friedman, 1979; Salop, 1978, 1979). Dixit (1980), Fudenberg and Tirole (1983) introduced strategic capacity choices to ensure the credibility of a commitment. Gilbert and Vives (1986) examined output commitment in a multiple-incumbent model. Bonanno (1987) theorized the entry-deterring power of product differentiation. Another plausible way out is to introduce imperfect information to beat the chain store paradox which has initiated a fresh lease of research (see Milgrom and Robert, 1982).

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The seminal paper of Milgrom and Roberts (1982) highlighted the likelihood that incumbent firms may control the entry decision, through prices, by influencing a potential entrant’s “perceptions of the profitability” when prices convey critical information about the exogenous determinants of post-entry profitability. The fundamental notion turns on an informational asymmetry between incumbents and potential entrants: the incumbents have a relevant piece of information which potential entrants do not possess. Matthews and Mirman (1983) examined the case where a potential entrant does not have critical information about the demand conditions. Milgrom and Roberts (1982) and Salop (1979a,b) developed signaling models where prices convey information about the cost conditions. These works demonstrate the rationale behind an incumbent’s decision to set prices below the short-run profit-maximizing level in order to forestall entry. These models firmly establish an interdependence between preentry price and the expected post-entry profit of the potential entrant and also spell out the rationale behind downward distortion of price. Hence, in such models, if sellers have any incentive to deviate post hoc from the limit price, then each would rather increase the price to make an extra profit. The upshot is that even if the dynamic approach to oligopoly seems to be the right paradigm to address the problem of chaotic discrimination, most of the models on limit pricing seems to be quite inadequate in shedding much light on it. The only exception is the pioneering and “provocative” works of Harrington (1986, 1987) who postulated positively correlated cost functions of the incumbent and the entrant to reverse the limit pricing result. In his works, the incumbent seller prices above the simple monopoly price, or Nash–Cournot price, to signal high cost and, hence, low post-entry profitability. Our basic premise is similar to that of Harrington (1986, 1987) as the entrant relies on price signals to learn about cost conditions. It seems possible from our analysis that one may rationalize chaotic price discrimination in the light of upward price distortion when potential entrants receive signal regarding their cost function from the current price of the incumbents.

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Once upward price distortion blocks entry and ensures long-run profits, incumbent sellers adopt price discounts to enhance their short-run profits. Thus, we establish chaotic discrimination as a subgame PNE. We raise two critical questions in this bedrock of analysis. First, the crucial question that we would turn to concerns the stability of such a tacit collusion. That is, whether the incumbents have any incentive to unilaterally deviate from such a pricing strategy. This issue is addressed in 1.3 and 1.10.

1.6 Is the Collusion Feasible and Stable? Under the postulated demand and cost conditions, the reaction functions of the incumbents are as follows (ignoring the time superscript): x1 = (a − c)/2b − x2/2,

(20a)

x2 = (a − c)/2b − x1/2.

(20b)

Under the tacit collusion, each seller sets the output at 4/3(ρ/b)1/2. Suppose Seller 1 produces 4/3(ρ/b)1/2, the following results trace out the optimal response of the second seller. Proposition 13. The optimal output and the resultant profit of the second seller in response to x1 = 4/3(ρ b)1/2 are respectively the following: = (a − c)/2b − 2/3m, x op 2

(21a)

P op = (a + c)/2 − 2/3bm,

(21a′)

= Π op 2

(21b)

[(a − c) /4b + 4/9bm] − 2/3(a − c)m, 2

where the superscript denotes the optimal deviation of the seller from the collusion and the consequent profit. Proof. Equation (21a) is arrived at by substituting 4/3m in Eq. (20b). Summing up the individual outputs, we arrive at the total output: = 2/3m + (a − c)/2b. X op = 4/3m + x op 2

(21c)

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Substituting Eq. (21c) in Eq. (13a), we arrive at the market price P op: P op = (a + c)/2 − 2b/3m. Substituting Eq. (21a) in Eq. (13c), we get Eq. (21b).

(21a′)

Proposition 14. The two-period profit of Seller 2 from deviating from the collusion, Π 2, is as follows: Π2 = [(a − c)2/4b + 4/9m] − 2(a − c/3) + m(a − c)2/16. (22a) Proof. We define Π2 as the following: Π2 = Πop + Πt+1 . 2 2

(22b)

op From Table 1.3, we know Πt+1 2 and from Eq. (21b), we know Π 2 . The substitution into Eq. (22b) yields (22a).

Proposition 15. The two-period profit of the second seller from the collusion is as follows: Π2t * + Π2t+1* = K(4/3m + 4/3m/b + ∆P/2b). Proof. See Result 2 for the derivation of Eq. (22c).

(22c)

Theorem 1. Tacit collusion becomes a Nash equilibrium if the values of a, b, and c are such that chaotic discrimination turns out to be Pareto superior to no-distortion Nash–Cournot equilibrium. This is true if the following condition holds: ∆P > [(a − c)2/8 − 8/3m,

(22d)

b > 8/3.

(22e)

Proof. Tacit collusion would be a Nash equilibrium if Eq. (22c) > Eq. (22a),

(23a)

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that is, (a − c)/2 < (2/3)mb + 4/3m (a − c − 8/3m),

(23b)

(a − c)/2 < (4/3) (a − c)m + 2/3m (b − 8/3).

(23c)

Since m > 1, hence so long as b > 8/3, Eq. (23c) would be valid and hence Eq. (23a) would hold. Hence if conditions (8a) and (8e) hold, then the collusion turns out to be a Nash equilibrium since there is no incentive for any incumbent to unilaterally deviate from the collusion. Incumbents maximize intertemporal profit streams by adopting the proposed rule of chaotic price discrimination. Thus, if the values of a, b, and c satisfy Eqs. (22d) and (22e), then chaotic price discounts, so long as it satisfies inequality (23a), would yield higher profits than that of the no-distortion Nash equilibrium. As a result, both the incumbent sellers would choose “chaotic discrimination” as optimal pricing strategy. The upshot, therefore, is that the collusion would be stable as no seller has any incentive to deviate from the “chaotic discrimination.” The critical question that we now turn to is why incumbent sellers cannot coordinate their price discounts to maximize profits. 1.7 Why are Secret Discounts Chaotic? It is postulated that incumbent sellers distort price upward to block entry when prices convey information to potential entrants about cost conditions (see Harrington, 1987). Once entry has been blocked, these incumbents strive for enhancing their market shares through secret price discounts. There are two critical elements in the market: First, incumbents, tacitly or openly, agree to coordinate at a posted price to deter entry. Second, the incumbents engage in secret price discounts to augment profits without triggering entry. Our primary concern in this section is to provide a theoretical foundation to these price discounts from the posted price.

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There are three important features that characterize the price discounts. First, price discounts are undertaken secretly after having forestalled entry by an upward price distortion. Price discounts are, therefore, determined in a game involving the incumbents. Second, the decision variable of an incumbent is the price variable and, hence, the relevant frame of analysis is the Bertrand model of price competition. Third, since the price discounts are secret, there exists informational asymmetry. Each incumbent knows his price discount which is not directly available to others. As a result, each incumbent must infer price discounts offered by other incumbents. In making such an inference, he must form conjectures about the price discounts of his rival. In a Bertrand–Nash equilibrium, such conjectures must be self-confirming. The optimal price discounts would, therefore, reduce to a rational expectations equilibrium involving self-confirming conjectures of incumbents about these secret price discounts. In what follows, we attempt to establish an equilibrium that would provide us with the optimal price discount of each incumbent seller. Assumption 1. Following Stiglitz (1987), we write the revenue function of the i th seller as follows: Ri = Mi χ

(24a)

where Mi is the number of customers who purchase from seller i and χ is the demand function of each customer. Assumption 2. We assume the following: Mi = Mi (P D, ∆Pi , ∆Pj),

(24b)

χ = χ(P , ∆Pi)

(24c)

D

where ∆Pi is the price discount undertaken by seller i, P D is the posted price that forestalls entry. We postulate the following (see Stiglitz, 1987): δMi/δP D < 0, δMi /δ∆Pi < 0, δMi /δ∆Pj > 0, δχ/δ∆Pi < 0. The implicit

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assumption is that buyers obtain information through “word-ofmouth” that will allow each seller to maintain a different price for a finite span (see Phelps and Winter, 1970). Assumption 3. For the sake of tractability, we linearize the above functions to generate:

χ = β1 − β2∆Pi,

(25a)

Mi = (α2∆Pj − α 1∆Pi)

(25b)

where α1, α2, β1, and β2 are all positive and the number of customers at P D is normalized to zero. The profit function of seller i, Πi, is reduced to the following: Πi = (β1 − β2∆Pi)(α2∆Pj − α1∆Pi) + (β1 − β2∆Pi)(α2∆Pj − α1∆Pi)∆Pi − c (β1 − β2∆Pi)

(26a)

where c is the average cost of production that is further normalized to zero for the sake of simplification without any loss of analytical bite. Theorem 2. The first-order condition for profit maximization reduces as follows: [−β1α1) + (β1 − β2)α2∆Pj] + 2∆Pi[−α1(β1 − β2) + β2α2∆Pj] + 3β2α1(∆Pi)2 = 0

(26b)

Proof. This follows from the profit function (26a) after substituting the derivatives of relevant instantaneous profit functions. We write Eq. (26b) as follows: A1 + A2∆Pi + A3(∆Pi)2 = 0

(27a)

where A1 = [(−β1α1) + (β1 − β2)α2∆Pj], A2 = 2[β2α2∆Pj − α1(β1 − β2)],

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and A3 = 3β2α1.

Theorem 3. The non-linear reaction function of seller i is given by the following: ∆Pi = [−A2 ± (A22 − 4A1A3)1/2]/2A3

(27b)

which is a function of ∆Pj . Proof. This follows from the profit-maximizing condition (27a) which is a quadratic function. Theorem 4. The optimal price discount/cut of seller i is given by the following: (∆Pi)opt = [−(β1 − β2)α2 ± {(β1 − β2)2α22 + 6β1α1}1/2/3 (28a) where we make the following simplifications, for the sake of tractability,

α1(β1 − β2) = 0,

(28b)

2β 2α2 =1,

(28c)

β2α1 = 1.

(28d)

Proof. The substitution of Eqs. (28b)–(28d) into Eq. (17b) yields the following: ∆Pi = −∆Pj ± (∆Pj2 − 2A1)1/2.

(29a)

Since both the sellers face identical conditions and the Nash equilibrium requires self-fulfilling expectations, we set (∆Pi)opt = (∆Pj)opt.

(29b)

Substituting Eq. (29b) in Eq. (29a) yields the following: 3[(∆Pi)opt]2 + 2(β1 − β2)α2(∆Pi)opt − 2β1α1) = 0.

(29c)

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From the quadratic equation (29c), we know the Nash equilibrium in the price discount is given by the following: (∆Pi)opt = [−(β1 − β2)α2 ± {((β1 − β2)2 + 6(β1α1)}1/2]/3. (30a) Theorem 4 establishes that in such a market, duopolist i would have two Bertrand reaction functions, Ri and R1i . For each pair of Bertrand reaction functions of these duopolists, Theorem 3 confirms, there are two self-fulfilling (equilibrium) price discounts: if each duopolist expects the same (equilibrium) discount, it will materialize as the profit-maximizing price discount. The tricky issue is that there are 1 four such equilibrium discounts. Note that Ri and Ri are a pair of Bertrand reaction functions for seller i. Points E1, E2, E3, and E4 represent the Bertrand–Nash (equilibrium) price discounts. If sellers can coordinate at one of these equilibrium discounts, all “chaotic, inconsistent, and arbitrary” elements in price discount will disappear. In the absence of a coordination device, such a market is beset with multiple Bertrand–Nash equilibrium that will lead to coordination failure: different sellers would be choosing different price discounts and, hence, price discounts will be characterized by “chaotic” elements such that secret price discounts will entail a “departure from a joint profit-maximizing pattern” (Bain, 1952, p. 430). 1.8 Politics, Conjectural Variations, and Degree of Rivalry 1.8.1 Basics The strategic trade and investment models attracted serious criticisms on two well-known grounds: First, their conclusions are extremely sensitive to the assumptions about the mode/nature of competition (Krugman, 1993, p. 363). Second, it is also highlighted that the optimal rent-seeking policy loses much of its gloss once we consider political costs associated with the policy (Dixit and Grossman, 1986, p. 234). An important step towards a better understanding of these issues requires us to endogenize the mode of competition and also to

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introduce explicit government policy making in this context. The proposed chapter makes both the nature of competition and the government policy making endogenous and, thereby, provides a framework in which industrial structures, conduct of firms, and political decisions are endogenously determined. Our central concern is to address two critical issues of government involvement in the context of strategic investment models: First, the nature of competition plays an important role in determining whether government policy has the intended and desirable effects. It is also important to model the nature of competition endogenously in this context since government policy can significantly influence the nature of competition through its effect on the firms’ costs structure (Dixon, 1986). Second, the promotion of one set of firms represents a “taxation” of others. Government policy thus entails a political cost that is an important ingredient for formulating government policy. The existing literature has a gap since it does not make both government policy and nature of competition endogenous. This is a major difficulty with the rent-extraction argument since political costs constrain the government’s behavior whilst the benefits from strategic government policy largely depend on the endogenous degree of competition. An optimal government policy will thus be misconstrued unless we determine these elements endogenously. We combine two distinct ideas — namely, the probabilistic voting model and the conjectural variations model — to endogenize the nature of competition and the government policy. First of all, the probabilistic voting model is a recent development in political theory to counter the time-honored predictions of the traditional political theory (Wittman, 1989): for centuries, social thinkers argued that democratic governments have been plagued by the absence of a stable electoral equilibrium and the risk of expropriation of minorities by majorities. The probabilistic voting model, by assuming a universally concave votes-to-offers curve, establishes the existence of a stable voting equilibrium and also that the expropriation argument is “an optical illusion.” The probabilistic voting model will allow us to endogenize the relevant government policy. Second, the conduct of firms has been made endogenous in a very important contribution of Bresnahan (1982) that is popularly known as the conjectural variations

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model. Latiner (1982), Bresnahan (1982), Kamien and Schwartz (1983), and Perry (1982) questioned the robustness of the Cournot model as an equilibrium concept by using the model of consistent conjectured reactions. A conjectural variation is a conjecture by one firm about how the other firm will adjust its decision variable in response to potential adjustments by the first firm. The consistent conjectural equilibrium is believed to be a rational expectations equilibrium that collectively confirms individual expectations about changes in the decision variables. It is argued that the Cournot equilibrium is not generally a consistent conjectural equilibrium. However, there are problems with this approach: the consistent conjectural equilibrium is not an equilibrium since each firm can unilaterally change its output to make more profits (Bresnahan, 1982, p. 937). Experimental evidence indicates that agents do not converge on the consistent conjectural equilibrium (Holt, 1982). It is also recognized that the conjectural variations parameter is not observable in principle. It has also been noted that these models lack a game-theoretic foundation (Shapiro, 1989). Yet it is widely held that conjectural variation models are still very important in examining scenarios underpinned by complex dynamic processes. The simplified story of our model subsumes the following: we examine government policy that concerns the allocation of public infrastructure between two industrial locations. It is argued that the location of public infrastructure will determine the short-run cost functions of firms in these locations. These costs of production will, in turn, determine the nature of competition in the product market.16 16

Arrow and Kurz (1970) and Barro (1990) have stressed the importance of public infrastructure being a substitute for private capital in the production function. Thus, an increase in public infrastructure in an industrial location, ceteris paribus, reduces the cost of production of all firms of that location. Alternatively, one may assume that public infrastructure reduces cost due to the “iceberg” effect of Samuelson (1954): if public infrastructure is inadequate, then a large portion of the goods produced will be wasted and will fail to reach the consumers. An increase in public infrastructure therefore reduces cost by facilitating trade. Public infrastructure has assumed significance in Europe as EC-funded infrastructure projects aim to create strategic advantages for the member nations (Martin and Rogers, 1995). As examples, the Channel Tunnel, highspeed rail network and new telecommunication networks have been undertaken in the recent years to boost industrial development and convergence in Europe.

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As a result, government policy will endogenously determine the degree/nature of competition in the product market. On the other hand, this allocation of public infrastructure also enables us to analyze the political cost: the promotion of an industrial location is an implicit taxation of firms in the other location. As the government increases public infrastructure in a location, voters from this constituency increase their political support for the incumbent government whilst this government loses votes from the other location. An allocation of infrastructure thus influences voters’ evaluation of the government and this evaluation constrains government policy on infrastructure that, in turn, impinges on voters’ evaluation. In the proposed equilibrium of the game, the government chooses the optimal allocation that influences the voters’ evaluation that, in turn, maximizes the probability of re-election of the incumbent government. The optimal allocation will determine the nature of competition in the product market. The game unfolds over two stages: In Stage I, the government allocates public infrastructure in order to maximize its probability of re-election given the voters’ preferences and characteristics. Thus, in Stage I, an electoral platform is formed. In Stage II, two firms compete for a unified market whilst their production bases are different. At the PNE of this sequential game, the government achieves an electoral equilibrium that maximizes votes cast in favor of the government. This optimum allocation of infrastructure provides a winning electoral platform to the incumbent government from which the costs of production for firms and the nature of competition in the product market will emerge. 1.8.2 The model We consider a market that has duopolists who have two distinct production locations. We assume that these locational choices have already been made and, hence, the location of a firm is part of the history. It is also assumed that the national economy consists of these locations. The government has a given amount of tax revenue that is to be distributed between these locations for creating public infrastructure.

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The impact of the public infrastructure is to reduce costs of production. Thus the larger is the public infrastructure in location i, vis-à-vis j, the lower is the cost of production of the firm at location i. We further assume that buyers are located in such a fashion that the cost of transport is zero and, hence, there is a single price that prevails in the market. The market is thus characterized by the following sequential game: In Stage I, the electoral equilibrium is achieved that, in turn, determines the distribution of public infrastructure. The distribution of infrastructure determines the costs of production of the oligopolists in Stage II of the game who engage in competition in the product market to capture the largest possible market shares (Fig. 1.4). The solution to the game is proposed in a recursive fashion. We first determine the market outcome at Stage II and then trace back to Stage I that is popularly known as the logic of backward induction. Rationality and complete information dictate that both these firms and the government will form their expectations by looking ahead and foreseeing the product market equilibrium of Stage II. If agents behave in this fashion, they are said to have rational expectations. In Stage I, all these agents adopt their optimal actions based on the rational expectations. The resultant outcome is the PNE of the proposed game. History:

• • • •

Tax revenues Location of firms Location of voters Characteristics of voters

•

•

Government allocates public infrastructure Electoral equilibrium is achieved

STAGE I

• •

Duopolists compete in the product market Product market equilibrium is achieved

STAGE II

TIME Figure 1.4.

Time-structure of decisions.

Source : Woodland, A. (ed.) (2002). Essays in Honour of Murray Kemp, Edward Elger, 2002.

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1.8.3 Stage II: Nature of competition in the product market We introduce the following assumptions to characterize the product market. The industry demand function (inverse) is linear: P = a − bX

(31a)

Where P and X are price and output, respectively, and a, b > 0. There are two production locations. We assume that Firm i is based at location i, for i = 1, 2. The cost of production of Firm i is as follows: ci = ci (Xi, Gi) = mXi2/Gi

(31b)

where Xi: output of Firm i, i = 1,2 Gi: allocation of public infrastructure to location i where firm i is located. The marginal cost is hence given as MCi: MCi = 2mXi/Gi.

(31c)

Thus MCt is increasing in Xi given Gi , and decreasing in Gi given Xi: δMCi/δXi = 2m/Gi > 0,

(31d)

δMCi/δGi = −2mXi/Gi2 < 0.

(31e)

The profit function of Firm i is as follows: Πi = Xi (a − bX) − mXi2/Gi.

(32a)

It is assumed that the firms have non-zero conjectural variation and, hence, we get the following for Firm 1: d P1 / dX 1 = a - 2bX 1 - bX 2 - bX 1(dX 2 / dX 1 ) - 2mX 1 /G1 .

(32b)

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We define the conjectural variations as follows: f1 = (dX 2 /dX 1),

f2 = (dX 1 /dX 2 ).

(32c)

Hence the reaction functions in the quantity decision of the duopolists are as follows: X 1 = (a - bX 2 )/ (2b + f1b + 2m/G1),

(32d)

X 2 = (a - bX 1)/ (2b + f2b + 2m/G 2 ).

(32e)

The consistency condition is that the change of X1with respect to X2 along Eq. (32d) must be self-confirming. That is, the slopes of the reaction functions must be equal to the appropriate conjectural variations. Hence f2 = [-b /(2b + bf1 + 2m / G1)],

(33a)

f1 = [-b /(2b + bf2 + 2m / G 2 )].

(33b)

The consistency conditions (4a) and (4b) give the following: 2bf2 + f1f2b + 2mf2 / G1 + b = 0,

(34a)

2bf1 + f1f2b + 2mf1 / G 2 + b = 0.

(34b)

Subtracting Eq. (31b) from Eq. (31a) will yield: (f2 / f1) = [b + (m/G 2 )]/ [b + (m/G1)].

(34c)

The more negative φ1 is, the more accommodating Firm 1 believes Firm 2 is. Thus, at the consistent conjectural equilibrium, all expectations are ex post confirmed and, hence, (φ2/φ1) is a measure of the relative competitiveness of Firm 1. Definition 1. We define (φ2/φ1) as the degree of competitiveness of Firm 1 vis-à-vis Firm 2. The larger (φ2/φ1) is, the more accommodating Firm 1 is and vice-versa. It is instructive to note that the degree of competition

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depends on the allocation of public infrastructure G1 and G2. We now turn to the explanation of G1 and G2 that will, in turn, determine the degree of competition. 1.8.4 Stage I: Electoral equilibrium Citizen voters have two entitlements: as an economic agent, each voter is entitled to returns from the firm of his location. We assume that the higher the profit of a firm, the larger the economic return of the citizen residing in the location in which the firm operates. As a voter, he is entitled to influence the rules of the game, that is, the allocation of infrastructure. This allocation, in turn, affects his economic returns. It is assumed that each citizen exercises the voting rights in one’s interests. The rational government chooses the allocation of infrastructure (rules of the game) that will give rise to nominal returns to voters that will, in turn, maximize its votes. The electoral equilibrium is the optimal allocation of infrastructure that maximizes the votes cast in favor of the incumbent government. In order to determine the allocation of public infrastructure G1 and G2, we now look at the electoral equilibrium of Stage I. We apply the probabilistic voting theorem to explain the electoral equilibrium (see Wittman, 1989). It is assumed that voters are located in two locations of the public infrastructure. In each location, voters have the identical preference for the infrastructure. Thus, there are two groups of voters and their preferences are represented by their utility functions U1 (G1 − G a) and U2 (G2 − G b), and S1 and S2 are the sensitivity parameters of these groups of voters. G a and G b are respectively the “ideal points” of voter groups 1 and 2 given their tax burdens. For instance, S1 represents the extent to which voters from group 1 based at location 1 decrease their support/vote for the political party in response to a divergence between G2 and these voters’ preferred allocation of public infrastructure Ga. We specify the votes-to-public infrastructure function as follows: V1 = 50 + n1S1 (U1(G1 − Ga)),

(35a)

V2 = 50 + n2S2 (U2(G2 − G b)).

(35b)

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Suppose G* is the total tax revenue to be distributed and group i of voters is located at production location i. Each group splits votes equally between two parties when both the parties offer the same infrastructure.17 Otherwise, a party loses votes as its public infrastructure offer deviates from the “ideal point” of a group. From Wittman (1989), we know that the vote-maximizing electoral equilibrium is ensured when the following first-order condition is satisfied18: n1S1 (∂U 1 / ∂G1) = n 2S 2 (∂U 2 / ∂G 2 ).

(35c)

Assumption 4. We specify the utility functions of the two groups of voters as follows: U1(G1 − G a) = −(G1 − G a)2,

(35d)

U2(G2 − G ) = −(G2 − G ).

(35e)

b

b

The above formulation of the utility function suggests that voters dislike both shortfalls and over-allocation of public infrastructure to their respective localities. The latter needs an explanation: voters may dislike an over-allocation simply to escape from the congestion and pollution that an over-allocation brings with it.19 Proposition 16. Equations (35d) and (35e) capture voters’ preferences and Eqs. (35a) and (35b) are the votes-to-(public infrastructure) offer functions. Then the optimal allocations G1 and G2 of the public infrastructure that maximize the votes of the incumbent government are given by: G1 = w1 (G* - G b) + G a (1 - w2 ) 17

(36a)

Why should voters care for infrastructure? One plausible explanation is that voters are the stakeholders of the firms both as shareholders and employees. 18 It can be checked that the second-order condition is automatically satisfied. 19 It is important to note that a simple concave utility function, where voters are happier the more infrastructure investment they get but decreasingly so, will provide similar results.

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where w1 = (n2S 2 )/ (n1S1 + n2S 2 ).

(36b)

G 2 = w2 (G* - G a) + G b (1 - w2 )

(36c)

w2 = (n1S1)/ (n1S1 + n2S 2 ).

(36d)

Similarly,

where

Proof. See Appendix.

Equations (35a)–(35d) establish that the political elements such as ni, S1, and S2 are the critical ingredients in determining G1 and G2 given G*. If the incumbent government wants to stay in office and voters want public infrastructure, then the vote-maximizing government will allocate public infrastructure in an optimal fashion to create an electoral equilibrium platform that is sensitive to voters’ characteristics. The vote-maximizing allocation of public infrastructure influences the nature of competition due to its effect on costs of production of duopolists. The higher the allocation that a particular location gets, the lower is the cost of production of the firm based there. This firm, due to its lower cost, will be able to extract larger profits from the output market. 1.8.5 Electoral equilibrium and nature of competition From Eqs. (36c) and (36d) it is evident that the allocation of government investment in infrastructure depends on w1 and w2 given the exogenously determined budget and the “ideal points” G a and G b. It is instructive to note that w1 and w2 depend on the sizes of these voter groups — n1 and n2 — and their political sensitivities, S1 and S1, to the non-fulfillment of their demand for infrastructure. From Eq. (5c) we know that the nature of competition in the product market depends on the ratio of G1 and G2 given the values of a and b. Hence, combining Eqs. (5c) and (7a) through to Eq. (7d), we argue that political elements such as the size of the voter groups (ni) and political

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sensitivities of these voters, S1 and S1, are the main determinants of the degree of competition, (φ2/φ1), in the product market. In order to highlight this finding, let us consider two special cases. Assumption 5. Suppose each group of voters wants all available funds, G*, to be ploughed back into their respective localities. Hence, G* = Ga = Gb.

(37a)

Proposition 17. In the PNE of the proposed sequential game, the degree of competition, (φ2*/φ1*), lies between the Cournot and Bertrand values and is sensitive to the political landscape of the simplified society. Proof. In the PNE, all agents hold rational expectations about the market outcome in Stage II which are given by Eqs. (3d) and (3e). The rational expectations outcome, in turn, depends on the allocation of public infrastructure G1 and G2 in Stage I. Given the rational expectations outcome, the incumbent government chooses G1 and G2 in Stage I to maximize votes. Suppose voters’ ideal points are given by Assumption 6, then we know: G1 = [(n1S1)/ (n1S1 + n 2S 2 )]G*

(37b)

G 2 = [(n2S 2 )/ (n1S1 + n2S 2 )]G*.

(37c)

and

Substituting Eqs. (34b) and (34c), we get: (f*2 / f* 1 ) = [bG * + m(n1S1 + n 2S 2 )/ (n 2S 2 )]/ [bG * + m(n1S1 + n 2S 2 )/ (n1S1)].

(37d)

Equation (38a) establishes that the equilibrium degree of competition, (φ2*/φ1*), is determined by the political factors (niSi) of the society — given the cost and demand conditions. It is also evident

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that the equilibrium values lie between the Cournot and Bertrand values. Now we turn to the comparative-static results. 1.8.6 Comparative statics The starting point of this section is that each group of voters would want the whole of public infrastructure G* (Assumption 5). In this scenario, we have the following comparative-static results that characterize the proposed PNE. Proposition 18. As the size of a group of voters increases — ceteris paribus — the degree of competition shifts against the interest of the other group. Proof. Details are available to readers upon request. Differentiating Eq. (9a) with respect to n2, we get: ∂(f2* /f* 1 )/ ∂n2 < 0.

(38a)

Thus, as n2 increases given the size of group 1, the competitiveness of Firm 1 based at location 1 goes down since the political power of its opponent increases. Similarly, we can show: ∂(f2* / f* 1 )/ ∂n1 > 0.

(38b)

Proposition 19. In the PNE, the competitiveness of firm i is an increasing function of Si and a decreasing function of Sj. Thus, voter sensitivity is an important determinant of the degree of competitiveness in the proposed equilibrium. Proof. Details are available to readers upon request. We find: ∂(f2*/ f1*)/ ∂S 2 < 0.

(38c)

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In an analogous fashion, we find: ∂(f2*/ f1*)/ ∂S1 > 0.

(38d)

The upshot is that a location gains a larger (smaller) chunk of the public infrastructure if voters residing in this location are more (less) sensitive about the deviation of the actual infrastructure from their desired allocation. Thus, if voters of a region are highly committed to the incumbent government, the region will receive a lower share of public infrastructure that will, in turn, impoverish the region and the voters of the region. 1.8.6.1 Comparative statics (under alternative assumption) It is presumed that voters want a fixed share of the public infrastructure and any deviation from this share lowers the welfare of the voters. One may rationalize this by assuming a congestion, or pollution, cost. We represent this idea under the following assumption. Assumption 6. Suppose each group of voters has the ideal point as follows: Ga = G b = λG*

(39a)

where 0 < λ < 1. Theorem 4. Let Eq. (11a) be the preference of the voters. The votemaximizing allocation of public infrastructure G1 and G2 are given by G1 = G* (w1 + λ + 2w1λ),

(39b)

G2 = G* (w2 + λ + 2w2λ).

(39c)

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As a result, the degree of competition in equilibrium is as follows: bG * + w (1 +bm2l) + l f2* 2 = . f1* bG * + w (1 +bm2l) + l

(39d)

1

Proof. Substituting Eq. (39a) into Eq. (32a) yields: G1 = G * (w1 + λ + 2w1λ),

(40a)

G2 = G * (w2 + λ + 2w2λ).

(40b)

similarly,

Substituting Eqs. (39b) and (39) into Eq. (33c) yields the degree of competition in equilibrium, which is given by (39d). Theorem 5. The competitiveness of Firm 1 in equilibrium is an increasing function in w1 and decreasing function in w2. Proof. Straight-forward differentiation of Eq. (39d) with respect to w1 and w2 yields the above. Details are available to readers upon request. Theorem 6. The weight wi is an increasing function of Si and a decreasing function of Sj. Proof. Differentiation yields the result.

Proposition 20. From Lemmas 2 and 3, we find that the competitiveness of Firm i in equilibrium is an increasing function of the political sensitivity of voters of group i. Proof. Combining Lemmas 2 and 3, we get f*

d f2* 1

dS1

f*

f*

∂ f2* ∂w ∂ f*2 ∂w 2 1 1 > 0. + 1 = ∂w2 ∂S1 ∂w1 ∂S1

(41a)

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Similarly, d (f2*/ f1*) / dn1 > 0, (df2*/ f1* )dn2 < 0, d (f2*/ f* 1 ) / dS 2 < 0. The comparative-static results show the precise nature of sensitivity of the degree of competition to changes in political factors. As examples, the degree of competition or competitiveness of Firm 1 goes up (down) as the number of voters in its production location (n1) goes up (down) ceteris paribus. The competitiveness of Firm 1 goes up (down) as voters in its production location become more (less) sensitive to the non-fulfillment of their demand for infrastructure. That is, the competitiveness of Firm 1 goes up (down) as S1 goes up (down). In an analogous fashion, the competitiveness of Firm 1 goes up (down) as n2 goes down (up) and S2 goes down (up). 1.8.7 Discussion and comments The Smithian perspective on competition highlights a congruence of interests of market participants: say, a buyer wants some milk and is ready to give some money to the milkmaid for it, and the milkmaid wants money and is, therefore, ready to give a carton of milk in exchange. This exchange allows each to achieve one’s goal and they, thereby, help each other. In a complex market mechanism, however, economic problems are often embedded in a conflicting situation. It is recognized that the market mechanism can easily handle congruent interests but may fail to resolve conflicts in a harmonious or fair fashion (see Sen, 1984). To redress such conflicts, the visible hand of the government has usually been invoked (Ostorm, 1987). In this chapter, we highlight two types of conflicts — namely, market conflicts and political conflicts — and, thereby, attempt to weave them together to illuminate an important intersection between the economy and the polity. We introduce conflicts at the market level in the usual fashion as market rivalry — two prototype firms compete against each other for market shares. By applying the simple game-theoretic reasoning, we obtained the equilibrium market outcome. However, the core of

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the problem remains that the emerging market outcome, the conduct of firms, market shares, and take-home profits of these rivals critically depend on the choice of their strategic variable and, hence, on the nature of competition.20 Dixon (1986) introduced consistent conjectural variations to make the degree of competition endogenous. He established that the degree of competition is driven by the investment decision of firms since capital stocks impinge on costs of production. We exploit this intuition of Dixon by focusing on the impact of public infrastructure, as opposed to private capital, on costs of production. The degree of competition in the product market is, therefore, driven by an allocation of public infrastructure. The introduction of public infrastructure in our model allows us to link the second type of conflict, namely, the political conflict with the first type. Since, the availability of public infrastructure is fixed, it is modeled that there is no congruence of interests of agents coming from two distinct locations, as Hirsch (1977) noted, “what winners win, losers lose.” An allocation of infrastructure will naturally entail political costs and benefits that a self-seeking government — driven by electoral motive — would try to exploit. An incumbent government will naturally choose an allocation to maximize the probability of its re-election. Our model on probabilistic voting has antecedents in the literature: Lindbeck and Weibull (1987) and Dixit and Londregan (1994) adapted the probabilistic model to examine public policies that redistribute income to narrow groups of voters. They assume that various groups differ in their preferences for the political parties and, thereby, identify political characteristics of a group that make it an ideal candidate for receiving political largesse. The upshot is that these authors mainly study the major determinants of the political

20

From an early work of Marshak and Nelson (1972), we know that if the production structure is inflexible, then the Cournot outcome is a natural conclusion. On the other hand, if production is completely inflexible, then the Bertrand outcome is the likely candidate. It is argued that production is more flexible the more steep the MC function is. The nature of competition is introduced as an external assumption in Brander and Spencer (1983, 1985), Dixon (1985), Dixit (1984), Eaton and Grossman (1986), and Yarrow (1985).

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success of a special interest group. On the contrary, we start off with the political characteristics of voters and then apply the probabilistic voting theorem to determine the electoral equilibrium that is driven by political largesse in the form of public infrastructure. This is how our model resolves political conflicts. The resolution of political conflict can have serious ramifications for the product market due to its impact on the allocation of public infrastructure. This is indeed a serious point to consider: the traditional political theory highlights the failure of the majority-rule voting caused by the absence of a stable electoral equilibrium. As a result, political instability can create significant instability in product markets. This is where we apply the probabilistic voting theorem to highlight the existence of a stable voting equilibrium to establish that democratic political markets are well-organized to promote the votemaximizing allocation of infrastructure that will, in turn, lend stability to the product markets: the model predicts that the vote-maximizing government adopts an optimal allocation of public infrastructure that induces an electoral equilibrium that, in turn, maximizes its chances of re-election. In this perspective, the nature of competition, the structure of the industry, and the conduct of firms in an oligopolistic market critically depend on this electoral equilibrium and, hence, on voters’ preferences and characteristics. The degree of competition is thus identified with the equilibrium allocation of infrastructure and becomes a continuous variable, rather than a binary variable. It captures intermediate situations between the pure Bertrand and Cournot cases. We also find important comparative-static results that show that the structure and conduct of firms, and the nature of competition in oligopolistic markets will be sensitive to political characteristics. Future extensions of the chapter are desired on two fronts: Voters’ preferences should be made dependent on the final good’s price and thus on the nature of competition. This extension can enhance our understanding of the nature of equilibrium by providing circular interdependence between government policy and market outcomes. Second, an important extension is possible by allowing voters to “vote with their feet.” This extension will once again introduce the circular interdependence between government policies and market outcomes.

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1.9 Concluding Comments We attempted to explain a particular form of price discrimination, known as chaotic discrimination: Sellers quote prices in an oligopolistic market which are almost uniform and part of the common knowledge. Each seller, in reality, engages in secret and arbitrary price discounts and, thereby, creates some unsystematic pattern of price discrimination. Thus, there are two critical elements in chaotic discrimination: common and high-posted prices, and secret, yet arbitrary and chaotic price discounts. The contribution of this chapter has been twofold: First, it provided a model to explain why sellers may choose a common and high-posted price. Second, we explained the “arbitrary” and “chaotic” nature of price discounts. Bain (1952) stressed the importance of such discrimination. He attempted to explain it mainly in terms of the stability of collusion of sellers while the burden of his argument turns on sellers’ irrationality concerning price making. We provided an alternative rationale behind chaotic discrimination on the basis of two sets of arguments: First, we argue that sellers may adopt upward price-distortion to prevent entry and, thereby, to maintain long-run market shares and profits. Thus the chapter establishes that chaotic discrimination as a pricing strategy is a subgame PNE. We, thereby, provided a strong theoretical justification for chaotic discrimination as an optimal pricing strategy. Second, we constructively demonstrate that sellers would fail to adopt profit-maximizing price discounts due to multiple equilibria in such a market. The price discounts will be uncoordinated, and, hence, “arbitrary” and “inconsistent” which would deviate from the profit-maximizing discounts. The upshot of the findings is that incumbent sellers may successfully deter entry by choosing an upward price-distortion, yet they would fail to coordinate price discounts to reap short-run profits owing to the multiplicity of equilibrium discounts. Appendix A Result 1. We know that Πit * + Πt+1i* = K(4/3m + 4/3m/b + ∆P/2b).

(A1)

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Profits from the strategy profile (PD, N–C): = 4/3mK + (a − c)2/9b.

(A2)

(A1) > (A2) if the following condition holds: ∆P > [2(a − c)2/9b − 8/3m].

(A3)

Result 2. Quasi chaotic discrimination entails the strategy profile (PD, PD − ∆P). The profit from this strategy profile to the seller is the following: Π it* + Π t+1i* = (PD − c)xi* + (PD − c − ∆P)x **. i

(A4)

Substituting values of P D, xi in (A4) yields the following: = 4/3mK + (K − ∆P)(4/3m/b + ∆P/2b).

(A5)

From chaotic discrimination, profits would be equal to 2(K − ∆P)(4/3m/b + ∆/2b).

(A6)

Chaotic discrimination dominates quasi chaotic discrimination if Eq. (A6) > (A5). Simplification yields K − 8/3m > ∆P,

(A7)

∆P < a − c − 16/3m.

(A8)

Result 3. Suppose sellers choose the no-distortion N–C strategy in period t, then in period t + 1, the entrant, enters. The profits accuring to a seller from such a strategy will be Πti** + Πt+1i** = (a − c)2/9b + (a − c)2/16b.

(A9)

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Secret price discount in period t + 1 will yield: P t+1 = (a + 3c)/4 − ∆P.

(A10)

This is evident from Table 1.2. Market demand will be X t+1 = 3/4b (a − c) + ∆P/b.

(A11)

Individual sales will be xi = (a − c)/4b + ∆P/3b.

(A12)

Individual profits would be Π it+1 = [(a − c)/4 − ∆P][(a − c)/4b + ∆P/3b]

(A13)

< (a − c) /16b − ∆P /b < (a − c) /16b.

(A14)

2

2

2

Since ∆P is positive, then if sellers choose the no distortion N–C in period 1, they would continue with it in period t + 1. Result 4. We know that Πti* + Πt+1i* = K [4/3m (1 + 1/b) + ∆P/2b].

(A15)

Profits from the strategy profile (N–C, N–C) would be, as we know from Tables 1.2 and 1.3: = 25/144b (a − c)2.

(A16)

For quasi chaotic discrimination to be optimal, we need (A15) > (A16) that can be reduced as follows: (a − c)2/8 − 8/3m > [(a − c)2/2.9K] −8/3m (1 + 1/b).

(A17)

The sufficient condition is the following: 2.9[a − c − 8/3m] > 8

(A18)

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or, a − c − 8/3m > 2.6.

(A19)

Appendix B Proof of Proposition 4: With the specified utility functions, the first-order condition (6c) is reduced to G1 - G a n 2S 2 = . G 2 - G b n1S1

(B1)

Since the amount of resources for investing in infrastructure is given at G*, the optimal allocation of G* is given by: G1 =

G* n 2S 2 - n 2S 2G b + n1S1G a , n1S1 + n 2S 2

(B2)

G *n1S1 + n 2S 2G b - n1S1G a . n1S1 + n 2S 2

(B3)

G2 =

We can simplify the above as G1 =

n 2S 2 n1S1 (G * - G b) + G a. n1S1 + n 2S 2 n1S1 + n2S 2

(B4)

Hence G1 = w1(G* − Gb) + Ga (1 − w)

(B5)

where w1 =

n2S 2 . n1S1 + n2S 2

(B6)

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Similarly, G2 = w2(G* − Ga) + Gb (1 − w2)

(B7)

where w2 =

n1S1 . n1S1 + n2S 2

(B8)

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Chapter 2

Politics of Campaign Contributions, Economics of Rivalry and Endogenous Market Structures

2.1 Introduction The main thrust of the literature on campaign contributions is on policy determination in representative democracies (see Grossman and Helpman, 1996, 1994). There is little attempt to understand the feedback between campaign giving and market outcomes. This chapter explores the pros and cons of campaign contributions in the context of a duopoly. We posit that campaign contributions of duopolists typically have an impact on their cost and demand functions. The fact that campaign contributions of these duopolists may affect their cost and demand functions implies that they can strategically choose campaign contributions in order to influence the market equilibrium. This chapter derives a perfect Nash equilibrium (PNE) volume of campaign contributions and establishes important comparativestatic properties of the equilibrium. This can be easily extended to oligopolies. It is of utmost importance to realize that campaign contributions have a far-reaching impact on the industrial structure through their effects on cost functions. Changed cost conditions alter market shares of firms and industrial concentration ratios, which thereby induce firms to take various actions to retain/enhance their market positions. These actions can take the form of product and technology 87

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developments, innovation and strategic acquisition, and endogenous mergers. The theory of endogenous merger argues that the decision to merge relies critically on the underlying industrial structure. As the industrial structure changes, it alters the incentives and constraints of firms to merge wherefrom one should observe new waves of merger activities. Static models of mergers typically consider mergers between exogenously given firms on the basis of pre-merger and post-merger profits and anticipated anti-trust rulings. We argue that campaign contributions alter cost functions and thereby open up new possibilities of mergers not captured by the static models of exogenous mergers. The model also highlights entry-inducing mergers associated with campaign contributions. A bulk of the literature on mergers finds the cost functions of firms involved in mergers and acquisitions to be the same, which is an inhibiting factor that undermines a realistic assessment of the effect of a merger on the firm and in the industry in which the merger is considered. To resolve this issue, we consider endogenous mergers in which the decision to merge is determined within the constraints of the firms’ operating and production choice. Gowrisankaran (1999) offers an endogenous and dynamic model of mergers. Gowrisankaran (1999) suggests that this type of analysis may be beneficial in assessing anti-trust considerations. Previous work on this issue of modeling mergers applied the game theory to find the implications on the welfare of mergers, e.g., Farrell and Shapiro (1990) who examined mergers in a static setting. Gowrisankaran (1999) argues that through a static analysis of the merger process, the conclusion, which may be intuitive to some, may suggest that a merger may lower social welfare through increased concentration and price effects. A dynamic analysis, however, may show that the increase in concentration in the market will be offset by the increased entry into the industry that may follow mergers. Furthermore, there is a suggestion by Gowrisankaran that static analysis may miss the benefit that a merger may have on an industry where languishing firms are merged into others, thus “preventing the dead-weight loss of discarding capital without a significant anti-competitive effect.”1 1

See Gowrisankaran (1999, p. 157).

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Politics of Campaign Contributions, Economics of Rivalry

89

The non-endogenous merger analysis will therefore be unable to predict the future welfare and industry effects of current policies. Furthermore, Gowrisankaran (1999) also argues that the relative profitability of merger vs. no merger is not a valid guide to whether a merger may occur. This is the case due to the strategic nature of the market where a firm may hold off merging to see if another firm merges with a third firm since this will have the effect of decreasing competition in the market. Similar issues are discussed in Polasky and Mason (1998) in terms of the ignorance of short-run and long-run effects of mergers in much of the literature where only one-shot static games are employed. Ignoring the distinction is a shortcoming in the literature, as firms may not have sufficient time to react to mergers in the short run. Allowing the merging group to form endogenously in a single merger case has been featured in Kamien and Zang (1990, 1991) and Gaudet and Salant (1992). In a sequential merger scenario, Kamien and Zang (1993) analyze the possible effect of monopolization in an industry if endogenously formed sequential mergers take place. The much-celebrated model of endogenous merger is given by Barros (1998). He provides a model that can predict merger partners, i.e., endogenous mergers, from the cost asymmetry of merger participants given the initial degree of market concentration. To put it differently, Barros (1998) proposes that mergers are endogenously determined by cost asymmetry. He then establishes, by means of the initial concentration of a market, that it can be forecasted which firms will be involved in a merger from the cost asymmetry. Our contribution, in this context, is the intuition that campaign contributions do affect the cost asymmetry and, thereby, trigger merger waves. The plan of this chapter is as follows: we present the prototype model in Section 2.2 and the comparative-static properties in Section 2.3. We introduce endogenous mergers in the context of campaign contributions in Section 2.4. In Section 2.5, we examine situations in which firms mimic a low-cost type and we conclude in Section 2.6. 2.2 The Model We consider a market that has duopolists (hereafter, agents) selling a product to a large number of buyers. The market is captured by a simple

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sequential game: in Stage I, agents engage in choosing campaign contributions that yield financial returns to them. We posit that the effect of campaign contributions materializes in Stage II of the proposed game. The effect is assumed to be threefold. First, campaign contributions of agent i enhance the market position of agent i. Secondly, campaign contributions of agent i yield private rents to agent i. Finally, the cost function of agent i is influenced by the campaign contributions of agent j and vice versa. Campaign contributions thus impinge on cost and demand functions in Stage II. In Stage II these agents engage in quantity competition to capture the largest possible market shares. The solution to the game is proposed in a recursive fashion. We first determine the market outcome in Stage II and then trace back to Stage I. Rationality and complete information about the structure of the game dictate that both agents will form their expectations by looking ahead and foreseeing the market outcome of Stage II. If agents behave in this fashion, they are said to have rational expectations. The resultant equilibrium is the PNE of the proposed sequential game. The PNE is an overall equilibrium in the two-stage model. It is a Nash equilibrium in campaign contributions since each agent’s overall profits can be given as a function of campaign contributions chosen in Stage I. Thus, in essence, the agent’s choice of campaign contributions is ipso facto a choice of reaction functions in the postulated duopoly. Stage II: Quantity competition in the duopoly The postulated market is characterized by the following assumptions: Assumption 1. The inverse demand function in the duopoly, without campaign contributions, is linear: p = a − bX

(1a)

where X is the market output, p is the price of good per unit, and a, b > 0. Assumption 2. We assume that campaign contributions lend a local monopoly power to these agents. Hence, campaign contributions

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funds of the ith agent increase the price of the product that he sells. We define pi as the price that agent i receives if agent i provides campaign contributions and Ti as to the winning party in the election. We define pi as: pi = p + αTi = a − bX + αTi

(1b)

for i = 1, 2 and j = 1, 2. In the absence of campaign contributions, the market turns out to be a bland duopoly with the inverse demand function given by Eq. (1a). Alternatively, one could have assumed the individual (inverse) demand function to be as Eq. (1b) in order to model campaign contributions. Assumption 3. We assume campaign contributions of agent j, Tj , to increase the marginal and average cost of agent i. The cost function of the ith agent is Ci which is postulated to be: Ci = (c + β Tj) Xi

(1c)

where c is the constant marginal cost of production in the absence of campaign contributions. Tj is the campaign contributions donated by the j th agent. Let us try to explore the imports of these two assumptions. First and foremost, in the absence of campaign contributions, this model reduces to the archetypal model of duopoly. With positive campaign contributions, more importantly, this model represents a scenario like this: each firm contributes Ti to the campaign fund of the winning political party. Each firm produces a homogenous product, say oil or coal, domestically and sells the product to a foreign market. Campaign contributions are a quid-pro-quo, these firms expect returns from the government in exchange for these contributions given at an earlier stage. The government negotiates with the foreign government for a slice of the foreign market for each of these campaign contributors. This is reflected in Eq. (1b): ceteris paribus as Ti increases, so does the market spoil for firm i from the foreign market. The government can secure a better price from the foreign

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firm, ceteris paribus. In order to sell this product in the foreign market, each firm incurs a transaction cost — maybe a transport cost and/or import duties. The government can reduce this transaction cost either by direct subsidy, or through negotiations with the foreign government. Both firms engage in pressure politics to raise the cost of the rival in order to have a more competitive position in the foreign market. This cost component is reflected in the second assumption as captured by Eq. (1c). The assumption is that the cost of firm i is larger as the contribution from its rival, Tj, ceteris paribus, increases. The necessity of these functional forms is to keep calculations tractable. All the results will be through with a general form for the profit function of firm i as in Eq. (2a): Πi = f (Ti, Tj) such that δ Πi/δ Ti < 0 and δ Πi/δ Tj > 0. Assumptions 2 and 3 together capture the effect of campaign contributions on the competitive positioning of these duopolists. Profits of agent i, Πi, in Stage II, are given by: Πi = aXi − bXi2 − bXiXj − cXi + αXiTi − βXiTj − Ti.

(2a)

Assumption 4. We posit that each agent also derives some pecuniary and nonpecuniary rents from donating campaign contributions in Stage I. It is assumed that the rent to each agent in Stage I is a constant, “r,” per unit of campaign contributions. Hence the rent of agent i from campaign contributions, Ti, is Mi: Mi = rTi.

(2b)

We now look at the market outcome at Stage II: maximizing the profit functions in Eq. (2a) with respect to Xi yields the Cournot equilibrium in the duopoly: X* 1 = [(a − c) + T2(α + 2β ) − T1(2α + β )]/(3b),

(3a)

X2* = [(a − c) + T1(α + 2β ) − T2(β + 2α)]/(3b),

(3b)

X* = X1* + X2* = [2(a − c) − (α − β )(T1 + T2)]/(3b),

(3c)

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p* = [(a + 2c) + (α − β )(T1 + T2)]/3,

(3d)

Πi = p*Xi* + (αTi − β Tj − c)Xi* − Ti

(3e)

It is evident from Eqs. (3a)–(3e) that the duopoly equilibrium in Stage II critically hinges on the values of T1 and T2 chosen in Stage I. This reveals the “strategic” role of campaign contributions, i.e., the incentive for agents to use campaign contributions to change the rivals’ output. This strategic role of campaign contributions is now addressed. Stage I: Strategic role of campaign contributions Campaign contributions have direct pecuniary and nonpecuniary rents to agents in Stage I. Campaign contributions also influence the market outcome of Stage II by affecting cost and demand conditions of these agents. Rational decision-makers must consider the effects of their campaign contributions of Stage I on the duopoly outcome of Stage II. The two-stage financial return of agent i, Ri, is: Ri = Mi + Πi = rTi + Πi (X1*, X2*).

(4a)

The first component on the RHS of Eq. (4a) is the private rent to agent i in Stage I that is given by Eq. (2b) of Assumption 4. The second term is the profit of the ith agent from the duopoly outcome in Stage II and given by Eq. (3e). To keep the analysis simple, we assume that the time rate of discount is zero for each agent. Maximizing profit functions in Eq. (4a) with respect to Ti yields the overall Cournot equilibrium in campaign contributions (T1*, T2*) in Stage I, whilst T1* and T2* are derived from the following first-order conditions: d P1 dR 1 =r + =0 dT 1 dT 1

(4b)

d P2 dR 2 =r + = 0. dT 2 dT 2

(4c)

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Proposition 1. The proposed sequential game has a unique PNE: in * Stage I, agents choose optimal campaign contributions, T* 1 and T 2 , such that: (a - c )(5b - 2a ) 9br T* = T *1 = T *2 = + . 2(a - b)(4b - a ) 2( a - b)( 4b - a ) e

(5a)

e

In Stage II, these agents sell optimal outputs X1 and X2 in the duopoly : X 1e = X 2e =

a - c (a - b) T*. b 3b

(5b)

The equilibrium (total) output X e and the equilibrium price p e in the duopoly are respectively : 2(a - c) 2( a - b ) T* , 3b 3b

(5c)

a + 2c 2( a - b ) + T * + bT *. 3 3

(5d)

Xe = pe =

Proof. T1* and T 2* are derived from the simultaneous equations (4b) and (4c). Since the proposed game is a symmetric game, T1* = T2* = T*. Substituting the value of T* from Eq. (5a) into Eqs. (3a) and (3b) yields Eq. (5b). Substituting Eq. (5a) into Eqs. (3c) and (3d), respec tively, yields Eqs. (5c) and (5d).2 2.3 Comparative-Static Properties In order to examine the comparative-static properties of the PNE given by Eqs. (5a)–(5d), we differentiate these equations with respect to relevant parameters to arrive at the following propositions. Proposition 2. An increase (decrease) in demand for information, “a,” increases (decreases) the equilibrium campaign contributions, 2

The second order condition is satisfied if (α − β)(4β − α) > 0.

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T*, if β > (2α/ 5). The equilibrium output, X e, of the duopoly goes up (goes down) as the demand parameter “a” increases (decreases). The equilibrium price, p e, of the informational duopoly increases (decreases) as the parameter “a” goes up (goes down), if (β 2 + 13αβ − 5α 2) > 0. Proof. Differentiating Eq. (5a) with respect to “a” yields:

δ T*/δa = (5β − 2α)/[2(α − β )(4β − α)] > 0.

(6a)

Since (α − β) > 0, and from the second-order condition, we know (4β − α) > 0, and hence (5β − 2α) > 0 for β > 2α/5. We know from the second-order condition that (α − β )(4β − α) > 0. Hence, δ T*/δa > 0, if β > 2α/5; otherwise, δ T */δ a < 0. Differentiating Eq. (5b) with respect to “a” yields:

δX ei /δa = β/[b (4β − α)] > 0.

(6b)

Similarly, we can find out the effect on the equilibrium price as

δp e/δa = [β 2 + 13αβ − 5α 2]/[3(α − β) (4β − α)].

(6c)

The impact of changes in “a” on the equilibrium output is unambiguous and expected. The impact of changes in “a” on the equilibrium price is ambiguous and can be perverse since in any market an increase in demand is expected to increase both the equilibrium price and the equilibrium quantity. This perverse result arises in our model if (β 2 + 13αβ − 5α 2) < 0 and, hence, δp e/δa < 0. This is due to the effect of a change in “a” on the equilibrium campaign contributions, T *, that in turn impinges on the equilibrium price. Proposition 3. An increase (decrease) in cost, c, reduces (increases) the (Nash) equilibrium campaign contributions if β > 2α/5. These changes have ambiguous and possible perverse effects on the equilibrium output and the equilibrium price of the proposed duopoly. Proof. It is instructive to note that

δ T */δc = −(5β − 2α)/[2(α − β )(4β − α)].

(7a)

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Hence, δT */δc > 0 for β < 2α/5 and δT */δc < 0 for β > 2α/5,

δX ei /δc = 1/(3b)(−1 + [(5β − 2α)]/[b (−α + 4β )]).

(7b)

Hence, δX ei/δc < 0 for β < (2α/5) and δX ie/δc > 0 for b < [(5β − 2α)/ (−α + 4β)]. Similarly,

δp e/δc = 2β (α − 1.75β ). Hence, δp e/δc > 0 for α > 1.75β and δp e/δc < 0 for α < 1.75β.

(7c)

The conventional wisdom is that an increase (decrease) in cost increases (decreases) the equilibrium price and reduces (increases) the equilibrium output in a duopoly. However, due to the effects of campaign funds on the output and prices, we note the possibility of perverse effects of changes in cost of production on the equilibrium output and the equilibrium price: δX ie/δc > 0 for b < [(5β − 2α)/ (−α + 4β)]δp e/δc < 0 for α < 1.75β. Proposition 4. An increase (decrease) in the pecuniary rent, r, from campaign contributions increases (decreases) the equilibrium campaign contributions, increases (decreases) the equilibrium price, and reduces (increases) the equilibrium output of each duopolist. Proof. We differentiate Eqs. (5a), (5b), and (5d) w.r.t. “r” to yield the following:

δT */δr = 9b (α − β )2/4 > 0,

(7d)

δX ei /δr e

= −(α − β ) (δT */δr)/(3b) < 0,

(7e)

δp /δr = 2(α − β ) (δT */δr)/(3b) > 0.

(7f)

Proposition 4 highlights the following: As the private rent from campaign contributions increases, each agent increases his campaign contributions that, in turn, raises the total cost of production of each agent. This increase in total cost, induced by an increase in T *, results

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in a rise in the equilibrium price and a decline in the equilibrium output of each agent.

2.4 Campaign Contributions and Endogenous Mergers in a Myopic Model We start off with a simple duopoly in which firms engage in quantity competition. For the sake of tractability, the demand function is postulated as q = [1 − (p/9)] by assuming a = 1, b = 1/9 in the demand function (1a). Both firms have constant and identical average cost of production C* in the absence of campaign contributions. It is now assumed that campaign funds have no impact on prices. Campaign funds however affect on transaction costs. Different transaction costs cause a difference in cost conditions. It is further assumed that these firms have constant marginal costs Ci for firm i, i = 1,2. Thus C1 = C* + λ1 and C2 = C* + λ2 where λi is the transaction cost that is determined by Tj. The model is myopic since firms do not use Tj s in a strategic fashion to embark on the most desirable endogenous merger. All firms in the model have made political contributions in a myopic fashion, which means these firms did not attempt to influence the industrial structure by making these campaign contributions. These firms expect some political favors from the political party if it gets elected. Thus firms only consider the short-term effects of campaign contributions on their profits. We assume that C1 < C2 since T1 > T2. We label the cost difference as ∆, hence ∆ = C2 − C1 = λ2 − λ1. Note that the transaction costs asymmetry as given by (λ2 − λ1) is determined by an asymmetry in campaign funds (T1 − T2). The profits of these incumbents from the Cournot–Nash equilibrium are: 2 Π* 1 = (1 − C1 + ∆) , 2 Π* 2 = (1 − C2 − ∆) .

* Since Firm 1 has a lower transaction cost, Π* 1 > Π2 .

(8a) (8b)

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We now consider a possible entry by Firm 3 who has a constant marginal cost C3. We assume this firm has made a prior contribution to the government and C3 = C* + λ3. We examine exogenous merger possibilities between Firms 1 and 2 as Firm 3 makes an entry — assuming that the merger does not attract flak from the regulatory authority. As Firms 1 and 2 merge into a single entity, the merged entity with the marginal cost C1 engages in Cournot competition with Firm 3. We represent the cost difference: C3 − C1 = λ3 − λ1 = ∆1. The profits from the Cournot–Nash equilibrium of the newly emerged duopoly are the following: * = (1 − C1 + ∆1)2, Π1,2 Π3* = (1 − C3 − ∆1)2.

(8c) (8d)

Equation (8c) gives the profits of the merged entity. We now examine the incentive of Firms 1 and 2 to merge. We first consider the possibility that C3 > C2. Suppose there is no merger, then the duopoly is turned into a triopoly as Firm 3 makes an entry. We label the cost difference between Firms 2 and 3 as ∆2, ∆2 = C3 − C2. The profits of these three firms from the Cournot–Nash equilibrium involving three firms are: Π1 = 9(1 − C1 + ∆ + ∆1)2/16,

(9a)

Π2 = 9(1 − C2 − ∆ + ∆2) /16,

(9b)

Π3 = 9(1 − C3 − ∆ − ∆2)2/16.

(9c)

2

A simple comparison will give us the incentive for the exogenous merger between Firms 1 and 2. Observation 1. The incumbents — following the entry of Firm 3 — have an incentive to merge if C3 > 2C1 + 3∆ − 1. Proof. Firms 1 and 2 have an incentive to merge if (1c) > (2a). That is, (1 − C1 + ∆1)2 > 9(1 − C1 + ∆ + ∆1)2/16. Simplification of Eq. (9d) yields the result.

(9d)

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2.4.1 Endogenous mergers The entry of Firm 3 leads to the possibility of three distinct mergers — Firms 1 and 2, Firms 1 and 3, and Firms 2 and 3. Assuming C1 < C2 < C3 and retaining the previous symbols, we label the post-merger *, profits of Firm i and j by Πi,j * = (1 − C1 + ∆1)2, Π1,2 2 Π* 1,3 = (1 − C1 + ∆) ,

(10b)

* = (1 − C2 − ∆) . Π2,3

(10c)

2

(10a)

* > Π* * From these values, we know Π1,2 1,3 > Π 2,3. Thus, both Firms 2 and 3 have an incentive to merge with Firm 1 whilst Firm 1 has an incentive to merge with Firm 2. Observation 2. Firms 2 and 3 have an incentive to merge if C3 < (1 + 2C2 − ∆)/3. * > Π2: Proof. Firms 1 and 2 have an incentive to merge if Π1,3 Substituting Eqs. (10b) and (9b) yields the result. From Observations 1 and 2, we offer the first result on endogenous mergers. Proposition 5. Assuming C1 < C2 < C3, Firms 1 and 2 will merge if C3 > (1 + 2C2 − ∆)/3 > 2C1 + 3∆ − 1.

(11a)

Firms 2 and 3 will merge if C3 < 2C1 + 3∆ − 1 < (1 + 2C2 − ∆)/3.

(11b)

There will be no merger if (1 + 2C2 − ∆)/3 < C3 < 2C1 + 3∆ − 1.

(11c)

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Firms 1 and 2 will merge if 2C1 + 3∆ − 1 < C3 < (1 + 2C2 − ∆)/3

(11d)

* > Π1,3 * > Π2,3 *. since Π1,2 Proof. Comparisons of Eqs. (8a)–(8c) with Eqs. (9a)–(9c), respectively, will yield the result. We now consider the case in which C1 < C3 < C2. That is Firm 3 is more efficient than Firm 2. Let us label the cost difference as: C3 − C1 = d, C2 − C1 = d1, and C2 − C3 = d3. The profits of these three firms from the Cournot–Nash equilibrium are: Π1 = 9(1 − C1 + d + d1)2/16,

(12a)

Π2 = 9(1 − C2 − d + d2) /16,

(12b)

Π3 = 9(1 − C3 − d1 − d2) /16.

(12c)

2

2

The post-merger outcomes are 2 Π* 1,3 = (1 − C1 + d1) , * = (1 − C1 + d)2, Π1,2

(13b)

* = (1 − C3 − d)2, Π2,3

(13c)

(13a)

* * while Π* 1,3 > Π1,2 > Π2,3 . We now offer the result for endogenous mergers. Proposition 6. Assuming C1 < C3 < C2, Firms 1 and 3 will merge if d < C1 + [(1 − C1 + d1)/3],

(14a)

C3 < (1 + C1 + C2)/3.

(14a′)

that is,

Firms 2 and 3 will merge if C3 > (3C2 − C1 − 1).

(14b)

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Firms 1 and 2 will merge if C3 > (3C2 − C1).

(14c)

There will be no merger if (1 + C1 + C2)/3 < C3

(14d)

(3C2 − C1) < C3.

(14e)

and

Proof. These results are derived from the above profit functions. 2.5 Mimicking a Low-Cost Entrant and Endogenous Mergers In order to introduce signaling and possible mimicking, we consider two periods and three firms. At date 1, Firms 1 and 2 form a duopoly and Firm 3 is an entrant. At date 1, as Firm 3 enters, there are three firms that engage in quantity competition in this market. At date 2, this entry can trigger an endogenous merger that depends on the cost of production of Firm 3 as articulated before. The entrant (Firm 3) knows its cost from the start while the incumbents do not know Firm 3’s cost. Because Firm 3 prefers to merge with Firm 1, Firm 3 intends to convey the information that it has a low cost such that C1 < C3 < C2, and C3 > (1 + 2C2 − ∆)/3 > 2C1 + 3∆ − 1. The problem is that it does not have a direct means to do that, even if the above inequalities were true. The indirect way is to signal by increasing its output. The knotty problem is that Firm 3 may want to increase its output at date 1 even if it has a high cost and the above inequalities do not hold. The loss in the first-period profit may be offset by the gain in the secondperiod gain from a merger with Firm 1. Does this mean that Firm 1 will merge with Firm 3 when observing a high output of Firm 3? It is not straightforward. A rational incumbent, Firm 1, knowing that it is in the entrant’s self-interest to “lie” in this manner, will not necessarily believe that the entrant has a low cost bounded within the above

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inequalities. In turn, the entrant knows about this incentive. We look at the much-famed separating equilibrium in which the entrant does not pick the same first-period price when his cost is low as opposed to the case when it is high. The first-period equilibrium then fully reveals the cost of Firm 3 to Firm 1. It is well-known that there are two necessary conditions for the existence of an equilibrium. First, the low-cost type does not want to pick the high-cost type’s equilibrium output and vice versa. In the separating equilibrium, the low-cost entrant’s output will induce a merger of Firm 1 with the entrant, Firm 3. In the separating equilibrium, the high-cost entrant’s output will not induce any merger. In order to derive the result, we assume the possibility of a subsequent de-merger if Firm 3 had “lied” about its cost in the earlier stage. The cost of the de-merger to the entrant is labeled as D. On the basis of this de-merger cost and the previous results, we offer the following findings. Proposition 7. An entrant, Firm 3, with cost C3 such that C1 < C2 < C3, does not mimic a low-cost firm, and the entry does not induce endogenous mergers if : (1 + 2C2 − ∆)/3 < C3 < 2C1 + 3∆ − 1,

(15a)

2C2 − C1 > 1/2,

(15b)

C3 > C2 − C1 + 2.

(15c)


Proposition 8. An entrant, Firm 3, with cost C3 such that C3 > C2 > C1, does not mimic a low-cost firm, and the entry triggers an endogenous merger between incumbents if : 2C2 − C1 > 1/2,

(15b)

C3 > C2 − C1 + 2,

(15c)

C3 > 2C1 + 3∆ − 1.

(15d)


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Proposition 9. An entrant, with cost C3 such that C3 > C2 > C1, does not mimic a low-cost firm and the entry induces an endogenous merger between the entrant and the less efficient incumbent, Firm 2, if : C3 < (1 + 2C2 − ∆)/3. Proof. Details are available from the author.

(16a)

Proposition 10. An entrant, with cost C3 such that C3 > C2 > C1, mimics a low-cost firm with cost C**, and the entry induces an endogenous merger and a subsequent de-merger between the entrant and the more efficient incumbent, Firm 1, if : C3 < C2 − C1 + 2, C ** 3 > 2C1 + 3∆ − 1,

(16b)

2C2 − C1 > 1/2,

(15b)

D > 0.

(16d)


(16c)

Proposition 11. An entrant, with cost C3 such that C3 > C2 > C1, mimics a low-cost firm with cost C**, and the entry induces an endogenous merger and a subsequent de-merger between the entrant and the less efficient incumbent, Firm 2, if: C3 < C2 − C1 + 2, C3** < 2C1 + 3∆ − 1.

(16b) (16c)

Proposition 12. An entrant, with cost C3 such that C3 < C2 < C1, mimics a low-cost firm with cost C**, and the entry does not trigger an endogenous merger if : C3 < C2 − C1 + 2,

(16b)

(1 + 2C2 − ∆)/3 < C3** < 2C1 + 3∆−1.

(17a)


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The above are all pooling-strategy equilibria. Let us now consider the possibility of a signaling equilibrium. Proposition 13. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2), and the entry triggers an endogenous merger between the entrant and the more efficient incumbent if: C*** < (1 + C1 + C2)/3.

(17b)

C2 < 2C1 − 3.

(17c)

This is possible if


Proposition 14. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2), and the entry triggers an endogenous merger between the entrant and the less efficient incumbent if : C2 > 3/2. Proof. Details are available from the author.

(17d)

Proposition 15. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2), and the entry does not trigger an endogenous merger if : C2 > 2C1 − 3. Proof: Details are available from the author.

(18a)

Proposition 16. A truly low-cost entrant signals a cost C*** = (C2 − C1 − 2), and the entry triggers an endogenous merger between the incumbents if : C2 < 1. Proof. Details are available from the author.

(18b)

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2.6 Concluding Comments We suppose campaign contributions impinge on cost and demand functions of duopolists and, thereby, influence their competitive positions. Duopolists spend campaign contributions to capture the largest possible market shares. From this extended model of duopoly, we derive the PNE in terms of campaign contributions. We note that an increase in market buoyancy, a decrease in the marginal cost of production, and an increase in private rents from campaign contributions funds will increase the equilibrium campaign contributions that each duopolist donates — given parametric restrictions. We similarly expect the equilibrium campaign contributions to decline with a decrease in market buoyancy, an increase in the marginal cost of production, and a decrease in private rents from campaign contributions — given parametric restrictions. We also noted perplexing comparative-static properties of the duopoly equilibrium in the presence of campaign contributions: parametric changes in demand and cost functions can have perverse effects on the equilibrium price and the equilibrium quantity of the proposed duopoly with campaign contributions. Our second proposal is that campaign contributions can have asymmetric effects on costs and will, therefore, cause cost asymmetry only. This cost asymmetry can be shown to trigger a gamut of endogenous changes. In this paper, we show the influence of this cost asymmetry on the incentives of firms to merge. A whole set of new results are offered: under a set of restrictions, we establish that the most efficient firm merges with the least efficient one. With a new restriction, we establish that less efficient firms will merge. Under another set of restrictions, we establish that more efficient firms will merge. What is important is that these restrictions are solely driven by differential impacts of campaign contributions on individual costs. Differences in campaign contributions can, therefore, drive a wave of endogenous mergers that cannot be explained by any other economic factors. The other important finding is that differences in campaign funds can create situations that induce the entry of firms in an industry that will in turn trigger endogenous mergers. Once again, such mergers and the merger-inducing entry cannot be explained by any other model.


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Chapter 3

Rivalry in Formation of Social Capital in Networks and Endogenous Social Norms

3.1 Introduction Social capital describes group benefits and network externalities that individual members can exploit to their advantage (see Sobel, 2002; Putnam, 2000; Glaeser et al., 2000; Bourdieu, 1986). The economic definition of individual social capital thus purports that an individual’s social characteristics can enable him to extract additional returns from interactions with others given the interrelationship within a group (Glaeser et al., 2000). We extend the concept of social capital to modern production within a firm that is peopled by a collection of diverse employees and managerial staff. The best way to visualize social capital within a firm is to think of social capital as additional efforts that workers and managers offer to increase a firm’s current profit so as to ensure its future sustainability, which is a common good for the firm. Individual effort thus creates positive externalities in a firm, which paves the way for studying social norms that describe the rules of conduct/ behavior that encourage social capital that promotes positive externalities (see Huck et al., 2006). Social norms are rooted in social preferences that encourage members to adopt activities that create positive externalities (see Akerlof, 1980; Moffitt, 1983; Besley and Coate, 1992; Lindbeck et al., 2002; Vendrick, 2003). Huck et al. (2006), in contrast to the existing 107

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literature, made social incentives for choosing social norms endogenous by making individual incentives dependent on the actions of the others. Their main concern is to offer a challenging finding of how contractual arrangements within a firm can impinge on the efficacy of social norms and model their impact on individual behavior. In contrast, we bypass the role of contractual arrangements in social norms by assuming that the management can enforce a social norm within a firm. For our model, the social norm within a firm entails the choice of social capital (effort level) that predicates the market spoils of a firm. Yet the choice of social capital by one firm will trigger similar choices in rival firms since the formation of social capital has a profit-snatching effect on others. We therefore explain an equilibrium social norm as a symmetric Cournot–Nash equilibrium in social capital (effort levels) that rival firms choose to maximize their individual profits. In order to make the model tractable, we introduce three simplifications: First and foremost, we assume a twostage game. In the first stage, each firm chooses social capital (effort levels). In the second stage, they compete as Cournot rivals in an integrated market. The second stage game is well-known, so we focus on the first-stage game. Second, we assume that the average cost of production of a firm is independent of the output level, but is dependent on its social capital (effort levels). This dependence is expressed as a U-shaped relationship, reflecting the notion that as social capital exceeds a certain level, control and supervision costs become very high within a firm and thus adversely affects the per unit production cost. Finally, managers who enforce social capital (effort levels) have an objective function that is a linear combination of profits and social capital per se. The proposed model establishes a number of interesting properties of the equilibrium social norms. First, endogenous social norms and capital can give rise to a multiplicity of symmetric Nash equilibria. We establish the existence of a high-effort equilibrium that coexists with a low-effort equilibrium. In our model, we find that the higheffort equilibrium is always unstable while the low-effort equilibrium is stable only under a condition. Thus the low-effort equilibrium becomes unstable if this condition is violated. The instability property

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of the high-effort equilibrium retains the possibility of reaching the maximum feasible social capital, if history or expectations dictate so. Path-dependency also assumes paramount importance. If both equilibria are unstable, the system becomes highly fragile and the initial condition, or history, and expectations can destabilize the system. The instability of equilibria can engender complex dynamics and trigger chaos. The plan of the work is as follows: we introduce the model in Section 3.2 and offer the results in Sections 3.3 and 3.4, and conclude in Section 3.5. 3.2 A Modeling of Social Capital and Formation of Group Norms 3.2.1 The main intuition Suppose there are two multinational enterprises: a Japanese and a US MNE from an industry seek additional social capital with employees (additional efforts) in order to lower their costs of production to achieve a better market positioning. Each MNE is aware of the possibility of reciprocal, or retaliatory, social capital formation by its rival. Our focus is on the simultaneous formation of norms on social capital by these global firms. At the outset, before the establishment of the norm of additional effort and social capital, there is a fixed marginal cost of production for each MNE. In order to enhance their market positioning, the two rival MNEs seek to increase social capital from their employees. Each MNE gains from social capital, and consequent additional efforts, since these additional efforts reduce costs of production. However, the increased formation of social capital by one MNE, say the Japanese, also triggers the social capital formation between the US MNE and its employees, which lowers the costs of the US MNE. The new market position of each MNE will depend on the relative changes in the costs of production, which will further drive future social capital formation. Forward-looking MNEs will strategize their current social formation in order to achieve a Nash equilibrium that involves mutual-best responses in terms of the formation of social

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capital by these two rivals. By the construction of the problem, the mutual-best responses determine the Nash equilibrium social capital. In what follows, we characterize a Nash equilibrium. 3.2.2 Preliminaries The market is characterized by a simple linear inverse demand function. P = a − bQ

(1a)

where P is price and Q is the quantity of the good produced. The industry is characterized by a duopolistic rivalry between the two MNEs. We explain the social capital formation between an MNE and its employees as follows: Assumption 1. The initial marginal cost of a typical MNE, h, is ch, which is exogenously given as ch = c0.

(1b)

Assumption 2. We label social capital as k. The positive impact of k on the marginal cost is assumed to be given by Eq. (1c): cj = f (kj)

(1c)

where kj is the social capital of MNE j. We will specify the cost function subsequently. The above idea is similar to the concept of scale economies highlighted by Alfred Marshall (1891, p. 485) who considered the outcome of a market in which firms with scale economies compete against each other. He argued that ultimately one firm monopolizes the industry, but which firm will take over cannot be predicted in advance. From this notion, one can derive the idea of agglomeration (see Krugman and Elizondo, 1996).

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Assumption 3. Two MNEs strategically form social capital by considering the mutual interdependence of their decisions to form social capital. Assumption 4. The equilibrium social capital is defined as the combination of mutual-best responses in terms of social capital, k1 and k2. Assumption 5. As long as the formation of social capital increases the profits of an MNE, both employees and managers have an incentive to form social capital in order to share the increased profits of the MNE. There is an implicit bargaining process that determines the allocation of increased profits between employees and managers. We have not modeled the bargaining process in this work. We do not model the bargaining process. The incentive of social capital formation derives from the increase in joint profits; this idea is similar to the search benefit as stated by Hall (2005). The two MNEs are firms with unknown social capital and hence unknown marginal costs, c1 and c2, and the Nash–Cournot output, price, and profits are: q1* =

(a - 2c1 + c 2 ) , 3b

(2a)

q *2 =

(a - 2c 2 + c1) , 3b

(2b)

p* =

(a + c1 + c 2 ) , 3

(2c)

p 1* =

(a - 2c1 + c 2 )2 , 9b

(2d)

p *2 =

(a - 2c 2 + c1)2 . 9b

(2e)

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With the formation of social capital, the marginal cost of production of each MNE changes. As the marginal cost of each MNE changes, it alters its relative position in the market. The incentive to form social capital derives from this change in the relative position of the MNEs that is driven by a change in marginal cost functions. 3.3 Managerial Returns from Firm Size and U-Shaped Costs: Fragility and Indeterminacy of Equilibrium Integration In this section, we will specify two important elements to model the proposed Nash equilibrium social capital of the previous section. The first is in the cost function that takes into account a supervision constraint that the senior management of an MNE faces as the size of social capital increases. Second, we introduce a utility function of the MNE management that will specify the managerial compensation function. We retain the usual assumption that managers of MNEs are compensated on the basis of their performance measured in terms of own-firm profits. We introduce the idea that the senior management of a global firm also derives benefits from social capital. This may be due to the manager’s enhanced power, prestige and camaraderie in the relevant firm, and also due to an improved position in the managerial labor market. The managerial labor market may reward the efforts of MNE managers who are more successful in forming social capital with their stakeholders. Note that the analysis in the previous section is based on an unspecified cost function driven by social capital as given in Eq. (1c). Our main argument is that social capital formation should result in a decreasing marginal and average cost for an MNE. However, we also posit that the management has a finite supervising capacity in building social capital. The marginal cost of production declines as social capital increases till it reaches a threshold. Beyond this threshold, social capital starts having a negative impact on the marginal cost of production due to managerial constraints. In order to highlight this aspect of the supervision limit of a firm, we introduce a specific average cost function of an MNE that is U-shaped in social capital.

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Assumption 6. As the social capital of MNE, i, increases, the average cost of production of MNE I declines till a particular level of social capital and then starts rising. That is, ci = c0 - c11ki + c12ki2 ,

c11 > 0,

c12 > 0,

dci = -c11 + 2c12ki . dki

(1d) (4a)

Hence (dci/dki) < 0 for ki < [c11/(2c12)] and (dc/dk) > 0 for ki > [c11/(2c12)]. We assume that the structure of the average cost is the same for each MNE. Assumption 7. The compensation, Ti, of the senior management of MNE, i, is given by: Ti = mki + π*i .

(4b)

The first component is the managerial return from social capital that increases with ki at a constant rate, m. The second component is the usual own-firm profits. The own-firm profit of an MNE is given in Corollary 1. Corollary 1. The profit functions of these MNEs are dependent on their social capital and given by: p 1* =

(a - c 0 + (2k1 - k2 )c11 - (2k12 - k22 )c12 )2 , 9b

(4c)

p 2* =

(a - c0 + (2k2 - k1)c11 - (2k22 - k12 )c12 )2 . 9b

(4d)

Proof. Substituting Eq. (1d) into Eqs. (2d) and (2e) yields Eqs. (4c) and (4d). Lemma 1. The first-order condition to maximize the compensation of management, i, is given by: ki = [9bm/(8zi) + ci1]/(2ci2) > [ci1/(2ci2)],

(4e)

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zi = [a − c0 + (2ki − kj)ci1 − (2ki2 − kj2)ci2] > 0. Proof. The results are from the usual first-order condition.

(4f)

In the rest of the work, we only consider a symmetric equilibrium of the social capital such that k1 = k2. Lemma 2. Assuming symmetry and hence k1 = k2, the optimal social capital of one firm in response to the optimal social capital of the rival firm is given by : (9bm)/[4(2c12k − c11)] = a − c0 + c11k − c12k2.

(5a)

Similarly, the optimal social capital of the other firm is given by Eq. (5a) because of the symmetry assumption. The second-order condition requires that 2

c 11 − c12(a − c0) + 5c11k + 5c12k2 < 0.

(5a′)

Note that conditions (4e) and (5a′) put two restrictions on the set of potential Nash equilibrium values of k. Condition (4e) gives the lower bound and condition (5a′) gives the upperbound on the set of potential Nash equilibria. Note that Eq. (5a) can be re-written as: k = β 0/β 1 − β 2/β 1 k 2 + β 3/β 1 k 3,

β0 = (a − c0)c11 + (9/4)bm, β2 = 4c11c12,

β1 = 2(a − c0)c12 − β3 = 4c122.

(5b) 2 c 11,

(5b′)

Thus, k = H(k) = β0/ β1 − β2/β1 k2 + β3/β1 k 3.

(5b′′)

Proof. Relevant substitutions yield the result. Equation (5a) is the (implicit) reaction function of each of the MNEs. We consider the equilibrium social capital from the reaction function (5b′′). We apply the simple notion of the Nash equilibrium: the

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equilibrium ks are the mutual-best responses in terms of alliances. By construction, the Nash equilibrium is given by the fixed point of Eq. (5b′′). In order to characterize the equilibrium social capital, we need the following. Corollary 2. Define k** as k** = (2β3)/(3β2) = (2c11)/(3c12)

(6a)

for 0 < k < k**,

H ′(k) < 0,

(6b)

for k > k**,

H ′(k) > 0.

(6c)

Proof. Simple differentiation of H(k) with respect to k yields the above. Corollary 3. The fixed point is given by the intersection between H(k) function and the 45° line passing through the origin. From Fig. 3.1, it is obvious that either there exist two equilibria of social capital, E1 and E2, or there does not exist any equilibrium social capital. It is an instructive note that there does not exist any equilibrium, if H(k**) < (4c12)/(9c11) = k**.

(6d)

On the other hand, there exist two equilibria, if: H(k**) > (4c12)/(9c11) = k**

(6d′)

where 2

2

H(k**) = [β0/β1 − β2/β1 [(4c11)/(9c 12)] 3

3

+ β3/β1 [(8c11)/(27c12)]

(6d′′)

Proof. The proof is straightforward and can be confirmed from Diagram 1.

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H(k)

H(k) A

E2

E1

k O

k1

k**

Figure 3.1.

k2

Multiplicity of equilibrium social capital.

Note : OA is the 45° line and the fixed points are E1 and E2, provided the sufficient condition (8d′) is satisfied. Note that E1 may be stable, or unstable, and E2 is always unstable. Note that k1 and k2 are the equilibrium social capital corresponding to E1 and E2.

Observation 1. We now characterize the equilibria as a high-social capital equilibrium (E2 and k 2) and a low-social capital equilibrium (E1, k 1). Equilibrium E2 is always unstable and equilibrium E1 is stable if |H ′(k1)| < 1. On the contrary, E1 is unstable if |H′(k1)| > 1. As a result, if |H′(k 1)| > 1 and if the initial value of k lies in the interval [0, k 2], the dynamics of social capital formation will take the system to k = 0. One may call k = 0 the zero-social capital outcome. If the initial k is greater than k 2, then the dynamics of the system takes the system to k = K in which the maximum social capital is formed. This K represents the maximum feasible social capital by construction. Thus, the instability property of the high-social capital equilibrium retains the possibility of reaching the maximum feasible social capital, if history or expectations dictate so (Krugman, 1991). If both equilibria are unstable, the system becomes highly fragile and the initial condition, or history, and expectations can destabilize the system.

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The instability of equilibria can engender complex dynamics and trigger chaos. Observation 2. Even when E1 is a stable equilibrium, parametric changes can cause a loss of stability for E1 and the dynamics will take the system to k = 0. We consider such bifurcation properties in Section 3.2. 3.3.1 Sufficient condition for the uniqueness of equilibrium integration and its stability properties In order to check the stability property of the equilibrium, it is useful to re-construct the fixed point problem (5b′′) as k2 = [k∆1 − ∆0)]/[((k − ∆2)], ∆1 = β1/β3,

∆0 = β0/β3,

∆2 = β2 /β3.

(6e) (6e′)

Note that the LHS of Eq. (6e) is an increasing function of k as drawn in Fig. 3.2. The RHS is a decreasing function, if k > ∆2 > (∆0/∆1)

and

∆0 < ∆2 ∆1

(6e′′)

Equation (6e′′) puts another restriction that ensures a unique equilibrium. The intersection between these two functions ensures the existence of unique equilibrium social capital. The equilibrium exists and is unique as long as (∆0/∆2) > 0 and inequality (6e′′) holds. In Fig. 3.2, we label the equilibrium as k e. The relevant question is if this equilibrium is stable. Corollary 4. The unique equilibrium integration k e is stable, if k e(k e − ∆0)2 > |∆0 − ∆2∆1|

(7a)

where || denotes the absolute value. Inequality (7a) can be further simplified as ∆0 < 2k e(k e − ∆0)2 + ∆2∆1.

(7a′)

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LHS, RHS

LHS

E

RHS

O

Figure 3.2:

ke

k

Sufficient condition for a unique equilibrium and bifurcation.

Note: RHS is the RHS of Eq. (6e) and LHS is the LHS of Eq. (6e). Conditions (6e′) and (6e′′) ensure that RHS is downward sloping and hence the equilibrium social capital ke is unique. The equilibrium also calls forth ∆0/∆2 > 0. If ∆0/∆2 < 0, there does not exist any equilibrium social capital. The stability of the equilibrium E depends on the values of the relevant parameters. Corollary 5 describes the bifurcation possibility of an otherwise stable equilibrium E.

Proof. For the stability we need at ke, the slope of the LHS of Eq. (6e) should be greater than the absolute value of the slope of the RHS and the inequality, (7a) ensures this. The expansion of Eq. (7a) by appropriate substitutions yields Eq. (7a′). 3.3.2 Bifurcation of the equilibrium From Eq. (7a′), we know the existence of a critical value of ∆0, ∆*, where ∆* = 2k e(k e − ∆0)2 + ∆2∆1.

(7a′′)

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Substitution converts (7a′′) into (a − c0)c11 + 9bm = 6β3k e(k e − ∆2)2 + 3β3∆1∆2.

(7b)

As long as ∆0 < ∆*, or the LHS of Eq. (7b) is less than the RHS of Eq. (7b), the equilibrium is stable. Due to parametric changes, if the LHS of Eq. (7b) exceeds the RHS of Eq. (7b), the stable equilibrium social capital, ke, loses its stability. Corollary 5. Given the parameters of the above system, there is a critical value of m, m*, given by m* = [−(a − c0)c11]/(9b) + [6β 3k e(k e − ∆2)2 + 3β 3∆1∆2]/(9b).

(7c)

For m > m*, ceteris paribus, the unique equilibrium, ke, loses its stability. In a similar fashion, we can derive the critical values of a, a*, and the critical value of c0, c*, from (7b) and explain the bifurcation, or the loss of stability of the unique equilibrium ke, if a > a* (or, c0 > c*). Proof. The proof is arrived at by examining the stability of the fixed point. We thus find that the stability of the unique equilibrium social capital is predicated on the values of the parameters of the system. For example, if the managers of Mi attaches too much weight to social capital and hence neglect profits, m > m*, the equilibrium can lose its stability. In a similar fashion, ceteris paribus, the equilibrium loses its stability if the market gets too buoyant (a > a*). The equilibrium is beset with bifurcation problems if the initial cost is above a critical value, c*, that is, the initial cost is too high. 3.3.3 The supermodular game of social capital and extremal equilibria and indeterminacy In this section, we impose sufficient conditions to transform the proposed game as a supermodular game. The supermodular game will

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endow us with the extremal equilibria given the sufficient conditions. In order to examine the existence of extremal equilibria, we reexamine the fixed point problem, (7e): k 2 = [k ∆1 − ∆0)]/[((k − ∆2)]

(7e)

where ∆1 = β1/(3β3), ∆0 = β 0/(3β 3), ∆2 = (2β 2)/(3β 3). Note that Eq. (7e) can be modified as k = [k∆1 − ∆0)]/[(k (k − ∆2)] = G (k).

(8a)

Note that k = 0 and k = K are the two extreme values of k. G(k) is the best-response function in terms of social capital. When k = 0, there is no social capital. When k = K, the social capital reaches the maximum, we call it maximal social capital. The value of k is thus bounded: 0 < k < K. Thus, the value of k belongs to a set, S, defined by the positive orthant {0, K}. It is instructive to note that S is non-empty and one can define a partial order ≥ as a binary relation since S is a subset of the positive orthant. It is important to note that the partial order ≥ is reflexive, transitive, and antisymmetric. By definition, Infimum of S = {k∈A, k ≤ G(k)} = 0,

(8a′)

Supremum of S = {k∈A, k ≥ G(k)} = K.

(8a′′)

Thus, the set, S, is a complete lattice since for any two values, k, we can define an infimum and a supremum, which belong to the set, S. We can therefore apply all the results to the lattice space (see Vives, 2005, p. 477–478). Corollary 6. The best-response function, G(k), is increasing in k, if the following conditions were satisfied: kmin < k < kmax,

(8b)

kmax = [(∆0/∆1) (1 + SQRT{1 − (4 ∆1∆2)/(∆0))})],

(8c)

kmin = [(∆0/∆1) (1 − SQRT{(1) − (4∆1∆2)/(∆0))})].

(8d)

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From Vives (2005), we know that since G’(k) > 0 when inequality (8b) is true, G(k) is supermodular and has increasing differences. Proof. Differentiation of the best-response function, G(k), establishes the above. Definition 1. Define S 1 as the subset of S such that k∈S1, if kmin < k < kmax. Corollary 7. Since S1 is a complete lattice and the best-response function, G(k), is supermodular and has increasing differences, if kmin < k < kmax. By applying the Tarski theorem, we establish that the best-response function, G(k), has two extremal equilibria, kmin and kmax , which are the fixed points involving social capital formation as summarized in Eq. (8a). The values of kmin and kmax are, respectively, given by Eqs. (8d) and (8c). In Fig. 3.3, B and B1 are the stable fixed points separated by an unstable fixed point B2. Proof. See Vives (2005) for the applicability of the Tarski theorem. Corollary 7 shows that the proposed game of social capital has at least two extremal equilibria and there is thus indeterminacy about the selection of an equilibrium (Arthur, 1994). The possibility arises that a high, or low, social capital equilibrium can be due to historical lockins that cannot be predicted a priori (see Arthur, 1994). This idea is similar to the question of indeterminacy highlighted by Alfred Marshall. Marshall (1891, p. 485) articulated this indeterminacy in the case when firms with scale economies compete against each other. He argued that ultimately one firm monopolizes over the industry, but which firm will take over cannot be deduced in advance. The historical path only reveals over time the winner and losers. In our model, the indeterminacy is created by the assumed production technology that displays both increasing and diminishing returns to scale due to social capital. One can easily argue for potential inefficiency and the non-predictability of equilibrium social capital because of this indeterminacy. The roles of history and expectations also assume prominence (Krugman, 1991). From Vives (2005), we know

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Economics of Rivalry, Conflict and Cooperation G(k)

A A1

B1

G(k)

B2

B A2

O

k kmax

kmin

Figure 3.3.

Extremal Nash equilibrium.

that the system monotonically converges to the extremal equilibrium, kmin, if k < kmin. The system converges to the extremal equilibrium, kmax, if k > kmax. There is a separatrix (depicted as B in Fig. 3.3) that divides the catchment areas of these equilibrium social capital. The separatrix is an unstable fixed point. All relevant integration take place in the box [A1B1A2B] in Fig. 3.3. Rationalizable outcomes, the mixedstrategy equilibrium and the correlated equilibrium must lie in the box [A1B1A2B]. Any kind of adaptive dynamics will take the system monotonically to either of the extremal equilibria (Vives, 1990). Also note that cyclical fluctuations can be generated (see Vives, 2005, p. 450). Properly mixed equilibria are unstable with respect to general adaptive dynamics.

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3.4 Discussion The purpose of these results is to explain the complex nature of the formation of social capital that has evolved due to historical and social reasons. In our understanding, the role of the social scientist, or business policy maker, is to master the relevant economic system to be able to adopt effective and appropriate policies that will lead to desirable outcomes, or will help prevent undesirable outcomes, in the future. The policy maker must be able to predict the outcome of current activities; the ability to do so is predicated upon an understanding of the relevant economic system. These models should help the rational policy maker to understand the dynamics of social capital in order to master it. What we purport is threefold: First and foremost, a small change in parameters can lead to major transformation of social capital in a firm — this is what is known as “chaos”, if we confine our attention to mathematical, or physical, systems. Political scientists use a phrase “crisis instability” to describe this extreme sensitivity of the political system to minor perturbations (see Saperstein, 1994). Second, we show the possibility that social capital as modeled can display remarkable stability in some circumstances driven by the values of relevant parameters (see Saperstein, 1984). We showed how history, or expectations, can determine whether a stable equilibrium, E1, gets established. We know that if the initial value of k lies in the interval [0, E2], then the system will steadily converge to E1. Expectations do play a similar role. The equilibrium social capital can display complex behavior if the system fails to converge to any equilibrium outcome. In our model, a minor and momentary right-ward departure from E2 destabilizes the entire system. Suppose E2 is reached and there is a sudden increase in k, the resultant outcome will be an ever-increasing k to reach the maximum feasible social capital. Instability can also be created by purely subjective factors. The switch from stability to chaos can also be triggered by the bifurcation properties of equilibrium, E1. From Saperstein (1984), we know that a chaotic economic system is a mathematical representation

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of a crisis-ridden and unstable economic system. Policy makers therefore must take extreme caution in tweaking the system, especially in certain circumstances. For policy making, it is important to predict the critical threshold beyond which the system becomes chaotic. For the policy maker, it will be important to avoid conditions, or circumstances, that will throw the system into crisis and instability. Finally, the model clearly demarcates a region of stability, (0, E2), vis-à-vis a region of instability, (>E2). Our argument is similar to the “edge of chaos theory.” Stacey (1991) adopted the “edge of chaos theory” in the social sciences to argue that the sustainability of a social system is achieved by the relevant decision-makers striving to remain at the confluence of the predictable “order” (the interval [0, E2] in Fig. 3.2). An unpredictable level of chaos sets in beyond E2 in Fig. 3.2. Chambers (1997) employed this concept of the edge of chaos to explain the sustainability of rural communities in developing nations. Ours is a first attempt to provide a model that can be stretched to explain the sustainability of business enterprises in the modern world of cascading forces of globalization. 3.5 Conclusion The model of social capital formation establishes a number of interesting properties of the proposed equilibrium social capital: First, there exist two Nash equilibria: one is a high-social capital equilibrium (E2 and k2) and the other represents a low-social capital equilibrium (E1, k1). We find that equilibrium E2 is always unstable and equilibrium E1 is stable only under a condition. Thus, E1 is unstable if this condition is violated. If both these Nash equilibria are unstable and the initial value of social capital (k) lies in the interval [0, k 2], the dynamics of social capital formation will take the system to a zero-social capital labeled as k = 0. If the initial level of social capital k is greater than a critical value k2, then the dynamics of the system takes the system to k = K, in which the maximal social capital is reached. Thus, the instability property of the high-social capital equilibrium retains the possibility of reaching the maximum feasible social capital, if history or expectations dictate so. If both equilibria are

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unstable, the system becomes highly fragile, and the initial condition, or history, and expectations can destabilize the system. The instability of equilibria can engender complex dynamics and trigger chaos. Even when E1 is a stable equilibrium, parametric changes can cause a loss of stability for E1 and the dynamics will take the system to zero-social capital (k = 0). We established these bifurcation properties of a stable Nash equilibrium, which render the business system/firm very fragile and even chaotic. It is well-known that a chaotic economic system is a mathematical representation of a crisis-ridden and unstable economic system. Policy makers therefore must take extreme caution in dealing with the system, especially in certain circumstances. For policy making, it is important to predict the critical threshold beyond which the business system becomes chaotic. Finally, the model locates a region of stability against the backdrop of a region of instability. Our argument is similar to the “edge of chaos theory.” Stacey (1991) adopted the “edge of chaos theory” for social sciences to argue that the sustainability of a business system is achieved by relevant decision-makers striving to remain at the confluence of the predictable “order” and an unpredictable level of chaos. Chambers (1997) employed this concept of edge of chaos to explain the sustainability of rural communities in developing nations. Ours is a first attempt to provide a model that can be strained to explain the sustainability of social capital in a modern firm.


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Chapter 4

Economics of Cooperation in Successive Markets

4.1 Introduction This work develops a simple game to examine the effects of cooperative retail and wholesale investment under two related market structure scenarios. Scenario I illustrates successive monopolies in the wholesale and retail markets. Scenario II is the evolution of Scenario I and represents the next stage of the natural development of a monopoly wholesale market with a duopoly retail market, resulting from a new entrant, to take a share of retail profits. We examine the effects of the wholesale-retail game for Scenario I and solve for the privately optimal levels of total output, retail prices, wholesale prices, retail profits, wholesale profits, total industry profits, consumer surplus, and social welfare. In Scenario I, it is shown that both the monopoly wholesaler and monopoly retailer do not have an incentive to, respectively, invest at socially optimal investment levels. That is, we have a Tragedy of the Commons where both the wholesaler and the retailer individually benefit the most from investing at their respective privately optimal investment levels, rather than at their respective socially optimal investment levels. Given that there is no incentive for either the monopoly wholesaler, or monopoly retailer, to invest beyond their respective privately optimal levels of investment, the government may engage in a social contract to punish any socially sub-optimal levels of investment by the wholesaler and retailer. This social contract is specified as

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a tax on the respective difference between the socially optimal levels of their investment and their actual investment level. In Scenario II, we present a two-tier game with one game being played between duopoly retailers — an incumbent firm and a new entrant — and the second game between the combined retail market and the sole wholesale market firm. Solving for each of the above listed variables as in Scenario I, we draw comparisons between these two related market structures as it evolves from Scenario I to Scenario II, and draw important lessons. Choe (1999) considers an example of the product of a monopolistic manufacturer sold in two separate markets at different retail prices. He states that whether this presents itself as a case of a manufacturer exercising third-degree price discrimination that requires, among others, the study of the retail market structure. Choe (1999) provides a partial answer to the question by assuming a theoretical situation in which both retail and wholesale demand functions are linear, and argues that the wholesale margin will be a function of the number of retailers currently within the market. Choe (1999) states, “The implication is that, if final demand functions are the same in two markets, then any difference in retail prices is entirely due to the difference in retail margins, not the price discrimination exercised by the manufacturers”. (p. 2)

Choe (1999) derives the basis of this work from an early paper written by Bresnahan and Reiss (1985), who by presuming the retailer was a price-taking agent, were able to develop a model of analysis on wholesale and retail margins. Bresnahan and Reiss’ (1985) results were canvassed as: •

•

“The ratio of retail margin to wholesale margin is greater than (equal to, less than, respectively) a half if the retail demand function is strictly convex (linear, strictly concave, respectively).” “The ratio of margins is equal to the change in the retail price when either the wholesale changes its wholesale price or the retailer’s selling costs are changed.”

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If the retailer is the only agent interacting with the wholesaler, then the assumption of a price taking downstream monopolist may be untenable.1 By generalizing the results from the Bresnahan and Reiss (1985) study, Choe (1999) allows for empirically testable results in the form of ratios related explicitly to the number of firms in the market and their respective price elasticity of demand values. The results are then applied to a case of third-degree price discrimination in vertically related markets. Choe (1999) concludes that the retail market structure is an important determinant in the question of whether there is a case of price discrimination exhibited by the manufacturer. Furthermore, by way of assuming a completely linear demand function for both agents, the eventual price reached in the retail market is fully dependent on the retail market structure, the manufacturer having no influence in its determination. We explore retail and wholesale markets with cooperative investment and consider the effects of evolving from Scenario I to Scenario II within the proposed game. It is important to note that contractual and non-contractual relations play a significant role in vertically related markets. Manufacturers of consumer goods rarely sell their products directly to consumers and they often enter into various contractual relations, and implicit and non-contractual relations, with retailers and dealers to create “consumer affection” in marketing a product. Prices and profitability in consumer goods markets depend on the nature of these relations, which, in turn, depends on the structure of wholesale and retail markets. Without the explicit consideration of these vertical relations, industry policies designed for those markets can be misleading. In this context, we introduce cooperative investment by wholesalers and retailers as their discretion is not bound by any enforceable contract. We show that cooperative investment by wholesalers and retailers can be mutually beneficial, yet strategic reasons can lead to a socially sub-optimal level of cooperative investment that calls forth an appropriate intervention by governments. This 1

In Choe (1997), a bargaining game between the wholesaler and the retailer is studied. It is shown that the final retail price is determined between the conventional double marginalization price and the vertically integrated price.

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work sets up a detailed model to examine this simple story. The plan of this work is to offer the prototype game in Section 4.2, then consider a linear model of the retail and wholesale markets in Section 4.3, and solve for key economic variables. In Section 4.4, the chapter introduces the case for cooperative investment, and solves for joint profits in Section 4.5. In Section 4.6, the Tragedy of the Commons is examined by constructing a government-written social contract to induce the wholesaler and the retailer to invest up to their respective socially optimal investment levels. Section 4.7 prepares the market structure evolution from Scenario I to Scenario II. Section 4.8 draws conclusions about the effects on market system variables. Finally, Section 4.9 presents concluding comments. 4.2 Retail and Wholesale Markets Relationships — Successive Monopolies Consider retail and wholesale markets with the following characteristics: The retail market demand function is assumed to be: p = a − bQ.

(1a)

p is the price and Q is the output in the retail market. We further assume one retailer and one wholesaler to start off with. The profit in the retail market, π R, is:

π R = pQ − cost,

(1b)

cost = (A + β)Q ,

(1c)

where

A: wholesale price, β: selling cost

π R = (a − bQ − β − A)Q = (a − β − A)Q − bQ2.

(1d)

We reduce the wholesale market profit, πW, to:

πW = (A − c)Q , c : marginal/average cost of production in the wholesale market.

(1e)

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Profit maximization in the retail market calls forth maximizing π R with respect to output decision. The first-order condition for profit maximization yields d π R/dQ = dπ R/dQ = a − β − A − 2bQ = 0,

(1f )

A = a − β − 2bQ .

(2a)

Equation (2a) is the wholesale demand function. The wholesaler uses (2a) as the inverse demand function in the successive stage (Bresnahan and Reiss, 1985). We now look at the wholesale market profit maximization. The profit function of the wholesaler, by substituting (2a) into (1e), is

πW = (A − c)Q = (a − β − 2bQ − c)Q = (a − c − β)Q − 2bQ2.

(2b)

The wholesaler maximizes π W with respect to Q ; so profit maximization requires maximizing πW = (a − c − β)Q − 2bQ 2 by an appropriate choice of Q. The first-order condition yields dπ W/dQ = a − c − β − 4bQ = 0

or

Q* = (a − c − β)/(4b).

(2c)

Substituting (2c) into (2a) gives the equilibrium wholesale price: A* = (a + c − β)/2.

(2d)

Substituting (2c) into (1a) gives the retail demand function: p* = (3a + c + β)/4.

(3a)

Further substitution in (1b) gives the maximized retail profit function:

π R* = (a − c − β)2/(16b).

(3b)

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Likewise, relevant substitution in (1e) gives the maximized wholesale profit function:

πW* = (a − c − β)2/(8b).

(3c)

4.3 The Case of Cooperative Investment Cooperative investments have received little attention, despite being common in practice and present in several classic settings.2 Cooperative investments generate a direct benefit for the trading partner. This is contrasted with a “selfish investment” in which a seller invests to reduce cost, or a buyer invests to increase the benefits from the procured good or service. In order to introduce cooperative investment in the context of successive monopolies, consider the following cooperative investment functions that affect β, c :

β = G (S),

G ′ < 0,

(4a)

c = F (B),

F ′ < 0,

(4b)

where S is the cooperative investment by the wholesaler, and B is the cooperative investment by the retailer that directly benefits the other party. We know c is the average (marginal) cost of the wholesaler that is affected by the cooperative investment of the retailer (B). While β is the average (marginal) selling cost of the retailer that is affected by the cooperative investment by the wholesaler. This is how we intend to introduce cooperative investment by one party that benefits the trading partner. In an emerging market following the privatization and entry of firms in wholesale and retail markets, there is good scope for cooperative investment between the retailer and the wholesaler. For example,

2

Chung (1991), MacLeod and Malcomson (1993), and Che and Chung (1996) offer the first theoretical treatments of cooperative investments. Bernheim and Whinston (1995) also observe difficulties with motivating cooperative investments.

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the General Motors–Fisher Body example entails Fisher Body’s decision to build a plant adjacent to General Motors. Such an investment resulted in supply reliability as well as reduced transport cost that brought benefits to both parties. This is a kind of hybrid investment. Other examples of cooperative investments include qualityenhancing R&D by suppliers. Asanuma (1989), Burt (1989), and Nishiguchi (1994) marshal evidence to establish the importance of cooperative investment. The problem with cooperative investment is the typical problem of hold-ups in negotiations (Che and Hausch, 1999). If different parties adopt projects that also benefit their partners, then contracting loses its value since the parties have the incentive to renege and abandon contracting. In the absence of a complete contract, the parties can also resort to opportunistic behaviors that can upset the market outcome. In the traditional literature, the absence of a complete contract, together with opportunistic behavior, is believed to lead to Paretoinferior investment (Grout, 1984; Williamson, 1985; Tirole, 1986). The hold-up problem has induced many authors to suggest the following prescriptions: • • • • •

vertical integration (Klein, 1978; Williamson, 1979), exchange of hostages (Williamson, 1983), allocating property rights (Grossman and Hart, 1986), allocating control rights (Aghion and Bolton, 1992), designing hierarchy (Aghion and Tirole, 1997).

Now we look at some of the important elements concerning cooperative investment in successive markets. Lemma 1. Joint profits (π*), net joint profits (Π*), consumer surplus (CS), and social welfare (W ) of the postulated successive markets, with cooperative investments, S and B, are given, respectively, by:

π* = πR* + πW* = [3(a − β − c)2]/(16b), Π* = π* − B − S,

(4c) (4d)

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CS = (a − c − β)2/(32b),

(4e)

W = 7(a − c − β)2/(32b).

(4f )

Proof. See Appendix A. 4.4 Cooperative Investment Analysis

We look at the effect of investment B and S on the market outcome. To do so, we first look at the effect of B and S on the wholesaler and the retailer. Assumption 1. We specify the average (production) cost of the wholesaler as a function of the cooperative investment by the retailer, B, as: c = C0 − C1B + C2B2,

(5a)

where C1 < C2 dc/dB = −C1 + 2C2B, d c/dB2 = 2C2 2

B* = C1/2C 2. If B < B* = C 1/2C 2,

then dC/dB < 0.

If B > B* = C 1/2C 2,

then dC/dB > 0.

Assumption 2. Similarly, we define the average (selling) cost of the retailer as a function of the cooperative investment by the wholesaler, S, as:

β = β 0 − β 1S + β 2S2 where β1 < β2, dβ/dS = −β1 + 2β 2S, d 2β/dS2 = 2β 2, S* = β1/2β 2. Similarly, we define S*, S* = β 1/2β 2. If S < S* = β1/2β 2,

then d β/dS < 0.

If S > S* = β1/2β 2,

then d β/dS > 0.

(5b)

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Lemma 2. Joint profits in terms of retail investment (B) and wholesale investment (S) are:

π* = (3/16b)(a − C0 + C 1B − C 2B 2 − β0 + β1S − β2S 2)2 (5c) while the relevant partial derivatives are (δπ*/δB) = (3/8b)[(a − C0 − β0) + C 1B + β1S − C 2B 2 − β2S 2] × (C 1 − 2BC 2),

(5d)

(δπ*/δS) = (3/8b)[(a − C0 − β0) + C 1B + β1S − C 2B 2 − β2S 2] × (β1 − 2S β2). Proof. See Appendix A.

(5e)

4.5 The Tragedy of the Commons In the Tragedy of the Commons, the social dilemma is defined by two properties. First, the social payoff to each individual agent for defecting behavior is higher than the payoff for cooperative behavior, regardless of what the other society members do. Second, “all individuals in the society receive a lower payoff if all defect than if all cooperate” (Dawes, 1980, p. 170). It should now be clear that social dilemmas are Prisoner’s Dilemmas on a large scale. Everyone has a dominating strategy to defect. Yet if everyone defects, then all are worse off than if they had cooperated. The problem of defection is often referred to as “free-riding.” In a situation where one suspects that the others will conserve (or supply) the public good, one is tempted to free-ride on them and not conserve (or supply). And it is the prevention of free-riding that is known as the problem of collective action. That is, how can society organize itself so that public goods will be conserved or supplied? We now examine the private optima and social optima differences for the monopoly wholesaler and monopoly retailer. In our case, as shown below, it is clear that both the monopoly wholesaler and monopoly retailer do not have an incentive to invest at

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socially optimal investment levels. That is, we have a Tragedy of the Commons where both the monopoly wholesaler and monopoly retailer individually benefit the most from investing at their respective privately optimal investment levels, rather than at their respective socially optimal investment levels. Given that there is no incentive for either the monopoly wholesaler or monopoly retailer to invest beyond their respective privately optimal levels of investment, the government may engage in a social contract to punish any socially sub-optimal levels of investment by the wholesaler and retailer. This social contract may be specified as a tax on the respective difference between the socially optimal levels of their investment and their actual investment level (Fig. 4.1). Theorem 1. Socially optimum level of cooperative investment by the wholesaler and the retailer are Ssop and Bsop that are given by : S sop = (β1 − C 1)/(2β 2 − C 2), B

sop

(6a)

= (β1 − C 1)/(4β 2 − 2C 2).

(6b)

π* R1 R2 A1 A2

M1

π*

M2 O

Figure 4.1.

B2

B1

B

Maximum profit/opportunity cost with respect to retailer investment.

Note: We represent the retailer investment along the horizontal axis and call it B. We represent the total profits in the industry π * along the vertical axis. The origin is O. The hill-shaped curve M2 π * is the gross profit function of the industry while the ray OR2 labels the total cost of retail investment. The line M1R1 is the slope of the profit function π*, which is equal to the slope of OR2. The socially optimal retail investment is OB1 that generates total industry profits of OA1. The private optimum is OB2 and generates OA2 profits and thus the surplus lost to the society from the free market equilibrium is (OA1–OA2).

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Proof. See Aappendix A.

137

The socially optimal retail and wholesale investment levels make sense when β1 > C 1 and 2β 2 > C 2, or when β1 < C 1 and 2β 2 < C 2. Theorem 2. Individually optimum levels of cooperative investment by the wholesaler and the retailer are Spop and Bpop that are given by : S pop = (2β1 − C 1)/(4β 2 − C 2), B

pop

= (2β1 − C 1)/2(4β 2 − C 2).

Proof. See Appendix A.

(7a) (7b)

The privately optimal retail and wholesale investment levels make sense when 2β1 > C 1 and 4β2 > C 2, or when 2β1 < C 1 and 4β 2 < C 2. The difference between the socially and privately optimal levels of wholesale investment is: S sop − S pop = (β1C 2 − 2β 2C 1)/[(4β2 − C 2)(2β 2 − C 2)].

(8a)

Reasonable assumptions hold that both 2β1 − C 1 > 0 and 4β2 − C 2 > 0 are necessary for economic sense. We notice that the difference between social optima and private optima is positive if β1C 2 − 2β 2C 1 > 0 and if β1/2β 2 > C 1/C 2 that is S* > 2B*. This is so since B sop − B pop = (β1C 2 − 2β2C 1)/[2(4β 2 − C 2)(2β 2 − C 2)].

(8b)

Lemma 3. The overall under-investment in an unregulated market is given as: (S sop + B sop) − (S pop + B pop) = (3(β1C 2 − 2β2C 1))/[2(4β2 − C 2)(2β2 − C 2)]. Proof. See Appendix A.

(8c)

Since there is a difference between socially and privately optimal levels of wholesaler and retailer investment, the government may set up a

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contract with each to ensure socially optimal levels of investment are reached. Currently, there is no incentive for either the monopoly wholesaler or monopoly retailer to invest beyond their privately optimal levels of investment. Given the difference between the socially and privately optimal investment levels, the government may engage in a social contract to punish any socially sub-optimal levels of investment by the wholesaler and retailer. This social contract is a tax on the difference between the socially optimal levels of their respective investment and their actual respective investment level. Theorem 3. Under the following punishment mechanism initiated by the government, the wedge between private optima and social optimal will disappear : T W = λW (S sop − S ), = 0,

if S sop > S if S

sop

< S,

T R = λR (B sop − B), if B sop > B = 0,

if B

sop

(9a) (9b)

< B,

where T W is the total social tax on social wholesale under-investment; T R is the total social tax on social retail under-investment; λW is the social wholesale tax rate on social wholesale under-investment; and λR is the social retail tax rate on social retail under-investment.

Proof. See Appendix A. 4.6 The Case of Wholesale Monopoly and Retail Duopoly

In this case, we have a two-tier game with a team game being played between duopoly retailers and a second game between the combined retail market and the sole wholesale market firm. Consider the case of two retailers — an incumbent and an entrant — and one wholesaler with the following new economic relationship: β is the total selling cost of the retail market,

β = βi + βn,

(10a′)

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where βi is the selling cost of incumbent retail firm; βn is the selling cost of new entrant retail firm; Q i is the output of the incumbent firm; and Q n is the output of the new entrant firm. Lemma 4. The incumbent ’s reaction function, entrant ’s reaction function, the output in the retail market, and the retail price are given by : Q i = (a − bQ n − A − βi)/(2b),

(10b)

Q n = (a − bQ i − A − βn)/(2b),

(10c)

Q = (2a − βi − βn − 2A)/(3b),

(11a)

A = (2a − βi − βn − 3bQ)/2.

(11b)

Proof. See Appendix A.

Lemma 5. In the Nash equilibrium, the wholesale market (equilibrium) output (Q*), price (A*) are given by: Q * = (2a − 2c − β)/(6b),

(11c)

A* = (2a + 2c − β)/4,

(11d)

In this equilibrium involving two retailers and a wholesaler, the total profits in successive markets (π*), the consumer surplus (CS ), and social welfare (W ) are given by:

π* = πR* + πW* = (16a2 − 30ac + 14c 2 − 28aβ + 27cβ + 10β 2)/(72b),

(12a)

CS = 1/2Q*(a − p*) = (2a − 2c − β)2/(72b),

(12b)

W = π* + CS = (20a2 − 38ac + 18c 2 − 32aβ + 31cβ + 11β 2)/(72b). Proof. See Appendix A.

(12c)

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4.7 Comparing Outcomes of the Two Case Scenarios Scenario I is for the successive monopolies in the wholesale and retail markets. Scenario II is the next stage off the natural development of Scenario I since it illustrates a monopoly wholesale market, together with a duopoly retail market, resulting from a new retail firm entrant intending to take a share of the retail monopoly profits. The results are summarized in Table 4.1. Finding 1. Since Scenario II entails an increase in competition, Q* increases in Scenario II. The increase in equilibrium output is (a − c + β). The higher (c − β) is, the larger is the increase in output (Q*) in Scenario II. In short, the creation of the duopoly retail market in Scenario II leads to overproduction. Finding 2. As we move from Scenario I to Scenario II, the equilibrium wholesale price A* increases by β/2. This is due to an increase in competition that enhances the equilibrium output in the retail market. Finding 3. Evolving from Scenario I to Scenario II will lead to a decrease in price p* by 2(a − c + β). The larger (c − β) is, the smaller will be the decline in p*. Finding 4. Scenario II reduces total retail profits of π R* as expected. The actual difference is given as 1 b (a 2 - 6ac + 5c 2 + 14a b - 12c b - 5b 2 ). 144 Table 4.1.

Q* A* p* π R* πW* π* CS W

Comparison of two case scenarios.

Scenario I

Scenario II

(a − c − β)/4b (a + c − β)/2 (3a + c + β)/4 (a − c − β)2/16b (a − c − β)2/8b [3(a − β − c)2]/16b (a − c − β)2/32b 7(a − c − β)2/32b

(2a − 2c − β)/(6b) (2a + 2c − β)/4 (4a + 2c + β)/6 [(2a − c − 7β)(2a − 2c − β)]/(72b) (2c − 2a − β)2/(24b) (16a 2 − 30ac + 14c 2 − 28a β + 27cβ + 10β2)/(72b) (2a − 2c + β)2/(72b) (20a 2 − 38ac + 18c 2 − 32a β + 31c β + 11β2)/(72b)

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It is important to note that, unlike Scenario I, if the total retail selling cost of β in Scenario II is at a sufficiently high level, then the total retail profits can be negative. The upshot of this is excessive overproduction which will lead to total retail market losses instead of profits. Finding 5. As intuitively expected, Scenario II increases wholesale profits of π W* by the amount of 1 b (a 2 - 2ac + c 2 + 2a b - 2c b - 2b 2 ). 24 One can safely conclude that wholesale profits will increase with the addition of another retailer, and wholesale profit sharing increases in comparison to the retail market. Finding 6. Moving from Scenario I to Scenario II shows a decline in total profits π * by -

1 b (5a 2 + c 2 - 7a b - 2a (3c + b )). 144

Finding 7. Moving to Scenario II shows an increase in consumer surplus by (a − c + 5β). Finding 8. Evolution to Scenario II results in the welfare reduction of 1 b (-17a 2 - 9c 2 + 2c b + 19b 2 + 2a (13c + b )). 288

4.8 Concluding Comments In Scenario I, the results establish that both the monopoly wholesaler and monopoly retailer do not have an incentive to, respectively, invest at socially optimal investment levels. That is, we unfolded a Tragedy of the Commons in which both the monopoly wholesaler and monopoly retailer benefit the most from investing at their respective privately optimal investment levels rather than their respective socially optimal investment levels. Given that there is no incentive for either the

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monopoly wholesaler or monopoly retailer to invest beyond their respective privately optimal levels of investment, the government may engage in a social contract to punish any socially sub-optimal levels of investment by the wholesaler and retailer. This social contract is a tax on the respective difference between the socially optimal level of their investment and their actual investment level. This is called Scenario I in this work. In Scenario II, we presented a two-tier game with one game being played between the duopoly retailers of an incumbent firm with a new entrant, and the second game between the combined retail market and the sole wholesale market firm. We drew comparisons between the two related market structures as it evolved from Scenario I to Scenario II, and found the following conclusions (Table 4.2). First, the creation of the duopoly retail market in Scenario II leads to overproduction with an increase in total output leading to an increase in wholesale demand and a decrease in retail prices. The consequence of this is a reduction in total retail market profits to the point that they can actually become losses with excessive overproduction and high marginal selling costs. Concurrently, the monopoly wholesale profits increase as the higher total industry fixed costs and wholesale production costs deliver a greater profit share to the wholesaler than to the duopoly retailers. That is, wholesale profits will

Table 4.2.

Resulting effects of moving from Scenario I to Scenario II.

Variable

Resulting Effect of Moving From the First to the Second Scenario

Output Wholesale price Retail price Retail profits Wholesale profits Total profits Consumer surplus Social welfare

Increased output leading to overproduction. Increase due to increasing retail variable cost. Decrease due to increased output. Decrease due to overproduction. It can even be negative. Increased wholesale profit levels and increased profit share. Decrease in total profits due to increased costs. Decrease. It can increase with total fixed costs and/or higher wholesale costs and/or lower variable retail costs. Decrease. It can increase for the same reasons as given for consumer surplus with added sensitivity to variable retail costs.

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increase with the addition of another retailer, and wholesale profit sharing increases in comparison to the retail market. An interesting result for the total industry is that total industry profits decline although a reduction in the total fixed costs to variable costs ratio will lead to an increase in total profits. The upshot of this is that a proportionately higher increase in the variable retail cost, compared to total fixed costs and average wholesale production costs, will increase total profits. This is consistent with the intuition that a relative reduction in the fixed to marginal costs of wholesale production and retail selling, increases total profits since the industry has less sunk costs. A further consequence of this evolving market structure is a reduction in consumer surplus. This reduction in consumer surplus will continue to grow the higher the total retail selling cost is in comparison to total industry fixed costs and variable wholesale production costs. The natural extension of this is that significantly higher total fixed costs and wholesale variable production costs, and a relative reduction in marginal retail selling costs, can actually increase the consumer surplus when evolving from Scenario I to Scenario II. For the same reasons, this market structure evolution also leads to a welfare reduction, and the driving sensitivity once again stems from the variable retail selling cost and the need to reduce it in comparison with total fixed costs and wholesale variable costs. Finally, reducing the variable retail selling cost relative to total fixed costs and variable wholesale production costs may actually lead to welfare gains. Appendix Proof of Lemma 1 The joint profit or surplus in the industry when substituted with (3b) and (3c) is:

π* = πR* + πW* = [3(a − β − c)2]/(16b).

(A1)

Net profit in the industry is Π* = π* − B − S.

(A2)

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Consumer surplus is: CS = 1/2Q*(a − p*) = 1/2((a − c − β)/4b)(a − (3a + c + β)/4) = (a − c − β)2/(32b).

(A3)

Therefore, social welfare is: W = π* + CS = 7(a − c − β)2/(32b).

(A4)

Substituting (4a) and (4b) into (4c) through (4f ) makes individual profits and the industry outcome dependent on cooperative investments, B and S. We now analyze cooperative investment in the proposed model. Proof of Lemma 2 Joint profits with respect to cooperative investment :

π* = (3/16b)(a − C 0 − C 1B − C 2B 2 − β0 + β1S − β2S 2)2,

(A5)

(δπ*/δB) = (3/8b)[(a − C0 − β0) + C1B + β1S − C2B − β2S2] 2

× (C1 − 2BC2).

(A6)

For B < C1/2C 2 = B*, then δπ*/δB > 0; for B > C1/2C 2 = B*, then (δπ*/δB) < 0. Joint profits with respect to wholesale investment: Similarly, using (5c) for joint profits, (δπ*/δB) = (3/8b)[(a − C0 − β0) + C1B + β1S − C2B2 − β2S 2] × (β1 − 2Sβ2).

(A7)

For S < β1/2β 2 = S*, then (δπ */δB) > 0; for S > β1/2β2 = S*, then (δπ*/δB) < 0.

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Proof of Theorem 1 Net profits to the industry are

πN* = (3/16b)(a − C0 + C1B − C2B 2 − β0 + β1S − β2S 2)2 − rB − rS,

(A8)

r : opportunity cost of investment capital. We depict the optimal cooperative investment of B in Fig. 4.1. For the optimal cooperative investment, S, equating dπ*/dS = r, we have (3/8b)[(a − C0 − β0) + C1B + β1S − C 2B 2 − β2S 2] × (β1 − 2Sβ2) = r.

(A9)

Let (a − C0 − β0) = X0, then (X0 + C1B + β1S − C 2B 2 − β2S 2) × (β1 − 2S β2) = (8br/3). (A10) Equation (A10) is the first-order condition for maximizing net profits with respect to S. Government-run Investment: Social Optima (3/8b)[X0 + C1B + β1S − C 2B 2 − β2S 2] × (C1 − 2BC 2) = r or, re-arranging, we have (X0 + C1B + β1S − C 2B 2 − β2S 2) × (C 1 − 2BC 2) = (8br/3). (A11) From (A10) and (A11), we solve (β1 − 2S β2) = (C1 − 2BC 2) to find the wholesale cooperative investment level of S which is S = (β1 − C 1)/2β 2 + (C 2/β 2)B.

(A12)

Since the profit-sharing rule is 1/3:2/3, then B:S = 1:2 or S = 2B. Substituting S = 2B into (A12) gives 2B = (β1 − C1)/2β2 + (C 2/β2)B.

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Solving and re-arranging for the socially optimal retail investment of B sop gives B sop = (β1 − C1)/(4β 2 − 2C 2).

(A13)

Since S = 2B, then the socially optimal wholesale investment of S sop is S sop = (β1 − C 1)/(2β2 − C 2).

(A14)

Proof of Theorem 2 Private-run investment: Private optima Retailer:

πR* = (a − c − β)2/16b

(as per 3b)

= (1/16b)[(a − C0 − β0) + C1B + β1S − C2B − β2S 2]. (A15) 2

Equating dπR*/dS = r, we have (1/8b)[(a − C0 − β0) + C1B + β1S − C 2B 2 − β2S 2] × (C1 − 2BC 2) = r.

(A16)

or, re-arranging and letting (a − C0 − β0) = X0, then (X0 + C1B + β1S − C 2B 2 − β2S 2) × (C1 − 2BC 2) = 8br.

(A17)

Equation (A17) is the first-order condition for maximizing retail profits with respect to S. Wholesaler: Similarly, for the wholesaler, we have (X0 + C1B + β1S − C 2B 2 − β2S 2) × (β1 − 2S β2) = 4br. (A18)

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Equation (A18) is the first-order condition for maximizing wholesale profits. From (A17) and (A18), we solve 2(β1 − 2S β 2) = (C 1 − 2BC 2) to find the wholesale cooperative investment level of S which is S = (2β1 − C 1)/4β2 + (C 2/2β2)B.

(A19)

Since the profit-sharing rule is 1/3:2/3, then B:S = 1:2 or S = 2B. Substituting S = 2B into (A19) gives 2B = (2β1 − C 1)/4β2 + (C 2/2β2)B. Solving and re-arranging for the privately optimal retail investment of B pop gives B pop = (2β1 − C 1)/2(4β 2 − C 2).

(A20)

Since S = 2B, then the privately optimal wholesale investment of S pop is S pop = (2β1 − C 1)/(4β2 − C 2).

(A21)

Proof of Lemma 3 Social investment shortfall/Under-investment Equations (8a) and (8b) define the investment shortfall or underinvestment in respect to the wholesaler and retailer investment, which is the difference between the socially and privately optimal level of investment for each. Total socially optimal investment: S sop + B sop = (β1 − C 1)/(2β2 − C 2) + (β1 − C1)/(4β2 − 2C2) = 3(β1 − C 1)/(2(β 2 − C 2)).

(A22)

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Equation (A22) is the total socially optimal level of investment by the monopoly wholesaler and the monopoly retailer. Total privately optimal investment: S pop + B pop = (2β1 − C 1)/(4β2 − C 2) + (2β1 − C 1)/(2(4β2 − C 2)) = 3(2β1 − C 1)/(2(4β2 − C 2)).

(A23)

Equation (A23) is the total privately optimal level of investment by the monopoly wholesaler and the monopoly retailer. (S sop + B sop) − (S pop + B pop) = (3(β1C 2 − 2β2C 1))/[2(4β2 − C 2)(2β2 − C2)].

(A24)

Equation (A24) is the difference between the total socially optimal and the total privately optimal investment, which is the difference between (A22) and (A23), and gives the total investment shortfall or under-investment. Proof of Theorem 3 Retail profit under social contract:

πR = πN(B) − λR(B sop − B).

(A25)

Wholesale profit under social contract:

πW = πN(S) − λW(S sop − S).

(A26)

Examining the first-order conditions for the retailer, we have dπR/dB = dπ N/dB − λR(d/dB)(B sop − B) which means if λR > (dπN/dB)/((d/dB)(B sop − B)), then the retailer will choose B pop = B sop.

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Considering the optimal level of the social retail tax rate λR*, we have

λR* = (dπN/dB)(B pop)/((d/dB)(B sop − B)) = − (d π N/dB)(B pop) > 0. Using the Envelope Theorem3 with (A16), we have dπR/dB = (1/8b)[(a − C0 − β0) + C1B + β1S − C 2B 2 − β2S 2] × (C 1 − 2BC 2) − r which gives

λR* > r − (1/8b)[(a − C0 − β0) + C1B + β1S − C 2B 2 − β2S 2] × (C1 − 2BC 2).

(A27)

Equation (A27) is greater than 0 for B > B pop. That is, the government can induce the retailer to undertake the socially optimal investment by writing the following social contract: TR = 0

for B ≥ B sop,

T R = λR*(B sop − B)

for B < B sop,

λR* > r − (1/8b)[(a − C0 − β0) + C1B + β1S − C2B 2 − β2S 2] × (C1 − 2BC 2). Similarly, the government can induce the wholesaler to undertake the socially optimal investment by writing the following social contract:

3

TW = 0

for S ≥ S sop,

T W = λW*(S sop − S)

for S < S sop,

The Envelope Theorem expresses a mathematical result where the change in the maximum value of a function brought about by a change in a parameter of the function can be found by partially differentiating the function with respect to the parameter when all other variables take on their optimal values.

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λW* > r − (1/4b)[(a − C0 − β0) + C1B + β1S − C2B 2 − β2S2) × (β1 − 2Sβ 2). Proof of Lemma 4 Retail market demand function: p = a − bQ

(as per 1a)

with two retailers and one wholesaler. Retail market profit function:

πR = p × Q − cost, where cost = (A + β)Q.

(as per 1b) (as per 1c)

Wholesale market profit function:

πW = (A − c)Q

(as per 1d)

where β : total selling cost of the retailer’s market,

β = βi + βn,

(A28)

βi: selling cost of incumbent retail firm; βn: selling cost of new entrant retail firm; Q i: output of the incumbent firm; Q n: output of the new entrant firm. Incumbent retail firm’s profit function:

πi R = p × Q i − (A + βi)Q i.

(A29)

By substituting for p, we have

π iR = (a − bQ i − bQ n)Q i − (A + βi)Q i = (a − bQ n − A − βi)Q i − bQ i2.

(A30)

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New entrant retail firm’s profit function:

π nR = p × Q n − (A + βn)Q n.

(A31)

By substituting for p, we have

πnR = (a − bQ n − bQ i)Q n − (A + βn)Q = (a − bQ i − A − βn)Q n −

n

bQ n2.

(A32)

Incumbent retail firm’s reaction function is given by dπR i /dQ i = a − bQ n − A − βi − 2bQ i = 0

gives

Q i = (a − bQ n − A − βi)/(2b).

(A33)

New entrant retail firm’s reaction function where dπnR/dQ n = a − bQ i − A − βn − 2bQ n = 0 Q n = (a − bQ i − A − βn)/(2b).

gives (A34)

Substituting Q n in (A33) yields the optimal incumbent retail firm output of Q i = (a + βn − A − 2βi)/(3b).

(A35)

Substituting Q 1 in (A34) yields the optimal new entrant retail firm output of Q n = (a + βi − A − 2βn)/(3b).

(A36)

Total retail output of Q* is obtained by adding together (A35) and (A36) which gives Q = (2a − βi − βn − 2A)/(3b).

(A37)

Re-arranging (A37) or substituting (A35) and (A36) into (A30) both give A = (2a − βi − βn − 3bQ*)/2.

(A38)

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Equation (A38) is the wholesale demand function. Similar to the first case scenario, the wholesaler uses (A38) as the inverse demand function in the successive stage (à la Bresnahan and Reiss, 1985). Proof of Lemma 5 Wholesale market profit maximisation: The profit function of the wholesaler by substituting (A38) into (1e) is

πW = (A − c)Q = ((2a − βi − βn − 3bQ)/2) − c)Q = ((2a − (βi + βn) − 3bQ*)/2 − c)Q.

(A39)

Since β = βi + βn, then

πW = (a − c − β/2)Q − 3bQ 2/2.

(A40)

The wholesaler maximizes πW with respect to Q , so profit maximization implies maximizing πW = (a − c − β/2)Q − 3bQ 2/2. First-order condition yields dπW/dQ = a − c − β/2 − 3bQ = 0

or

Q* = (2a − 2c − β)/(6b).

(A41)

Equilibrium wholesale price: Substituting (A41) into (A38) gives the wholesale price: A* = (2a + 2c − β)/4.

(A42)

Substituting (A41) into (1a) gives the retail demand function: Q* = (2a − 2c − β)/(6b).

(A43)

Further substitution in (1b) gives the retail profit function:

πR* = [(2a − c − 7β )(2a − 2c − β )]/(72b).

(A44)

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Likewise, substitution in (1d) gives the wholesale profit function:

πW* = (2a − 2c − β)2/(24b).

(A45)

The joint profit or surplus when substituted with (A44) and (A45) is given as:

π* = π R* + πW* = (16a 2 − 30ac + 14c 2 − 28aβ + 27cβ + 10β 2)/(72b).

(A46)

Consumer surplus : CS = 1/2Q*(a − p*) = (2c − 2a + β)2/(72b).

(A47)

Social welfare: W = π* + CS = (20a 2 − 38ac + 18c 2 − 32aβ + 31c β + 11β 2)/(72b).

(A48)


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Chapter 5


5.1 Introduction Many product markets contain aspects of localized competition with different firms competing directly with different groups of rivals. In such markets, different firms have different private information about their rivals’ past actions. This may lead to market segmentation. In the absence of an information exchange mechanism, firms cannot observe the past actions of all firms. Communication, hence, becomes a serious problem in these markets. Early models of Hotelling (1929), Chamberlin (1933) and Kaldor (1935) highlighted the problems of the localization of competition (see Anderson et al., 1992, for details). Schmalensee (1985) marshals evidence that the morning breakfast cereal industry is characterized by localized competition. Feenstra and Levinsohn (1995) offer econometric evidence of localized competition in the car market. Scherer and Ross (1990) discuss interesting anti-trust issues in markets with localized competition. Papers by Stigler (1964) and Green and Porter (1984) highlight the problem of imperfect public information with uncertain demand functions, even in non-localized markets. Game theoretic models also examine serious difficulties in homing on the equilibrium when agents play repeated games with private information (Ben-Porath and Kahneman, 1996; Kandori and Matsushima, 1994). The communication problem can

155

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create enormous difficulties in such markets for two sets of reasons: First and foremost, a collusive arrangement cannot be sustained in such markets due to this communication problem. Second, such markets can be beset with non-equilibrium behaviors as firms may fail to reach a full-information Nash equilibrium. In this context, chaotic discrimination may become terribly important since firms may fail to adopt equilibrium strategies. Joseph Bain (1952) offers examples of various forms of price discrimination as arbitrary and non-profit-maximizing, and therefore labels them as purely unpredictable. He calls these forms of price discrimination “chaotic.” Price discrimination is chaotic since it does not conform to profit maximization and, as a result, this form of pricing does not constitute equilibrium in the Nash sense (Gangopadhyay, 2000, 2005). Since these prices do not form the Nash equilibrium, there remains scope for sellers to unilaterally enhance their individual profits. Yet sellers fail to do so. The market is beset with a nonequilibrium and an inefficient outcome. The precise aim of the present study is to apply the recent developments in non-linear and deterministic dynamic system to explain chaotic discrimination. Despite being an important component of industrial economics (Shepherd, 1985), this is the first attempt to explain chaotic discrimination in terms of a cohesive model. During the last three decades, the discovery of chaotic dynamics in simple non-linear deterministic systems has been a milestone in scientific research. The issue at stake is that even though all time paths of a deterministic dynamic system are bounded, trajectories that start close together diverge, or separate, exponentially. A significant import of chaotic behavior is that a precise prediction in deterministic models is not possible. Deterministic models can thus display fundamental randomness. A gradual collection of information does not remove this randomness nor make prediction feasible. For economics science, the study of chaotic behavior assumes great significance since the core of deductive equilibrium approach relies on the mutual consistency and fulfillment of expectations, or predictions, of agents. Typically, industrial economists focus their attention on economic models with

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regions of local stability on the assumption that regions of instability are of little importance and more of a pathological case (Gangopadhyay, 2005). The fundamental argument is that industrial economics does not find exploding time paths of any significant variable. However, the development of chaotic behavior significantly undermines this dismissal of regions of instability that can actually generate complex, yet deterministic, dynamics within bounds. The meeting point between chaotic dynamics and chaotic discrimination is the common feature of non-equilibrium behavior. Bain (1952) identified two principal forms of price discrimination as chaotic discrimination. The fundamental characteristic of such discrimination, he argued, embodies an element of irrationality in the pricing decision. As a result, such prices are believed to be arbitrary and non-profit-maximizing (Bain, 1952). The first form is popular as the Basing-Point Pricing. Many goods are sold at delivered prices, which are the factory prices plus shipping mark-ups while sellers are disparately located. Every seller quotes a delivered price at a delivery point that equals the base price of the nearest seller plus the shipping mark-up from the nearest seller. As a result, price discrimination may emerge if buyers do not buy from the nearest seller. This form of discrimination is labeled as chaotic since the delivered prices are inconsistent with joint-profit-maximization. Such a scheme of pricing evolved between the 1880s and 1949 in cement, steel and certain other industries but, after 1949, it gradually declined (See Shepherd, 1985). The second type of chaotic discrimination emerges when sellers quote a common price but secretly engage in arbitrary price discounts. As a result, different buyers pay different prices. Such price discrimination, Bain (1952) argued, does not conform to a pattern of joint-profitmaximization and, hence, is arbitrary and non-profit-maximizing. Bain (1952) rationalized such discrimination as an effort by oligopolists to avoid an open price war. In his opinion, there may exist a uniform pricing rule that would engender higher individual as well as joint profits. Yet the chaotic price discrimination is omnipresent in modern markets. What we understand is that this form of discrimination may

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not be underpinned by the instrumental rationality of sellers and may not be an equilibrium phenomenon. This scheme of pricing, hence, came to be termed as chaotic discrimination that embodies a systematic departure from a profit-maximizing equilibrium pattern. This form of chaotic discrimination is an important element of modern markets, but what causes it remains unclear. The explanation of Bain is inadequate for two reasons: first, we do not understand why sellers fail to arrive at an efficient equilibrium confirming conjectures/ predictions of each of others’ price discounts. Second, we know very little about the forces that stop sellers from secretly making Paretoimproving price discounts and converging on a Nash equilibrium. The main purpose of this study is to address the second form of chaotic discrimination to answer these questions. A stylized case of chaotic discrimination was considered: the incumbent sellers choose a common posted price, but they engage in “secret” price discounts from the posted price. We develop a model to argue that such discrimination may derive from the regions of instability of a dynamic model of price discounts. We finally offer an econometric evaluation of price discounts in a localized market that lends support to chaotic price discrimination as price discounts that are arbitrary and nonprofit-maximizing. The plan of the chapter is as follows: Section 5.2 offers the model; Section 5.3 discusses the precise ramifications of the proposed model; Section 5.4 offers econometric evaluation; and Section 5.4 concludes. 5.2 The Model We consider localized competition in the following manner: the market may have many oligopolists but the market is split into duopolies that compete directly with each other. We focus on the classic case of a duopoly in which two sellers compete against each other. We do not attempt to model the entire industry/market dynamics. Instead we focus only on the dynamics of a duopoly, which is a segment of the entire market. In this model, the strategic variable is price discounts. Each firm in a duopoly simultaneously

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chooses a price discount that impinges on its own and rival profits. A price discount by seller i affects the number of customers of seller j (cross effect) while the price effect works through the individual and downward-sloped demand function. Let us now characterize the game: Assumption 1. We write the revenue function of the i th seller as the following: Ri = Mi χ (PD − ∆Pi),

(1a)

where Mi is the number of customers who purchase from seller i and χ is the demand function of each customer. ∆Pi is the price discount undertaken by seller i and PD is the posted price. This assumption about the revenue function comes from Stiglitz (1987). Assumption 2. We also assume the following: Mi = α(PD − ∆Pj),

(1b)

χ = β1 − β2 (PD − ∆Pi)

(1c)

Once again, it follows. The general restriction is that δMi/δ∆Pj < 0, δχ/δ∆Pi > 0. The implicit assumption of (1b) is that buyers obtain information through “word-of-mouth” that will allow each seller to maintain a different price for a finite span (Phelps and Winter, 1970). Note that (1c) is the usual downward-sloped demand function. The profit function of seller i, Πi is reduced to the following: Ri = Πi = α(PD − ∆Pj)[β1P D + (β2 − β1)∆Pi − β 2∆Pi2]

(2a)

β 1 = β1 − β2P D.

(2a′)

where

For the sake of simplification, we assume — without any loss of analytical bite — the cost of production is assumed to be zero.

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Assumption 3. At date t + 1, seller i makes incremental changes in the price discount as: ∆Pi (t + 1) = ∆Pi (t) + H1[δΠi(t)/δ∆Pi (t)].

(2b)

[δ Πi(t)/δ∆Pi (t)] is the marginal change in profits for a small change in the price discount at date t. H1 is a positive coefficient. The story is that a seller starts with a price discount and then gropes for the best discount by changing the discount: he raises the discount at date t + 1 by a factor H1 if the discount at t increased his profits. He lowers the discount at date t + 1 by the factor H1 if the discount at date decreased his profits. This type of dynamics has been studied in Gangopadhyay (1997). Assumption 4. We further assume the existence of a symmetric Nash equilibrium. That is, at equilibrium ∆Pi = ∆Pj = ∆P.

(2c)

Theorem 1. The price dynamics is then reduced to the following : ∆P (t + 1) = λ − θ ∆P (t) + γ [∆P (t)]2,

(2d)

where λ = H1αPD((β2 − β1), γ = 2αH1β2, θ = H1(β2 − β1)α + 2αH1β2PD − 1. Proof. Differentiating (2a) with respect to ∆Pi, then substituting it in (2b) and using (2c) yields (2d). Theorem 2. The dynamics as represented by (2a) has two fixed points : ∆P* = [1 + θ + SQRT{(1 + θ)2 − 4λγ }]/[2γ],

(3a)

∆P** = [1 + θ − SQRT{(1 + θ) − 4λγ }]/[2γ].

(3b)

2

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Both these equilibria are the steady state of the above dynamics. It is instructive to see that the first equilibrium given by (3a) is unstable. The second equilibrium given by (3b) is stable if: SQRT{(1 + θ)2 − 4λγ} < 2.

(3c)

Proof. Substituting ∆P (t + 1) = ∆P (t) = ∆P into Eq. (2d) yields the quadratic equation whose two roots give the steady state of the above dynamics. Evaluating the slope of Eq. (2d) for ∆P* and ∆P ** will give us the rest of the theorem. Theorem 3. It is now simple to rescale the variables to arrive at the following dynamics : Yt+1 = BYt (1 − Yt),

(4a)

Yt = γ (∆P* − ∆P(t))/B,

(4b)

B = 1 + SQRT{(1 + θ)2 − 4λγ }.

(4c)

where

Equation (4a) is the much-celebrated logistic equation expounded by May (1976) and Feigenbaum (1978). From May (1976), we know that chaotic behavior sets in for B ≥ 3.57. Proof. The proof, being simple, is omitted.

5.3 Discussion It is now possible to characterize the dynamics: for 1 < B < 3, the dynamics of price discounts converge to the stable equilibrium, ∆P**. This is the region of stability that plays an important role in the equilibrium analysis as discussed in Gangopadhyay (1997). If B is increased above 3, ∆P** becomes unstable and the price discounts converge to a stable two-period cycle. As B is increased further, the stable period cycles of n bifurcates into cycles of period 2n. From

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Feigenbaum (1978), we know that the range of A values for which the nth cycle is stable shrinks at a geometric rate. For B > 3.57, the price discounts evolve through a cycle of infinite period. The price discounts are within the relevant bounds but never repeat. For a higher order, price discounts may look like a random process but these discounts are fully deterministic. 5.4 Empirical Findings 5.4.1 Empirical methods The primary aim of this study is to understand to what extent price discounts in localized competition are explained by underlying economic factors. The economic factors are four-fold: purchasing power of customers, age profile of customers, ethnic composition of customers, and price discounts chosen by local competitors. The industry that we focus on is the retail fuel market along a long stretch of suburban Sydney in Australia. It is some kind of an ideal representation of Hotelling’s spatial competition model with localized aspects. These fuel stations sell an identical product that is unleaded fuel. Neighboring fuel stations compete with each other, which gives rise to localized competition. These fuel stations are located at different spots on a 40 km stretch of Sydney. These fuel stations are all located within a 5 km radius of a train station. Two neighboring ones compete against each other for customers due to their positions on highways and busy streets that make the search cost quite high for customers. We visualize each fuel station catering to a particular region of Sydney suburb. For each station, we collected evidence of price discounts and also various characteristics of customers. A natural starting point would be to estimate a model in which price discounts are dependent on the factors that determine price discrimination since these discounts represent some kind of spatial discrimination. To put it in simple terms, price discrimination results from two sets of factors. First and foremost, price discrimination arises

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due to differences in the demand elasticities of customer groups. Second, the degree of competition and rivalry in a localized market can also influence on price discrimination. 5.4.2 Differences in demand elasticities The most important factor in price discrimination is the income groups that different customers come from (purchasing power). We choose the asset price of a region within this 40 km stretch of suburban Sydney as a proxy of purchasing power of customers. We control the selection of fuel stations in such a fashion that customers are almost equi-distant from rail stations, so that the scope for the substitution of fuel is more or less similar across customers (similar elasticity of demand). However, a weakness is that we fail to take into account the differences in the quality of coach/bus services across suburbs. In order to lessen the impact of this weakness, we ignore fuel prices within the inner-city where bus services are excellent and a good substitute for private vehicles. In our chosen region, we tend to think that rail services and private vehicles are close substitutes. The demand for fuel in a region is also dependent on the age profile of its population. We expect that a working family with children will need to rely more on vehicles than a family of retirees and empty-nesters. In order to incorporate this effect, we have chosen the percentage of working families in a region as a determining factor of price discrimination. The impact of social factor on the choice of optimal mode of transport and also on the search behavior of customers for a cheaper fuel price is taken into account by considering the ethnic composition of the people in a region. 5.4.3 Degree of competition/rivalry in localized markets Finally, we take into account the degree of competition among sellers as a determining factor of these discounts. We choose the neighboring discounts (in a unidirectional fashion representing the flow of traffic) as a proxy for localized rivalry/competition.

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5.4.4 Simple model of regression Thus, the simple equation that determines the price discounts is postulated as X1 = a1 X2 + b X3 + a2 X4 + a3 X5 + a5 X1(−1)

(5a)

X1: Price discounts, X2: Asset price, X3: Constant (=1), X4: Percentage of people born in Australia, X5: Percentage of people working, b: Unknown factors, X1(−1): Discounts offered by relevant fuel stations. 5.4.5 Data sources The primary data are on price discounts (X1). These data are collected before the coalition attack on Iraq when the maximum price of fuel was expected to be $1(Australian). It was a kind social custom to expect the price of fuel to be less than $1. The primary data were collected on the eve of Easter holidays when the demand for fuel is the strongest in Australia. Any price less than the $1 is chosen as a discount in the study. It is also noteworthy that the Iraq war led to an increase in expected price to $1.10. Our primary data were collected before the Iraq war. Thus, price discounts are calculated from the sample as: X1 = 1 − Actual Fuel Price on the Easter Holiday eve on 1 March 2004. (5b) The secondary data were collected from the web site domain.com.au, which lists the property prices of different Sydney regions (X2), the ethnic composition (X4), and the percentage of working families (X5) in every region. 5.4.6 Results We posit that the price discounts in the proposed fuel market are a linear function of the purchasing power of customers, their ethnic

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composition, their age profile and working status, and degree of rivalry between the competitors. The empirical results are negative, which suggest that the current data set cannot statistically explain the price discounts as a function of the aforementioned variables. There are various shortcomings that beset the empirics: first and foremost, the data set may not be large enough. Second, there are omitted variables. Finally, the functional specification may be incorrect (Table 5.1). Yet these results are in perfect consonance with the theoretical models of chaotic discrimination that we propose. Due to the nonlinearities, the price discount model is beset with chaotic dynamics, due to which agents fail to predict mutual-best responses. As a result, the market fails to achieve the Nash equilibrium. Actual discounts are chaotic in the sense of Bain (1952), these discounts are arbitrary and non-profit-maximizing. Therefore, the empirical finding — i.e., the aforementioned variables fail to explain the price discounts statistically — can support one possibility that these price discounts are purely arbitrary and non-optimal. 5.5 Conclusion We consider price discounts in a dynamic context. Customer flows to a seller are influenced by secret prices and price discounts chosen by its rival. The demand function of each customer is linear and downward sloped in prices. Since price discounts are secret, an instantaneous Nash equilibrium is not arrived at. Sellers start off with initial price discounts and gradually update these discounts, t, to enhance their profits. We have shown that the dynamic path of price discounts will be characterized by chaotic behavior in the region of instability. The finding has important bearings: it is typically assumed in the deductive equilibrium approach to modern economic theory that the Nash equilibrium dispels all systematic prediction errors and the economic system settles in an equilibrium characterized by self-confirming and mutual-best responses. This approach has its most dominant influence on modern industrial economics, popularly known as industrial organization. The deductive equilibrium analysis has contributed to a better understanding of modern industrial economics. However,

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Economics of Rivalry, Conflict and Cooperation Table 5.1.

Regression results.

Ordinary Least Squares Estimation Dependent variable is X1 33 observations used for estimation from 1 to 33 Regressor X2 X3 X4 X5

Coefficient

Standard Error

T-Ratio [Prob]

−.5844E-5 14.0515 −.092514 −7.2409

.9804E-5 21.8338 .072580 37.0850

−.59607 [.556] .64356 [.525] −1.2747 [.213] −.19525 [.847]

R-Squared .069471 S.E. of Regression 5.2944 Mean of Dependent 7.0758 Variable Residual Sum of 812.8918 Squares Akaike Info. −103.6925 Criterion DW-statistic 1.7621

R-Bar-Squared −.026790 F-stat. F(3, 29) S.D. of Dependent Variable Equation Loglikelihood Schwarz Bayesian Criterion

.72169[.547] 5.2249 −99.6925 −106.6855

Diagnostic Tests Test Statistics*

LM Version*

F Version

* * * A:Serial Correlation*CHSQ(1) = .35144[.553]*F(1, 28) = .30140[.587] * * * B:Functional Form *CHSQ(1) = 1.6163[.204]*F(1, 28) = 1.4420[.240] * * * * C:Normality *CHSQ(2) = 1.8273[.401]* Not applicable * * * D:Heteroscedasticity*CHSQ(1) = 2.4775[.115]*F(1, 31) = 2.5163[.123] A: Lagrange multiplier test of residual serial correlation, B: Ramsey’s RESET test using the square of the fitted values, C: Based on a test of skewness and kurtosis of residuals, D: Based on the regression of squared residuals on squared fitted values.

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little attention has been given to the regions of instability. We established that the postulated price discount dynamics can exhibit chaotic behavior. Firms now fail to see systematic errors. Firms also fail to make long-run predictions with certainty even though they act in a deterministic world. Time profiles of prices and quantities, which start very close together, will separate exponentially. The strength of the Nash equilibria gets terribly emasculated. We suggest that an application of standard results of chaotic behavior can be a very important step forward to understand the dynamics of industrial economics. We marshal some evidence to explain price discounts as a function of some relevant variables in a market characterized by localized competition. The results are negative. There are some shortcomings in the empirical section. Yet the empirical study supports the theoretical model that price discounts may be arbitrary and non-optimal in the sense of Bain (1952) in oligopolies with localized competition.


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Chapter 6

Globalization, Market Hostility and Endogenous Mergers among Rivals

6.1 Introduction The issue of endogenous and reciprocal mergers has emerged recently. The literature is still evolving. Theoretical models typically examine the incentives of firms to merge in response to mergers among their rivals. As a set of firms merge, the new entity poses a challenge to other rivals in the market, which precipitates some kind of a conflict for market shares. The rivals engage in alliance formation for survival, which further induces other firms to seek an alliance. Endogenous and reciprocal mergers reflect some kind of ologopolistic rivalry for market shares and ensuing conflicts among big players. The question that the literature poses is simple: who will merge with whom? The decision to merge by firms can significantly alter the industrial structure and profit opportunities that can, in turn, trigger further mergers and cause instability — akin to an avalanche in an Alpine resort. Mergers can thus cause turbulence and complexity in an industry. This idea has been advanced more than 30 years ago by Knickerbocker (1973) in the context of oligopolistic disequilibrium and strategic rivalry. The oligopolistic disequilibrium and rivalry form the central focus that, we argue, has assumed significance in the globalized economy.

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Industrial issues concerning globalization are rooted in the internationalization theory. The basis of this theory stems from the economic benefits to a firm in acquiring tangible assets from another firm through the process of merger or acquisition. These benefits make mergers and acquisitions profitable. The tangible assets are knowledge-based assets and also research and development resources. They must have zero running costs within the firm, along with high transaction costs, so that a merger is the least-cost method of acquiring these assets. These commonly recognized assets by competitors in the market generally provide a competitive advantage if acquired through increased profit. This is a reason why this theory is seen to best explain the existence of horizontal mergers in the international context. As Dunning (1981) states, “Internalisation is thus a powerful motive for take-overs or mergers, and a valuable tool in the strategy of oligopolists” (p. 54).

A firm will strategically choose its merging partner that will result in a beneficial change in capital structure, thus ensuring a more competitive position in the market as the cost function changes. Globalization offers an unprecedented opportunity to firms to internationalize in order to exploit knowledge-specific assets. As the era of globalization gathers momentum, there were sweeping changes in the German industry during the 1990s. First of all, the German economy in the 1990s was characterized by a strong structural change. The share of the industry in the gross value-added decreased gradually and accounted for around 30% while the share of the service sector shot up to 69%.1 In spite of this trend, the industry was still an important part of the German economy. In 1997, the roughly 44,500 industrial enterprises employed close to 6.2 million people — this is 16.66% of all German employees. But only about 1.7% of these industrial enterprises were large companies with more than 1,000 employees. Nevertheless, these large firms employed 1

http://www.bmwi.de/textonly/Homepage/Politikfelder/Branchenfocus/Branchenfocus.jsp.

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about 31% (2.1 million) of the total workforce in the industrial sector and accounted for about 40% of the industry’s total turnover. Many of these firms were known worldwide such as the automobile manufacturers, Daimler-Chrysler, Volkswagen and BMW, the chemical corporations, Hoechst, Bayer and BASF, the energy groups E.ON and RWE, as well as the electrical equipment manufacturer, Siemens. The remaining 98.3% constitute the German “Mittelstand” which means companies that employ fewer than 500 workers. Nearly three quarters were even firms with fewer than 100 employees.2 Thus, the great majority of industrial enterprises in Germany were of small or medium size and a few very large enterprises accounted for a considerable share of all industry activities. This implies a low concentration ratio for the German industry. The theory of endogenous merger argues that the decision to merge relies critically on the underlying industrial structure. As the industrial structure changes, it alters the incentives and constraints of firms to merge wherefrom one should observe new waves of merger activities. Due to globalization, structural changes in the industrial sector and the gathering momentum of the European Union in the 1990s, the German industry has become the testing ground for alternative theories. We want to test the model of endogenous mergers in the light of the recent experience of the German industry since 1994. A bulk of the literature on mergers focuses on the cost functions of firms involved in mergers and assume these cost functions to be identical, which is an inhibiting factor towards a realistic assessment of the effect of a merger on these merging firms and on the industry in which the merger is considered. To resolve this issue, we consider endogenous mergers in which the decision to merge is determined within the constraints of the firms’ operating and production choice. Gowrisankaran (1999) develops an endogenous, dynamic model of mergers. The expected results are obtained in the study on the effect of a merger on entry, investment, industry equilibrium, and other

2

cp. http://www.foreign-direct-investment.de/index.html?w=gges.

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factors that we are interested in observing and have discussed in previous sections. Gowrisankaran (1999) suggests that this type of analysis may be beneficial in assessing anti-trust considerations. Previous works on mergers apply game theory to find the welfare implications of mergers, e.g., Farrell and Shapiro (1990) examine mergers in a static setting. Gowrisankaran (1999) argues that though a static analysis of the merger process may suggest that a merger may lower social welfare through increased concentration and price effects. A dynamic analysis, however, may show that the increase in concentration in the market will be offset by the increased entry into the industry that may follow mergers. Furthermore, there is a suggestion by Gowrisankaran that a static analysis may miss the benefit that a merger may have on an industry where languishing firms are merged into others, thus “preventing the dead-weight loss of discarding capital without a significant anti-competitive effect.”3 A non-endogenous merger analysis will therefore be unable to predict the future welfare and industry effects of current policies. Furthermore, Gowrisankaran (1999) also argues that the relative profitability of merger vs. no merger is not a valid guide to whether a merger may occur. This is the case due to the strategic nature of the market where a firm may hold off merging to see if another firm merges with a third firm since this will have the effect of decreasing competition in the market. Similar issues are discussed in Polasky and Mason (1998) in terms of the ignorance of short-run and long-run effects of mergers in much of the literature where only one-shot and static games are employed. Ignoring the distinction is a shortcoming in the literature, as firms may not have sufficient time to react to mergers in the short-run. Allowing the merging group to form endogenously in a single merger case has been featured in Kamien and Zang (1990, 1991) and Gaudet and Salant (1992). In a sequential merger scenario, Kamien and Zang (1993) analyze the possible effect of monopolization in an industry if endogenously formed sequential mergers take place.

3

Gowrisankaran (1999, p. 57).

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The much-celebrated empirical model of an endogenous merger is given by Barros (1998). He provides a model that can predict merger partners, i.e., endogenous mergers, from the size asymmetry of merger participants given the initial degree of market concentration. To put it differently, Barros proposes that mergers are endogenously determined that means that the decision to merge is dependent on constraints that firms face in operation and production choices. He then establishes, by means of the initial concentration of a market, that it can be predicted which firms will be involved in a merger. In this chapter, we test this model in the context of the German mergers in the industrial sector. The plan of the chapter is as follows: Section 6.2 provides the baseline model of endogenous mergers and industrial concentration. Section 6.3 offers an overview of the relevant issues concerning the German industry during 1994–2001. Section 6.4 outlines the data sources and the collection of data. Section 6.5 furnishes empirical results on endogenous mergers in the German industry. Finally, Section 6.6 concludes. 6.2 Size Asymmetry and Endogenous Mergers: The Baseline Model The model starts off with a Cournot oligopoly with three firms of different efficiencies (see Barros, 1998). The inverse demand function is given by P = 1 − Q. It is assumed that the firms have different constant marginal costs of production (c1 < c2 < c3) which implies different efficiency levels characterized by c1 + 2∆ = c2 + ∆ = c3 where ∆ > 0 is the summary index of asymmetry. The assumption of constant marginal costs implies that after a merger, the less efficient firm ceases production. Furthermore, the asymmetry index is defined by = ∆/ (1 − c1) and the initial market concentration is measured by the Herfindahl–Hirschman-Index (HHI). The relationship between these two variables is assumed to be positive. This indicates that an increase in the asymmetry between firms leads to a redistribution of output production from the less to the more efficient firm because of rationalizing and welfare improving effects. A market with three firms offers the

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following merger formations: {{1,2},3},{{1,3},2},{{1,{2,3}}. In the first step, Barros analyzes the conditions under which each type of these mergers is carried out. The first condition says that a merger will only take place if the post-merger profit of the merging firms exceeds the sum of the pre-merger profits. Second, it is required that the merger needs to be stable. That means the outside firm cannot make a more profitable offer to one of the two merging firms to prevent/ destroy this merger. The outside firm would have an incentive to make a counteroffer because in the case of a merger between the two other firms, the outside firms’ profit would decrease while the merging firms profit will increase. If more than one merger is stable, the merger with the larger internal gain is selected. In the next step, Barros observes if these two conditions are simultaneously fulfilled, the following is valid: If d is very small (χ[0,0.034]), firms are of equal size and, thus, are equally efficient. In this case, no redistribution effects can be obtained and a merger would lead to a loss for the participating firms because they would reduce their output after the merger. Consequently, for very small asymmetry indices, no mergers will occur. More significant asymmetry levels are related to companies of different size and efficiencies. In this case, a merger between the two firms is profitable because positive effects from the output redistribution towards the least cost firm can be achieved. The size of this gain depends on the difference of the costs, and the pre-merger output volume of the least efficient firm. The smaller this output, the higher are the welfare surpluses. Thus, for the moderate values of the asymmetry index, d (χ(0.034, 0.152]), the most profitable merger occurs among the less and the most efficient firms, because of the sizable output effect of the latter. For large asymmetries between firms (χ(0.152, 0.200]), the efficiency differences are so high that in comparison to the best efficient firm, the production of the less efficient one is insignificantly low which results in an output-redistribution effect that is almost zero. Thus, the merger takes place between the two most efficient firms.4 4

These findings are valid for any number of firms in a market. They are not restricted to markets with only three firms.

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Summarizing these results, it can be said that the higher the asymmetry index , the less asymmetric/more symmetric/similar are the participating firms of a merger. Or the other way around the lower the asymmetry index (except for very small d) the more asymmetric the firms that merge. Recalling the positive relationship between the asymmetry index and the concentration index H from above, it can be concluded that the asymmetry between the merger participants should be higher when the initial concentration is low. That means a negative relation between these variables should be expected.

6.2.1 Evidence from Portugal To see if this association is tenable, Barros offers an empirical test based on a data set containing 18 Portuguese mergers spanning over different industries. The plot of the merger participants’ asymmetry against the initial market concentration (HHI) in Fig. 6.1 shows a significant negative relationship. 1.2

Asymmetry Index (A)

1

0.8

0.6

A

0.4

0.2

0 0

1000

Figure 6.1.

2000

3000 4000 5000 Concentration Measure (H)

6000

7000

The Portuguese experience with endogenous merger.

8000

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For markets with a higher concentration, Barros interprets this negative association as follows: (i) firms with a large market share attempt to reinforce their market position; (ii) or firms with a small market share try to gain critical scale of operation by joining efforts with other firms of similar sizes. According to the theoretical model, in higher concentrated markets, merging firms are less asymmetric. This is reason to believe that the first interpretation is dominant. From this model, Barros also argues that the joint initial market share of merging firms should be higher in markets with a higher concentration. This is compatible with interpretation (i), but not with (ii). The empirical analysis of the Portuguese data in Fig. 6.2 shows a positive association between the combined market share of the merger participants and the initial concentration, which supports the dominance of the first explanation. A negative association would have given stronger support to the second interpretation.

90

80

Combined Market Share (MS)

70

60

50 Series1 40

30

20

10

0 0

Figure 6.2.

1000

2000

3000 4000 5000 Concentration Measure (H)

6000

7000

8000

Combined sizes of merging firms and initial concentration measures.

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6.3 A Brief Note on the German Industry Since 1994 To get a more precise overview of the concentration issues, we look at the following sectors: Beginning with the chemical industry, it can be said that it is principally based on three large corporations, Hoechst, Bayer, and BASF, which account for 21.7 of the total turnover. In addition to these large firms, there are also a multitude of successful smalland medium-sized firms, which hold the concentration low. The HHI for this sector is only 23.81. The other industrial sectors included in this study are the food and beverage sector, the coffee roaster sector and the cigarette-manufacturing sector. All three industries are lowconcentrated with a HHI ranging from 17.707 for the beer brewing industry to 107.09 for the coffee roaster sector and 266.49 for the cigarette manufacturers. According to the CR-3 of these sectors (all are below 15%), there are firms dominating these industries. Looking at the banking sector, it can be seen that this sector is still characterized by a low concentration although the consolidation process in recent years has led to a slight increase in concentration in this sector. The five biggest German banks account for only 21% of the market and the bank ranked 20th among the biggest German banks has only a market share of a round 1%. In comparison with the European market where the average CR-5 is 57%, the German concentration level is still one of the lowest.5 The insurance sector shows a similar situation. There are also a large number of insurance companies. Only the 22 largest insurance firms have a market share of more than 1%. The two dominating firms are the Allianz and the Munich Re, accounting for around 25% of the market. All the following companies have a market share of less than 5% (except the Generali Group with 7.7%). The roller-bearing industry shows a similar situation. The overall concentration with a HHI of around 37.875 is low. This industry is dominated by two firms, FAG Kugelfischer AG and INA Schaeffler KG, which have a combined market share of 27%6 before their merger in 2001. After that, they 5 6

For a more detailed analysis of the banking sector, see Chap. 4.1. Estimated since INA has never published any company details.

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became the leading roller-bearing firm in Germany and the second largest in the world. But not all sectors of the German economy show a low concentration. In particular, the markets for power, petrol stations, tourism, and media advertising are highly concentrated. Above all of them are the power companies. After two mergers among the biggest German power companies in 2000, the market is now controlled by a duopoly. The two largest companies, namely E.ON AG and RWE AG, have a combined market share of more than 70%. But before their mergers, the sector’s concentration was already high with a CR-3 of around 66.5%. A similar observation is also valid for the TV advertising market. The three largest television groups account for 70.3% of the net advertising turnovers before the merger between Pro7 and Sat.1 (which constituted the second and third largest corporations). Nowadays, the two largest TV groups account for this market share. The high HHI of 1,843 highlights the high concentration. The market for petrol stations is also characterized by a duopoly. After the two mergers between Deutsche Shell GmbH and DEA AG (being a subsidiary of RWE AG), and Deutsche BP AG and E.ON’s Aral, the combined market share of the two new firms is approximately 50%. The market share of the three largest companies is 61%. To prevent a market-dominating position of the two post-merger firms, the merger control commission required them to reduce the number of their petrol stations after the merger. But this process is not finished and the market-dominating position still exists. The initial market share before these two mergers had already increased with a CR-3 of around 43%. Also, the retail and mail-ordering sector should be mentioned. The conglomerate merger of Karstadt and Quelle created the leading department store and mail-order company in Europe. In Germany, this new company has a market share of 36% in the department store and a market share of 30% in the mail-order sector. Finally, Germany’s tourism industry market has become more and more concentrated in recent years. Only a few years ago, there was a multitude of different travel agencies. Nowadays, most of them belong to big companies

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Globalization, Market Hostility and Endogenous Mergers among Rivals Preussag 22%

Miscellaneous 32%

Öger 2% Alltours FTI 4% 5%

Figure 6.3.

REWE 17%

179

Miscellaneous 32%

Karstadt Quelle 18%

Öger 2% Alltours FTI 4% 5%

CR-3 57%

Market shares of leading firms in the German tourism industry.

such as the REWE AG which combines ITS Reisen, Jahn Reisen, Tjaereborg, ITSBilla Reisen, Meier’sWeltreisen, DERTOUR, ADAC Reisen, Atlasreisen, DER Business Travel, DER Reisebüro, DER Deutsche Reisebüro DERPART, and LTU. It should be mentioned that before 1988, REWE was only a food retailer with no activities in the tourism industry. The other main players are Karstadt Quelle with Neckermann Reisen, Condor Individuell, Air Marin, Terramar, Aldiana, Bucher Reisen and Kreutzer Touristik, and Preussag AG with Hapag Lloyd and TUI, to name only the three most important. Figure 6.3 makes the situation clearer. Increasing concentration is the fact as some of these firms have also a stake in other tourism companies. Due to the fact that most of the acquired firms have retained their names, the high concentration is not immediately obvious. Summarizing, it can be said that most of the sectors observed in this study have a large number of firms, thus resulting in low HHIs. But many of the sectors are dominated by only a few big enterprises as well. The average CR-3 ratio in this study is 30%, indicating a moderate concentration.7 6.4 Collection of Data and Data Sources The collection of the data set proved to be pretty difficult. Data on various important factors are not publicly provided. It is difficult to 7

If CR-4 is higher than 40%, an oligopoly is rearing its head.

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get appropriate data for early mergers. Therefore, most of the mergers observed in this study took place around the end of the 20th and the beginning of the 21st century. To be more precise, the data range from 1994 to 2001 representing the German activities in the 5th merger wave. Furthermore, the study mainly consists of significant German mergers. Data for mergers between small- and medium-sized firms are rare because these mergers are not required to be approved by the German Federal Cartel Office. These companies do not meet the specified criteria to trigger mergers. They are, furthermore, not required to publish company reports with useful information about their financial situation. For bigger firms meeting the criteria, information could be collected from the decision papers of the Federal Cartel Office, or the European Merger Control Commission. These published decisions contain information on the market shares of these firms and the situation of the related market. But in some cases, these reports did not provide the necessary data because they were company secrets! When that was the case, market shares were estimated by the means of firm reports, or information provided in the ranking of the 500 biggest German firms published by the newspaper “Die Welt.” Sometimes market shares of companies were published in newspapers such as the “Financial Times Deutschland,” in sector reports, or notifications of the respective industry associations. Concerning the banking sector, we benefited from useful information provided by the magazine “Die Bank” that publishes a ranking of the 100 biggest German credit institutions every year. With the given information, the market shares of the banks were calculated. Information about the situation in the banking sector can be found in the monthly reports of the “Deutsche Bundesbank” and its statistics. The HHI and concentration ratios are published there. The only sector for which comprehensive data on industry concentration exist is the production industry and the commerce sector. These data are published in the “Hauptgutachten” of the German Monopoly Commission and its appendices, which are published every two years.

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Leaving out the mergers for which not all of the necessary information could be collected, the sample for this study consists of 40 mergers spanning over different industries. Specifically, there are eleven mergers in the banking sector; six in the insurance sector; three in each power market and the tourism sector; two for each petrol stations, the TV, and the beverage sector; one of each chemical, the roller bearing, the coffee roasting, and the retail industry. It should be mentioned that some of these 40 mergers are counted twice because these mergers had an impact on two different sectors, as in the case of the four conglomerate mergers. The same applies to the mergers in the Tourism and TV sectors because they influenced different markets within a special sector for example, the sector for business and private travels has impacts on the audience and advertising market. Finally, these mergers were not chosen by any specific selection process. They were only chosen because of the availability of the necessary data. 6.5 Empirics of Endogenous Merger Models in the Light of German Mergers and Concentration Before Barros’ theory can be used for the German data set, the merger participants’ asymmetry8 has to be calculated, which is defined as A=

s1 - s 2 max{s1 , s 2}

with s1 and s2 being the market shares of the two participating firms. Index A takes value 1 in the case of maximum asymmetry and value 0 if firms are of equal sizes. A must always be lower than 1 because A = 1 is only possible if one of the firms has a zero market share. In this test, this happens five times because the respective merging partner

This should not be mixed up/confused with from the theory section, which measured the asymmetry of all firms in a market and not the one between the merging partners. 8

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was not active in the market of the other firm before the merger. This is characteristic of conglomerate mergers. After calculating the asymmetry index A, it is plotted against the initial concentration. We use the CR-3 instead of the HHI because HHI is not available for all mergers of this study. Figure 6.4 shows that there is a slightly negative and statistically significant relationship between the asymmetry index and the initial market concentration. The estimates of a linear regression prove/ confirm/support this finding. The correlation coefficient is obtained by taking the value −0.187. To show this correlation clearly, the regression straight line is additionally drawn in Fig. 6.1 which is A = −0.0012* CR-3+ 0.625.9 Next, we plot the combined market share of the participating firms against the initial concentration (CR-3). As can be seen in Fig. 6.5, a significant positive correlation between these two variables exists. The correlation coefficient in this case takes value 0.595 and the regression straight line is MS = 0.143*CR-3+ 10.12.10 As can be seen from these results above,

1,0000 0,9000 0,8000

Asymmetry (A)

0,7000 0,6000 0,5000 0,4000 0,3000 0,2000 0,1000 0,0000 0

10

20

30

40

50

60

70

80

Concentration (CR-3)

Figure 6.4.

9

Asymmetry and initial concentration.

The complete calculations and estimates can be found in Appendix A. See the regression results in Appendix A.

10

90

100

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183

45 40

MS of participating firms

35 30 25 20 15 10 5 0 0

10

20

30

40

50

60

70

80

90

100

Concentration (CR-3)

Figure 6.5.

Size of merging firms and initial concentration.

Barros’ theory is also confirmed for the German data set. There is a negative relation between the initial concentration and the asymmetry. But it is not as significant as the Portuguese relation. Therefore, also in German markets with higher concentrations, large firms merge to reinforce their market share. Due to the low concentration in most of Germany’s industries, the asymmetry between the merging partners should be high, which indicates that in these industries, the less and the most efficient companies merge. From such mergers, high rationalizing effects can be gained due to the redistribution of the output production from the less to the more efficient firm. On the other hand, for German markets showing a higher/high concentration, one can predict that symmetric firms will merge. But in the second case, the welfare effects for the merging firms are small. Looking at the impact of the mergers on the competition in these markets, it can be said that in both cases, competition will be reduced. But this impact will be higher in markets with higher concentrations. Because in markets with higher concentrations, mergers mainly occur among larger and more efficient companies. Market-dominating positions will be achieved faster in

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such markets with higher concentration ratios. A simple example will illustrate this effect. If in a high concentrated market firm A with a market share of 20% would merge with an equally efficient firm B having a market share of 25% while the post-merger market share will be 45%. The market share of an efficient firm — in a market with low concentration ratios — would increase marginally due to its merger with a small and less efficient firm. Negative welfare effects would be higher after a merger in a higher-concentrated market than in a lowerconcentrated one because the competition-reducing effect in the first case is much higher than in the latter. 6.6 Concluding Comments It is only recently that economists have turned their attention to the question of endogenous mergers. The literature is still evolving. Theoretical models typically examine the incentives of firms to merge. As a set of firms merge, the new entity poses a challenge to other rivals in the market, which precipitates some kind of a conflict for market shares. The rivals engage in alliance formation for survival, which further induces other firms to seek alliance. The question that we pose is simple: who will merge with whom? At the empirical level, the question seeks to quantify the relevant market data that can explain “who would merge with whom.” At this level, the question that motivates researchers is plainly put as: Should we expect merging firms in more concentrated markets to be more asymmetric? Recent research has marshaled some evidence on the basis of two empirical findings: first, there is a negative correlation between the merger participants’ asymmetry and the initial market concentration ratio. Second, there is a positive correlation between the size of merging firms and initial concentration ratios. From these twin observations, one concludes that the large firms in an industry will merge to reinforce their market shares if the concentration ratio is high in the industry concerned. The German economy is a prime mover of the global economy both in terms of its per capita national income of roughly US$40,000

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and its ever-expanding FDI. Moreover, during the 1990s, the German economy faced unprecedented changes and challenges: reunification, the formation of the European Union, the increased pace of globalization, and significant sectoral shifts in German industries. All these events have led to the far-reaching changes in the industrial structure, incentives, and constraints of firms. As a result, it is expected that firms in the new juncture may have different incentives to merge. We therefore look at the question of endogenous mergers in the German industry in recent years. We are able to confirm that the large firms in a German industry have merged to reinforce their market shares if the pre-merger concentration ratio had been high in the concerned industry. Due to the prevalence of low concentration ratios in many German industries, the asymmetry between the merging partners should be high, which indicates that in these industries, the less and the most efficient companies have incentives to merge. Our results confirm this. From these mergers, high rationalizing effects can be gained due to the redistribution of production from the less to the more efficient firms. On the other hand, for German industries with high concentration ratios, one tends to expect symmetric firms to merge. Our results confirm this. Negative welfare effects would be higher after a merger in an industry with high concentration ratios than in industries with lower concentration ratios. This is so because the competition-reducing effect of mergers is significantly larger in the first case than in the latter case. Appendix A The relationship between the asymmetry index and the initial concentration can be estimated with the help of the linear regression. The correlation coefficient is calculated as (CR - 3, A) =

COV (CR - 3, A) V (CR - 3)V (A)

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with COV(CR-3,A) being the covariance of CR-3 and A n

COV (CR - 3, A) = Â (CR - 3i - CR - 3)(Ai - A) i =1 n

= Â (CR - 3i )Ai - n(CR - 3)A i =1

and V(CR-3) and V(A) being the variance of CR-3 and A n

n

i =1

i =1

V (CR - 3) = Â (CR - 3i - CR - 3)2 = Â (CR - 3i )2 - n(CR - 3)2 n

n

i =1

i =1

2

V (A) = Â (Ai - A)2 = Â Ai2 - nA . – A is the average of A with A=

1 n Â Ai n i =1

and CR - 3 is the average of CR-3 with CR - 3 =

1 n Â (CR - 3)i . n i =1

Furthermore, the following is valid: −1[ (CR − 3, A) [1. Results with −1[ (CR − 3, A) < 0 are negative correlated. Results with 0 > (CR − 3, A) µ 1 are positive correlated. Results with (CR − 3, A) = 0 are uncorrelated.

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The estimation of the asymmetry index on the initial concentration gives the regression straight line which is A-A=

COV (CR - 3, A) (CR - 3 - CR - 3). V (CR - 3)

In our case, the following results were obtained: (CR − 3, A) = −0.18, COV(CR − 3, A) = −45.60, V(CR − 3) = 1473.39, V(A) = 4.02, A = −0.001* CR −3 + 0.62, n = 40. Following the same procedures for the relation between the combined market share of the merging firms and the initial market concentration gives: (CR − 3, MS) = 0.595, COV(CR − 3, MS) = 5216.07, V(CR − 3) = 14731.39, V(MS) = 5216.14, MS = 0.143*CR − 3 + 10.126, n = 40.


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Chapter 7


7.1 Introduction Vertical markets have assumed paramount importance in the theory of international trade. The research, in this context, has focused on two related issues. First, a large number of papers explore the incentive of the integrated firm to foreclose the downstream market to limit actual competition (e.g., Jones, 1996; Bernhofen, 1996; Spencer and Jones, 1991, 1992). Vertical foreclosure therefore involves some kind of a market conflict in which a powerful player, in order to increase its market share, forces out its rivals from a market. The vertical arrangement in such markets is hardly a level-playing field. One typically wonders how to control the vertical foreclosure. Second, many papers also examine the discriminating tariff policy that can prevent such anti-competitive behavior (e.g., Spencer and Jones, 1991, 1992; Chang and Kim, 1991; Chang and Chen, 1994). In their paper, Ishikawa and Lee (1997) introduce the entry/exit of foreign firms and demonstrate that the discriminatory tariffs may turn out to be counterproductive since they may have adverse effects on the profits of the domestic firms. However, relatively little attention has been paid to the collusive behavior among the incumbent firms in vertical markets that can seriously warp competition and may cause significant deadweight losses. Our primary objective is to analyze the collusive behavior in vertical world markets.

189

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An important issue in this context is potential competition which is driven by the entry of new firms in the downstream market. The existing literature has neglected the impact of a non-integrated foreign firm’s entry into the retail market on potential competition. Our purpose is to fill this gap. We do this by analyzing the possible entry of a non-integrated foreign firm in the domestic downstream market.1 The focus of Ishikawa and Lee (1997) in their recent paper is the impact of tariffs on the entry/exit decision of a foreign firm, which is shown to lead to adverse effects of tariffs on domestic firms. On the contrary, our focus is on the impact of collusive activities of the incumbents on the entry decision of the non-integrated foreign firm under dubious information. Hence, we examine the dynamic analysis of the vertical market in international trade. We posit the global/ international market as a formation whose privileges are constantly threatened by entry. We follow Bain (1956), Sylos-Labini (1956), Milgrom and Roberts (1982), Harrington (1986, 1987), Bagwell and Ramey (1991) among others adopting the theory of limit pricing to examine the dynamics of entry and extend the analysis to vertical markets in international trade. We examine a stylized industry where an integrated home firm has monopolistic control over the supply of a key input in the upstream market and competes with non-integrated foreign firms in the downstream market. The downstream retail market is characterized by Cournot competition while the integrated home firm enjoys monopolistic power in the upstream input market. The key question for the incumbents, both home and foreign firms, is how to ward off entry in order to maintain the status quo. This is a time-honored problem in the theory of oligopoly (see Bagwell and Ramey, 1991): Bain (1956), Modigliani (1958) and Sylos-Labini (1969) advanced the notion of limit pricing which involves incumbents choosing a low price to convince a potential entrant that entry will be unprofitable. 1

There is only one paper that has examined the impact of entry/exit in vertical markets: Ishikawa and Lee (1997) examined the impact of entry/exit of an integrated foreign firm while we analyze the entry of a non-integrated foreign firm. Our focus is also different as we concentrate solely on the collusive behavior in such markets.

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The limit price signals a lower post-entry profit to the entrant. Thus, the main intuition of limit pricing is that the current price may signal the probable nature of the incumbent’s policy if entry occurs. The incumbent firm indicates its commitment/threat to maintain output consistent with the low limit price. If the threat is credible, then the potential foreign entrant is deterred by a low price and high output.2 The seminal paper of Milgrom and Roberts (1982) highlighted the likelihood that incumbent firms may control the entry decision, through prices, by influencing a potential entrant’s “perceptions of the profitability” when prices convey critical information about the exogenous determinants of post-entry profitability. The fundamental notion turns on an informational asymmetry between incumbents and potential entrants: the incumbents have a relevant piece of information which potential entrants do not possess. Matthews and Mirman (1983) examined the case where a potential entrant does not have critical information about the demand conditions. Milgrom and Roberts (1982), Salop (1979a,b) developed signaling models where prices convey information about the cost conditions. These works demonstrate the rationale behind an incumbent’s decision to set prices below the short-run profit-maximizing level in order to forestall entry.

2

These early works highlighted a commitment linkage whereby the incumbents are able to pre-commit to a higher output if entry occurs (see Bagwell and Ramey, 1991). However, such a threat by the incumbents may not be credible since the incumbents may have an incentive to deviate from the committed output once entry occurs. Friedman (1979) forcefully argued that such a commitment cannot be sustained in a perfect Nash equilibrium. However, most of the earlier studies ignored the credibility problem (see Kamien and Schwartz, 1971, 1975; Gaskins, 1971; Pyatt, 1971). Subsequently, the commitment to maintain a low price is justified in terms of an irreversible decision such as plant investment, advertising (see Flaherty, 1980; Friedman, 1979, 1983; Salop, 1979). Dixit (1980), along with Fudenberg and Tirole (1983), introduced strategic capacity choices to ensure credibility of commitment. Gilbert and Vives (1986) examined output commitment in a multiple-incumbent model. Bonanno (1987) theorized the entry-deterring power of product differentiation. Another plausible way out is to introduce imperfect information to beat the chain store paradox which has initiated a fresh lease of research (see Milgrom and Roberts, 1982).

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These models firmly establish an interdependence between preentry price and the expected post-entry profit of the potential entrant, and also spell out the rationale behind the downward distortion of price to prevent entry. The only exception is the pioneering and “provocative” works of Harrington (1986 and 1987) who postulates positively correlated cost functions of the incumbent and of the entrant in order to reverse the limit pricing result. In his works, the incumbent firm prices above the simple monopoly price, or the Nash–Cournot price, to signal high cost and, hence, low post-entry profitability. Our basic premise is similar to that of Harrington (1986, 1987) since the foreign entrant relies on the price signals to learn about the cost conditions. We extend the literature by applying the model of informational linkage to vertical international markets with multiple incumbents. We adopt a particular form of information asymmetry in this context: we assume that a foreign entrant does not know the local cost of production and expects the cost to be positively correlated with the cost of production of the incumbents. The potential foreign entrant observes the price statistic to infer about the cost of production. As a result, the incumbents have an incentive to distort the price upward in the retail market to signal high cost and, hence, low post-entry profit to the potential foreign entrant.3 We develop a model to examine the effects of this informational asymmetry in vertical markets in international trade. We establish that an equilibrium exists in which the incumbents can strategically deter entry by conveying to the potential foreign entrant that this industry is a high cost one with limited/zero post-entry profit. Our primary contribution to the literature is two-fold: first, we extend the information-based model of limit pricing to the important case of vertically related markets in international trade. Assuming a particular type of informational asymmetry, we establish that the 3

Harrington (1987) writes, “By virtue of having been a supplier in past periods, an incumbent firm generally possesses some advantages over a potential entrant. One obvious source of advantage is that an incumbent firm has first-hand experience with the production process; while a potential entrant does not....it is then reasonable to assume that an incumbent firm will hold private information on cost function” (p. 211).

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input price plays a critical role in deterring entry into vertical markets. A pre-commitment to an input price by the integrated firm acts as a commitment linkage in such markets that can effectively deter entry and, thereby, limit potential competition. We are thus able to identify the bounds on input price for which an upward price distortion will act as a collusive device to deter entry and would, thereby, limit potential competition. Second, we show that the control of input price can successfully thwart collusion among the incumbents and, hence, will promote potential competition in such markets. The plan of the chapter is as follows: in Section 7.2, we present the static model of vertical markets in which a given number of incumbents compete for shares in the downstream market. In Section 7.3, we examine the issues related to entry in the retail market. We analyze strategic entrydeterrence by upward price distortion. In Section 7.4, we establish that the strategy of upward price distortion is an optimal collusive device to deter entry. We establish that the control of the input price can effectively forestall such anti-competitive behavior of the incumbents. We conclude in Section 7.5. 7.2 A Static Model of Vertical Markets 7.2.1 An outline We postulate an industry that supplies a single final product. Each unit of it is produced by combining necessary input from the upstream industry with labor and other inputs from the competitive markets. The upstream home firm is an integrated firm which has a monopolistic control over the supply of a key input and competes with the downstream foreign firm in the market for the final product.4

4

In order to simplify the analysis, we assume that there is a single non-integrated foreign firm in the downstream market and, hence, this market is postulated to be a duopoly. The conclusions will extend to the case with a finite number of firms. We also assume that the non-integrated firm is a foreign firm. It is perfectly possible that this firm is a home firm. We maintain this assumption for stylistic reasons. What is crucial is that the potential entrant is from foreign market and, hence, confronts asymmetric information about the local conditions that determine the cost of production.

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The precise market structure in the downstream sector entails a duopoly. We postulate Cournot quantity competition in the downstream market while the integrated home firm has naturally monopolistic power in the upstream market. The downstream foreign firm is competitive in the input market as it takes the access price as a datum. The implicit assumption is that there are infinitely many foreign firms that buy the inputs from the integrated domestic firm but not all compete with this domestic monopolist in the same downstream market. Only a few foreign firms engage in quantity competition in the downstream market. Thus, one may assume that there is also a third market as in Brander and Spencer (1985). Alternatively, there is a unified world market for the final goods and at least part of the market is in the domestic economy (see Brander and Spencer, 1988, pp. 228–229). We thus make the assumption that the foreign firm takes the input price as given. Production takes place in two discrete stages: In the first stage, the key input is produced and priced by the integrated home firm by using natural monopoly technology. The second stage is potentially competitive as the integrated firm engages in Cournot quantity competition with the vertically separated foreign firms. Hence, all the foreign firms rely on the integrated home firm for the supply of the essential input. 7.2.2 The static framework We assume a highly stylized framework which is the bedrock of the modern analysis of the vertical markets and is latent in Jones (1996), and Spencer and Jones (1992, 1991). The integrated home firm faces a duopolist in the downstream (final product) market while it wields naturally monopolistic power in the upstream (input) market. During the first stage, or Stage I, the integrated home firm sells the essential input to the non-integrated foreign firm. During Stage II, both integrated home and non-integrated foreign firms will compete as Cournovian duopolists in the downstream market to sell the final product. If the information is complete in the static market, in the relevant rational expectations equilibrium, both the firms correctly

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predict the Cournot–Nash equilibrium of the second stage, or Stage II, competition and both the firms will seek to maximize their profits in Stage II given the input price of Stage I. We need the following preliminary to characterize the market equilibrium: Definition 1. The profit accruing to the integrated home firm (Πm) is given as: Πm = (A − w)qn + (P (Q ) − c − w)qm

(1)

where Q (= qm + qn) is the market output of the final product; qm is the output of the integrated firm; qn is the output of the nonintegrated firm; A is the input price; w is the cost of producing the essential input; c is the cost of producing the final good for both firms; and P (Q ) is the inverse market demand. Definition 2. The profit accruing to the non-integrated foreign firm from the downstream market: Πn = (P (Q ) − c − A)qn.

(2)

Assumption 1. We assume the inverse demand function to be linear: P (Q ) = a − bQ .

(3)

Based on the above, we derive the Cournot–Nash equilibrium of the duopoly at Stage II. 7.2.3 Cournot–Nash equilibrium of the duopoly in the static market In Stage II, the integrated home firm earns Πm1 from the sales of the final product: Π m1 = (P (Q ) − c − w)qm.

(1a)

Substituting (3) in (1a) and simplifying would yield: Πm1 = (a − c − w)qm − bqnqm − bqm2 .

(1b)

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Similarly, the profit function of the non-integrated foreign firm reduces to: Π n = (a − c − A)qn − bqmqn − bqn2 .

(2a)

Maximizing the profit function (1b) yields the reaction function of the integrated home firm which is essentially the first-order condition to maximize (1b) with respect to qm taking qn as datum. This would yield qm = [(a − c − w)/(2b) − (qn/2)].

(4a)

Similarly, from the maximization of (2a) with respect to qm, we obtain the reaction function of the non-integrated foreign firm as: qn = [(a − c − A)/(2b) − (qm/2)].

(4b)

The Cournot–Nash equilibrium of the downstream duopoly is determined by the solution to the simultaneous equation systems (4a) and (4b). Table 7.1 presents the Cournot–Nash equilibrium. (5a) and (5b) are derived from the solution to the simultaneous equation systems (4a) and (4b). And q* i labels the Cournot–Nash equilibrium output of firm i and we derive Eq. (5c) by adding (5a) and (5b). Substituting (5c) into Eq. (3), we obtain the Cournot–Nash price of the final product as given by Eq. (5d).

Table 7.1. The Cournot–Nash equilibrium of the downstream market (without entry). qn* = [(a − c − 2A + w)/(3b)] qm* = [(a − c + A − 2w)/(3b)] Q* = [(2(a − c) − (A + w)]/(3b)] P* = [(a + 2c + A + w)/(3)]

(5a) (5b) (5c) (5d)

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We substitute Eq. (5a) through (5d) into Eq. (1) to yield the maximized profit of the integrated home firm as the following: È (a - c - 2w + A) 2 (a - c + 3w) 2 2 w(a - c + w) ˘ +A Pm** = Í A ˙ ... 9b 3b 3b 3b ˙˚ ÍÎ

(6a) The profit accruing to the non-integrated foreign firm, Π n*, from the downstream duopoly is: Πn* = (P* − c − A)qn*.

(6b)

Substituting q n* by (5a) and P * by (5d) into (6b) yields: P

n*

=

(a - c + w - 2A)2 . 9b

(6c)

Equations (6a) and (6c) represent the profits of the incumbent firms in a static market characterized by fixed number of competitors, stable demand, and cost conditions. The excess profits of these incumbents attract new firms from overseas into the retail market which opens up the dynamic issues that we now turn to in Section 7.3.

7.3 The Threat of Foreign Entry and Strategic Entry Deterrence 7.3.1 Post-entry competition in the retail market We consider a stylized market in which there are two incumbent firms that engage in quantity competition in the retail market. Suppose there is a single potential foreign entrant that is deciding whether to enter this retail market or not. The market is characterized by information asymmetry: the incumbent firms have full information about the cost and demand conditions while the potential foreign entrant has sketchy information about the cost of production. The potential foreign entrant infers the cost of production from the price statistic.

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The game unwinds in a market in which the demand and cost conditions remain invariant through time. Suppose the potential foreign entrant decides to enter the retail market, then there will be three competitors in the downstream retail market engaging in quantity competition that leads to the following post-entry market configuration. Proposition 1. The post-entry Cournot–Nash outputs and price are given by : ** = (a − c + 2A − 3w)/(4b), qm qn** = (a − c − 2A + w)/(4b), qe** = (a − c − 2A + w)/4b),

(7b)

P** = (a + 3c + 2A + w)/4,

(7d)

Q** = (3a − 3c − 2A − w)/(4b).

(7e)

(7a) (7c)

where qe is the output of the foreign entrant. Proof. The derivation is exactly similar to that of Section 7.2.3. Instead of having two firms and two reaction functions, we now have three firms and three reaction functions which form the simultaneous equation system. The solution to the system gives the optimal outputs of the firms as represented by (7a), (7b), and (7c). The price follows from the demand function. Proposition 2. The post-entry profits of the three Cournot competitors are as follows : Πm** = n1 + n2A + n3A2,

(8a)

where È (a - c - 2A + w)2 3w(a - c + w) ˘ n1 = Í ˙ ,... 16b 4b ÍÎ ˙˚ (3a - 3c + 5w) 3 ,... n 3 = n2 = 4b 4b Πn** = s1 + s2A + s3A2,

(8b)

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where s1 =

(a - c - 2A + w)2 1 a -c +w ,s 2 = , s 3 = 16b 4b 4b Pe** =

(a - c - 2A + w)2 . 16b

(8c)

Proof. We get (8a) by substituting (7a), (7b), (7c), and (7d) into (1). We get (8b) by substituting (7b) and (7d) into (6b). Equation (8c) is arrived at in the same fashion as (8b). 7.3.2 Entry prevention by upward price distortion If entry occurs, then the post-entry outcome is the three firm Cournot–Nash equilibrium with complete information as outlined in Propositions 1 and 2. All information before entry is common knowledge except the cost of production in the retail market which remains private information to the incumbent firms.5 Since the incumbents have asymmetric information on the cost, their preentry outputs and the resultant market price contain information about the cost and demand parameters. As a result, the entry decision hinges critically on the pre-entry price which is derived from the Cournot competition between the incumbents (see Milgrom and Roberts, 1982). Thus, the post-entry profit of the potential foreign entrant is decreasing in the pre-entry price of the retail market. The rationale is that a high pre-entry price brings a signal to the potential foreign entrant that this is a high-cost industry that will, in turn, signal low post-entry profit. The fallout is that the incumbent firms may have an incentive to strategically distort price upward in the retail market to signal high cost and low post-entry profits (see Harrington, 1986, 1987). The rest of the section is 5

Note that while considering the entry-issues, we refer to the integrated (home) incumbent firm and the non-integrated (foreign) incumbent firm as the integrated home incumbent and the non-integrated foreign incumbent, respectively.

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devoted to the analysis of the rationale and feasibility of such price distortion in vertical markets. Theorem 1. The distorted price signal, P D, that conveys a message of high cost and low, or, zero profitability to the potential foreign entrant which will, thereby, forestall entry is given by : PD =

a - A +w . b

(9a)

Proof. Since the potential foreign entrant does not know the unit cost of production c, hence the incumbents set a price P such that the profit accruing to the entrant, Πe, is reduced to zero and, hence, the foreign entrant will stay away from the market. Thus, the foreign entrant does not enter if: Πe = 0.

(9b)

We substitute (8c) into (9b) to yield: (a - 2A + w - c* )2 = 0, 16b

(9c)

where c* is the distorted cost that will signal zero profitability in the concerned market. From (9c), we derive: c* = a − 2A + w.

(9d)

Substituting (9d) into (7d) yields the distorted price signal PD: PD = (a − A + w)/b.

(9a)

The distorted price signal PD is determined by Eq. (9a) which signals high cost c* given by Eq. (9d), that will convey low (zero) post-entry profits to the potential foreign entrant. Hence, the foreign entrant will be deterred by this price statistic, P D.

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7.4 Is Upward Price Distortion an Optimal Strategy? 7.4.1 The integrated home incumbent and upward price distortion In this section, we turn to the important question of whether the incumbent firms have an incentive to adopt the strategy of upward price distortion as laid out in Theorem 1. In order to find that, we need to compare their profits from such distortion with their profits from the no-distortion market equilibrium. The strategy of upward price distortion is optimal only when it yields higher profits to the incumbents vis-à-vis their profits from the no-distortion equilibrium. We set the stage with the following: Theorem 2. The profit, Π m***, accruing to the integrated home incumbent from the strategy of upward price distortion, is given by the following : Πm*** = m1 + m2 A + m3 A2,

(10a)

where (ab - a - w)(a - bc - (b - 1)w) , 2b 3

(10b)

(ab - a + w)(b - 1) + (a - bc - (b - 1)w) , 2b 3

(10c)

m1 =

m2 =

m3 = (b − 1)/(2b3).

(10d)

Proof. At price PD, the quantity demanded, QD, in the retail market is: QD = (a − PD)/b = (ab − a + A − w)/b2.

(11a)

Assuming the incumbents have tacit agreement about market shares, we simplify the analysis by an equal output share. Hence, their outputs and profit of the integrated home incumbent from the retail market, respectively, are: Qm*** = Qn*** = (ab − a + A − w)/b2

(11a′)

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È (ab - a + A - w) ˘ È a - (A - w) + b (A - w) - bc ˘ Pm*** = Í ˙˚ ÍÎ ˙˚ b 2b 2 Î (11b) is expanded to yield (10a).

(11b)

Definition 3. We define GM as the gains, or increase, in profit from the price distortion strategy of the integrated home incumbent, which is given by: GM = Πm*** − Πm**,

(11c)

where Πm*** is the profit accruing to the integrated home incumbent from price distortion strategy while Πm** is its profit from the no-distortion strategy which allows entry. Observation 1. The gains from price distortion, GM, can be reduced to the following: GM = h1 + h2A + h3A2,

(11d)

where h1 = (m1 − n1), h2 = (m2 − n2), h3 = (m3 − n3). We define AC: AC = (n2 − m2)/[2(m3 − n3)]

(11e)

and for A > AC, GM is an increasing function of A, and for A < AC, GM is decreasing in A. We substitute Eq. (8a) and (11b) into (11c) to yield (11d) and find: dG M > 01. dA

(12a)

2h3A + h2 > 0

(12b)

If

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or, A > AC = (n2 − m2)/[2(m3 − n3)].

(12c)6

Theorem 3. The integrated home incumbent will adopt an upward distortion of the price of the final good if the input price A is such that: A < A* 1

(13a)

A > A* 2

(13b)

or,

where A*1 =

-h 2 - h 22 - 4h 1h 3 2h 3

(13c)

and -h 2 + h 22 - 4h 1h 3 = . A* 2 2h 3

(13d)

Proof. We set GM equal to zero and from the resultant quadratic equation, we derive two roots, A*1 and A*2 . For any A, such that * A* 1 < A < A2 , GM < 0 and hence the integrated home incumbent has no incentive to distort price since the no-distortion equilibrium yields larger profits than what the upward price distortion does. On the other hand, if the input price lies outside this range, the integrated home incumbent gains from an upward distortion of the price of the final good. See that the denominator of (12c) is always positive if b > 1 and we assume n2 > m2 to get a positive critical value of A, AC. Also note that the second derivative of GM with respect to A is positive for b > 1. These restrictions give us a bell-shaped function for GM as depicted in Diagram 1. 6

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Thus, we establish that the integrated home incumbent will adopt an upward distortion of price as an optimal strategy to deter entry if the proposed conditions (13a) and/or (13b) were satisfied, and if the nonintegrated foreign incumbent were to also adopt the price distortion strategy. We now turn to the question of whether the non-integrated foreign incumbent has an incentive to distort the price upward. 7.4.2 The non-integrated foreign incumbent and upward price distortion The non-integrated foreign incumbent sells Q D/2 at a price of P D if it colludes to distort the price upward. From the quantity sold and the price, we are to determine its profit Πn*** from the strategy of price distortion. Proposition 3. The non-integrated foreign incumbent sells Q D/2 at a price of PD and, hence, its profit, Πn***, from the price distortion strategy is given by : Πn*** = t1 + t2A + t3A2,

(14a)

where (a - bc + w)(ab - a - w) , 2b 3

(14b)

a - bc + w - (b + 1)ab + a (b + 1) + w(b - 1) , 2b 3

(14c)

t1 = t1 =

t3 = −1/(2b2).

(14d)

Proof. We know that the profit accruing to the non-integrated foreign incumbent from price distortion is: Πn*** = (PD − c − A)QD/2.

(14e)

Substituting PD by Eq. (9a) and QD by Eq. (11a), we arrive at (14a).

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Definition 4: The gains from the price distortion strategy for the non-integrated foreign incumbent, GN, are defined as: GN = Πn*** − Πn**.

(15a)

Observation 2. Substituting Πn*** by (14a) and Πn** by (8b) yields the following: GN = H1 + H2A + H3A2,

(15b)

where H1 = (t1 − s1), H2 = (t2 − s2), H3 = (t3 − s3). Theorem 4. The non-integrated foreign incumbent will adopt an upward distortion of the retail price to forestall entry if the following conditions were satisfied: A > A** 1

(16a)

A < A**, 2

(16b)

or,

where A** 1 = and A** 2 =

-H 2 - H 22 - 4H 1H 3 4H 3

(16c)

-H 2 + H 22 - 4H 1H 2 . 4H 3

(16d)

Proof. The non-integrated foreign incumbent is indifferent between price distortion and the non-price distortion strategy, if GN is zero. That is: H1 + H2A + H3A2 = 0.

(16e)

Thus, there are two roots of the quadratic Eq. (16e) for which the non-integrated foreign incumbent is indifferent between two

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alternative strategies. The roots are given by (16c) and (16d). Since H3 < 0 and H2 > 0, hence GN > 0 for (16a) and (16b) since the first derivative of GN is positive until a critical value of A, ACC, such that ACC = [−H2/(H3)]. Now we combine GN and GM in the above diagram to consider the possibility of whether both the incumbents will collude to deter entry by the strategic distortion of the price of the final good. From the above, it is evident that the crucial determinant of such a collu* sion is the value of the input price. If the input price lies {A** 2 , A1 } * ** and/or {A2 , A1 }, then the upward distortion of the price yields a larger profit for each incumbent than its profit from the no-distortion strategy. Thus, we come to the following: Statement 1. The upward price distortion strategy is chosen by the colluding incumbents to deter foreign entry and the potential foreign entrant decides not to enter the retail market, if one of the following conditions holds: ** A* 1 − A2 > 0, * A** 1 − A2 > 0.

(17a) (17b)

* and the actual input price lies within the bounds {A** 2 , A1 }, or {A2*, A** 1 }. Statement 2: The collusion to strategically deter entry fails if one of the condition holds: ** A* 1 − A2 < 0, * A** 1 − A2 < 0.

(17c) (17d)

Statement 3. It is important to note that such an anti-competitive strategy inflicts a cost on the consumers as they pay a high price for the final product. They not only pay a high price due to limited actual competition, but also due to upward price distortion which does not conform with the cost of production.

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Statement 4. Can the regulatory authority control such anticompetitive behavior to limit potential competition?7 From the finding, one can see that the regulatory authority can break such a collusion by simple price capping. If the maximum input price is set below A** 2 , then the collusion collapses since the non-integrated foreign firm has no incentive to adopt the price distortion strategy. Thus, by strictly regulating the input price, the regulatory authority can forestall such entry-deterring and anti-competitive price distortion. 7.4.3 Trigger strategy equilibrium From sub-section 7.4.2, we have learned that incumbents have an incentive to collude by adopting the upward price distortion strategy to deter foreign entry. Under a set of conditions, such a collusive strategy is also shown to be successful in deterring entry. However, collusion gives rise to the familiar problem that each incumbent has an incentive to defect, when its rival abides by the collusive agreement. As is usual in the supergame theory, we assume that incumbents deter defection from the collusive agreement by employing the trigger strategy to punish defection: incumbents abide by the collusive agreement unless one firm cheats. If an incumbent cheats, they revert to the non-cooperative Cournot–Nash equilibrium for once. We now explore the possibility that an infinite repetition of a profile ***, and qn***, which makes the incumbents better off than of PD, qm defection in terms of their respective profit functions, can be sustained as a subgame perfect equilibrium by means of a trigger strategy with a one-shot Nash reversion (see Tirole, 1988). As long as both incumbents stay in equilibrium, profits are Πm***, Πn***. The integrated home incumbent chooses to stay on 7

We shelve the question of why the regulatory (domestic) authority will intend to enhance domestic competition by allowing foreign firms. Instead we suppose that the regulatory authority seeks to foster competition. If so, our question is what should they do to control such anti-competitive activities of the incumbents.

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the equilibrium path if and only if the following incentive compatibility no-defection constraint were satisfied: ’m (DF ) - ’m***
[Πm (DF) − Πm***]/GM.

(18e)

Inequality (18b) is satisfied so long as

δ > [Πn (DF) − Πn****]/GN.

(18f )

We define δ m* and δ n* as the following:

δ m* = [Πm (DF) − Πm***]/GM,

(19a)

δ n* = [Πn (DF) − Πn***]/GN.

(19b)

It is important to note that (18a) and (18b) will hold so long as δ > δ m* and δ > δ n*. We complete the proof by deriving Πm (DF) and Πn (DF), and substituting the relevant values in (19a) and (19b). Derivation of Π m(DF) The non-integrated incumbent sticks to the collusive agreement and produces output given by Eq. (11a′). Substituting (11a′) in the reaction function of integrated incumbent, (4a), we get the optimal defection output of the integrated firm, Qm (DF), Qm (DF) = (a − c − w)/(2b) − (ab − a + A − w)/(4b2).

(19c)

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The resultant price, P m (DF), when the integrated firm defects is Ê a - c - w ab - a + A - w ab - a + A - w ˆ P m (DF ) = a - Á + ˜¯ . (19d) Ë 2 4b 2b We substitute (11a′), (19c), and (19d) into Eq. (1) to get Πm (DF) as: Πm (DF) = [a − (a − c − w)/2 + (ab − a + A − w)/(4b) + (ab − a + A − w)/(2b) − c − A][(a − c − w)/(2b) − (ab − a + A − w)/(4b2)].

(20a)

Substituting (20a) into (19a) yields (18c). Following similar steps, we derive (18d).


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Section B

Rivalry, Conflict and Cooperation: Goliath against Goliath


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Chapter 8


8.1 Introduction In the 1990s, there has been a perceptible increase of academic interest in the institutional structure of the monetary system. It has, however, been a gradual development. In the 1950s and the 1960s, the dominant theme turned on the Keynesian principle of “managed money.” The collapse of the Breton Woods system in the 1970s paved the way for adopting flexible exchange rates and monetary targeting as the order of the day. The 1980s and the first half of the 1990s witnessed a series of passionate debates over central bank independence. An important view has emerged that such independence is desirable for developed nations. The arguments in favor of central bank independence pivot on four major issues: first, the inflationary experience of most G-7 countries in the 1960s and 1970s continually deteriorated. In the United States, the average inflation rate rose from 2.8% to 9.9% between 1960 and 1980. Similar hikes in inflation rates were observed in the United Kingdom, France, Italy, Canada and Australia. Despite serious challenges, the issue has been settled in favor of the monetarist position that an excessive growth of monetary aggregates was the major source of the inflationary experience. Second, the available evidence suggests an inverse longer-term relationship between inflation and growth rates. There has been a series of attempts to run the causality from high inflation to lower rates of growth, albeit the theory and 215

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evidence both share some inescapable holes. Combining the above two arguments, one may naturally champion the monetarist advice for tighter monetary control. The tricky question is why we cannot leave tighter control to the discretion of the central bank! A tentative answer is given on the basis of the following twin arguments that form the remaining two issues. The third issue revolves around the argument that the discretionary monetary policy carries an inflationary bias since unanticipated inflation hinges critically on the revenue needs of the government. This argument of dynamic inconsistency, therefore, stresses the inability of the central bank to credibly commit to a low rate of inflation. And finally, a number of recent studies reveal a significant negative relationship between the average rate of inflation and central bank independence. As a result, a view has been gathering momentum to grant independence to central banks in order to achieve price stability. If price stability is desirable, then central bank independence is naturally a “desirable policy goal.” Therefore, if the fundamental tenet is that central bank independence is a desirable policy goal, then the obvious key point is how to implement the policy. In the Australian context, the work of Hendy and Evans (1995) posits the analysis exactly here: “The paper starts from the premise that Reserve Bank independence is a desirable policy goal. This article, therefore, is more about successful policy implementation” (p. 50).

The purpose of this chapter is two-fold. First, we would outline the pitfalls of the above set of arguments and put forward a number of reasons that may challenge the notion that central bank independence is a desirable policy goal. Second, the implicit foundation of this recommended independence, or actual independence as in Australia, Canada, Germany, New Zealand and the UK is based on the muchcelebrated contracting models involving government and central bank. Under a set of restrictions, such models show that central bank independence enables the society to reach the first best solution by eradicating the inflationary bias arising out of dynamic inconsistency.

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This is indeed a possibility under a set of strong, undue and imaginary restrictions. In a more realistic scenario, this chapter would argue that such independence may not only fail to deliver the much needed price stability, but may also impose serious costs on the society. As a consequence, it becomes a moot point whether central bank independence is a desirable policy or not. In articulating this possibility, we will draw heavily from the US experience during the last two decades. The chapter may therefore explain why the custodians of the monetary management in Australia fear to tread in such a treacherous area. As Hendy and Evans (1995) write, “Nevertheless, Mr Fraser, while supporting the need for independence, parts company with many others in his publicly stated belief that the degree of independence currently practised by the Reserve Bank is satisfactory” (p. 58).

The crux of the matter is that central bank independence is a mixed bag and one must carefully balance the costs and benefits before making a final decision. More importantly, this chapter also argues why an attempt to grant independence to central banks may meander into pseudo-independence that may impose significant costs on society. 8.2 Evolution of Central Banking In 1668, the world’s first central bank, the Riksbank, was instituted in Sweden. However, the formation of the Bank of England in 1694 marked the emergence of a new era that saw the need for a state bank in the contemporary economic and social milieu. The driving force behind the bank was the Anglo-French war that necessitated the raising of money by the government of William and Mary. Merchants of London who were called upon raised 1.2 m pounds and a royal charter was quickly granted. By the royal charter, the Bank of England became a monopoly since it was the only joint stock bank allowed. In the 18th century, the Bank was regularly raising money on behalf of the government by selling government bonds. It was

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gradually felt that other joint stock banks could help the ever-expanding business activities. In 1826, the Banking Act allowed for other banks that not only increased the number of banks, but also led to occasional spurts of bank runs. In 1844, a new act gave the Bank a virtual monopoly on the note issue. The Bank was nationalized in 1946, and banking legislations confirmed and re-confirmed its fiduciary power in 1979 and 1987. Events during the First World War and the Second World War showed that the Bank was an arm of the government and not independent! All that changed in 1998 when the Bank was made independent, run by a body called the “Court”, headed by a Governor, two Deputy Governors, and 16 non-executive directors. The mandate of the Bank was to maintain price stability. In 1800, Napoleon set up the Bank of France to control the quality of bank notes and bank runs during the difficult years of the French Revolution. It was a joint stock company with Napoleon as a major shareholder. A total of 1,848 witnessed the event as the Bank of France became nationalized in 1945 and was granted the power to issue bank notes. In 1973, its power and organization were revamped. In 1993, the Bank was given independence. Japan chose the Bank of England as the ideal model and set up its own central bank in 1885. In 1889, the Japanese central bank became the sole issuer of notes. Technically, the bank was granted independence from the government in 1998. The German Bundesbank (called the Reichsbank) was founded in 1876 and remained a private bank until 1920. Due to the hyperinflation problems of 1920s, the Banking Act of 1924 made the bank independent of the government. The Nazi era took full control of the Bundesbank. A two-tier system was introduced after the conclusion of the Second World War and further refined in 1957. In 1992, after the reunification, the Bundesbank was made independent of government instructions (though a close association has been maintained). The story is far more complicated for the US. The art of central banking posed a serious challenge to the US. In 1789, the Treasury was entrusted with the management of the US currency. In 1791, the Bank of the United States was formed to issue the dollar bill and control public debt. The Bank of the United States faced stiff opposition from member states and failed to get the bank’s charter renewed in

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1811. It was started again in 1816, leading to severe competition with state banks. As a result, in 1841, the Bank of United States went bankrupt. The Act of 1863 introduced a two-tier system — the federal banks (national banks) and state banks came into being. By 1880, there were about 2,000 National banks that were all issuing bank notes. It created enormous problems in ensuring the quality of notes and in avoiding bank runs. As a result, the Federal Reserve System was formed in 1913 with a single central bank controlling note issue and operating it through 12 Federal Reserve Districts. The Chairman and the Board of Governors of the Federal Reserve are appointed by the President of the USA. The Federal Reserve is not officially given any independence. There is a great cleavage between the institutional structure of the US central bank and that of other developed nations. Many developed nations chose to grant independence to their central banks through formal legislation while the Federal Reserve seems to act as an arm of the US government. The move to independent central banks in the 1990s can be best understood by looking at the direct effects of the high interest rate policy in OECD nations. Table 8.1 shows the overall budget balance as a percentage of GDP in 1992 when all countries except Japan had significant deficits. All countries, except Japan, had significant deficits and government interest payments were as high as 14% of the GDP in Greece. Table 8.1.

Government deficits and primary balances in 1992 (percentage of GDP).

Country

Budget balance

Interest payments

Primary balance

USA Japan Canada Germany France Italy UK Spain Greece

−4.7 1.3 −5.8 −3.2 −2.8 −11.1 −6.6 −4.7 −13.2

2.2 0.4 5.5 2.6 2.6 10.9 2.1 3.3 13.6

−2.5 1.7 −0.3 −0.6 −0.2 −0.2 −4.5 −1.4 0.4

Source: UNCTAD, Trade and Development Report, 1993, p. 75.

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The third column shows that most countries would have almost achieved a balanced budget once the interest payments were taken out. The problem of budget deficits in most advanced countries came to be viewed as partly due to high interest payments owing to high interest rates, which were due to the poor monetary policy over and above the lack of fiscal discipline. The cocktail of these twin irresponsibilities (fiscal and monetary) led to interest payments of between 5% and 10% of their GDP for OECD nations. With a high debt–GDP ratio (between 60% and 100%) and growth rates between 3% and 6%, the public debt in the developed world became unsustainable. The only way governments in the developed world could maintain constant debt ratios and come close to balancing budgets was if the monetary policy could accommodate public debts by lowering interest rates. It was strongly felt that the central banks could lower interest rates if they could control inflation rate. To control the inflation rate, central bank independence was felt to be necessary. This led to a significant herding in the developed world when governments gave independence to central banks to combat inflation. In the next section, we look at the obvious pitfalls. 8.3 Inescapable Pitfalls There are three crucial points that form the basis of an argument in favor of central bank independence. We take one issue at a time and examine its tenability in light of current evidence and existing theories. 8.3.1 Inflationary bias and the conflict between rules and discretion The principal hypothesis in this context is that monetary policy is one component of the government revenue-raising process. Under this hypothesis, often labeled as the optimal seigniorage hypothesis, the government has three sources for raising revenues: (a) levying taxes, (b) issuing bonds, and (c) printing money. The government utilizes these three sources in such a way as to minimize the deadweight losses

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associated with taxes and the inflation, subject to pre-determined budget constraints (see Mankiw, 1987; Poterba and Rotemberg, 1990; Trehan and Walsh, 1990). The upshot is that inflation is a tax that is not very explicit to the public and, hence, a government can succumb to the temptation of overusing it. On top of that, the natural rate models suggest that a surprise inflation could reduce unemployment. Hence, if the public anticipates x % inflation, then the government gains by creating an inflation in excess of x %. This excess not only brings extra revenue to the exchequer, but also reduces unemployment. Therefore, there appears to be a large marginal benefit that the government derives from surprise inflation. Kydland and Prescott (1977), and Barro and Gordon (1983) argue that an equilibrium rate of inflation is produced such that at that high rate of (surprise) inflation, the marginal benefit from seigniorage and the reduction in employment are equal to the marginal cost of surprise inflation. In a world with complete information, the public fully anticipates this inflation which prevents unemployment from falling below the natural rate. The economy is characterized by a Pareto-dominated Nash equilibrium of an inflation blow-out. Cuckierman (1992) listed two more factors behind inflationary bias: namely, interest rate smoothing and the balance of payments motive. There are two separate arguments in favor of central bank independence to reduce inflationary bias. First, central bank independence is argued to separate fiscal motive from monetary policy. Hence the removal of inflation tax would lead to a decline in the inflation rate (see Debelle, 1994a; Debelle and Fischer, 1994). But the problem with this argument is that the proposal may appear to be a bit dated. The seigniorage motive may have been quite strong in the 1960s and 1970s; but in the 1990s, there was very little reason, or evidence, to support the significance of the fiscal motive (see Froyen and Waud, 1995). Moreover, it is extremely difficult to empirically isolate the seigniorage motive from the hypothesis of interest rate smoothing (see Barro, 1989). Hence, it is at best a moot point that central bank independence would reduce the inflationary bias. Second, in order to reduce inflationary bias, central bank independence is sought to bypass the dynamic inconsistency problem. There

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are two distinct views: First, one strand of thought argues for independence with strict monetary feedback rules so that the independent central bank has no power to pursue active policy (see Friedman, 1959; McCallum, 1994). But this may engender the possibility that the central bank is tied down to an inappropriate and outdated monetary rule (see Sayers, 1958, p. 7). The heart of the problem is the recently observed instability in the money demand function that renders the rule inappropriate. One must hence balance the cost associated with a discretionary monetary policy vis-à-vis the cost of pursuing an inappropriate monetary rule. The second strand, however, allows for an activist monetary policy to stabilize the real economy. To reduce the inflationary bias, Rogoff (1985), and Lohmann (1992) propose that the principal (society) must appoint a conservative central banker with a very high degree of inflation aversion. The practical problem with these games is the well-known problem of preference revelation. The central banker, being driven by tactical considerations, may distort his actual preferences (see Gangopadhyay, 1994). The argument is similar to the one proposed by Crawford and Varian (1979) to analyze the effect of distortion of utilities on the solutions to the bargaining game. The dominant strategy of the potential bankers would be to report the least possible aversion to inflation that leads to a random appointment. As a result, the society may fail squarely to appoint a conservative central banker. The lesson is that independence may not solve the problem of discretionary policy. More importantly, the problem of discretionary policy appears to be quite flimsy in the real world where the central bank cares about its long-run reputation (see Backus and Driffil, 1985; Gangopadhyay, 1999; Gangopadhyay and Varoufakis, 2000). There is, hence, no propelling reason to establish an independent central bank just to redress the problem of dynamic inconsistency. 8.3.2 The trade-off between inflation and growth In the 1990s, there emerged a strong theoretical conviction and an empirical corroboration that inflation and growth bear a negative

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long-run relation. The theoretical models turn on the intuition that inflation warps price signals and thereby adversely impinges on the ability of agents to plan intertemporal decisions. The increased uncertainty along with a reduced ability of private agents to plan mesh in with the malfunctioning price signals to lower economic growth (see Howitt, 1990; Aghion and Howitt, 1992, 1994; Gangopadhyay, 1997). A cross-country and time series analysis established the negative relation between inflation and growth over the 1951–1992 period (see Smyth, 1994; Smyth and Schalivy, 1994, Fischer, 1993). It has been further empirically observed that capital accumulation and productivity growth have demonstrated significant negative relations to inflation. The proponents of central bank independence hastily juxtapose the theoretical models and empirical evidence to assume that an increase in inflation results in lower economic growth. The obvious policy implication is to establish an independent central bank to reduce inflation and thereby pave the way for higher economic growth. But there is a faux pas in the argument. Despite such a statistically strong inverse relation between inflation and growth, there is absolutely no confirmation that there exists a causal relationship running from inflation to lower growth (see Fischer, 1993). In fact, Rudebusch and Wilcox (1994), in their attempt to ascertain the nature of causality, found empirical support that inflation causes productivity growth. They further demonstrated that the statistical relationship between inflation and growth turns out to be insignificant if one makes an adjustment for the cyclical element in the aforementioned relationship. There is a strong belief that such a negative relationship may have been triggered by the endemic supply shocks which reduced growth and increased inflation (see Fischer, 1993). The bottom line is that there is neither any robust model nor any empirical evidence to argue that high inflation resulted in lower growth between 1951 and 1992 (see Gangopadhyay, 1996, for further details). Therefore, it may be quite incorrect to blame the status of the central bank as the source of the poor economic performance of the G-7 countries during the last 40 years.

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8.3.3 On the presumed inverse relationship between central bank independence and inflation The empirical evidence for the inverse relationship between central bank independence and inflation rate is a bit muddy to draw any definitive conclusion. Debelle and Fischer (1994) derived a significant negative relationship for the industrialized nations. But in Cuckierman (1992), with an expanded data set, the relationship turns out to be rather positive. It is far from clear whether granting independence to the central bank would definitely result in decreased inflation or not. Hence one may be persuaded to think that the question of central bank independence as a desirable policy goal is still unsettled. Any serious discussion on central bank independence must marshal sufficient support to demonstrate the tenability of the assumption that such independence is irrefutably a desirable goal. In the rest of the chapter, we will attempt to establish a significant cost that may emerge from independence. 8.4 Optimal Contract and Independence In the 1990s, a handful of models constructively argued the efficacy of a well-designed and explicit contract between the society and the central bank such that the central bank adopts monetary policies in order to pursue the public interest (see Walsh, 1993; Persson and Tabellini, 1993). Such a contract embodies a set of policy goals and a set of incentive schemes to induce the central bank to act in the public interest. In case the central bank fails to act in the public interest, the notion of accountability requires that the central bank faces adverse consequences. In an optimal contract, the central bank and the society share mutuality of interests and hence the central bank implements policy goals just to pursue its own interests. This is so since a failure would bring adverse consequences. Two distinct types of models have evolved in this context: The first posits that the central bank has limited control in setting up the goals as the central bank has to negotiate with the government to agree on a target. The second

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type allows the central bank almost full autonomy in deciding the targets. These models further empower the central bank to pursue discretionary monetary policy to achieve the targets. Under a set of restrictions, it has been demonstrated that the central bank would achieve the first best solution. In recent years, a number of countries have adopted the contracting model to hammer out an optimal monetary policy. In New Zealand and in Canada, the central banks have to negotiate with the government to set targets for monetary variables. In France and in Germany, the central banks have the discretion to decide the targets. All these banks, however, enjoy the discretion to adopt the policies in achieving the targets. What is crucial is the observation that the central goal of monetary policy in these four nations is price stability. There are two polar opinions that have evolved in this context. First, Hendy and Evans (1995) proposed a rewriting of the Reserve Bank Act 1959 in Australia by deleting all other objectives except price stability. The “prime objective” of monetary policy would, therefore, be to achieve price stability, however defined. There are some perceived gains from such a policy rule: monetary policy would be more consistent due to an absence of conflicting objectives, stricter enforcement of accountability and lower inflationary expectations would be achieved (see Fraser, 1991). This view is similar in spirit to the monetary rules as proposed by Friedman (1959). The common thread is that monetary management, without a well-articulated guiding rule, would inevitably meander into excess activism and thereby destabilize the otherwise stable economy. I have already discussed some of the weaknesses associated with such a view while analyzing the problems arising from dynamic inconsistency. The major difficulties with this view are the following: First, in order to alleviate the inflationary bias of discretionary monetary policy, one must either bind the central bank to a policy rule, or tie the central bank down to a pre-planned price level targeting, albeit with some flexibility. The critical problem arises from the tyranny of the status quo. That is, the central bank is bound to follow inappropriate goals or rules since the underlying economic forces are rarely static. There are a few interesting theoretical developments to side-step

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such a problem (see Rogoff, 1985). Yet the practical implementation of the models has limitations. The upshot is that such a rewriting of the Reserve Bank Charter may entail a cost due to the tyranny of the status quo; yet there has been no attempt to address the cost (see Fischer, 1994, p. 289). Second, at the theoretical level, Barro and Gordon (1983) persuasively argued for the need for an active monetary policy in the short run even when the central bank is bound by monetary rules. This is due to the irrefutable fact that monetary policy is a “balancing factor” in bridging the gap between macro-objectives and the formulation of other policies. This derives from the stark reality that both fiscal policy and wage-income policies lack short-term flexibility. Hence the burden of adjustment falls on the monetary policy if the economy suffers from instabilities. As M.J. Phillips (1991), the ex-Deputy Governor of Reserve Bank of Australia, articulated, “So, the only area of macro-economic policy where flexibility is practicable (as distinct from appropriate) is monetary policy. The Reserve Bank Board meets regularly; the Bank operates in financial markets on a daily basis; interest rate shifts can be initiated (within limits) at virtually any time” (p. 424).

As a result, it may not be pragmatic to throw away the flexibility of the activist role of the monetary policy, even though such flexibility imposes a cost on the society. Third, such price level targeting would create two powerful enclaves whose interests are mutually conflicting: namely, the government with an inflationary bias and the central bank with a deflationary bias. It may be quite possible that their mutually counter-balancing forces on price stability would engender a desirable policy outcome. Yet the possibility looms large that a conflict of interests may result in a costly distortion in the short-run management of the economy (see Fischer, 1994, p. 293). This is so since the self-seeking motive of the central bank, in such an institutional set-up, would prompt them not to adopt countercyclical monetary policy, especially during a downturn. These problems with price level targeting pave the way for a more mature view that allows an independent central bank to pursue a

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broader and more flexible set of goals. According to the second view a central bank is entrusted with the mandate of price stability, but no numerical targets. This gives the central bank a better position to pursue both price stability and the much trusted role of monetary policy as a critical balancing element of the national economic strategy. This approach has been adopted in Germany and France. In Canada and New Zealand, some degree of flexibility has also been ingrained by providing an explicit formula for the adjustment of the inflation target for coping with supply shocks and fiscal changes. But in Canada and New Zealand, the dominant idea is that the primary objective of the monetary policy is price stability and the monetary policy is relied on to provide an optimal and dynamically consistent inflation rate, albeit with some scope for adjustment if there were to emerge supply, or fiscal, shocks. The underlying theme has been the age-old currency/ monetarist position which assumes the fundamentals of the economy to be stable while monetary activism, excessive or otherwise, would destabilize the economy. This is indeed a moot point and the profession has witnessed two great debates on this issue. In the first half of the 19th century, the Banking School and the Currency School fervently debated the desirability and the mechanism to achieve currency stability. Between 1960 and the early 1980s, the Monetarists and the Keynesians ardently debated the causes and the cures of inflation. The Monetarist School highlights the monetary causes of inflation and advocates a strict monetary rule to achieve currency stability (à la Friedman, 1959). On the contrary, the Keynesians raised the importance of the non-monetary supply shocks as the major forces behind inflation. Despite a great deal of work, these issues have not been settled in favor of any particular school. A pragmatic compromise has been reached by agreeing on the fundamental differences between the two schools: the Monetarists assume a stable real sector while the Keynesians postulate an intrinsically unstable real sector. And the dichotomy between the short run and long run apparently reconciled the conflicting positions of these two schools (see Howitt, 1994, p. 764). The upshot is that it is highly controversial whether price stability ought to be the sole objective of monetary management. In particular, in the Australian context, the

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custodians of the monetary management persuasively articulated the “practicability” of an activist monetary policy as the “balancing element” in the national economic strategy. In both Germany and France, the central banks have been accorded some leeway to participate in the management of the economy as the policy goals of the central banks are not precise. Therefore, in spite of the fact that monetary activism may be costly and inappropriate, the realism demands some short-run “fine tuning.” Hence, one must address the desirability of central bank independence and its ramifications in a more general framework in which the central bank pursues a number of policy goals. Otherwise, the discussions would remain incomplete. The work of Hendy and Evans (1995) has just initiated the problem by assuming a scenario in which the central bank pursues the sole objective of price stability. My arguments not only unravel some of the weaknesses in the arguments of Hendy and Evans (1995), but also set the problem in the right perspective in which the central bank is willy-nilly locked in a number of policy goals. 8.5 Activism Price Stability and Accountability The point of departure is that the primary objectives of monetary policy encompass both price stability and better economic performance. The activist stance is that the central banks react to inflation and the growth of national income. Phillips, the ex-Deputy Governor of RBA, puts it succinctly: “The end objective of monetary policy has not varied of course. Basically, it remains non-inflationary sustainable growth” (1989, p. 315).

In this light, it could be argued that central bank independence may be accompanied by a lack of accountability. This lack of accountability would further be shown to have a far-reaching consequence on the conduct of monetary management. The train of logic subsumes the following: the esoteric nature of central banking derives from two sources. First, if central banks pursue countercyclical policies to

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stabilize income and employment, then a typical central bank would undertake a series of actions that hinge on the anticipation of the central banks. As a result, some of these actions may not be rational post hoc since the ex ante information is not available at the outset. Due to a lack of precision of the information, monetary management turns a great deal on the “educated guess” of the management of the central bank. This element of “educated guess” adds to the esoteric nature of central banking. Second, the monetary policy is typically shrouded in secrecy, ambiguity, and mystery which result in an esoteric art of central banking as persuasively argued by Brunner (1981): “The possession of wisdom, perception and relevant knowledge is naturally attributed to the management of Central Banks. The relevant knowledge seems automatically obtained with appointment and could only be manifested to holders of the appropriate position. The mystique thrives on a pervasive impression that Central Banking is an esoteric art. Access to this art and its proper execution is confined to the initiated elite. The esoteric nature of the art is moreover revealed by an inherent impossibility to articulate its insights in explicit and intelligible words and sentences. Communication with the uninitiated breaks down” (p. 5).

The immediate spin-off is that central bank accountability becomes a slippery issue. This is so mainly for three sets of reasons. First, due to the nature of anticipatory actions, the central bank can hide behind their “honest mistakes.” Second, the necessity of secrecy would require the non-disclosure of certain information which would make accountability to the public quite difficult. Third, a lack of precise information and the “difficult-to-follow technical nature of reports” would render accountability a difficult task. Consequently, central bank independence without accountability may have a significant deleterious effect on the management of monetary variables. 8.5.1 Activism and anticipatory monetary policy The principal actions taken by the central banks attempt to impinge on money and credit markets in order to control domestic demand

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and inflation at desirable levels. In an economy with deregulated financial markets, as in Australia, the central bank achieves the goals by judicious trading in securities. The purchase, or sales of securities acts through changes in interest rates which have a direct bearing on domestic demand, domestic price level, and external balances. The central bank also closely monitors the foreign exchange market to ensure greater stability in the market. A critical role is the “prudential” supervision of banks in the deregulated environment so that banks achieve a desirable mix of risks and returns. The other dominant interest of the central bank in the financial markets is to keep a close watch on the “bigger players” and to act to promote overall financial stability. Australia is critically integrated with the global financial market and, hence, changes in the international markets have a significant impact on the Australian financial markets. Therefore, many of the challenges that the RBA faces cannot be foreseen. More importantly, monetary policy has its usual lags before it becomes effective. Therefore, the conventional wisdom is that “forewarned is forearmed.” This feeling lays down the founding stone of anticipatory monetary policy. As Phillips aptly summarized the situation: “The medicos tell us that most sun cancers acquired in middle age are the result of exposure to the sun during one’s youth. In other words the lag between cause and effect can be very long. The economy is a bit like that... Policy decisions must be taken, not on the basis of conditions here and now, but on the basis of forecasts and informed guesses about how conditions will be six or twelve months down the track, or even further ahead” (1991, p. 424).

The art of central banking not only relies on sketchy information, but also hinges on “educated guesses” in a scenario in which the policy suffers from a significant lag to produce the desired effects. This makes it difficult to arrive at cut-and-dried optimal actions. The central bank

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also confronts a significant challenge about the timing of its actions. Phillips drove this point home: “Possibly the most often quoted definition of a central bank’s purpose in life is to take away the punch-bowl just as the party is getting started... Of course, closing the bar early with a group of thirsty revellers lined up is not calculated to be popular” (1991, p. 426).

The upshot is that the act of central banking involves difficult decisions characterized by a timing problem which forces the bank to be forward looking in order to achieve better management. To quote Phillips yet again: “Monetary policy makes its best contribution to society when it looks ahead and focuses on prevention rather than when it looks back and searches for cure. That is what medium term means” (1991, p. 426).

It is obvious that the central bank must have a medium-term focus in terms of price and demand stability. The crucial balancing act of the central bank is how to reconcile the short-run policies with the medium-run objective of low and stable inflation (see Phillips, 1990, p. 353). The knotty problem is two-fold: First, the short-run and long-run dichotomy may not be feasible as the short-run and longrun problems may be critically enmeshed. For example, suppose there is a severe supply shock which leads to a recession in the short run. The short-run monetary policy leans against the wind by focusing on boosting demand which may be argued to stand in contrast to the medium-term objective of price stability. Even when the short-run management is very conservative, the medium-term goal of price stability may not be attained due to the nature of the problem. There are, therefore, reasons to believe that such a compromise between the short run and longer run may not be feasible (see Howitt, 1994).

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Second, both short- and medium-term policies are based on sketchy information about future variables. Therefore, the central bank management may make honest forecast errors and thereby fail to achieve the short-run, or medium-run, targets. As a result, policy failures cannot easily be reduced to the dynamic inconsistency. This constitutes a serious blow to accountability as it is difficult to pin down the precise causes of policy failures. 8.5.2 The rationale for a dose of secrecy in central banking In the US, there is a deep-rooted conviction that the central bank, that is, the Federal Reserve, has a penchant for secrecy about its precise goals and actions (see US Congress, 1983; Petzinger, 1983). At the theoretical level, Barro (1976, pp. 21–25), Backus and Driffil (1985), Barro (1986) and Cuckierman and Meltzer (1986) rationalized the observed secrecy as a fallout of the value of private information that allows the central bank to enjoy an output benefit from surprise inflation. The classic example is the legal proceedings of D.R. Merrill vs. Federal Open Market Committee in 1975 (see Federal Reserve Annual Report, 1975). In the US Supreme Court, the Committee was asked to defend its deferment and concealment of information, and the Committee provided six reasons for practicing secrecy. On the basis of the available evidence, the US Supreme Court allowed secrecy on the grounds that the immediate release of information “would significantly harm the Government’s monetary functions or commercial interests” (Federal Reserve Regulatory Service, Volume III). Otherwise, the Court upheld that the Federal Reserve must practice immediate disclosure of information. The crucial reasons that the Federal Reserve garnered are the following: (a) prompt disclosure may adversely affect the orderly execution of its statutory functions; (b) the disclosure may result in unfair advantages by speculative trading in securities; (c) the disclosure would destabilize the securities market; (d) the disclosure would make open market operations costly;

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(e) the disclosure would interfere with the macroeconomic management of the economy; (f) the disclosure would reduce the effectiveness of financial transactions with foreign bankers with significant adverse impact. The non-disclosure of information is argued to reduce the operating costs of open market operations. There are two acceptable tenets behind this argument. First, disclosure is argued to increase the fluctuations in short-run interest rates and hence increase the risks borne by the distributing dealers. As a result, the borrowing cost of the Treasury goes up with disclosure. The logic therefore is to conceal relevant information to prevent a drain on the resources of the Treasury. Second, non-disclosure is said to reduce the competition with Account Managers in the market and, therefore, relevant secrecy reduces the cost of open market operations. A second important accepted rationale for secrecy is the argument that disclosure would increase the abrupt changes in interest rates. As a result, the concealment of information is said to prevent swings in short-run interest rates. Hence, a disclosure of information is not considered warranted if it makes interest-rate smoothing more difficult. The upshot is that the act of central banking entails a host of esoteric elements. Due to the anticipatory factors behind monetary management, it is almost impossible to have full accountability. The problem is further complicated by the appropriate dose of secrecy that central banks adopt for the smooth functioning of monetary policy and for furthering the commercial interests of the government. The veil of secrecy would make it difficult to ascertain the precise goals and the efficacy of the monetary policies. The lack of precise information, the technical nature of revealed information and the possibility of human errors mean that the accountability of the central bank to the public is quite minimal. Therefore, the crucial issue is to understand the ramifications of central bank independence with almost no accountability.

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8.6 Independence Without Accountability: The Road to Conflicts and Central Bank “Bashing” The relevant framework comprises two powerful enclaves in the national economy, namely the government and the independent central bank. The central bank leans against the wind by responding to inflation and output growth, and also provides leadership to the financial community. One may conveniently reduce these twin objectives to the following: First, the central bank attempts to improve the performance of the economy. Second, the central bank attempts to improve the “prestige,” or “reputation,” of the management to the financial community (see Kane, 1990, p. 286). It is evident that the central bank has mutually contradicting objectives and adopts mutually conflicting actions. Quite naturally, some of these actions favor the government and some do not. The aim of the government is to influence the management of the central bank to maximize favorable actions and minimize unfavorable ones. Thus, the government attempts to achieve this by designing a clandestine incentive mechanism. As Kane (1990, p. 286) forcefully argued, “Round by round, politicians like some of the Fed’s potential moves and dislike others. The goal of the play is to influence the Fed to make moves they favour and to avoid moves they disfavour” (p. 286).

The implicit assumption is that the government can deliver political and bureaucratic rewards, and inflict effective punishment an the management. There are three important elements in this argument: First, the central bank is finally accountable to the government for pursuing seemingly contradictory policies. Second, in a parliamentary democracy, the government reserves the right to control, and if necessary, change the monetary framework. As Kane (1990, p. 286) put it, “In the United States, society authorises citizens elected to the Presidency and Congress to control jointly the framework of monetary policy. Politicians may at any time change the policy-making

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arrangements that define the rules that apply in the future plays of the game. This ability to redefine the rules of the games reinforces politicians’ ability to influence the central bank’s monetary policy” (p .286).

Third, the government has a close control over the training, grooming, and selection of the top management of the central bank. This political “horse trading” extends government control over the central bank (Kane, 1990, pp. 290–291). The central bank management and the elected officials participate in a “repeated game” in which the government has imperfect control over the monetary policy. The monetary management is believed to be a long-run equilibrium of the strategic interdependence (see Kane, 1990, p. 286). One possible equilibrium is the mutual best responses of the central bank and the government such that the central bank adopts policies that favor, or partially favor, the government in exchange for optimal “bureaucratic rewards.” The government derives additional benefits during politically, or economically, difficult times by blaming the “misguided monetary policies of an independent Federal Reserve System” (Kane, 1990, p. 287). Since there is no accountability, no one has any incentive to unilaterally deviate from this arrangement. Such an equilibrium outcome is called “Fed Bashing.” In such an equilibrium, the government can distance itself from policies that may have a political cost at that juncture. On the other hand, the central bank management may gracefully bear the responsibility for three sets of reasons: First, there is no clear-cut accountability since the management can easily hide behind “honest mistakes.” Second, it is almost impossible to enforce discipline on the management by inflicting a cost for the mistakes. Finally, the management may receive significant bureaucratic privileges such as budgetary autonomy. As a result, the independence of the central bank may turn out to be a sham in such a scenario. Kane (1975) succinctly describes such a precarious independence in the following way: “The Fed is independent so long as the Congress wants it.” The crucial lesson is that central bank independence without well-defined accountability may degenerate

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into pseudo-independence that may impose significant external costs on the society. Hence, it is crucial that the central bank is “separate from the everyday functioning of government”; yet a carelessly drawn charter of independence may turn out to be exceedingly hazardous. The current Reserve Bank Governor Bernie Fraser has been reported to be very cautious on this issue: “Nevertheless, Mr Fraser, while supporting the need for independence, parts company with many others in his publicly stated belief that the degree of independence currently practised by the Reserve Bank is satisfactory” (see Hendy and Evans, 1995, p. 58).

Ex-Deputy Governor Phillips (1988) masterfully put it as: “Our autonomy is not unlimited of course — no statutory body could be wholly autonomous. Which is why I think of the Bank being ‘separate’ — rather than “independent” (p. 281).

8.7 Concluding Comments It is imperative that the central bank must maintain an “effective relationship” with the government since the parliament and hence the government “retain ultimate responsibility for monetary policy.” Yet it is absolutely crucial that the central bank preserves its “capacity to form its views and determine its policies free of party political pressures” (Phillips, 1992, p. 469). Therefore, for the efficacy of monetary management, the central bank needs to maintain some optimal “separateness” from the government, yet a complete autonomy may not be at all desirable. The bottom line, therefore, is that the art of central banking is a difficult balancing act and the actual independence of central bank depends much on the capability of governors as tightrope walkers. Since 1992, many G-7, OECD and other developed countries have chosen to create an independent central bank by enacting specific legislations to sever central banks as a legislative arm from the

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exchequer of their national governments. Our detailed examination in preceding sections does not find any overriding economic reason for such a strong convergence in opinions amongst developed nations concerning their monetary and financial institutions. From the informed opinions of the renowned central bankers and governors, as articulated in previous sections, we could not find any support for central bank independence in the 1980s and 1990s. Yet it became a reality that, in our opinion, could pose a serious challenge to the developing world. We will articulate our concerns in the following thematic points that deserve a closer empirical look once the global economy gathers more data: •

•

•

•

First and foremost, central bank independence in many developed countries acted as a coordinating device through which many of these nations have come to home on a convergence on macroeconomic policies. The developing world does not have any agenda to coordinate its macro and tax policies. It foretells a further consolidation of the bargaining position of the developed world in global and oligopolistic markets. Some observers argue that the immediate spin-off of central bank independence has been a drastic reduction in inflation rate and interest rate, which provided a big boost to the global and regional economies. In the developing world, we see a gradual decline in financial repression; yet the interest rates in the developing world have been significantly higher than the ones in the developed world. This has caused an unprecedented flow of “hot money” into developing nations in a quest for bigger returns. The “hot money” has exacerbated the financial instability and economic crises in various regions. The interest rate advantage of the developed world over the developing world, along with lower inflation rates in the developed world, has gradually altered the comparative advantage in favor of the developed world in high-tech products. The lowering of interest rates in the developed world, following central bank independence, has lowered the debt-servicing burden of many developed nations. It has helped them reduce the budget

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deficit and get back to a balanced, or even a surplus, budget. More importantly, as the pressure of debt servicing eased (as discussed in Section 8.2), governments in developed nations could spend more money on investment, infrastructure, R&D, and higher education. According to various reports by the World Bank, this increase in government expenditure has boosted the endogenously driven growth of the developed countries. Only a handful of developing countries such as India and China could compete with the developed nations in capturing the dynamic comparative advantages driven by the high-tech sectors. This is where we see emerging divisions within the developing world. We will have to fully understand these problems of dynamic comparative advantages and take appropriate measures to address these problems for many developing nations.

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Chapter 9

Intellectual Property Rights and SIDS: Vertical Foreclosure and the Role of Ethics in Cooperation

9.1 Introduction Small Island Developing States (SIDS) increasingly rely on emerging new opportunities in the high-tech, and information and technology sectors to overcome limitations of isolation and remoteness. For example, the sunrise industries for SIDS have been enumerated as e-commerce, telecommunications and telemedicine, and distance learning. In this quest, a geographic information system (GIS) and other information systems are believed to play a significant role. As a result, a significant emphasis has been placed on the development of national, regional, and supra-national information and database centers. It is therefore not an overstatement that information and communication technologies (ICT) are a critical ingredient in the pursuit of sustainable development in most SIDS. The economic performance of these states over the decade has been mixed: most states, except the ones with the least development, have registered positive economic growth since 1994. In particular, most of these nations achieved very satisfactory human development

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indices mainly in literacy and health. Most of these economic successes have been identified due to: • • •

appropriate economic diversification, tourism, development of niche markets in goods and especially services.

Many of the success stories of SIDS relied heavily on the high-tech sectors while the Bahamas, Barbados, and Mauritius specialized in financial services. As an example, the contribution of the financial services sector to the gross domestic product of Mauritius increased from 10.1% in 1992 to over 20% by 2005. The emergence of hightech sectors must be viewed against the steady decline in the terms of trade of primary products in which these countries specialized before. It is also important to note the increase in the transport costs to export bulk products due to energy price shocks. Because of these twin factors, one has come to realize that the knowledge sector and the management of this sector will drive the future prosperity of these nations. To take a simple observation to support our point, between 1980 and 2000, the share of SIDS in global merchandise trade went down by 50% while their share in the global trade of services stayed unchanged mainly due to telecommunications and high-tech service sectors. The sticking point is that high-tech sectors are hardly a level playing field because of intellectual property rights (IPR), which has given rise to a digital divide among nations belonging to the SIDS. It is widely argued that the presence of IPR promotes innovation that drives economic growth and economic prosperity (see Demestz, 1966; Boldrin and Levine, 2002). Strong property rights are therefore regarded as a collective good. This perception is based on a simplistic notion that strong property rights provide appropriate incentives for the production of any goods and services. If this perception is correct, then one will just need to add that strong and well-defined property rights are a prerequisite for the production of ideas as well. Unfortunately, this perception is at best a howler, since ideas and knowledge are typically considered a produced means of

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production — inputs for the production of other goods and services. The problem is that the presence of strong IPR takes away from the purchaser the freedom in the way s/he wants to utilize this input. This gives rise to what is known as “intellectual monopoly”. This work develops a vertical market model to argue a case against strong IPR especially for SIDS who need knowledge-based products for their economic progress and also for attenuating their vulnerabilities due to poor transport and communication technologies. It calls forth an appropriate regulatory framework to control royalties by international players like the United Nations. The gist of the work can be appreciated through the words of Boldrin and Levine (2002): “When you buy a potato, you can eat it, throw it away, plant it, or make it into a sculpture. Current law allows producers of CDs and books to take this freedom away from you. When you buy a potato you can use the ‘idea’ of a potato embodied in it to make better potatoes or to invent French fries. Current law allows producers of computer software and medical drugs to take this freedom away from you” (p. 209).

The goal of this chapter is to establish the point that strong IPR can lead to serious anti-competitive behavior in industries that rely on knowledge. The plan of this chapter is as follows: Section 9.2 offers a review of IPR in a global forum; Section 9.3 develops a game appropriate for examining IPR in a vertically related industry; Section 9.4 examines the need for regulation in the light of the proposed game; and Section 9.5 discusses the findings. 9.2 Intellectual Property Rights and Global Forum The World Trade Organization (WTO) is a recent development in the context of IPR agreements. The World Intellectual Property Organization (WIPO) has been a relevant forum since 1967, when a convention in Stockholm instituted it. The WIPO is based in Geneva. It administers more than 20 international IPR treaties. The WTO has an interesting IPR agreement, known as the agreement on trade-related

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intellectual property rights (TRIPs). When the agenda for the Uruguay Round was being set in the mid-1980s, serious opposition was mounted against the inclusion of the idea of TRIPs. Two main arguments were advanced against its inclusion. First, it is widely held that IPR and international trade are unrelated. At face value, this may seem to be true. But a proper analysis will show that this view is incorrect. If India exports computer software to Germany, one cannot argue that the protection granted to software has nothing to do with trade. If German firms export computer hardware to India, one cannot argue that the protection granted to hardware is a non-sequitur for traderelated issues. The upshot is that trade is usually predicated on investments. So if foreign direct investment (FDI) into a nation is hamstrung by a lack of IPR protection, one cannot convincingly argue that IPR and international trade are unrelated issues. The second argument against the inclusion of IPR in a trade agenda is more convincing. One may argue that the WIPO already exists and the WIPO already has agreements on IPR. Why do we need the WTO to safeguard IPR? It is widely held that the WIPO is not effective for various reasons. Just in terms of inclusiveness, the WTO has 145 members. In contrast, very few countries are signatories to various WIPO conventions or treaties. One may also argue that coalescing IPR into the WTO fold has several advantages. Not only are more countries members of the WTO, more importantly, the WTO provides an effective dispute resolution mechanism and this can be used against countries that fail to protect IPR. Following a dispute, thus, retaliatory action can be taken against a country that breaches IPR conventions. The WTO as a threat/retaliatory mechanism is far more credible, which is why IPR was brought into the WTO. The forms of IPR covered in the WTO are copyright and related rights, trademarks, geographical indications, industrial designs, patents, layout designs (topographies) of integrated circuits, and undisclosed information. On transitional arrangements, nations are to gradually achieve higher norms. Developing countries had until 2005 for patents. In some sectors, some countries only allowed process patents, food, chemicals, and drugs being the examples for India.

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There will have to be product patents for all sectors, the choice between a process patent and a product patent is usually left to the applicant. At the conclusion of the WTO’s Fourth Ministerial Meeting in Doha in 2001, the least developed countries (LDCs) were given until 2016 to implement higher norms. Other than product patents in addition to process patents, patent protection has to be uniformly implemented in 20 years. Compulsory licensing provisions have been tightened. These provisions are used when a patent is not workable. The government can instruct the patent-holder to compulsorily execute a license in favor of another manufacturer. There are three main issues that give rise to concern in South Asia about the TRIPs agreement. India and Brazil have asked for dilution of the Uruguay Round’s TRIPs agreement. The Commission on Intellectual Property’s document, “Integrating Intellectual Property Rights and Development Policy”, 2002 represents one of the best examples of the concerns. This Commission was set up by the British government. On health issues, there are also various reports brought out by the Global Forum for Health Research, WHO. The expression “10/90 gap” is now used, meaning that less than 10% of global spending on health research is devoted to diseases or conditions that account for 90% of the global disease burden. There is a concern that patent protection in the pharmaceutical sector will result in monopolies, increase drug prices and prevent access to health care. Similar concerns are also expressed about monopolies in fertilizers and seeds. Given the spread of AIDS, countries in Sub-Saharan Africa and South Asia have also been concerned about the costs of public health and this was reflected in a WTO Ministerial Declaration in Doha on TRIPs and access to public health. On public health issues, there are three kinds of concerns — price controls, parallel imports, and compulsory licensing. The major concerns with IPR at the global level are the following: 1. monopolization of an idea; 2. IPR protects and promotes monopoly power; 3. how an idea is to be utilized is at the discretion of the owner;

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4. every time an idea is used, a royalty is to be paid by the licensee to the owner, which can seriously warp competition. The following section offers a game based on the issues (1), (2) and (4) to examine an anti-competitive element in the entire set-up. 9.3 Formalization of the Model 9.3.1 Ecological footprints of economic progress: The relevance of knowledge assets Environmental economics, economic development, and sustainability have triggered one of the most interesting debates in modern civilization. On the one hand, one strand of thought headed by leading natural scientists argues that the current interrelationship between human beings and nature is vitiated by a deep “malaise” as the current standard of living of the average human is not ecologically sustainable. One tends to interpret this negative opinion as a prediction of a doomsday awaiting humanity when the ecological system collapses and fails to sustain our future economic wellbeing. The other strand of thought, mainly led by economists and business specialists, tends to marshal the fact that the standard of living of the average human being today is better off in many ways than what was enjoyed in the part. On a secondary note, they argue that there is no impending crisis and the foundation of the doomsday prediction may be an overreaction. It is early days for anyone to make a clear and definitive judgment about the empirical tenability of either of these opposing views. Yet what is at stake is a seemingly fragile ecological system that can suffer irreversible damages from unbridled economic development, which is especially of severe concern for SIDS. If over time, the first strand of thought prevails over the second strand, many societies — especially the SIDS — will have virtually little option to turn back the clock and quickly achieve a sustainable development program to instantly rectify ecological damages. If these ecological damages are serious enough, the survival question for many societies in SIDS will be on the wall. So a critical question for SIDS is how to

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contain ecological damages that typically accompany economic development within some reasonable and acceptable bounds. In this chapter, we call these damages rather euphemistically the “ecological footprints of economic progress”, or simply ecological footprints. In what follows, we constructively argue two important drawbacks of economic development in the context of ecological sustainability: •

•

First and foremost, we will argue that the economic development strategy of SIDS can achieve ecological sustainability by promoting industries that intensively use “knowledge assets” in their production. One may call these industries “knowledge-specific industries.” These industries, we will establish, have relatively smaller ecological footprints. Second, we will argue that the nature of knowledge-specific industries is such that SIDS cannot rely on the global market mechanism to achieve ecologically sustainable economic progress. It is therefore mandatory that SIDS collectively engage in multilateral negotiation/bargaining with advanced nations in regulating and controlling royalties of knowledge assets.

Let us take a quick glimpse at the implication of ecological footprints of economic development/progress. Economic activities directly, or indirectly, utilize natural resources. Natural resources are directly used in consumption and indirectly used as inputs in the production system. The main natural ingredients in production are oil, coal and natural gas, which have an adverse impact, like water and air pollution on our environment. In modern work, natural resources are considered natural assets that create a complex ecosystem on which life is based. These natural assets provide a complex gamut of services to all living organisms in a specific ecosystem. The most important element of our argument is that economic activities leave an irreversible impact on the ecosystem and different industries have different kinds of impact on the ecology. What we argue here is the adverse impact of pollutants from the production process of an industry. In most cases, the concomitance of economic development and pollutants results in a degradation of ecosystems. Economic

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development also causes a deterioration of various environmental assets (like water and air quality). The environment is the proverbial sink and pollution is an unintended consequence of economic development on the quality of environmental goods. For us, one of the important quests of economic sustainability is to minimize the deterioration of environmental assets as a result of the turning of the economic wheel of progress. What follows is a constructive argument that SIDS can significantly arrest the environmental degradation by choosing an optimal development strategy that focuses on industries that intensively utilize knowledge assets in their production. In order to drive our point home, we offer the consumption, or utilization, of energy by an industry as a proxy for the measure of its ecological footprint. The measures give an estimate of the pollution directly caused by production in each industry. We examine 22 industrial sectors from the United States and their energy consumption in the year 2002. The industry classification codes (NAICS), and their names and various measures of energy consumption are presented in Table 9.1. The details are given at the bottom of the table. For our argument, it is important to note two of the measures, CPE and CPV, as proxies for ecological footprints. The index CPE is the consumption of energy per employee and CPV is the consumption of energy per value added. For our reference, Industry 334, Industry 335 and Industry 336 are knowledge-specific industries. These industries intensively utilize knowledge assets. In Fig. 9.1, we present the energy consumption, or CPE measure, of each industry and it is evident from the figure that the ecological footprint of Industries 334, 335, and 336 are significantly lower than the others. These are the high-tech and knowledge-specific industries. In Fig. 9.2, we present the CPV measure of energy use for 22 industries, which graphically describes how the ecological footprints of Industries 334, 335, and 336 are close to zero. Thus, our main argument is that knowledge-specific industries and their development in SIDS can play an important role in ensuring economic development without compromising their ecological sustainability. What we argue in the next section is that we cannot leave the development of these important industries to the vagaries of

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Table 9.1. Price and consumption of energy by the American manufacturing industries in 2002. NAICS 311 312 313 314 315 316 321 322 323 324 325 326 327 331 332 333 *334 *335 *336 337 339

Sectors

POE

CPE

CPV

CPVS

Food Beverage and tobacco products Textile mills Textile product mills Apparel Leather and allied products Wood products Paper Printing and related support Petroleum and coal products Chemicals Plastics and rubber products Non-metallic mineral products Primary metals Fabricated metal products Machinery Computer and electronic products Electrical equipment, appliances, components Transportation equipment Furniture and related products Miscellaneous

6.42 7.53 7.73 7.38 11.16 9.66 3.95 4.78 12.54 3.97 5.03 10.9 4.66 4.94 10.39 11.38 9.24 6.84

6.766 6.508 6.683 5.844 4.622 5.025 6.609 8.525 5.028 10.354 8.481 5.928 7.798 8.336 5.555 5.059 4.949 5.353

6 1.6 11.2 4.7 1.8 2.4 10.6 31.1 1.8 91.3 15.3 2.9 20.7 34.61 3 1.4 0.9 1.9

2.6 1 4.3 1.6 0.9 1.1 4.2 15.2 1.1 15 8.5 2.1 11.7 4.2 1.7 0.7 0.5 1

8.65 8.82 13.26

630 4.734 4.620

1.8 1.6 0.9

0.7 0.9 0.6

Source: Energy Information Administration, U.S. DOE (2002 index), Department of Energy survey data on energy intensity in industrial sectors. Notes: NAICS: North American Industry Classification System, POE: Average Price of Purchased Energy, CPE: Consumption of Energy Per Employee, CPV: Consumption of Energy per Value Added, CPVS: Consumption Per Dollar Value Shipment.

the global market mechanism. The global market can significantly marginalize the SIDS and thereby compromise their future development. 9.3.2 Vertical markets and regulatory issues: A digression In vertically related industrial structures, global firms are the upstream firms that wield natural monopoly power in the production

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Ecological Footprints of Specific US Industries in 2002 12

10

CPE

8

CPE

6

4

2

0 305

310

315

320

325

330

335

340

345

Industry Classification

Figure 9.1.

Specific industries and their ecological footprints (CPE measure).

Source: Computed from Table 9.1.

Ecological Footprints of Industrial Sectors in the USA in 2002 100 90 80 70

CPV

60 50

CPV

40 30 20 10 0 305

310

315

320

325

330

335

340

345

Industry Classifications

Figure 9.2.

Specific industries and their ecological footprints (CPV measure).

Source: Computed from Table 9.1.

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and supply of key knowledge-specific inputs while local and downstream firms are competitive in the supply of the final product.1 Thus, such an industry is characterized by vertical integration between “naturally monopolistic and potentially competitive” activities. The critical feature of the industry is that the naturally monopolistic firm of the upstream input market competes with competitive firms in the downstream market for the final products. It has been commonly held that such monopolistic power of the vertically integrated firm may lead to serious market distortion and the consequent marginalization of the downstream non-integrated firms (OECD, 1993; Hilmer et al., 1993). One may call this conventional wisdom. In order to restrain the monopoly power of the vertically integrated upstream firm, conventional wisdom recommends the strict control of the price of the key input (royalty in our model). Thus, to protect the non-integrated firms, a set of special regulatory measures have to be introduced in such industries. An important element of the regulatory measures is the input price control: input prices in the upstream market are directly controlled by the regulatory bodies to protect the rivals in the downstream markets (Hilmer et al., 1993; OECD, 1993). The regulation of the input price thus became a common feature in the UK and Australia in such industries, especially for telecommunications industries until the mid-1990s (see King, 1997).2 1

As an example, in telecommunications, the long-distance operations are potentially competitive while local network operations are characterized by natural monopoly. The deregulation of the market has created a special industrial structure: for example, British Telecom was privatized and now faces competition in the downstream long-distance market, mainly from Mercury. Yet British Telecom retains its naturally monopolistic power in the local network operations. We observe a similar structure in the Australian telecommunications industry: Telstra has a natural monopoly in the local network while both Telstra and Optus Communication compete in the downstream long-distance market. In both countries, the firms in the downstream market pay the network-owners an access fee, which is subject to active regulation to promote competition (see Armstrong et al., 1994; Vickers, 1995; Damania, 1996; Hilmer et al., 1993). Similar structures have emerged in the gas, railways, water supply, and electricity industries. 2 Rate-of-return considerations also emerge as important issues in this context: input prices hinge on the access providers earning reasonable returns on their capital (King, 1997).

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In the context of a Cournot duopoly with two stages of production, it is well-known that the regulation of input prices is unambiguously beneficial to consumers. However, since the mid-1990s, it has also been argued that such regulation of the input price does not necessarily benefit the non-integrated downstream rivals. There exists a set of conditions under which an increase in input price will raise the profits of both the integrated firm and its rivals. The apparent rationale behind this argument is the possible role that the input price may play as a collusive device to restrict outputs in the downstream market and, thereby, to enhance profits accruing to both firms. One may call this a challenge to conventional wisdom. A critical weakness of this line of reasoning (the challenge) is that they neither explain nor consider the determination of the optimum input price in an unregulated industry. They rather assume that the regulatory authority exogenously sets the input price. In such a scenario, Damania (1996) and Vickers (1995) consider the comparativestatic results for variations in input prices. In light of these results, they reverse conventional wisdom to argue that input price control may make the non-integrated firms worse off. One therefore seems to incorrectly entertain this argument: if the objective of the regulator is to protect the non-integrated firm, input price regulation may turn out to be “ineffectual and counterproductive” since such regulation may restrict the profits of the non-integrated firm. Suppose we fully concur with this conclusion and the regulator removes the control over the input price. What would be the effects of such deregulation on the non-integrated firm? Would both the firms be better off? The current works do not shed any light on these questions since they do not explain the input price when the market is unregulated. Yet these are not trivial questions. In order to judge the merits of the regulation of input price in protecting the nonintegrated firm, one must make an appropriate comparison: the welfare losses associated with the regulation must be pitted against the losses in the absence of such regulation. Otherwise, the exercise will remain incomplete and may even be incorrect. To put it baldly, suppose the removal of regulation reduces the profits of the non-integrated

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firm even further, yet the existing models argue that input price control is ineffectual in protecting the interests of the nonintegrated firms.3 The relevant question, arises: Is input price regulation “ineffectual and counterproductive” in protecting the nonintegrated firms? To answer this question, we need to know the welfare implications of the unregulated market outcome. Impressive as the existing literature is, however, it is the contention of this chapter that it may be significantly incomplete and possibly flawed. The major contribution of the next section is to present a simple model to develop this claim. In this chapter, we introduce an explicit determination of the optimum input price in the context of the Cournot duopoly with two stages of production. The perfect Nash equilibrium (PNE) of the game unravels an interesting twist in the theoretical result: in the absence of regulation, the integrated firm will choose (in equilibrium) the optimum input price to reduce his non-integrated rival’s profits to zero and thus induce the rival to leave the market.4 The upshot is that our new finding is in complete consonance with the conventional wisdom that an active regulation of input price is a necessary ingredient for fostering competition in such markets. More importantly, quite contrary to the received doctrine, if the objective of the policy makers is to protect the downstream and non-integrated rivals, a strict regulation of the input price will be mandatory. We will establish that an increase in input price is beneficial to integrated firms. We will also establish that such an increase cannot benefit both the integrated and non-integrated firms. 3

Both Damania and Vickers have shown explicitly that regulation enhances consumer welfare. Such regulation is, however, shown to lower aggregate welfare since it lowers the profits of both the firms. We expressly ignore consumer welfare and concentrate solely on the profits in this chapter. 4 An important distinction has to be made in this context: our argument does not rely on any kind of predatory pricing. Instead we drive our point home on the basis of a sequential game which is implicit in Vickers (1995). The conceptual difference between the standard models and our arguments lies in our attempt to determine the (unregulated) input price from the perfect Nash equilibrium of the proposed sequential game.

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9.4 The Optimal Royalty 9.4.1 An outline We postulate an industry that supplies a single final product. Each unit of it is produced by combining necessary input, called a knowledge asset, from the upstream industry with labor and other inputs from competitive markets. The upstream firm is an integrated firm which has a monopolistic control over the supply of knowledge asset and competes with the downstream firm in the market for the final product.5 The downstream firm is competitive in the input market as it takes the input price as a datum. We postulate Cournot–type quantity competition in the downstream duopoly market while the integrated firm has naturally monopolistic power in the upstream market. It is natural that the degree of (actual) competition in the downstream market is determined by the royalty/price of the knowledge asset of the upstream market. 9.4.2 The sequential game and the Cournot–Nash equilibrium in the downstream market We assume a highly stylized sequential game that is played out over two time periods. The integrated firm faces a duopolist in the downstream (final product) market while it wields naturally monopolistic power in the upstream market (knowledge asset). During the first time period, or Stage I, the integrated firm announces the royalty at which it will sell the knowledge asset in the second period, or Stage II, to the rivals in the downstream market. During Stage II, both the integrated and non-integrated firms will compete as Cournot duopolists in the downstream market to sell the final product. If the information is complete, in the relevant rational expectations equilibrium, both firms correctly predict the Cournot–Nash 5

In order to simplify the analysis, we assume that there is a single non-integrated firm in the downstream market and, hence, this market is postulated to be a duopoly. The conclusions will extend to the case with a finite number of firms.

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equilibrium of Stage II competition and both firms will seek to maximize their profits in Stage II given the royalty determined in Stage I. When the integrated firm chooses the royalty in Stage I, it seeks to maximize the overall profits in Stages I and II.6 Thus, in order to solve the game, we will apply the logic of backward induction: we start with Stage II and characterize the Cournot–Nash equilibrium of the duopoly game. Rationality and complete information dictate that both firms and the regulatory body will form their expectations by looking ahead and foreseeing the duopoly outcome. If agents behave this way, they are said to have rational expectations. In Stage I, relevant agents adopt their optimum actions based on their rational expectations. The resultant outcome is the solution to the sequential game, which is called the PNE. In order to derive the PNE, we need the following details: Definition 1. The profit of the integrated firm (Πm) is given as: Πm = (A − w)qn + (P (Q) − c − w)qm

(1)

where Q (= qm + qn) is the market output of the final product while qm is the output of the integrated firm, qn is the output of the non-integrated firm, A is the royalty for each unit of final output produced by the non-integrated firm, w is the cost of producing the essential input, c is the cost of producing the final good for both firms, and P (Q) is the inverse demand function. Definition 2. The profit accruing to the non-integrated firm from the downstream market is: Πn = (P (Q) − c − A)qn.

(2)

Assumption 1. We assume the inverse demand function to be linear: P (Q) = a − bQ. 6

(3)

Profits accrue to the integrated firm from two sources: First, it receives profits from the sales of knowledge assets. Second, it receives profits from the sales of the final product.

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Based on the above, we derive the Cournot–Nash equilibrium of the duopoly at Stage II. 9.4.3 Stage II: Cournot–Nash equilibrium of the duopoly in the downstream market In Stage II, the integrated firm earns Πm1 from the sales of the final product: Πm1 = (P (Q) − c − w)qm.

(1a)

Substituting (3) into (1a) and simplifying would yield: Πm1 = (a − c − w)qm − bqnqm − bqm2 .

(1b)

Similarly, the profit function of the non-integrated firm reduces to: Πn = (a − c − A)qn − bqmqn − bqn2 .

(2a)

Maximizing the profit function (1b) yields the reaction function of the integrated firm which is essentially the first-order condition to maximize (1b) with respect to qm taking qn as datum. This would yield the reaction function of the integrated firm in the downstream market: qm = [(a − c − w)/(2b) − (qn/2)].

(4a)

Similarly from the maximization of (2a) with respect to qn we obtain the reaction function of the non-integrated firm as: qn = [(a − c − A)/(2b) − (qm/2)].

(4b)

The Cournot–Nash equilibrium of the downstream duopoly is determined by the solution to the simultaneous equation systems (4a) and (4b). The Cournot–Nash equilibrium of the downstream market: qn* = [(a − c − 2A + w)/(3b)],

(5a)

* = [(a − c + A − 2w)/(3b)], qm

(5b)

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Q* = [(2(a − c) − (A + w)/(3b)],

(5c)

P* = [(a + 2c + A + w)/(3)].

(5d)

Equations (5a) and (5b) are derived from the solution to the simultaneous equation systems (4a) and (4b). And q*i labels the Cournot–Nash equilibrium output of firm i, and we derive Eq. (5c) by adding (5a) and (5b). Substituting (5c) into Eq. (3), we obtain the Cournot–Nash price of the final product as given by Eq. (5d). 9.4.4 Stage I: The optimal royalty and the perfect Nash equilibrium of the sequential game In an unregulated industry, the integrated firm fully controls the royalty A. It also has the full knowledge of the Cournot–Nash equilibrium of Stage II and expects the rival to respond by Eq. (5a). In Stage I, the integrated firm thus sets A to maximize (1), subject to the Cournot–Nash equilibrium of Stage II, as given by Eqs. (5a)–(5d). This outcome is the PNE of the two-stage game. Theorem 1. In the PNE of the proposed sequential game, the optimal royalty, AE, as set by the integrated firm in Stage I, is given by Eq. (6b). This optimal royalty in turn determines the equilibrium output response of the non-integrated firm, q nE , equilibrium output of the integrated firm, qmE , and the equilibrium market price, P E, at Stage II as 7: P E = [(a + 2c + AE + w)/3],

(6a)

A = [(a − c + w)/2],

(6b)

E

qmE qnE

= [(a − c − w + A )/(3b)],

(6c)

= [(a − c + w − 2AE)/(3b)].

(6d)

E

Proof. We know that in Stage II, the Cournot–Nash equilibrium price P*, and optimal quantities, qm* and qn*, are given by Eqs. (5d), (5a), and (5b), respectively. From these equations, we also know that 7

Here, what we mean by an equilibrium is the perfect Nash equilibrium of the proposed sequential game.

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P *, qm*, and qn* at Stage II are functions of the royalty A which is optimally chosen at Stage I. So once we determine the optimum value of A, AE, in Stage I, AE will in turn determine the PNE values of P E, qmE , and qnE, from the relevant Eqs. (5a)–(5d). To derive the optimum A, AE, we substitute Eqs. (5a)–(5d) into Eq. (1) to yield: È (a - c - 2w + A)2 (a - c + 3w) 2 2 w(a - c + w) ˘ +A Pm = Í A ˙ .... 9b 3b 3b 3b ÍÎ ˙˚ (7a) The first-order condition to maximize (7a) with respect to A yields8: AE =

(a - c + w) . 2

(6b)

Substituting (6b) into (5a), (5b), and (5d) will yield (6a) through (6d). Theorem 2. In the PNE of the sequential game, the optimal royalty, AE, of the integrated firm will drive the profit of the rival (non-integrated firm) to zero. Hence the non-integrated firm will leave the downstream market if the industry is unregulated. Proof. If A is the royalty, then the profit of the rival non-integrated firm, Πn*, from the downstream duopoly, will be: Πn* = (P * − c − A)q n*.

(8a)

Substituting qn* by (5a) and P * by (5d) into (8a) yields: ’n* =

(a - c + w - 2 A ) 2 . 9b

(8b)

We know that the optimum A of the integrated firm is given by Eq. (6b). Hence to derive the profit of the non-integrated firm from 8

One may check that the second-order condition is satisfied as:

∂ 2Πm/∂A2 = (−10/9)b < 0. where ∂ represents partial derivative.

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the PNE, we substitute A in (8b) by (6b). Substituting (6b) into (8b) yields: Πn* = 0.

(8c)

Since it earns zero profits, the non-integrated firm would leave the downstream market. Also note that for A > AE, Πn = 0. In an unregulated and vertically integrated industry, as captured by the above sequential game, the resulting equilibrium is one in which the integrated firm chooses AE in Stage I to maximize its overall profits. At this pre-committed price AE, the non-integrated rival will make zero profits and hence quit the industry, leaving the vertically integrated firm to enjoy the monopoly profits. Thus, if the royalty for the knowledge asset is not subject to regulation, such an industry will be characterized by significant market distortions. The integrated firm will have anti-competitive incentives and the ability to choose a royalty rate for knowledge assets, which will eventually evict its rivals from the downstream sector. In order to protect the nonintegrated firms, the regulator must therefore introduce caps on the royalty to avoid AE. From the profit functions, it is evident that both the firms cannot simultaneously gain from an increase in the input price. From these results, we make the following remarks: Remark 1. It is evident that for A < AE: d Pm > 0, dA

(8d)

d Pn < 0. dA

(8d′′)

Remark 2. It is evident that for A > AE: d Pm < 0, dA d Pn = Pn = 0. dA

(8e)

(8e′′)

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One can establish (8d) and (8e) and (8d′′) and (8e′′) by differentiating (7b) and (8b), respectively. The above results show that the regulator must introduce restrictive measures in the upstream market to protect the non-integrated firm. Otherwise the integrated firm can use its power in the upstream market to “leverage”9 itself into a position of power in the downstream market. It is interesting to note that the optimal royalty of the integrated firm may not be too high or too low: it is the price of the knowledge asset that raises the cost and lowers the market share of the non-integrated firm in order to drive the nonintegrated firm’s profit to zero. At this optimal royalty, the integrated firm maximizes its profit and, hence, this anti-competitive behavior appears to be an equilibrium phenomenon. To prevent this equilibrium vertical foreclosure, it is necessary to regulate royalties in such markets. 9.5 Comments and Discussion One of the major characteristics of SIDS is their isolated nature. It is also important to note that isolation creates geographical distances among these states and from major global markets. More often than not, the transport network and communication network in SIDS are poorly developed, maintained and managed. Poor long-term planning is partly responsible for this. It is of utmost importance that the fragmented nature of these nations and their linkage problems with the rest of the world is redressed in order to lend economic and social stability to SIDS. The tyranny of geographical distance in conjunction

9

This argument is similar in spirit to the equilibrium vertical foreclosure as propounded by Ordover et al. (1990) who consider a market in which the supply of inputs is competitive. After the merger, the upstream division of the now integrated firm refuses to supply necessary inputs to the rivals in the downstream market. Thus, the input-supply to the rivals is foreclosed which leads to increased input price as well as increased output prices. The integrated firms benefit from the reduction in competition, resulting in price hikes. Ordover et al. (1990) provided a coherent model to argue that anticompetitive foreclosure arises as an equilibrium phenomenon in a four-stage game.

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with high fuel costs further isolates these nations. These challenges are substantial and will determine the fate of these small and fragmented economies as the forces of globalization take different turns with the energy price shocks of 2007–2008. There is an increasing reliance of these nations, their economic advisors and also among experts from the United Nations, on the rapid development of ICT to establish the missing and weak networks with the regional and global markets. With ever increasing hunger, these nations are gaining access to and implementing technologies to modernize their relevant sectors. Unfortunately, the global market of high-tech sectors is dominated by a few firms and IPR are a major characteristic of these technology-savvy sectors. We offer an insight into this with a stylized model: there is an integrated global firm that develops the knowledge, technology, and also the final product. A typical local firm from the SIDS only produces the final product by using the “knowledge” as input. There is a royalty that the integrated and global firm charges for selling the “knowledge,” which is mainly establishing IPR. It is important to note that the integrated global firm will need to set the royalty in such a fashion that the resultant profit of the non-integrated firm from SIDS is below a threshold, which will induce the non-integrated SIDS firm to exit from the downstream market. In our work, we have set this threshold as the zero supernormal profit. Our analysis remains unaffected for any finite profit threshold. We therefore argue in favor of introducing controls on the price of knowledge assets, the royalty, by providing the determination of the optimal royalty in a vertical industrial structure. If the industry is unregulated, we are able to establish the conventional wisdom: the PNE of the proposed sequential game shows that the integrated and global firm will adopt its profit-maximizing royalty that will force the local rivals to leave the downstream market. Even if this integrated firm does not adopt the strategy of vertical foreclosure, it has a leveraged position in the downstream market since this vertical foreclosure looms as a credible threat to non-integrated local rivals.

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This threat can seriously compromise competition in vertical markets. In order to promote competition and protect the rival firms in the downstream market, it is essential to introduce controls and regulation in the pricing of knowledge assets. It is important for the international organizations to intervene in knowledge-specific markets to control the royalty. In the absence of such regulation, the pursuits of SIDS in beating isolation, fragmentation, and geographical distance can prove unproductive. 9.6 Ethics in Cooperation: An Australian Case Study In the Australian context, the Hilmer Committee Report (1993) underpins the regulatory framework. The Hilmer Committee report (1993)10 defines the Competition Policy in Australia as the conscious efforts to facilitate effective competition in order to promote efficiency and economic growth without jeopardizing the public interest. The Trade Practices Act is the most important vehicle to promote effective competition as it embraces the twin aims: • •

to eliminate anti-competitive conduct and thereby promote competition and efficiency (Part IV of the Act), to ensure that consumers’ interests are adequately protected in their dealings with producers and suppliers (Part V of the Act).

Prior to the adoption of the Competition Policy, Australian cooperatives were insulated from foreign competition. In recent years, many of them are being forced to confront the gale of internationalization and consequent challenges of global competition. As a response to the onslaught of competition, many cooperatives in Australia have adopted strategic mergers which have serious effects on effective competition (e.g., agricultural marketing cooperatives after deregulation in 1995). Since such cooperatives represent agreements between competitors 10

Hilmer et al. (1993). National Competition Policy, AGPS, Canberra.

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which may have anti-competitive consequences, the Trade Practices Act treats such agreements as a breach of the Act and, hence, illegal. However, such agreements are accorded legitimacy on the grounds of public interest. Such agreements will not breach the Act if they create significant public benefits that can outweigh the associated cost. Thus, the Trade Practices Commission is guided by some kind of economic rationalism in deciding whether a cooperative agreement is illegal or otherwise. As a result, a potential conflict will arise between the Trade Practices Act, hence the Competition Policy, and the cooperatives.11 The rationale behind a cooperative agreement in Australia turns on the following: 1. 2. 3. 4. 5.

it it it it it

reduces transaction costs, reduces supply uncertainty, economizes on information, fosters competition, enhances the bargaining strength of the members.

As a result, there are significant benefits from the formation of cooperative agreements which may in turn have serious anti-competitive consequences. The primary purpose of this chapter is to argue that the application of economic rationalism cannot resolve the conflict between the Competition Policy and cooperative agreements since the public benefits and associated costs from such agreements naturally hinge on the prisoner’s dilemma-type interactions among cooperative members, and between members and non-members. The outcome of cooperative agreements is further clouded by tactical rent-seeking activities such that individual self-seeking activities may engender 11

Ian Langdon of Australian Cooperative Foods stated that “Trade Practices in Australia have got a preoccupation with maintaining maximum competition within Australia even if it means that the players that provide competition are too small to be effective on an international basis and we will take the Trade Practices Commission on it if we have to.”

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significant collective costs on the public interest, leading to a breach of the Act. How to resolve such conflicts? We constructively argue that ethics play a significant role in controlling damages from the prisoner’s dilemma-type interactions, which have precipitated potential conflicts between the Competition Policy and cooperatives in Australia. The layout of the chapter is as follows: we provide an outline of the Competition Policy and cooperatives in Australia in Section 9.6. In Section 9.7, we examine the impact of the Competition Policy on the cooperatives in Australia. Section 9.8 analyzes the recent intensification of cooperative activities, mainly the mergers between existing cooperatives induced by the implementation of the Competition Policy. Section 9.9 highlights the need for conflict-resolution through business ethics. We conclude in Section 9.10. 9.6.1 The Competition Policy in Australia The Competition Policy in Australia during the 1990s embraced efforts to facilitate effective competition in order to promote efficiency and economic growth without jeopardizing the public interest. The major channels through which the Competition Policy worked were two-fold: First, the bankruptcy threat to non-performing business enterprises; and second, the capital market threat in the form of takeover. The simple philosophy of the Competition Policy may be reduced to the adage of “perform or perish.” There are, however, ground rules that business enterprises cannot transgress in pursuit of profits: the market principle is that no player in the market should be able to engage in anti-competitive conduct against the public interest. Within the preordained rules, the Competitive Policy recommends the market to have a free reign if the participants do not wield any market power. This is the broad context within which the Competition Policy works in Australia. 9.6.2 Roles of cooperatives in Australia At first sight, the formation of cooperatives may appear as a step away from the forces of competition. Hence, one may rationally argue that

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the formation and the development of cooperatives will infringe on the basic postulates of competitive markets. In order to set the stage, let us take a cursory glance at the major reasons behind the formation of a cooperative. There are two major reasons: 1. To enhance the bargaining strength/position of the members. 2. To enable members to add value to their products. One may safely conclude that the second reason is less controversial. The first one, however, needs careful analysis as this reason has serious pitfalls and is potentially hazardous. This reason recommends tampering with the market mechanism so that members of cooperatives are better positioned in markets, which may result in the appropriation and continuance of excess profits. The pitfall lurks simply because we are unable to determine how much market tampering is justified. One may argue that this is a case of pure value judgment since cooperatives necessarily imply market tampering to some extent. The usual guidepost is that the formation of a cooperative should bring benefits that should not be surpassed by its cost to other agents. This is a straitjacket application of economic rationalism, which may accept the legitimacy of a cooperative in terms of the economic calculus. The major issue that we want to highlight is that the formation of cooperatives will inevitably lead to costs which will be borne by uncompensated players. As a result, there may emerge a conflict of interests and ensuing disputes between affected parties. There must be an accompanying low-cost system of dispute resolution. Otherwise, the operation of cooperatives may lead to costly legal wrangles and consequently the gradual emergence of undue market power. The upshot is that cooperatives are compatible with the Competition Policy only under certain restrictions and the benefits from such cooperatives are not unambiguous. In other words, cooperatives and the Competition Policy have partly symbiotic and partly antagonistic relations. One needs to be very careful in such a treacherous area.

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9.7 The Impact of Australian Competition Policy on Cooperatives If we cast a look at the environment within which a business is located, the following picture emerges. A typical business enterprise has the following strategies: • • • •

try to tune the environment in your favor, adjust to the environment, emigrate to a new environment, die.

The major impact of the Competitive Policy is to get rid of the artificial barriers that create market power and allow businesses to create their own cocoons to evade the gale of competition. The Competition Policy will also enhance competition all across the economy and hence the importance of Options 1 and 3 will be partially reduced. Thus, in a new economic order, the business must decide to adapt to the market conditions or just pass away. In a world of cut-throat competition, we expect the market participants to form more and more cooperatives in pursuit of survival. Let us take a cursory look at the cooperatives in Australia. There are 2500 cooperatives in Australia. Their turnover is estimated at $6b. This figure excludes the turnover of financial cooperatives. The asset base of all Australian cooperatives is estimated at $4b. Among the top 500 private companies, there are 36 cooperatives (7%). Among the top 500 exporters, there are 19 cooperatives. In NSW, in 1996, 894 cooperatives were listed on the NSW Register with 1,038,630 members, $608m worth of exports and 14,901 paid employees. The dominant cooperatives are in the dairy industry, rice milling industry, and cotton industry. The main exports are dairy products, rice, grain and flour, cotton, meat and meat products, lobster and abalone, citrus and fresh fruit, canned fruit and vegetables, and agricultural seeds.

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9.8 The Australian Competition Policy and Cooperatives To answer this question, let us have a look at the rationale behind cooperatives in Australia: • • • • •

it it it it it

reduces transaction cost, reduces supply uncertainty, economizes on information cost, fosters coordination, enhances the bargaining strength of its members.

In the new economic order — created by the Australian Competition Policy — the survival of a business enterprise will hinge critically on its cost savings. As we can clearly see, cooperatives provide a host of cost savings and hence will be a natural selection among existing business enterprises to evade the threats of bankruptcy and capital market takeovers. For a better perspective, let us have a look at the formation of cooperatives in Australia in the recent years (Table 9.2). In recent times, the following developments have highlighted the depth of the problems associated with the intensification of mergers between cooperatives which may have anti-competitive implications. Pecuniary penalties under the restrictive trade practices provisions have increased from a maximum of $250,000 to $10m for a corporation, Table 9.2.

Formation of cooperatives in Australia.

Year 1991/1992 1992/1993 1993/1994 1994/1995 1995/1996 Source: Fells (1995).

Number of cooperatives formed 35 46 24 38 42

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and in the case of an individual, it has gone up to $500,000. The penalties under the fair trade and consumer protection provisions have doubled. In order to reduce anti-competitive activities, the Courts have taken punitive actions in all the sectors of the economy. In the past, the fines never exceeded the $250,000 mark. In recent times, the penalties have made a quantum jump: • • • •

TNT/Ansett/Mayne Nickless — $16.3m, Toyota Dealers — $644,000, Holland Stolte — $1.7m, Sims/Normetal — $572,500.

The Courts now hold individual executives responsible for the infringement of the Trade Practices Act. The AMP case saw a refund of $50m to customers; insurance and superannuation markets were streamlined; and Telstra and Optus were forced to correct their advertisements. 9.9 Conflicts and Cooperatives: The Role of Ethics 9.9.1 Private benefits and public costs Members form cooperatives in order to achieve a critical mass in the concerned market to enhance their bargaining position. Thus, the benefits are largely private ones for members of the cooperative and are not available to non-members. However, the costs — inefficiency associated with increased market power — is a public cost which is borne by all the market participants. As a result, one may expect some kind of conflict between cooperatives. To put this point baldly, consider the following game: suppose there are two regional cooperative bodies in the dairy industry, namely, cooperative A and cooperative B which individually deal with an outside distributor. Each cooperative has two possible actions: (i) bargain aggressively with the outside distributor for the price and quantity and (ii) accept the market rates. The distributor has an outside option of buying from a third party if

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the price is too high (say, an international seller). We can summarize the game as the following: Game Matrix 9.1.

Cooperative A Bargain

Bargain

Accept

100, 100

70, 250

250, 70

150, 150

Cooperative B Accept

What is the outcome? The Nash equilibrium of the above game is (bargain, bargain) since the cooperatives cannot trust each other. From there emerges a conflict: cooperation between A and B will give $150m to both, yet they fail to reach an instant agreement since the dominant strategy is to bargain. Thus, cooperatives in their pursuit of maximizing private benefits inflict a public cost as the distributor turns away from the regional market. This is an example of the much-celebrated idea of the prisoner’s dilemma: agents driven by their self-seeking motives and lack of trust fail to achieve an optimal scenario. How to resolve such a conflict? We shall examine this question soon. 9.9.2 Conflicts between insiders and outsiders Consider the three dominant cooperatives in Australia: construction, property and business service, and finance and insurance. If they merge, they will gain significant market control. The merger is nationally beneficial as the price in the short run is expected to go down since such a merger leads to some kind of vertical integration. Hence, the Australian Competition & Consumer Commission (ACCC) may find that the merger is in the national interest since the buyers get the benefits from the decline in prices. What is the impact on the non-integrated producers? In the short run, they will be forced to reduce their prices and they may vanish in the long run, thus giving monopoly power to the integrated industry. Thus, there arises a conflict of interest between the

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insiders, the integrated cooperative, and the outsiders, the non-integrated cooperatives. We can model this in the following game: Game Matrix 9.2.

ACCC Integrate

Penalise

Do not Penalise

−50, 100

10, 201

−100, 10

15, 200

Cooperatives Do not

The Nash equilibrium of the above game is (do not penalize, integrate) which yields the payoffs (10, 500) in the short-run. In the long run, however, such an integration may inflict a high cost on the society as the outsiders are gradually pushed out of the market. The optimum social outcome is (15, 200) where social welfare is maximized in the long run. But such a cooperative outcome which yields the maximum social welfare is not feasible if the agents are driven by self-interest and individual profits. This will lead to the prisoner’s dilemma once again. 9.9.3 Tactical rent-seeking Now suppose that the cooperatives try to influence government policy. If successful, the ACCC is persuaded that such mergers are in the public interest. As a result, there may emerge a political influence game leading to the prisoner’s dilemma. Consider two cooperatives A and B which are trying to influence government policy: Game Matrix 9.3.

Cooperative A Bribe

Bribe

Do not Bribe

50, 50

10, 70

70, 10

60, 60

Cooperative B Do not

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The natural outcome of the above game is the Nash equilibrium in which each cooperative attempts to influence government policy in its favour, leading to a sub-optimal scenario (bribe, bribe) and yielding payoffs (50, 50). This is yet again a case of the prisoner’s dilemma. 9.9.4 Ethics, morality, and the prisoner’s dilemma In social life, the prisoner’s dilemma is presumed to be a common incident (see Taylor, 1976; Stinchcombe, 1978). The source of the problem is a lack of trust which results in an inferior social state. In the prisoner’s dilemma, there is a cooperative outcome which yields a higher benefit for every individual but each individual has an incentive to defect from such a cooperation. Such a problem does not arise if the agents are not driven by their “cunning of reason,” or rationality. Instead, if agents are actuated by morality, then defection becomes a non-sequitur and the problem disappears (see O’Neill, 1989). This argument hinges on Kant’s theory of morality from social ethics. Titmuss (1970) argued that the voluntary blood donation system functions better than the more commercial ones. He further unraveled that the compelling reason behind voluntary blood donation is the “desire to help others” which is not actuated by self-interest. In a similar fashion, Hardin (1982) argued that environmental and other volunteer organizations operate on a volitional basis: “people play fair if enough others do”. Thus, one may argue that the problems of the prisoner’s dilemma can be avoided if individuals are morally motivated (see Hollis, 1987; Sen, 1970). The prisoner’s dilemma arises since the agents attach full weight to their instrumental rationality such that defection is a dominant strategy. If agents were influenced by norms, then defection would vanish into thin air. The anthropological literature is rife with examples of how spontaneous cooperation emerges due to social and cultural norms (see Turnbull, 1963). In the First World War, Christmas fraternization spontaneously emerged when opposing trenches stopped aggression cooperatively during the Christmas period (see Ashworth, 1980; Axelrod, 1984). In economics, we see similar evidence in solving

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the problems of the prisoner’s dilemma: North (1991) argued that the norms of the Confucian society resolved these problems without costly contracting and monitoring activities. Akerlof (1983) reported the loyalty filter which explains the relative superior performance of the Quaker groups in North America due to their respect for the norm of honesty. Peters and Waterman (1982) argue in their bestseller that the culture of a company is crucial to its performance. Thus, the key to the resolution of conflict between the Competition Policy and cooperatives in Australia depends on the cooperation between parties. Such cooperation may not emerge naturally since all or some parties have incentive to defect. Such defection can be stopped by decisions which are derived from ethical and moral judgments. Thus we fully concur with Polanyi (1945): “The outstanding discovery of recent historical and anthropological research is that man’s economy, as a rule, is submerged in his social relationships. He does not act so as to safeguard his individual interest in the possession of material goods; he acts so as to safe-guard his social standing, his social claims, his social assets. He values material goods only in so far as they serve this end” (p. 53).

9.10 Concluding Comments In the view of the present author, cooperatives and competition bear a tenuous relation: there may be both uses and abuses of cooperatives in a competitive system. If there are strict and enforceable ground rules, then cooperatives and competition may enjoy a mutually beneficial existence. It seems that cooperatives, as an organization, will fit in the framework of competition only under cautiously devised rules of the game. More importantly, the moral, ethical and social values will play a significant role in settling the differences between the Competition Policy and cooperatives in Australia.

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Chapter 10


10.1 Introduction In developing countries, as in developed countries, local governments typically respond to incentives and abide by constraints that they confront wherefrom the local expenditure is derived. It is a moot point whether local expenditures in developing nations are economically efficient and politically acceptable. To be efficient, local governments must be entrusted with a significant role in raising revenues and allocating expenditure, and be given sufficient incentives to act in a responsible and efficient way. It is widely held that local governments in the developing world have little autonomy in raising revenues and little flexibility in determining local tax rates (Bird, 1994). This lack of autonomy and flexibility is believed to have deleterious consequences for the standard of living of millions (Bird et al., 1995; Bird, 1993). At the same time, it is well understood that unconditional grants and limited conditionality of transfers from central governments usually lead to the fungibility of money, the cannibalization of resources, and the diversion of funds for non-local use and rampant corruption (Bird and Wallich, 1992; Shah, 1991). Thus, the fiscal outcome in developing nations is a product of institutional and behavioral peculiarities that offer specific incentives and create relevant constraints for central governments and local governments.

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What follows is a simple model that characterizes a fiscal equilibrium in the context of a set of institutional and behavioral peculiarities that capture the typical features of the landscape of local governments in developing nations. Based on the proposed fiscal game and this fiscal equilibrium, we characterize successful reforms. Section 10.2 provides the model and Section 10.3 concludes. 10.2 The Model A typical local government has two levels of accountability. The first level of accountability is to local taxpayers for the use of resources mobilized from their residents. The second level of accountability is to the central government for the appropriate use of transfers. We posit that a typical local government is more accountable to the local residents than to the central government. To make our model tractable, we assume that local governments cannot divert resources that it collects from local residents through local taxes while it is possible to divert intergovernmental transfers for other purposes. Thus, the corruption in our model entails a simple diversion of untied transfers. This is a well-known feature of developing nations that has prompted perceptive observers to recommend matching and tied grants to replace transfers (Bird et al., 1995). The reality is that most transfers are still untied (Gangopadhyay and Nath, 2001a, b). Another facet of local governance in developing nations is the little flexibility that local governments enjoy in setting taxes. For modeling purposes, we assume that local taxes are set by the central government while the revenues are collected and utilized by local governments. In the above scenario, the fiscal game unfolds in the following fashion: The central government sets the local taxes to maximize its payoff/welfare given the diversion of funds by the local government. The local government chooses the level of corruption (diversion of funds) to maximize its payoff/welfare given the local taxes and intergovernmental transfers. The resultant Nash equilibrium entails the combination of taxes and diversion of funds that are self-confirming.

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10.2.1 Local government The payoff function of an incumbent local government is as follows: ER = αθ (Y − T )

(1)

where α is the probability of re-election of the incumbent local government, Y is the total funds available to the local government, T is the tax revenue collected by the local government, (Y − T ) is the untied fund that the local government can divert, and θ is the proportion of untied funds that the local government diverts. θ is the choice variable of the local government. It is further postulated that an incumbent can divert funds for personal use that is not raised locally. This is an extreme version of the celebrated flypaper effect. We also postulate that α is given by 1

α = α1 (1 − θ) (Y − T ) − α1 T, 1

= α1 (1 − θ) Y − [α1 (1 − θ) + α1]T,

α = α1 (1 − θ) Y − α2 T

(2a) (2)

where 1

α2 = [α1 (1 − θ) + α1].

(2b)

The probability of the re-election of the incumbent local government is positively related to the utilized fund, (1 − θ) Y, for local goods and negatively related to the resources raised locally, T, while α1 and α2 > 0. Hence the expected payoff of the incumbent local government is given as: ER = α1θY 2 − α1 θ 2Y 2 − α2TθY − α1θ Y T + α1θ 2YT + α2θ T 2. (3) The first-order condition to maximize ER with respect to the choice variable θ is given by: (dER/dθ) = α1Y 2 − 2α1θY 2 − α2T Y − α1Y T + 2α1θYT + α2T 2 = 0.

(4a)

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The second-order condition is (d 2ER/dθ 2) = 2Y(T − Y)α1 < 0.

(4b)

The second-order condition is satisfied if Y > T. The first-order condition yields the reaction of the incumbent local government. The slope of the reaction function of the incumbent local government is given by: (dT/dθ)LG = [2Y(Y − T )α1]/[(2α 2T − Y )α2 + α1 Y(2θ − 1)]. (5) 10.2.2 Central government We assume that the central government intends to improve the welfare of citizens. The welfare of a typical citizen, U(c), is assumed to be the following1: U(c) = c(K − T )

(6)

where c is the consumption of local goods, T is the tax burden of citizens and K is their income such that: c = (1 − θ)(Y − T) + T = Y − (Y − T)θ.

(7)

The central government has an opportunity cost of λ for each dollar of (Y − T ) that it transfers to the local government. For tractability, we set λ = 0 without losing any analytical bite. Thus, the first-order condition to maximize (6) with respect to T, given Eq. (7), yields the reaction function of the central government: T = [Kθ − (1 − θ)Y]/[2θ].

1

(8)

We assume that there are N identical citizens in the jurisdiction of the local government and we normalize by setting N =1. In a more general case, we will have N at the denominator of Eqs. (6) and (7). To our knowledge, the normalization does not affect the analytical results.

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The second-order condition yields: (d2U/dT 2) = −2θ < 0.

(9)

The slope of the reaction function of the central government (dT/dθ)CG is: (dT/dθ )CG = [(K + Y) − 2T]/(2θ).

(10)

10.2.3 Equilibrium configurations The Nash equilibrium of the proposed game is given by the values of (T, θ) that simultaneously satisfy Eqs. (4a) and (8). From Eq. (8), the slope of the reaction function of the central government (dT/dθ )CG has the following characteristics: (dT/dθ )CG > 0,

for T < (Y + K)/2,

(11a)

(dT/dθ)CG < 0,

for T > (Y + K)/2,

(11b)

Thus, the reaction function of the central government slopes upward till T reaches the value (Y + 1)/2 and then slopes downward. It is also instructive to note the curvature of the reaction function: (d 2T/dθ 2)CG > 0,

for T < (Y + K)/2,

(11c)

(d T/dθ )CG < 0,

for T > (Y + K)/2.

(11d)

2

2

From the reaction function of the local government (4a), we know that its slope (dT/dθ)LG: (dT/dθ)LG = [(2Tα2 − Y)α2 + (2θ − 1)α1Y]/[2Y(Y − T)α1], (11e) (dT/dθ )LG > 0,

if T/m + θ/n > 1,

(12a)

(dT/dθ)LG < 0,

if T/m + θ/n < 1

(12b)

where m = Y(α1 + α2)/(2α2), n = (α1 + α2)/(2α1).

(12c)

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The curvature of the reaction function of the local government can be shown from (11e): (d 2T/dθ 2)LG > 0, (d 2T/dθ 2)LG < 0,

for (dT/dθ)LG > 0,

for (dT/dθ)LG>

2 α2 /[2Yα1].

(12d) (12e)

We provide a qualitative exposition of the Nash equilibrium in the following diagrams. We dichotomize the model into two scenarios: Scenario 1 is the one in which the local government is beset with a severe resource scarcity (Y < K) whilst in Scenario 2, the local government has resources beyond a critical level (Y > K). We expound the possible equilibria in these scenarios in the following diagrams: Scenario 1: Severe Resource Crunch (Y < K) Case 1. Multiple Equilibria without a Stable Equilibrium (Y < K) Figure 10.1 demonstrates the possibility of multiple equilibria such that none of these equilibria is stable. It is instructive to note that this possibility arises when the intercept of RCG on the θ axis is Y/(Y + K) such that Y/(Y + K) < θ** and θ** is the intercept of RLG on the θ axis. This implies (Y/(Y + K) < (1/2) and hence Y < K. There are two equilibria, E1 and E2; E1 is patently unstable while E2 is unstable if (dT/dθ)LG< (dT/dθ)CG at E2. Case 2. Multiple Equilibria with a Stable Equilibrium (Y < K) This possibility arises when the intercept of RLG (θ**) on the θ axis is such that θ** < n so that RLG is positively sloped with (d2T/dθ 2)LG > 0 for (dT/dθ)LG > 0, if T/m + θ/n > 1 as given by (12a). Assume also θ** > Y/(Y + K) (see Fig. 10. 2.) E2 is the unstable equilibrium. At E1(dT/dθ)LG < (dT/dθ)CG for E1 to be stable. Thus, E1 is a stable equilibrium if (2θ )/[(K + Y) + 2T] > [2Y(Y − T)α1]2/[(2α1Y(Y − T)) 2 *(2α 2 + 2Y dθ/dTα 1) + (2Tα 2 − Y)α 2 + α 1Y(2θ − 1)].

(13a)

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θ

R LG

R CG

E2

N θ**

E1 Y/K+Y O

Figure 10.1.

M

T

Multiple Nash Equilibria with severe resource scarcity (Y < K).

RLG represents the reaction function of the incumbent local government while the reaction function of the central government is depicted as RLG. The Nash equilibria are E1 and E2. The stability of these equilibria depends on the absolute values of the slopes of RLG and RCG at E1 and E2. Patently, E2 is unstable whilst E1 is unstable if the absolute value of the slope of RLG is steeper than the slope of RCG. Also note OM = m = Y(α1 + α2)/(2α2) and ON = n = (α1 + α2)/2α1. The reaction function RLG has a negative slope in the region within the triangle OMN and a positive slope outside this triangle. The slope of the reaction function of the central/national government is positive.

Case 3. Non-Existence of a Pure-Strategy Nash Equilibrium (Y < K) This possibility arises if reaction functions are as in Fig. 10.3. Scenario 2: Local Resources Above a Critical Level (Y > K) Case 4. Unique and Stable Nash Equilibrium From Fig. 10.4, we can see that a unique and stable equilibrium exists if 2/(Y − K) > −α2/[2Yα1],

for Y > K.

(13b)

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θ

R LG R CG E2

N

E1

O

M

T Figure 10.2.

Multiple Nash Equilibria with severe resource scarcity (Y < K).

RLG represents the reaction function of the incumbent local government while the reaction function of the national government is depicted as RCG. The Nash equilibria are E1 and E2. The stability of these equilibria depend on the absolute values of the slopes of RLG and RNG at E1 and E2. The reaction function RLG has a negative slope in the region within the triangle OMN and a positive slope outside this triangle. The slope of the reaction function of the central/national government is positive. E2 is unstable while E1 is stable if the stability condition is fulfilled.

The equilibrium can be stable if the equilibrium is situated to the right of the separatrix T = (K + Y)/2. To the right of the separatrix, (dT/dθ)CG < 0, hence the stability calls forth 2θ/[(K + Y ) − 2T] > [2Y(Y − T)α1]2/[(2α1Y(Y − T)) 2 * (2α2 + 2Y dθ/dTα1) + (2Tα2 − Y)α2 + α1Y (2θ − 1)].

(13c)

Case 5. Unique and Unstable Nash Equilibrium It is instructive to note that this possibility arises when the intercept of RCG on the θ axis is Y/(Y + K) such that n > Y/(Y + K) > θ ** = 1/2

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Local Governance: Fiscal Decentralization and Conflicts in LDCs θ

279

R CG

R LG N

O

M

Figure 10.3.

T

No Nash Equilibrium in pure strategies.

RLG represents the reaction function of the incumbent local government while the reaction function of the national government is depicted as RCG. In the above case, there does not exist an equilibrium.

where θ**(= 1/2) is the intercept of RLG on the θ axis. The slopes of RCG and RLG at the θ intercept are such that: 2θ/(Y − K) > −α2/[2Yα1],

for Y > K,

(14a)

(2θ)/[(1 + Y)−2T] < [2Y(Y − T)α1] /[(2α1Y(Y − T))* 2

2

× (2α 2 + 2Y dθ/dTα1) + (2Tα2 − Y)α2 + α1Y(2θ − 1)].

(14b)

Equation (14b) is true if there is an intersection between RLG and RCG as it is obvious from Fig. 10.5 if the intersection takes place to the left of the separatrix, that is, to the left of the line T = (K + Y)/2. Hence, if there exists an equilibrium E, it must be unstable, since (14b) must hold if (14a) holds if the equilibrium is situated to the left of T = (K + Y)/2. 10.2.4 Fiscal instability and fiscal reforms If local governments have a severe resource crunch (Y < K), the main result is threefold: First, the proposed fiscal equilibrium may not exist.

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θ

R LG

M

E

R CG

O

N

Figure 10.4.

(Y+K )/2

T

Unique and stable equilibrium (Y > K).

RLG represents the reaction function of the incumbent local government while the reaction function of the national government is depicted as RNG. OM = Y(α2 + α1)/(2α2) and ON = (α1 + α2)/(2α1). The reaction function RLG has a positive slope outside this triangle. E is a stable equilibrium if the absolute value of the slope of RCG is greater than the slope of RLG.

Second, when such an equilibrium exists, it may not be unique. Finally, there may not exist a stable equilibrium. The consequence is instability in the local government system driven mainly by coordination failure. More importantly, the possibility of multiple equilibria lifts the lid off the Pandora’s box: A momentary departure from an equilibrium, or a minor perturbation in expectations, can have a lasting influence on the fiscal equilibrium. Multiple equilibria also cause the standard indeterminacy. The multiplicity of equilibria makes the political system extremely fragile that can have serious consequences for the local economy (Gangopadhyay, 2002). Consider Case 2 as in Fig. 10.2. History determines whether the stable equilibrium E1 gets established. If the initial values of T and θ are contained within E2, then the system will

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θ R LG R CG E

N

O

M

Figure 10.5.

(Y+K )/2

T

Unique and unstable equilibrium (Y > K).

RLG represents the reaction function of the incumbent local government while the reaction function of the national government is depicted as RCG. The reaction function RLG has a positive slope outside this triangle NOM. E is the unique and unstable equilibrium.

steadily converge to E1. Otherwise, the system fails to converge to any equilibrium outcome. Expectations play a crucial role in determining the equilibrium outcome. If all agents expect E1 to be established, then E1 gets established. On the other hand, if all agents expect E2 to get established, then the system reaches the unstable equilibrium E2. A minor and momentary right-ward departure from E2 can destabilize the entire system. Suppose E2 is reached and there is a sudden increase in T. The resultant outcome is an ever-increasing T matched by an increase in corruption in the form of a continued diversion of funds. There is no equilibrium to which the system now converges. Such instability can be created by purely subjective factors if players anticipate changes in T, or θ, to the right of E2. Similar instability is expected for Case 1 in

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Fig. 10.1 as both these equilibria E1 and E1 are unstable. We expect similar instability for Case 3 (as in Fig. 10.3) since E is an unstable equilibrium. Such instability can trigger conflicts among groups of citizen voters as the coalition of voters supporting the incumbent government can become unstable (see Gangopadhyay, 2000). Any fiscal reform that takes the system to a serious deficiency of resources (Y < 1) can lead to irreversible damage to the system as the fiscal system is beset with instability as discussed above. The most meaningful reform entails a transition from Scenario 1 (Y < K) to Scenario 2 (Y > K). In the absence of such a reform, there is a severe resource crunch so that the fiscal outcome is beset with a serious instability (Case 1–Case 3). In the post-reform scenario, the central government will need to pour resources beyond the critical level (Y + K)/2, that is when T > (YL + K) where YL is locally raised revenue and equals Y − T. Does it lend stability to the fiscal system by ensuring the establishment of the stable equilibrium of Case 4 (Fig. 10.4)? It is important to note that the transition to the stable equilibrium is feasible only when (dθ/dT)LG is very low so that the reaction function of the local government is very flat. In other words, the reform can establish the stable equilibrium if and only if the corruption of the local government rises at a slower pace than the increase in T in the region T ∈ (0, (Y + K)/2). One may call the reform package that triggers the transition to Case 5 a Pareto-improving reform (PTR). Otherwise, the reform will take the system to Case 4 in which the system is still beset with an unstable equilibrium, and consequent fragility and instability. Even making sufficient resources available to the local government may thus fail to deliver the good since the system may fail to reach a stable equilibrium, if bureaucrats at the local level have high incentives for corruption. Hence a successful reform program must address two key issues: • •

increase in intergovernmental transfers beyond a critical level (YL + K); creation of significant disincentives to corruption.

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We also note three important facets of PIR: • • •

the larger the locally raised resources (YL), ceteris paribus, the larger will be the required transfer to achieve a PIR; the richer local residents are (K), the larger will be the required transfer to achieve a PIR; with increased opulence of local residents over time, the central government will have to make more and more transfers to retain the inequality T > (YL + K) in order to maintain the unique and stable equilibrium of Case 5.

Finally, a fiscal reform that takes the system from Case 5 to Scenario 1 is a highly dangerous and deleterious one. Before reforms, the system is perched on a stable equilibrium with low corruption and high T. Such reforms will trigger a disappearance of this stable equilibrium of Case 4 and the system will be beset with the serious instability of Case 1 and Case 3 of Scenario 1. 10.3 Conclusion Local governments must have reasonable autonomy in determining local taxes. This is necessary for making local governments accountable. The art of local governance is a delicate balancing act: autonomy and accountability will allow a local government to vary local taxes in order to collect larger revenues to finance higher levels of local services, if the local government so chooses. This would allow the local government to establish a linkage between revenues and expenditure. Local revenues ought to be collected from local residents in proportion to the perceived benefits from local services for them. Such decentralization entails fiscal disequalization — as richer zones will collect more revenues. In order to offset this disequalization, intergovernmental transfers are designed to endow local governments with sufficient revenues to provide a “standard” level of local expenditure. Sensible local governance is thus built on fiscal autonomy and accountability of local governments along with appropriately

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designed transfers. Incorrect designs of transfers and a lack of true accountability can cause serious distortions in the provision of local goods. We developed a simple game involving local and central governments to characterize potential (Nash) equilibrium outcomes. In the proposed model, fiscal reforms are successful when they establish a stable equilibrium. We are successful in isolating a threshold of local resources such that for local resources below this threshold (Y < K), the fiscal scene is beset with significant uncertainty and instability caused either by multiple equilibria, or by an absence of pure-strategy Nash equilibrium. Fiscal reforms that fail to yield local resources above this threshold will fail to improve economic conditions at the local level. We also endogenously derive a critical value of transfers from central governments to local governments. For transfers below this critical value (T < (Y + K)/2), fiscal reforms are doomed to fail. We find that fiscal transfers beyond this critical point can establish a stable equilibrium. Whether fiscal transfers can establish a stable equilibrium depends on the flatness of the reaction function of the local government: if the corruption of local government rises at a sluggish rate with respect to increases in transfers from central government within a relevant zone, then fiscal reforms will be successful. Successful and Pareto-improving fiscal reforms therefore entail a transition from a scenario in which Y < K to a scenario where T > (Y + K)/2 such that the post-reform game is characterized by a unique and stable Nash equilibrium. This is feasible only when corruption at local levels can be restrained.

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Chapter 11

Multinationals and Labor Unions in LDCS: Cooperation vis-à-vis Conflicts

11.1 Introduction Multinational enterprises play an important role in shaping international competition (see Brainard, 1997). Rugman (1988) provided an estimate that the 500 largest multinational firms control more than 50% of global trade flows that constitutes one-fifth of the global GDP. The multinational production-location decision is explained by a trade-off between maximizing proximity to consumers and concentrating production to reduce the cost of production (see Krugman, 1983). In imperfectly competitive models, this trade-off arises since a multinational enterprise has proprietary advantages that are internally exploited by spreading production across nations due to asymmetric information, technology diffusion and quality control (see Ethier, 1983; Dunning, 1988; Raff, 1992). The primary purpose of the internationalization of the production base is to achieve cost efficiency given the distribution of global customers. The cost structure of multinational enterprises, their production-location decision and internationalization will, therefore, depend critically on the outcome of local labor market and government tax policies. This is so since the cost structure is seriously influenced by wages, taxes and subsidies. Recent years have witnessed the emergence of a literature that addresses an important area of interface between internationalization and multilateral tax reforms (see Keen, 1987, 1989a, 1989b; TurunenRed and Woodland, 1990). The current interest is partly fuelled by 285

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the emergence of the European Union that has accorded a high priority to multilateral tax reforms in member nations. With the increased pace of internationalization in the 1990s, explicit trade barriers in the global markets have been steadily on the wane. As a corollary, policy advisers have recommended multilateral tax reforms to reduce potential and actual trade distortions and to increase internationalization (Keen and Lahiri, 1993). These tax reforms have taken two major forms: first, a uniform contraction of all taxes and tariffs and, second, the harmonization of commodity taxes. The major concern of the existing literature is to assess whether a common or harmonized tax is better, in welfare-theoretic terms, than distinct and distorting tax systems in different nations. An important implication of multilateral tax reforms is its influence on the production-location, or investment, decisions of multinational corporations (MNCs) that in turn propel the forces of internationalization. National governments traditionally offer tax concessions to the MNCs to attract foreign investment. In this context, the institutional structure of labor markets has surfaced as an important element in determining the “international competitiveness” of firms involved in the global markets (Brander and Spencer, 1988; Matsuyama, 1990). It is generally recognized that unionization and labor market asymmetries have a strong influence on the investment decisions of MNCs that, in turn, impact on the process of internationalization. The conventional wisdom is that a strong labor union in a nation will increase the wage rate above their opportunity cost and, thereby, lower the profits of both domestic and foreign firms. This will indeed damage the competitive position of these firms located in highly unionized nations (Brander and Spencer, 1988). Therefore, the strong unionization of a labor market is commonly regarded as an entry-deterrent for MNCs. Both tax reforms and the institutional structure of the labor market have strong influences on the production-location decisions of MNCs. The innovation in this chapter is to offer a two-country model that makes the production-location decision of MNCs, national tax policies, and union-government wage bargaining endogenous, and thereby provides a framework in which the optimal

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tax policy, optimal multinational investment, and the equilibrium labor market outcomes are explained. The model allows us to determine endogenously the tax policies and labor market outcomes within national boundaries that will, in turn, propel the optimal investment decisions of MNCs and, thereby, fuel the process of internationalization. The upshot is that the proposed model reverses a much-abused conventional wisdom that argues that a strongly unionized labor market acts as an entry-deterrent for MNCs. Contrarily, we show that a strong union may enhance the flow of multinational investment into a nation. The economic rationale for this finding is that a tax concession to multinational firms offered by a domestic government is an implicit tax on the domestic sector, especially on the wage income. If a labor union is powerful, then the base of (labor) income tax is large and also the wage income is high since the wage rate is above the opportunity cost. As a result, if the government passes the tax to the wage earners, the political cost will be less for two reasons: First, since the tax base is large, the tax burden is small. Second, the target income of the workers is achieved by a powerful union and so workers have less incentive to fight the tax increase (i.e., decline in wage income) tooth and nail. On the other hand, suppose the union is weak, the workers are poorly paid; the tax base is small. As a result, when the tax gets shifted to workers, the decline in wage income will cause a significant decline in the welfare of workers that can generate strong opposition to tax concessions to MNCs from the union. Such labor trouble is a sheer nuisance to multinationals that have an incentive to evade such problems.1 The nuts and bolts of the two-country model are as follows: a national government in each country can, ceteris paribus, increase

1

Let us put it more baldly. Suppose we are confronted with two mutually exclusive alternatives: either to dine with a pack of hungry, lean and mean wolves, or to dine with a fat, well-fed and lazy lion. We may have a better chance of survival with this lion in comparison with an almost instant annihilation by the pack of wolves. Our basic intuition in the chapter is analogous to this diner’s dilemma.

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national income, employment and economic growth by attracting MNCs through tax incentives. A typical multinational firm looks for product space, and weighs tax rates and cost conditions in each nation before making an investment decision. Each national government attempts to minimize the tax burden of the multinational firm to induce the firm to invest in the domestic economy — given the tax rates and cost conditions of the competing country. But such efforts are not costless since the national government must pass the tax to the domestic producers/consumers; otherwise they must reduce the budget deficit. We offer a two-tier decision problem: The tier-one game is played out between the national governments in a noncooperative fashion — given the expected union-government agreements on wage bills and tax rates. The tier-two game is a two-person game played out between the government and the labor union in each country, that come to an agreement about the wage bill and the taxes on the wage income. The cooperative solution to the game is of the Nash type. Given the anticipated labor market outcome and the wage tax, these national governments choose the equilibrium tax rates for the MNCs that are the mutual best responses. We characterize the equilibrium tax rates. The plan of the chapter is as follows: We present the fundamentals of the postulated economy in Section 11.2. In Section 11.3, we analyze the multinational production-location decision in the context of international tax competition. In Section 11.4, we examine the wage negotiation between national governments and labor unions. In Section 11.5, we provide a solution to the proposed two-tier game and analyze the sensitivity of multinational investment to the outcome of wage negotiations in the domestic economy. We conclude in Section 11.6. 11.2 The Economy We present the major economic relationships and variables in Table 11.1.

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Multinationals and Labor Unions in LDCS Table 11.1.

289

Major economic relationships and variables. P Y = Wg + Πg + tCP Y + (1 − x)ΠF

(1a)

P Y: Nominal National Income, P: Price level, Y: Real National Income, Wg: Gross wage bill, Πg: Gross profits of domestic firms, (1 − x)ΠF: Retained gross profits of multinational enterprises. Πn = Πg (1 − tΠ)

(1b)

Wn = Wg (1 − tw)

(1c)

n ΠF

(1d)

= (1 − x)ΠF (1 − tF)

Πn: Net profits of domestic firms, Wn: Net wage bill, ΠFn: Net retained profits of multinationals, tΠ: Profit-tax on domestic firms, tw: Wage tax, tF: Profit-tax on multinationals. Wg = wL

(1e)

w: Nominal wage rate, L: Employment L = bY

(1f )

Equation (1f ) represents the linear production function. P = ϕ wb

(1g)

Equation (1g) represents the mark-up pricing rule.

Basic macro relationships are explained as the following: 11.2.1 The macro picture Savings-Investment Balance: PI = SwWn + S ΠΠn + (1 − x)ΠF I: Real investment

(2a)

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Budgetary Balance: PG = T = tΠΠg + twWg + tc P Y + tF ΠF

(2b)

G: Real government expenditure, T: Tax revenue, tc: Tax on final goods and services such as VATs. Distribution of Investment: PI = PIF + PID

(2c)

IF: Foreign investment by MNCs, ID: Investment by domestic firms. We assume: IF = f (ϕ, w, tF)

(2d)

such that

δf/δϕ > 0,

δf/δw < 0,

δf/δtF < 0.

(2e)

We assume that domestic investment increasing in net profits of the domestic firms: PID = αΠn.

(2f)

PI = Pf (ϕ, w, tF) + αΠn,

(3a)

Hence,

P g f (j ,w, t F ) (1 - x )P F (1 - t F ) S W (1 - t W ) Y. = (1 - t P) (1 - t P)(S P - a ) j (1 - t P)(S P - a) P

(3b)

The distribution of profits will always be such that: P g Y [j (1 - t c) - 1] (1 - x )P F = . P j P

(4a)

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11.2.2 Equilibrium national income Combining (4a) and (3b) yields the equilibrium national income and profits: Y * = A1/k + A2/k

(5a)

A1 = Pf (ϕ, w, tF),

(5b)

A2 = ϕ [ΠF (1 − x)(1 − tF)][(1 − t Π)(S Π − α)− P],

(5c)

Ê P g ˆ* j (1 - t C) - 1 È A 1 + A 2 ˘ P F (1 - x)(1 - t F) . ÁË P ˜¯ = ÍÎ ˙˚ k P j

(5d)

where

Observation 1. Increase in foreign investment boosts the equilibrium national income since dY* = 1/k > 0. dA1

(6a)

Increase in profits of multinationals increases the equilibrium national income: dY* > 0. dA 2

(6b)

Observation 2. Increase in foreign investment increases profits of domestic firms. On the other hand, as profits of multinational enterprises go up, the real profits of domestic firms decline: d (P g /P )* dA 1, A 2

= 1/k > 0,

d (P g /P )* d PF

< 0.

(6c)

(6d)

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Observation 3. Increase in tax on wage increase (tw) and reduction in tax on multinational (tF) will increase equilibrium national income Y * and employment since: d (P F /W )* 1 = >0 d tw wb (1 - t w)2

(7a)

and since dY* > 0, d PF

dY* dY* d (P F /W )* = > 0. d t w d PF dt w

Similarly, dY* dY* d P F < 0, = dtF d PF d tF

(7b)

since Y * and ΠF bear a positive relationship and ΠF and tF are negatively related. Statement 1. The national government can increase national income and employment by increasing tw and reducing tF. The prescription may be too simplistic. In reality, the thorny question is twofold: Can the national government effectively lower the (net) wage rate by raising tw? Will the government attract multinational enterprises by just reducing tF ? Our innovation is to make both tw and tF endogenous. We determine tw from the wage bargaining between the national government and the nation-wide labor union. We determine tF from the international tax competition among nations. The optimal tax policies and the optimal investment decisions of the multinationals will propel international competitiveness. 11.3 Tax Competition and Production-Location Decision of Multinationals Consider the multinational production-location decision in a simple set-up of two competing nations. The multinational firm uses production space, Hi, as an input to produce final goods in nation i.

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We assume the following production function for multinational nation i: Qi = Hi.

(7c)

The demand of the multinational firm for production space in nation i is as follows: j

i

Hi = Qi = m − n1tF + n2tF .

(7d)

Ceteris paribus, the larger the tax rate in nation i, tFi, the lower is the demand for the production space of the multinational in nation i. The greater is the tax rate in nation j on multinationals, the greater is the demand for production space in nation i. Hence, the tax liability of a typical multinational firm in nation i, TFi, is

(

i

i

i

i

)

j

TF = (P − ci) m tF − n1 (tF )2 + n2tF tF .

(8a)

P and ci are the exogenously determined price and cost of production. We assume that the cost depends solely on the wage rate. Hence

i TF

(

ci = wi,

= (P − wi) mtFi −

(8b)

i n1 tF 2

( )

+

i j ntF tF

).

(8c)

Assumption 1. The national government in nation i attempts to minimize the tax burden TFi to give incentive to multinational firms to invest in the domestic economy given the tax rate in nation j. i

Proposition 1. The optimal tax rate of nation i on multinationals, tF , is j an increasing function of tF and is given by the following reaction function: i

j

tF = m/(2n1) + n2/(2n1)tF .

(8d)

Proof. The national government i seeks to minimize the tax burden of the multinational firm: i

(

i

i

j

Minimize = TF = (P − ci) mtF − n1(tF)2 + n2tFitF {tFi}.

)

(8d′)

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The first-order condition is i

j

(P − wi) (m − 2n1tF + n2 tF ) = 0.

(9a)

From (9a), we derive (8d) by minor manipulation. In an analogous fashion, we define the demand for production space in nation j as: j

i

Q j = Hj = L1 − L2tF + L3tF .

(9b)

The reaction function of nation j in tax rate on the multinational firm is j

i

tF = L1/(2L 2) + L3/(2H1)tF ,

(9c)

Proposition 2. The Nash equilibrium tax rates on the multinationals — i j (tF )e and (tF )e — that derive from the international tax competition are the following: (t Fi )e =

2m L 2 + M L 1 , 4 n 1L 2 - n 2L 1

(10a)

(t Fi )e =

wL 1n 1m L 1 . 4n 1L 2 - n 2L 1

(10b)

Proof. The Nash equilibrium tax rates are given by the solution to the simultaneous equation systems (9b) and (9c). Proposition 3. The equilibrium tax rate on wage income in nation i, (twi) e, is given by: (t wi )e = (a / b)(W gi / ’iF )

2m L 2 + L 1n 2 . 4n 1L 2 - n 2L 1

(10c)

Proof. From the internal equilibrium, we know: tFi/twi = b/a ΠFi/Wgi. Substituting tFi by Eq. (10a) yields (10c).

(10d)

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Statement 2. Equation (10d) plays an important role in reversing conventional wisdom. The profits of the multinational firm ΠF* are: i i ’* F = a / bW g / t w

2m L 2 + L 1n 2 . 4n 1L 2 - n 2L 1

(10e)

From (2d), (I F )i is

(I F )i

Ê ˆ 2m L 2 + L 1n 2 i = f Áa /b W g / t wi ˜ , Ë ¯ 4n 1L 2 - n 2L 1

f ¢ > 0.

(10f)

Foreign investment in nation i bears a positive relationship to the gross wage bill, Wgi, and a negative relationship to the tax on wage income in nation i, twi. From Eq. (10f ), we know that Wgi and twi work in opposition: given twi, the foreign investment is the greater — the greater is Wgi. Given, Wgi, foreign investment is the lesser — the greater is twi. 11.4 Wage Bargaining in the National Arena Let Y be the national income, W be the share of workers ignoring subscript i for nation i. It is postulated that the union demands the largest possible share W and the national government demands the maximum share, Y − W, for the rest of the economy. The bargaining game is a cooperative one and the Nash product µ is defined as:

µ = λg Log(Y − W − G 0) + λL log(W − W 0)

(11a)

where λg and λL are, respectively, the bargaining strengths of the government and the labor union. G 0 and W 0 are the shares if the national bargaining breaks down. Proposition 4. The solution to the proposed cooperative game is the wage share WE such that W E = (Y − G 0)1/(λg/λL + 1) + W 0/(λg/λL).

(11b)

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Proof. The solution to the proposed game is given by the wage share W that maximizes the Nash product. The first-order condition to maximize (11a) with respect to W is as follows: -l g dm lL = + = 0. 0 dW Y - W - G W -W 0

(11c)

Reorganizing (11c), we get WE: W E = (Y − G 0) [1/(1 + λg/λL)] + W 0 [1/(λg/λL + 1)]. (11d) 11.5 Multinational Investment and Wage Bargaining In the first tier game, national governments engage in a tax competition to attract multinational investment. National governments choose the tax burdens at this stage of the game. In tier two of the proposed game, each national government negotiates with the labor union to determine the wage income and individual tax on labor. If information is complete, in the relevant rational expectations equilibrium, the multinational firm and the national governments correctly predict the cooperative outcome of wage bargaining in tier two of the game. Given the outcome of tier two and the internal equilibrium, the optimal tax policy is chosen at tier one. The production-location decision is the solution to the two-tier game that is popularly known as the perfect Nash equilibrium (PNE).2

2

In order to solve the game, we apply the logic of backward induction: we start with the tier-two game and characterize the cooperative Nash solution to the wage bargaining game (Section 11.3). Rationality and complete information dictate that both national governments and the multinational firm will form expectations by looking ahead and foreseeing the cooperative Nash solution. If agents behave in this fashion, they are said to have rational expectations.

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297

Proposition 5. The optimal investment of the multinational firm in country i, (IF )i, is derived as the PNE of the proposed two-tier game and is given by:

(I F )i

Ê ˆ a 2mL 2L 1n 1 1 ˜ =fÁ . (Y i - G 0 + W 0) l g i Á b 4n(1L 2 - n 2L 1 ˜ ( ) +1 Ë ¯ lL

(12a)

Proof. Since the multinational firm is endowed with rational expectations, hence Wgi is given by Eq. (11b). Thus, in the tier-one game, the multinational firm correctly predicts the wage share of the tiertwo game and invests in response to ex ante profits ΠFi. Substituting (11d) into (10f ) yields (12a) that is the PNE. Proposition 6. The optimal foreign investment of the multinational enterprise in nation i, (IF)i, is an increasing function of the bargaining strength, (λL)i, of the labor union of the nation i in its wage negotiation with the national government. That is, d (I F )i > 0. d (l L)i

(12b)

Proof. Differentiating (12a) yields: d (I F )i d

(ll )i g

L

È a 2m L 2 + L 1n 1 1 = - f ¢ ÍÍ (Y - G 0 + W 0) l b 4n 1L 2 - n 2L 1 1 + lg ÍÎ l

˘ ˙. 2˙ ˙˚

( ( )) i

(12c)

Since f ′ > 0, hence d (I F )i d

lg i lL

( )

< 0.

(12d)

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Since d (I F )i d (I F )i 1 = l . (l g )i i g i i ˘2 d (l L) d È ) ( l L lL Î ˚

( )

(12e)

From (12d) Eq. (12b) follows. 11.6 Concluding Comments The unionization of the labor market has far-reaching consequences in imperfectly competitive markets since it affects the cost of production of firms. In a similar vein, direct and indirect taxes impinge on the cost of production and, hence, on the equilibrium market outcome. We examine the investment decision of a multinational firm that faces an international product market. Its main economic decision is regarding the location of its production base. There are mainly two critical elements that influence the investment decision: First, the institutional structure of the labor market that determines wage rates and, hence, costs of production. Second, taxes and fiscal incentives directly influence the cost of production of MNCs. Multinational firms significantly contribute to the economic development of a country. National governments hence engage in competition with each other to attract multinational firms mainly through their tax policies. We model this competition between national governments as a non-cooperative game. The outcome of the non-cooperative game is sensitive to the wage cost which will determine the net profit of the multinational firm. The wage rate, hence, is a critical element in the decision problem of the multinational firm. As a result, labor market conditions and asymmetries between nations will be very important to secure a competitive position for the multinational firms in the global market. The investment decision of a multinational firm is therefore sensitive to both tax policies and labor market outcomes. The conventional wisdom is that the unionized labor market acts as an entry-deterrent for multinational firms since strong unionization

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raises the wage rate above the opportunity cost of labor. Thus, if one country has a more powerful union than the other, then the multinational firm based in the former will have lower “international competitiveness” because of a higher cost of production. If everything else is identical, then a multinational firm will naturally shun the former country. National government in that country must offer larger tax incentives to the multinational firms. We reverse this conventional wisdom by establishing that the optimal foreign investment by multinationals will be an increasing function of the equilibrium wage share. We observe that if the union is strong, then the base and rate of labor tax will be, respectively, high and low since the wage and employment are high. Thus, it will be easier for the national government to pass the implicit tax of fiscal concessions to the wage earners. On the contrary, with a weak labor union, such a shift of tax can precipitate a labor crisis. A fully informed and rational multinational firm will thus have an incentive to invest in the highly unionized country. Given the equilibrium tax rates on the multinationals, the larger the share of the labor in the national income, the greater the flow of multinational investment into this country. This analysis thus suggests that the “international competitiveness” of a country with powerful labor union will not necessarily be in jeopardy.


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Chapter 12


12.1 Introduction Only a generation ago, large cities filled the urban landscape of advanced industrial nations. Today, developing nations house the many mega-cities of our globe (see Krugman and Elizondo, 1996). To many observers, such an urban sprawl in developing nations is a sheer economic disaster as Bairoch (1988) poignantly labeled these mega-cities as “Romes without empires.” These cities are often a home ground for poverty, destitution and deprivation while the urban problem has been exacerbated by a blatantly inadequate supply of local goods. In a number of important studies on local governance in developing nations, it has been asserted that the inadequacy of local goods in cities of developing nations is a temporary phenomenon. It is generally recognized that urban crises will gradually disappear with economic progress and the democratization of urban society (World Bank, 1985; Government of West Bengal, 1986; Zakaria, 1978). However, there is little evidence that there has been any perceptible improvement in the quality of life of millions living in the urban sprawl (Gangopadhyay and Nath, 2001; Government of India, 1980–88; UNDP, 1993; Gangopadhyay and Nath, 1989). On the contrary, urban crises continue unabated in developing nations after many decades of high rates of economic growth and significant social progress. Why do local governments in developing nations fail to redress urban crises? This simple question drivers this chapter. 301

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The central concern of this chapter is to explain the nagging persistence of urban crises that have dogged developing nations decade after decade. We develop a simple game to argue that the inadequate supply of local goods in cities of developing nations is an equilibrium phenomenon. There is, hence, a reason to suspect that economic growth and social progress can fail to resolve urban crises. We argue that the source of the problem is an incorrect tax scheme that is propelled by the electoral motive of local governments. We highlight the need to reform local taxes and introduce Tiebout-type competitive forces in local governance in developing nations. The plan of the chapter is as follows: We examine the problems of globalization in Section 12.2 and look at theoretical issues in Section 12.3. Section 12.4 offers a model and Section 12.5 concludes. 12.2 Relevant Issues of Globalization Globalization is a multidimensional issue with various important facets entailing economic, financial, technological and social and political processes that continually transform the global economy, society and polity. It is generally recognized that the process of globalization has been significantly aided by the fall in the costs of communication and transportation that has led to an inevitable shrinkage of our globe into a quasi “global village” — characterized by an integration typically observed in traditional village communes. We therefore view globalization as a complex process that gradually unleashes a series of transitions: the process starts off with an increased integration of the world economy through trade and investment networks. It is well understood that the harbinger of this stage of increased integration turns on the pivot of decreasing transaction costs associated with trans-border trade and investment. Declining transactions costs are typically explained in terms of technical progress that reduces the cost of communication and transportation. Declining transaction costs have a direct and positive impact on cross-border trade and portfolio and direct investment. The economic consequence of this increased integration is twofold: First, nations become more interdependent in economic

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terms. Second, there arises a perception that trans-border trade and investment offer tremendous and often unprecedented economic opportunities for a nation. The first transition thus results in an increased integration of the world economy — through a mesh of multinational investment, trade flows, and flows of financial capital — with an equally important transition in the perception about the importance of trans-border trade and investment as a vehicle of economic progress and prosperity for a nation. The second transition affects the realm of national management as national governments actively respond to this new perception that trans-border trade and investment offer great benefits to those nations that entertain relevant openness to foreign trade and investment. As a number of nations vie against each other to take home the spoils of the world economy, policy makers have come to agree that the main barrier to the access of these spoils lies in the domestic economic structure characterized by the labyrinth of controls that has been a by-product of the Keynesian era of de-globalization. This leads to the third transition that paves the way for the homogenization of economic ideologies, the convergence of macroeconomic and trade policies and the consequent adoption of measures of domestic liberalization. For any national government, options are pretty limited — either it chugs along with the pre-existing regime of economic control with limited global trade as pursued by China and India, or the nation must ditch the olden economy and substitute it with a functional market mechanism, openness to trans-border trade, the liberalization of domestic and external sectors and exchange rates, and the privatization of state-owned enterprises. The hard fact is that during the 1980s and 1990s, the majority of nations went for the second option, representing an unprecedented convergence of economic ideologies. This common act of nations, as though to the dictate of a common script, has further consolidated the process of integration of the global economy. The final transition typically takes place in the social and economic spheres of our globe as a direct consequence of these previous transitions. The process of globalization can thus be reduced to this simple and uncomplicated fable. Within this simple fable highlighting various, possibly virtuous, transitions lies a plethora of terribly complicated subplots without

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which it is impossible to understand the process, consequences and ramifications of globalization. 12.3 Theoretical Underpinning The decentralization theorem of Oates (1972) suggests that local governments in advanced nations are effective in balancing the preferences and cost and, thereby, achieving a mix of local goods that efficiently satisfies the local demand. However, such an effective allocation may be blocked by interest group influence (see Borge and Rattsø, 1993; Borge et al., 1995) that could lead to inefficiency in allocation even in advanced nations. It is quite likely that conflicting interests of urban settlers in developing nations can also block efficient allocation. The median-voter model posits that local goods are supplied through a majority-rule voting process. As a result, the supply response of a local government coincides with the preferences of the median voter (see Rubinfeld, 1987; Bowen, 1943; Downs, 1957). Such a notion is inconsistent with a local government that provides many local goods and is influenced by powerful political parties (see Borge et al., 1995, p. 137). In such a scenario, different groups of voters struggle to enforce their influence on the local government (see Craig and Inman, 1985; Renaud and van Winden, 1991). As a result, the paradigm of direct democracy has severe limitations in explaining the supply responses by local governments even in advanced industrial nations. The median-voter model may have very limited applicability in developing nations. In the context of advanced industrial nations, the Tiebout (1956) hypothesis provides the theoretical underpinning of efficient local expenditure. This hypothesis invokes the “invisible hand” principle to solve the public goods problem as posed by Samuelson (1954). The precise import of the hypothesis relies on the competitive market fable: profit-maximizing local governments offering tax-local goods package come into economic contact with utility-maximizing residents who “vote with their feet.” This interaction engenders the usual forces of equilibration that effectively guide the allocation of resources towards a Pareto-efficient outcome if local governments

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maximize their land values (see Henderson, 1985). Despite serious criticisms by Bewley (1981), the Tiebout hypothesis remains a “challenging reference” for advanced nations. In developing nations, the lack of mobility of residents causes market failure as the residents do not “vote with their feet.” The Tiebout hypothesis has been less tenable in developing nations also due to an absence of competition between local governments. We instead apply the probabilistic voting theorem (see Wittman, 1989) to explain an electoral equilibrium that, in turn, determines the supply of local goods.1 The heart of the matter is that local taxes and goods typically entail political costs and benefits that a self-seeking government, driven by electoral motive, will like to exploit (see Gangopadhyay, 2001). An incumbent local government will naturally choose a tax-service package to maximize the probability of its re-election. We start off with the political characteristics of voters and then apply the probabilistic voting theorem to determine the electoral equilibrium to determine the equilibrium urban tax-service package. 12.4 The Model We postulate that there are N residents in an urban jurisdiction and these residents belong to two distinct groups of voters — namely, the rich and the poor. Out of these N voters, NR are rich and NP are poor. To keep the analysis tractable, we also assume that the budget is to be allocated between two local goods — water supply (W ), and roads and maintenance (M). We develop a two-stage game to determine the equilibrium provision. In Stage I, the incumbent government announces local tax rates. Given the grants and aids, these tax rates will determine the size of the budget of the local government. 1

The probabilistic voting model is a recent development in political theory to counter the time-honored predictions of traditional political theory: for centuries, social thinkers argued that democratic governments are plagued by the absence of a stable electoral equilibrium and the risk of expropriation of minorities by majorities. This model establishes the existence of a stable voting equilibrium.

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In Stage II, the incumbent allocates the budget between local goods, W and M. An election takes place at the local level at the end of Stage II. The goal of the incumbent is to get re-elected. We assume that voters have ideal points in terms of the allocation of budget.2 Voters from the same group have the same ideal point. As the actual allocation diverges from the ideal point of a group, more and more voters from this group will withdraw electoral support for the incumbent government. On the other hand, we assume both groups dislike to pay taxes; hence the higher (lower) the tax rate on a group, the lower (higher) the political support by this group for the incumbent. An electoral outcome is reached at the end of Stage II — given these tax rates in Stage I and the allocation of budget in Stage II. The incumbent maximizes votes in the election by choosing these taxes at Stage I and the budgetary allocation at Stage II, given the expected electoral outcome at the end of Stage II. If information is complete, in the relevant rational expectations equilibrium, all players of the game correctly predict the electoral outcome and the incumbent adopts optimal taxes in Stage I and optimal budgetary allocation in Stage II wherefrom the overall equilibrium of the game evolves. In order to solve this game, we apply the logic of backward induction: we start off with Stage II and characterize the electoral outcome. Rationality and complete information ensure that all players will form expectations by looking ahead and foreseeing the electoral outcome. At the overall Nash equilibrium of the game, the incumbent chooses local taxes and a budgetary allocation to achieve an electoral outcome that maximizes the votes and, thereby, the probability of its re-election. 12.4.1 The precise sequence of moves The game has two stages when specific decisions and events take place. We highlight these stages as Stage I and Stage II of the game.

2

It is important to note that a simple concave utility function will provide similar results.

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Before the game unfolds, important determinants of the game are exogenously given and we call them the history. We now describe the sequence. History • •

•

Local government receives grant, aids, and project-tied funds that we label as F. F is given exogenously. There are two distinct groups of residents/voters, namely the rich (R) and the poor (P) who have ideal points in the allocation of the local government budget. Voters’ characteristics are a part of history.

Stage I • • •

Local government announces individual tax rates, TR and TP , on the rich and the poor, respectively. These tax rates yield the revenue T of the local government. Thus, the budget of the local government B is determined as: B = T + F.

(1a)

Stage II •

Local government allocates B between W and M. That is, B = W + M = T + F.

•

(1b)

The election takes place after the allocation of budget B at the end of Stage II.

We provide Fig. 12.1 to summarize the time-structure of these decisions. 12.4.2 Budgetary allocations of Stage II and payoffs functions In our simple model, there are two groups of residents, R and P, and two local goods, W and M. The preferences of these two groups over

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HISTORY: • • • •

Grants and Aids Types of Voters Preferences of Voters Characteristics of Voters

•

•

Local Government Sets Tax Rates and Enforcement Efforts

•

Allocation of Local Budget is Undertaken

Local Budget is Determined

•

Election Takes Place

STAGE I

STAGE II

TIME

Figure 12.1.

Table 12.1.

R P

Time-structure of decisions.

Ideal points of residents/voters. W

M

φR φP

1 − φR 1 − φP

R: Rich, P: Poor, W: Water Supply, M: Roads and Maintenance.

these two local goods are assumed to be quasi-linear. The ideal points are presented in Table 12.1. φR and (1 − φR) are, respectively, the split of the budget into W and M as desired by the rich. As the actual allocation deviates from φR, a typical rich resident suffers a welfare loss. We similarly define it as φP. Let φ be the actual allocation of the budget by the local government. The utility function of a rich resident, UR, is specified as UR = −(φR − φ)2.

(1c)

The utility function of a typical poor resident is UP: UP = −(φ P − φ)2.

(1d)

Let us call V the total votes that the incumbent receives in the municipal election at the end of Stage II and VR and VP the votes cast in

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favor of the incumbent by the rich and the poor, respectively. The goal of the incumbent is to maximize the probability of its re-election by maximizing votes. The payoff function of the incumbent, UG, is simply the total votes that it receives in the election: UG = VR + VP.

(2a)

12.4.3 Electoral framework of Stage II In order to determine the provision of local goods, we now look at the electoral equilibrium in Stage II. We apply the probabilistic voting theorem to explain the electoral equilibrium. It is assumed that the government seeks political support from both of these groups. It is possible that the local government succumbs to sectarian interests and rent-seekers and, hence, adopts a tax-service package for the benefit of one group of voters only (see Craig and Inman, 1985; Renaud and van Winden, 1991). However, under certain conditions, it can be shown that the local government has an incentive to represents a coalition of both these groups (see Gangopadhyay, 2000). Within a group, voters have identical preferences. Their preferences are represented by utility functions (1c) and (1d). Following the basic tenet of the probabilistic voting theorem, we write SR and SP as the sensitivity variables of these groups of voters. SR represents the extent to which rich voters decrease their support/vote for the political party in response to a unit divergence between the actual allocation and these voters’ preferred allocation. SP is defined in a similar fashion for poor voters. We specify the votes-to-offer function of the rich as the following: VR = NR (1 + SRUR) λR

(2b)

where V R labels the votes that the incumbent receives from the rich, NR denotes the total number of rich residents, and λR is the proportion of rich residents who vote for the incumbent if the allocation equals the ideal point of the rich. We write the votes-to-offer function of the poor as the following: VP = NP (1 + SPUP) λP,

(2c)

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where VP labels the votes that the incumbent receives from the poor, NP and λP, respectively, denote the number of poor residents and the proportion of poor residents who vote for the incumbent if the allocation equals the ideal point of the poor resident. Given the tax rate TR on the rich, we express the sensitivity variable of the rich, SR, as the following: SR = 1−[(φR − φ)2/TR] < 1.

(3a)

Similarly, we write SP as: SP = 1−[(φP − φ)2/TP] < 1.

(3b)

It is important to note that the sensitivity variable is positively related to the tax burden of voters and also to the divergence between the ideal point and the actual allocation. It is assumed that (φR − φ) > 0 and (φP − φ) > 0. Otherwise, we express the sensitivity function in terms of (1 − φR) and (1 − φP). Based on the above, we offer the main result of this chapter in the following proposition. Proposition 1. An under-provision equilibrium characterizes the proposed game in which the incumbent maximizes its probability of re-election by simply choosing low taxes and inadequate provision of local goods. Proof. The goal of the incumbent is to maximize (2a) by optimally choosing φ at Stage II and setting TR and TP at Stage I. Substituting (2b) and (2c) into (2a) yields the following optimization scheme for the incumbent at Stage II: Maximize {NR (1 + SRUR) λR + NP (1 + SPUP) λP} {φ} Subject to (3a) and (3b).

(3c)

The first-order condition for the above optimization at Stage II is reduced to the following: (φR − φ)NR λR(1 − (φR − φ)2/TR) + (φP − φ)NP,

λP(1 − (φP − φ)2/TP) = 0.

(3d)

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In the overall equilibrium, the incumbent chooses TR and TP at Stage I to maximize its probability of re-election in Stage II. One set of values of TR and TP at Stage I that will maximize votes cast in favor of the incumbent in the election is the following: (1 − (φR − φ)2/TR)) = 0.

(4a)

TR* = (φR − φ)2, TP* = (φP − φ)2.

(4b)

That is,

(4c)

What is interesting is that the incumbent has the leeway to choose φ. One possibility to get re-elected is to set φ = φP, TP = 0, and TR* = (φR − φP)2. At this equilibrium, the poor pay no taxes for local goods while the rich pay a little. The result is an under-provision equilibrium in which the local government raises very little resources locally and supplies inadequate local goods. This equilibrium leads to the vicious cycle of urban poverty: • • •

Why are local goods inadequate in supply? Because local governments have little resources. Why do local governments have little resources? Because local taxes are low. Why are local taxes low? Because local governments supply very little local goods.

12.5 Conclusion In conclusion, we find that the main problem of local governance in developing nations is an inability, or lack of willingness, of local governments to balance the preference and the cost of providing local goods to residents. Thus, from the decentralization theorem of Oates (1972), we know that local governments will fail to achieve efficiency in satisfying the local demand. The heart of the problem is the low level of local taxes, driven by the electoral motive of local governments.

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At these low taxes, local governments are simply unable to provide adequate local services. Yet this tax-service package creates an electoral equilibrium that ensures the political survival of a local government through time. Hence, there is no incentive for these governments to improve local goods by increasing local taxes. Increases in grants and aids will have little effect on local goods as they will end up in the coffers of corrupt bureaucrats and politicians. This is akin to the problem of incorrect pricing of a product in a market insulated from the forces of competition. How to improve the quality of local services? There are two ways in which one can expect an improvement. First of all, it is necessary to revamp the local tax system so that residents pay a decent price for a decent service and also ensure minimum resources are spent on these services (Zakaria, 1978). Second, in consonance with the era of decentralization and deregulation, we suggest that it may be necessary to introduce Tiebout-type competitive forces in providing local goods in order to redress urban crises in developing nations. Local tax reforms and forces of competition are necessary to break the electoral equilibrium that taxes little and provides little of local goods.

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Concluding Comments: Whither Rivalry, Conflicts and Cooperation?

In Chapter 1, we examine various forms of rivalry, conflict and collusion in oligopolies with market segmentation. The primary intuition is that market segmentation creates an opportunity (potential rivalry) for a business firm to enter into other markets that can have a serious impact on the overall equilibrium configuration through the effects of potential entry on the incentives of and constraints on incumbent firms. On a similar note, market segmentation offers new scope for cooperation among incumbents to forestall entry and potential rivalry. There is little literature on this important issue examined in Chapter 1. Entries and exits, through their effects on the cost asymmetry in a segmented market, can trigger a series of endogenouslydriven changes in a market. Some important considerations are the following: •

•

One of the major key endogenous changes is the endogenous partnership formation, or collusion, of business alliances that is driven by these changes in the efficiency/cost asymmetry. We developed a model of endogenous alliance formation, which we believe to be the first of its kind to shed light on the incentives for firms to form coalitions and alliances endogenously in the context of threatened entry in a segmented market. In Chapter 1, we examine a model of endogenous alliance formation in the highly simplified context of an oligopoly with a linear demand function. In this model, firms form alliances in order to 313


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reduce their marginal cost of production, or improve efficiency. They also form alliances to capture the largest possible market spoils by acting as a single entity to enhance their market power in the relevant market segment. We start off with a simple duopoly and examine the exogenous possibilities of a potential merger between these incumbents. We then consider the entry by a firm into this duopoly that opens up the possibility of endogenous mergers/collusion/cooperation, or alliance formation. Based on the (marginal) cost differences/asymmetry in efficiency, we were able to determine the driving forces behind the endogenous alliance formation in this triopoly. Traditionally, collusion is an integral component of competition analysis, which entails some measures of conjectural variations. Based on the traditional measures of rivalry and collusion, we examined the Australian banking industry to explore the presence of endogenous collusion and alliance in a segmented industry such as this. The sample used for the study comprises 10 domestic Australian banks. The study covers the time period between 1995 and 2005 in order to capture the changes within the Australian banking industry that occurred following the Wallis Inquiry. Hence, the base year of 1995 represents the year before the announcement of the Wallis Inquiry in 1996 while the post-Wallis period commences after the publication of the inquiry’s Final Report in 1997. Two observations are in order: 1. The collusion index is significantly different from the value of one (1), implying significant collusive arrangement in the Australian banking industry, which represents some form of departure from intense rivalry and costly conflicts. 2. Second, the value of the index is not stable and fluctuates over time. It is also important to note that the value of the index has gradually stabilized towards the expected value of −1, which is a reflection of increasing rivalry and a decreasing degree of collusion since 2000. Thus on the empirical evidence, one can argue that powerful players can peacefully settle their conflicts, but the cooperation device gradually becomes weaker.


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The caveat is that it is a restrictive form of alliance that we consider in this work. Upon the formation of an alliance between two firms, the new entity sells off the assets of the less efficient business in the relevant segment and offers appropriate compensation to all old shareholders and workers of this less efficient organization. The implicit assumption is that the value of the less efficient firm is less than the competing claims of its owners and workers. In order to shed light on endogenous market segmentation and consequent price discrimination in local segments, we introduce an important type of price discrimination known as chaotic discrimination: sellers quote prices in an oligopolistic market which are almost uniform and part of the common knowledge. Each seller, in reality, engages in secret and arbitrary price discounts and, thereby, creates some unsystematic pattern of price discrimination. Thus, there are two critical elements in chaotic discrimination: a common and high posted price, and secret, yet arbitrary and chaotic price discounts. The contribution of this book is twofold: • •

First, it provides a model to explain why sellers may choose a common and high posted price. Second, we explain the “arbitrary” and “chaotic” nature of price discounts. Bain (1952) stressed the importance of such discrimination. He attempted to explain it mainly in terms of the stability of collusion of sellers while the burden of his argument turns on sellers’ irrationality concerning price making.

We provide an alternative rationale behind chaotic discrimination on the basis of two sets of arguments: First, we argue that sellers may adopt upward price-distortion to prevent entry and thus maintain long-run market shares and profits. Thus the chapter establishes that chaotic discrimination as a pricing strategy is a subgame perfect Nash equilibrium (PNE). We, thereby, provide a strong theoretical justification for chaotic discrimination as an optimal pricing strategy. Second, we constructively demonstrate that sellers would fail to adopt profit-maximizing price discounts due to multiple equilibria in such a market. The price discounts


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will be uncoordinated and, hence, “arbitrary” and “inconsistent,” which would deviate from the profit-maximizing discounts. The upshot of the findings is that incumbent sellers can successfully deter entry by choosing an upward price-distortion, yet they would fail to coordinate price discounts to reap short-run profits owing to multiplicity of the equilibrium discounts. Finally we introduce a political element in the determination of the degree of rivalry in an oligopoly by considering the allocation of public infrastructure that impinges on the cost of production of two or more oligopolists that are based in different geographical locations. In traditional models of competition, such political factors have not been examined. The Smithian perspective on competition highlights a congruence of interests of market participants: say, a buyer wants some milk and is ready to give some money to the milkmaid for it, and the milkmaid wants money and is, therefore, ready to give a carton of milk in exchange. This exchange allows each to achieve one’s goal and they, thereby, help each other. In a complex market mechanism, however, economic problems are often embedded in a conflicting situation. It is recognized that the market mechanism can easily handle congruent interests but may fail to resolve conflicts in a harmonious or fair fashion (see Sen, 1984). To redress such conflicts, the visible hand of government has usually been invoked (Ostorm, 1987). In this work, we highlight two types of conflicts — namely, market conflicts and political conflicts — and, thereby, attempt to weave them together to illuminate an important intersection between the economy and the polity. We introduce conflicts at the market level in the usual fashion as market rivalry — two prototype firms compete against each other for market shares. By applying the simple game-theoretic reasoning, we obtain the equilibrium market outcome. However, the core of the problem remains that the emerging market outcome, the conduct of firms, market shares, and the take-home profits of these rivals critically depend on the choice of their strategic variable and, hence, on the nature of competition. Dixon (1986) introduced consistent conjectural variations to make the degree of competition endogenous. He established that the degree of competition is driven by the investment decision of firms since capital stocks impinge on costs of production.


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We exploit this intuition of Dixon by focusing on an impact of public infrastructure, as opposed to private capital, on costs of production. The degree of competition in the product market is therefore driven by an allocation of public infrastructure. The introduction of public infrastructure in our model allows us to link the second type of conflict, namely, political conflict, with the first type. Since the availability of public infrastructure is fixed, it is modeled that there is no congruence of interests of agents coming from two distinct locations, as Hirsch (1977) noted, “what winners win, losers lose”. An allocation of infrastructure will naturally entail political costs and benefits that a self-seeking government — driven by electoral motive — would try to exploit. An incumbent government will naturally choose an allocation to maximize the probability of its re-election. Our model of probabilistic voting has antecedents in the literature: Lindbeck and Weibull (1987), and Dixit and Londregan (1994) adapted the probabilistic model to examine public policies that redistribute income to narrow groups of voters. They assume that the various groups differ in their preferences for the political parties and, thereby, identify the political characteristics of a group that makes it an ideal candidate for receiving political largesse. The upshot is that these authors mainly study the major determinants of the political success of a special interest group. On the contrary, we start off with the political characteristics of voters and then apply the probabilistic voting theorem to determine the electoral equilibrium that is driven by political largesse in the form of public infrastructure. This is how our model resolves political conflicts. The resolution of political conflict can have serious ramifications for the product market due to its impact on the allocation of public infrastructure. This is indeed a serious point to consider: the traditional political theory highlights the failure of the majority-rule voting caused by the absence of a stable electoral equilibrium. As a result, political instability can create significant instability in product markets. This is where we apply the probabilistic voting theorem to highlight the existence of a stable voting equilibrium to establish that democratic political markets are well-organized to promote the votemaximizing allocation of infrastructure that will, in turn, lend stability


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to the product markets: the model predicts that the vote-maximizing government adopts an optimal allocation of public infrastructure that induces an electoral equilibrium that, in turn, maximizes its chances of re-election. From this perspective, the nature of competition, the structure of the industry, and the conduct of firms in an oligopolistic market critically depend on this electoral equilibrium and, hence, on voters’ preferences and characteristics. The degree of competition is thus identified with the equilibrium allocation of infrastructure and becomes a continuous variable, rather than a binary variable. It captures intermediate situations between the pure Bertrand and Cournot cases. We also find important comparative-static results that show that the structure, the conduct of firms, and the nature of competition in oligopolistic markets will be sensitive to political characteristics. Future extensions of the book are desired on two fronts: First, voters’ preferences should be made dependent on the final good’s price and thus on the nature of competition. This extension can enhance our understanding of the nature of equilibrium by providing circular interdependence between government policy and market outcomes. Second, important extension is possible by allowing voters to “vote with their feet”. This extension will once again introduce the circular interdependence between government policies and market outcomes. In Chapter 2, we continue with a standard oligopoly, or duopoly, model that we introduced in Chapter 1. Since the oligopolists, or duopolists, are aware of the impact of the public infrastructure on their individual cost functions and their take-home profits, it is likely that these firms will try to influence the distribution of public infrastructure. One mechanism to do that is by the use of campaign contributions these firms make to politicians to seek favor. In Chapter 2, we examine the impact of campaign contributions on the market outcome. We suppose campaign contributions impinge on the cost and demand functions of duopolists and, thereby, influence their competitive positions. Duopolists spend campaign contributions to capture the largest possible market shares. From this extended model of duopoly, we derive the PNE in terms of campaign contributions. We note that the increased market buoyancy, the decrease in marginal cost of production and the increase in private rents from campaign contributions funds will


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increase the equilibrium campaign contributions that each duopolist donates — given parametric restrictions. We similarly expect the equilibrium campaign contributions to decline with decreased market buoyancy, an increase in the marginal cost of production and a decrease in private rents from campaign contributions — given parametric restrictions. We also note perplexing comparative-static properties of the duopoly equilibrium in the presence of campaign contributions: parametric changes in demand and cost functions can have perverse effects on the equilibrium price and the equilibrium quantity of the proposed duopoly with campaign contributions. Our second finding is that campaign contributions can have asymmetric effects on costs and will, therefore, cause and intensify cost asymmetry. This cost asymmetry can be shown to trigger a gamut of endogenous changes. In this work, we show the influence of this cost asymmetry on the incentives of firms to merge. A whole set of new results on rivalry and cooperation are offered: under a set of restrictions we establish that the most efficient firm will merge with the least efficient one. With a new restriction we establish the less efficient firms will merge. Under another set of restrictions, we establish that the most efficient firms will merge. What is important is that these restrictions are solely driven by the differential impacts of campaign contributions on individual costs. Differences in campaign contributions can therefore drive a wave of endogenous mergers that cannot be explained by any other economic factors. The other important finding is that differences in campaign funds can create situations that induce the entry of firms in an industry that will in turn trigger endogenous mergers and the degree of rivalry in an industry. Once again, such mergers and the merger-inducing entry cannot be explained by any other models. In Chapter 3, we consider the formation of networks of firms that usually creates social cohesion and alliance within a network, which significantly lessens intense rivalry and costly competition within the group. This is usually referred to as social capital within a network. In Chapter 3, we examine the formation social capital within a group of firms and model an equilibrium group rivalry. What we examine is the formation of social capital within a group when multiple groups are


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engaged in mutual rivalry and conflicts, which are akin to the formation of endogenous and competitive norms. In our model, we bypass the role of contractual arrangements in social norms by assuming that the management can enforce a social norm within a firm. For our model, the social norm within a firm entails the choice of social capital (effort level) that predicates the market positioning and market spoils of a firm. Yet the choice of social capital by one firm will trigger similar choices in rival firms since the formation of social capital has a profit-snatching effect on others. We therefore explain an equilibrium social norm as a symmetric Cournot–Nash equilibrium in social capital (effort levels) that rival firms choose to maximize their individual profits. The following observations are made: •

•

Social capital describes group benefits and network externalities that individual members can exploit to their advantages (see Sobel, 2002; Putnam, 2000; Glaeser, Laibson and Sacerdote, 2000; Bourdieu, 1986). The economic definition of individual social capital thus purports an individual’s social characteristics that enable him to extract additional returns from interactions with others given the interrelationship within a group (Glaeser et al., 2000).

We extend the concept of social capital to the organization of modern production within a firm that is peopled by a collection of diverse employees and managerial staff. The best way to visualize social capital within a firm is to think of social capital as additional effort that workers and managers offer to increase a firm’s current profit that ensures its future sustainability, which is a common good for the firm. The individual effort thus creates positive externalities in a firm, which paves the way for studying social norms that describe rules of conduct/behavior that encourage social capital and in turn promotes positive externalities (see Huck et al., 2006). The important lessons are as follows: •

In order to make the model tractable, we introduce three simplifications: first and foremost, we assume a two-stage game. In the


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•

•

321

first stage, each firm chooses social capital (effort levels). In the second stage, they compete as Cournot rivals in an integrated market. As the second-stage game is well-known, we focus on the first-stage game. Second, we assume that the average cost of production of a firm is independent of output level, but is dependent on its social capital (effort levels). This dependence is expressed as a U-shaped relationship, reflecting the notion that as social capital exceeds a certain level, control and supervision costs become very high within a firm and thus adversely affect the production cost per unit. Finally, managers who enforce social capital (effort levels) have an objective function that is a linear combination of profits and social capital per se. The proposed model establishes a number of interesting properties of the equilibrium social norms. First, endogenous social norms and capital can give rise to a multiplicity of symmetric Nash equilibria. We establish the existence of a high-effort equilibrium that coexists with a low-effort equilibrium. In our model, we find that the high-effort equilibrium is always unstable while the low-effort equilibrium is stable only under a condition. Thus the low-effort equilibrium becomes unstable if this condition is violated. The instability property of the high-effort equilibrium retains the possibility of reaching the maximum feasible social capital, if history or expectations dictate so. Path-dependency also assumes paramount importance. If both equilibria are unstable, the system becomes highly fragile and the initial condition, or history, and expectations can destabilize the system. The instability of equilibria can engender complex dynamics and trigger chaos. The model of social capital formation establishes the following: First, there exist two Nash equilibria: one is a high-social capital equilibrium (E2 and k2) and the other represents a low-social capital equilibrium (E1, k1). We find that equilibrium E2 is always unstable and equilibrium E1 is stable only under a condition. Thus E1 is unstable if this condition is violated. If both these Nash equilibria are unstable and if the initial value of social capital (k) lies in the interval [0, k2], the dynamics of social capital formation will take the system to a zero-social capital labeled k = 0. If the initial


322

•

•

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level of social capital k is greater than a critical value k2, then the dynamics of the system takes the system to k = K in which the maximal social capital is reached. Thus, the instability property of the high-social capital equilibrium retains the possibility of reaching the maximum feasible social capital, if history or expectations so dictate. If both equilibria are unstable, the system becomes highly fragile and the initial condition, or history, and expectations can destabilize the system. The instability of equilibria can engender complex dynamics and trigger chaos. Even when E1 is a stable equilibrium, parametric changes can cause a loss of stability for E1 and the dynamics will take the system to zero-social capital (k = 0). We established these bifurcation properties of a stable Nash equilibrium, which render the business system/firm very fragile and even chaotic. It is well-known that a chaotic economic system is a mathematical representation of a crisis-ridden and unstable economic system. Policymakers therefore must take extreme caution in dealing with the system, especially in certain circumstances. For policymaking, it is important to predict the critical threshold beyond which the business system becomes chaotic. Finally, the model locates a region of stability against the backdrop of a region of instability. Our argument is similar to the “edge of chaos theory”. Stacey (1991) adopted the “edge of chaos theory” for social sciences to argue that the sustainability of a business system is achieved by the relevant decision-makers striving to remain at the confluence of the predictable “order” and an unpredictable level of chaos. Chambers (1997) employed this concept of edge of chaos to explain the sustainability of rural communities in developing nations. Ours is the first attempt to provide a model that can be strained to explain the sustainability of social capital in a modern firm.

In Chapter 4, we examine an important topic of business alliance, rivalry and cooperation. In this setup, we have two or more business partners that have the opportunity to undertake cooperative


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investment. The cooperative investment increases the partner’s profits and can thereby create a win–win situation if all partners could agree to invest in cooperative projects. This chapter develops a simple game to examine the effects of cooperative retail and wholesale investment under two related market structure scenarios. Scenario I illustrates successive monopolies in the wholesale and retail markets. Scenario II is the evolution of Scenario I and represents the next stage of the natural development of a monopoly wholesale market with a duopoly retail market, resulting from a new entrant taking a share of the retail profits. We examine the effects of the wholesale-retail game for Scenario I and solve for the privately optimal levels of total output, retail prices, wholesale prices, retail profits, wholesale profits, total industry profits, consumer surplus, and social welfare. In Scenario I, it is shown that both the monopoly wholesaler and monopoly retailer do not have an incentive to respectively invest at socially optimal investment levels. That is, we have a tragedy of the commons where both the wholesaler and the retailer individually benefit the most from investing at their respective privately optimal investment levels rather than at their respective socially optimal investment levels. Given that there is no incentive for either the monopoly wholesaler, or monopoly retailer to invest beyond their respective privately optimal levels of investment, the government may engage in a social contract to punish any socially sub-optimal levels of investment by the wholesaler and retailer. This social contract is specified as a tax on the respective difference between the socially optimal levels of their investment and their actual investment level. In Scenario II, we present a two-tier game with one game being played between the duopoly retailers — an incumbent firm with a new entrant — and the second game between the combined retail market and the sole wholesale market firm. Solving for each of the above listed variables as in Scenario I, we draw comparisons between these two related market structures as it evolves from Scenario I to Scenario II, and draw important lessons. First, the creation of the duopoly retail market in Scenario II leads to overproduction with an increase in the total output leading to an


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increase in wholesale demand and a decrease in retail prices. The consequence of this is a reduction in the total retail market profits to the point that they can actually become losses with excessive overproduction and high marginal selling costs. Concurrently, the monopoly wholesale profit margins increase, fixed costs in the industry, which will increase the profit share of the wholesaler compared to the profits of the retailers. That is, wholesale profits will increase with the addition of another retailer, and wholesale profit sharing increases in comparison to the retail market. •

•

An interesting result for the total industry is that total industry profits decline although a reduction in the total fixed costs to variable costs ratio will lead to an increase in total profits. The upshot of this is that a proportionately higher increase in the variable retail cost, compared to total fixed costs and average wholesale production costs, will increase total profits. This is consistent with the intuition that a relative reduction in the fixed to marginal costs of wholesale production and retail selling increases total profits since the industry has less sunk costs. A further consequence of this evolving market structure is a reduction in consumer surplus. This reduction in consumer surplus will continue to grow the higher the total retail selling cost is in comparison to total industry fixed costs and variable wholesale production costs. The natural extension of this is that significantly higher total fixed costs and wholesale variable production costs, and a relative reduction in marginal retail selling costs, can actually increase the consumer surplus when evolving from Scenario I to Scenario II. For the same reasons, this market structure evolution also leads to a welfare reduction, and the driving sensitivity once again stems from the variable retail selling cost and the need to reduce it in comparison with total fixed costs and wholesale variable costs. Finally, reducing the variable retail selling cost relative to total fixed costs and variable wholesale production costs may actually lead to welfare gains.


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In Chapter 5, we re-visit the issue of price discounts as introduced in Chapter 1. In this chapter, we focus on the dynamics of price discounts as oligopolists, or duopolists, try to outsmart each other, which is form of dynamic rivalry and conflicts. To our understanding, this is the first model that examines the dynamics of conflicts without a footing to the much-celebrated model of consistent conjectural variations. We consider price discounts in a dynamic context. Customer flows to a seller are influenced by secret prices and price discounts chosen by its rival. The demand function of each customer is linear and downward sloped in prices. Since price discounts are secret, an instantaneous Nash equilibrium is not arrived at. Sellers start off with initial price discounts and gradually update these discounts to enhance their profits. We have shown that the dynamic path of price discounts will be characterized by chaotic behavior in the region of instability. The finding has important bearings: it is typically assumed in the deductive equilibrium approach to modern economic theory that the Nash equilibrium dispels all systematic prediction errors and the economic system settles in an equilibrium characterized by self-confirming and mutual-best responses. This approach has its most dominant influence on modern industrial economics, popularly known as industrial organization. The deductive equilibrium analysis has contributed to a better understanding of modern industrial economics. However, little attention has been given to the regions of instability. We established that the postulated price discount dynamics can exhibit chaotic behavior. Firms now fail to see systematic errors. Firms also fail to make long-run predictions with certainty even thought they act in a deterministic world. Time profiles of prices and quantities, which start very close together, will separate exponentially. The strength of Nash equilibria gets terribly emasculated. We suggest that an application of standard results of chaotic behavior can be a very important step forward in understanding the dynamics of industrial economics. We marshal some evidence to explain price discounts as a function of some relevant variables in a market characterized by localized competition. The results are negative. There are some shortcomings in the


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empirical section. Yet the empirical study supports the theoretical model that price discounts can be arbitrary and non-optimal in the sense of Bain (1952) in oligopolies with localized competition. Thus, the formation of alliance and collusion is difficult to sustain in the dynamic context as firms can get easily locked in rivalry and open, or tacit, conflicts. In Chapter 6, we consider a very special type of cooperation and collusion that firms can choose instead of getting locked into rivalry and conflicts. It is commonly known as endogenous mergers. It is only recently that economists have turned their attention to the question of endogenous mergers. The literature is still evolving. Theoretical models typically examine the incentives of firms to merge. As a set of firms merge, the new entity poses a challenge to other rivals in the market, which precipitates some kind of a conflict for market shares. The rivals engage in alliance formation for survival, which further induces other firms to seek alliance. The question that we pose is simple: who will merge with whom? Alternatively, one may call this a case alliance formation that examines the economics of partnership in a simple oligopoly. Our observations are in order: •

•

At the empirical level, the question is how to quantify the relevant market data that can explain “who would merge with whom”. At the empirical level, the question that motivates researchers is baldly put as: Should we expect merging firms in more concentrated markets to be more asymmetric? Recent research has marshaled some evidence on the basis of two empirical findings: First, there is a negative correlation between merger participants’ asymmetry and initial market concentration ratio. Second, there is a positive correlation between the size of merging firms and initial concentration ratios. From these twin observations, one concludes that the large firms in an industry will merge to reinforce their market shares if the concentration ratio is high in the concerned industry. The German economy is a prime mover of the global economy both in terms of its per capita national income of roughly US$40,000 and its ever-expanding FDI. Moreover, during the 1990s the German economy faced unprecedented changes and


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challenges: reunification, formation of the European Union, increased pace of globalization, and significant sectoral shifts in German industries. All these events have led to the far-reaching changes in the industrial structure, incentives, and constraints of firms. As a result, it is expected that firms in the new juncture may have different incentives to merge. We therefore look at the question of endogenous mergers in the German industry in recent times. We are able to confirm that the large firms in a German industry merged to reinforce their market shares when the pre-merger concentration ratio is high in the concerned industry. Due to the prevalence of low concentration ratios in many German industries, the asymmetry between the merging partners should be high, which indicates that in these industries, the less and the most efficient companies have incentives to merge. Our results confirm this. From these mergers, high rationalizing effects can be gained due to the redistribution of production from the less to the more efficient firms. On the other hand, for German industries with high concentration ratios, one tends to expect symmetric firms to merge. Our results confirm this. Negative welfare effects would be higher after a merger in an industry with high concentration ratios than in industries with lower concentration ratios. This is so because the competition-reducing effect of mergers is significantly larger in the first case than in the latter case.

Chapter 7 argues that vertical markets are of paramount importance in the theory of global trade. The existing research, in this context, has focused on two related issues: First, a large number of papers explore the incentive of the integrated firm to foreclose the downstream market to limit actual competition (e.g., Jones, 1996; Bernhofen, 1996; Spencer and Jones, 1991, 1992). Vertical foreclosure therefore involves some kind of a market conflict in which a powerful player, in order to increase its market share, forces out its rivals from a market. The vertical arrangement in such markets is hardly a level playing field. One typically wonders how to control vertical foreclosure. Second, many papers also examine the discriminating tariff policy that can prevent


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such anti-competitive behavior (e.g., Spencer and Jones, 1991, 1992; Chang and Kim, 1991; Chang and Chen, 1994). In their paper, Ishikawa and Lee (1997) introduce the entry/exit of foreign firms and demonstrate that the discriminatory tariffs may turn out to be counter-productive since they may have adverse effects on the profits of the domestic firms. However, relatively little attention has been paid to the collusive behavior among the incumbent firms in vertical markets that can seriously warp competition and may cause significant deadweight losses. Our primary objective in this chapter is to analyze the collusive behavior in vertical world markets. An important issue in this context is potential competition that is driven by the entry of new firms in the downstream market. A gap in the existing literature is the neglect of the impact of non-integrated foreign firm’s entry into the retail market on potential competition. Our goal is to fill this important gap. We fill the gap in the existing literature by analyzing the possible entry of a non-integrated foreign firm in the domestic downstream market.1 The focus of Ishikawa and Lee (1997) in their paper is the impact of tariffs on the entry/exit decision of a foreign firm which is shown to lead to adverse effects of tariff on domestic firms. On the contrary, our focus is on the impact of collusive activities of the incumbents on the entry decision of the non-integrated foreign firm under sketchy information. We develop the dynamic analysis of the vertical market in international trade. We posit the global/international market as a formation whose privileges are constantly threatened by entry. In other words, we have examined an extension of the information-based approach to entry deterrence to the important case of vertical markets in international trade. We consider a market in which two incumbent firms face the danger of entry by a foreign firm. The entry of a foreign firm has the potential for market related conflicts. Can the incumbents take 1

There is only one paper that has examined the impact of entry/exit in vertical markets: Ishikawa and Lee (1997) examined the impact of entry/exit of an integrated foreign firm while we analyze the entry of a non-integrated foreign firm. Our focus is also different as we solely concentrate on collusive behavior in such markets.


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appropriate measures to avoid this type of potential conflict? Being a foreign firm the potential entrant has sketchy information about the local cost condition. This sketchy information unravels the possibility of collusion between incumbents to block the foreign firm. Assuming an information asymmetry about the cost of production, we find that the integrated home and non-integrated foreign firms can effectively deter entry into the retail market by an upward distortion of the price of the final good. We find, under a set of conditions, that an effective collusion among the incumbents is feasible if the integrated home firm can freely commit to an input price before foreign entry occurs. Thus, we establish a new commitment linkage whereby the integrated home firm is able to pre-commit to an input price if entry occurs. We also find that the regulation of the input price will effectively control such anti-competitive price distortion and, hence, would promote potential competition in vertical markets in international trade. Chapter 8 examines how rivalry and conflicts can pervade the arena of policy making, which can have far-reaching ramifications for both economic agents and the overall state of economic well-being of a nation. Typically, the economics of rivalry and conflicts are restricted to two sub-fields: The first is the field that is commonly known as market rivalry and Chapters 1–7 examine the rationale for and consequences of rivalry and conflicts in a market apparatus. The second sub-field of rivalry and conflict is examined in the Hirshleifer type of models in which economic agents engage in a contest to lay a claim on some pre-determined economic benefits, or prize (see the Introduction for details). In what follows, we introduce intrastate conflicts and rivalry among different social and economic classes, and powerful players and agents. In what happened in the previous chapters, our focus was riveted on rivalry and conflicts between firms/producers and we now extend our horizon by examining the rivalry and conflicts between nonfirm players in an economy. In order to understand policy related conflicts, we examine the making of a monetary policy in an advanced nation. In the making of a monetary policy, there is apparent rivalry between central banks and governments. It is imperative that the central bank must maintain an “effective relationship” with the government since the parliament and


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hence the government “retains ultimate responsibility for monetary policy”. Yet it is absolutely crucial that the central bank preserves its “capacity to form its views and determine its policies free of party political pressures” (Phillips, 1992, p. 469). Therefore, for the efficacy of monetary management, the central bank needs to maintain some optimal “separateness” from the government; yet a complete autonomy may not at all be desirable. The bottom line, therefore, is that the art of central banking is a difficult balancing act and the actual independence of a central bank depends considerably on the capability of its governor as a tight rope walker. Since 1992, many G7, OECD, and other developed countries have chosen to create an independent central bank by enacting specific legislations to sever central banks as a legislative arm from the exchequer of their national governments. Our detailed examination in preceding sections does not find any overriding economic reason for such a strong convergence in opinions amongst developed nations concerning their monetary and financial institutions. From the informed opinions of the renowned central bankers and governors, as articulated in previous sections, we could not find any support for central bank independence in 1980s and 1990s. Yet it became a reality that, in our opinion, can pose a serious challenge to the developing world. We will articulate our concerns as the following thematic points that deserve a closer empirical look once the global economy gathers more data: •

•

First and foremost, central bank independence in many developed world acts as a coordinating device through which many of these nations have come to reach a convergence on macroeconomic policies. The developing world does not have any agenda to coordinate their macro and tax policies. It foretells a further consolidation of the bargaining position of the developed world in global and oligopolistic markets. Some observers argue that the immediate spin-off of central bank independence has led to a drastic reduction in inflation rates and interest rates, which have provided a big boost to the global and regional economies. In the developing world, we see a gradual


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decline in financial repression; yet the interest rates in developing world have been significantly higher than in the developed world. This has caused an unprecedented flow of “hot money” into developing nations in search of bigger returns. The “hot money” has exacerbated the financial instability and economic crises of various regions. The interest rate advantage of the developed world over the developing world, along with lower inflation rates in the developed world, has gradually altered the comparative advantage in favor of the developed world in high-tech products.

The lowering of the interest rates in the developed world, following central bank independence, has lowered the debt-servicing burden of many developed nations. It has helped them reduce the budget deficit and get back to a balanced, or even a surplus, budget. More importantly, as the pressure of debt servicing has eased (as discussed), governments in developed nations can spend more money on investment, infrastructure, R&D, and higher education. According to various reports of the World Bank, this increase in government expenditure has boosted the endogenously driven growth of the developed countries. Only a handful of developing countries such as India and China can compete with the developed nations in capturing the dynamic comparative advantages driven by the high-tech sectors. This is where we see emerging cleavages within the developing world. We will have to fully understand these problems of dynamic comparative advantages and take appropriate measures to address these problems for many developing nations. In Chapter 9, we examine an important and new rivalry and consequent conflicts in the global context. In recent years, when the global economy has been on the ascendant with unprecedented growth of global output, a group of economies have become dropouts from the growth league. These economies, known as “smallisland developing states” (SIDS), can create serious and costly conflicts. One of the major characteristics of SIDS is their isolated nature. It is also important to note that isolation creates geographical distances between these states and major global markets. More often


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than not, the transport network and communication network in SIDS are poorly developed, maintained, and managed. Poor long-term planning is partly responsible for this. It is of utmost importance that the fragmented nature of these nations and their linkage problems with the rest of the world must be redressed in order to lend economic and social stability to SIDS. The tyranny of geographical distance, in conjunction with high fuel costs, further isolates these nations. These challenges are substantial and will determine the fate of these small and fragmented economies as the forces of globalization take different turns with the energy price shocks of 2007–2008. There is an increasing reliance of these nations, their economic advisors, and also among experts from the United Nations, on the rapid development of ICT for establishing the missing and weak networks with the regional and global markets. With an ever increasing apperite for new technology, these nations are gaining access to and implementing technologies to modernize their relevant sectors. Unfortunately, the global market of high-tech sectors are dominated by a few firms and intellectual property rights are a major characteristic of these technology-savvy sectors. We offer insights with a stylized model: there is an integrated global firm that develops the knowledge, technology, and also a final product. A typical local firm from the SIDS only produces the final product by using the “knowledge” as input. There is a royalty that the integrated and global firm charges for selling the “knowledge”, which is mainly for establishing intellectual property rights. The integrated global firm will set the royalty in such a fashion that the resultant profit of the non-integrated firm from SIDS is below a threshold in order to induce the non-integrated SIDS firm to exit from the downstream market. In our work, we have set this threshold as the zero supernormal profit. Our analysis remains unaffected for any finite profit threshold. We therefore argue in favor of introducing controls on the price of knowledge asset, royalty, by providing the determination of the optimal royalty in a vertical industrial structure. If the industry is unregulated, we are able to establish the conventional wisdom: the PNE of the proposed sequential game exhibits that the integrated and


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global firm will adopt its profit-maximizing royalty that will force the local rivals to leave the downstream market. Even if this integrated firm does not adopt the strategy of vertical foreclosure, it has a leveraged position in the downstream market since this vertical foreclosure looms as a credible threat to non-integrated local rivals. This threat can seriously compromise competition in vertical markets. In order to promote competition and protect the rival firms in the downstream market, it is hence essential to introduce controls and regulation of the pricing knowledge asset. It is important for the international organizations to intervene in knowledge-specific markets to control royalties. In the absence of such regulation, the pursuits of SIDS in beating isolation, fragmentation, and geographical distance can prove unproductive. In the view of the present authors, cooperatives and competition bear a tenuous relation: there may be both uses and abuses of cooperatives in a competitive system. If there are strict and enforceable ground-rules, then cooperatives and competition may enjoy a mutually beneficial existence. It seems that cooperatives, as an organization, will fit in the framework of competition only under cautiously devised rules of the game. More importantly, the moral, ethical, and social values will play a significant role in settling the differences between the competition policy and cooperatives in Australia. Chapter 10 examines the rivalry and potential conflicts in the making of a fiscal policy. One important aspect of a fiscal policy in developing nations is what is known as fiscal decentralization. Fiscal decentralization calls for local governments to have reasonable autonomy for determining local taxes. This is necessary for making local governments accountable. The art of local governance is a delicate balancing act: autonomy and accountability will allow a local government to vary local taxes to collect larger revenues to finance higher levels of local services, if the local government so chooses. This would allow the local government to establish a linkage between revenues and expenditure. Local revenues ought to be collected from local residents in proportion to perceived benefits of local residents from local services. Such decentralization entails fiscal disequalization — as richer zones will collect more revenues.


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In order to offset this disequalization, intergovernmental transfers are designed to endow local governments with sufficient revenues to provide a “standard” level of local expenditure. Sensible local governance is thus built on the fiscal autonomy and accountability of local governments along with appropriately designed transfers. Incorrect designs of transfers and a lack of true accountability can cause serious distortions in the provision of local goods. Our central concern in this chapter is to examine the possibility of rivalry and conflicts between local and regional/federal governments that can seriously impinge on the economic welfare of millions of local residents in developing nations. We develop a simple game involving local and central governments to characterize potential (Nash) equilibrium outcomes. In the proposed model, fiscal reforms are successful when they establish a stable equilibrium. We are successful in isolating a threshold of local resources such that for local resources below this threshold (Y < K ), the fiscal scene is beset with significant uncertainty and instability caused either by multiple equilibria, or by an absence of pure-strategy Nash equilibrium. Fiscal reforms that fail to yield local resources above this threshold will fail to improve economic conditions at the local level. We also endogenously derive a critical value of transfers from central governments to local governments. For transfers below this critical value (T < (Y + K )/2), fiscal reforms are doomed to fail. We find that fiscal transfers beyond this critical point can establish a stable equilibrium. Whether fiscal transfers can establish a stable equilibrium depends on the flatness of the reaction function of the local government: if the corruption of local government rises at a sluggish rate with respect to increases in transfers from the central government within a relevant zone, then fiscal reforms will be successful. Successful and Pareto-improving fiscal reforms therefore entail a transition from a scenario in which Y < K to a scenario where T >(Y + K)/2 such that the post-reform game is characterized by a unique and stable Nash equilibrium. This is feasible only when corruption at local levels can be restrained. In Chapter 11, we consider rivalry and conflicts between two powerful players in any society — namely, the labor union and the


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industrial lobby led by a multinational enterprise (MNE). The contest between these two powerful and extra-market players not only determines the shares of workers in the national income but also impinges on the general economic condition of a nation. We examine in detail the economic contest between these two powerful players mainly in the context of a developing nation. The unionization of labor market has far-reaching consequences in imperfectly competitive markets since it affects the cost of production of firms. In a similar vein, direct and indirect taxes impinge on the cost of production and, hence, on the equilibrium market outcome. We examine the investment decision of a multinational firm that faces an international product market. Its main economic decision is regarding the location of its production base. There are mainly two critical elements that influence the investment decision: First, the institutional structure of the labor market that determines wage rates and, hence, costs of production. Second, taxes and fiscal incentives directly influence the cost of production of MNEs. Multinational firms significantly contribute to the economic development of a country. National governments hence engage in competition with each other to attract multinational firms mainly through their tax policies. We model this competition between national governments as a non-cooperative game. The outcome of the non-cooperative game is sensitive to the wage cost which will determine the net profit of the multinational firm. The wage rate, hence, is a critical element in the decision problem of the multinational firm. As a result, labor market conditions and asymmetries between nations will be very important to secure a competitive position for the multinational firms in the global market. The investment decision of a multinational firm is therefore sensitive to both tax policies and labor market outcomes. The conventional wisdom is that unionized labor market acts as an entry-deterrent for multinational firms since strong unionization raises the wage rate above the opportunity cost of labor. Thus, if one country has a more powerful union than the other, then the multinational firm based on the former will have lower “international competitiveness” because of a higher cost of production. If everything


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else is identical, then a multinational firm will naturally shun the former country. The national government in that country must offer larger tax incentives to the multinational firms. We reverse this conventional wisdom by establishing that the optimal foreign investment by multinationals will be an increasing function of the equilibrium wage share. We observe that if the union is strong, then the base and rate of labor tax will be, respectively, high and low since the wage and employment are high. Thus, it will be easier for the national government to pass the implicit tax of fiscal concessions to the wage earners. On the contrary, with a weak labor union, such a shift of tax can precipitate a labor crisis. A fully informed and rational multinational firm will thus have an incentive to invest in the highly unionized country. Given the equilibrium tax rates on the multinationals, the greater is the share of the labor in the national income, the greater is the flow of multinational investment into this country. This analysis thus suggests that the “international competitiveness” of a country with powerful labor union will not necessarily be in jeopardy. In Chapter 12, we examine why local governments fail to allocate resources efficiently in local economies in developing nations, which adversely affect the economic and social well-being of more than a billion people. The consequent urban ghettos are a breeding ground of corruption, crime, and terrorism. It is only recently that these urban ghettos in developing nations are believed to play an important role in driving global terrorism. So the critical question for this chapter is why local governance typically fails in the provision of local goods. In conclusion, we find that the main problem of local governance in developing nations is an inability, or lack of willingness, of local governments to balance the preference and the cost of providing local goods to residents. Thus from the decentralization theorem of Oates (1972), we know that local governments will fail to achieve efficiency in satisfying the local demand. The heart of the problem is the low level of local taxes that is driven by the electoral motive of local governments. At these low taxes, local governments are simply unable to provide adequate local services. Yet this tax-service package creates an electoral equilibrium that ensures the political survival of a


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local government through time. Hence, there is no incentive for these governments to improve local goods by increasing local taxes. Increases in grants and aids will have little effect on local goods as they will end up in the coffer of corrupt bureaucrats and politicians. This is akin to the problem of incorrect pricing of a product in a market that is insulated from the forces of competition. How to improve the quality of local services? There are two ways in which one expects an improvement. First of all, it is necessary to revamp local tax system so that residents pay a decent price for a decent service and also ensure minimum resources be spent on these services (Zakaria, 1978). Secondly, in consonance with the era of decentralization and deregulation, we suggest that it may be necessary to introduce Tiebout type of competitive forces in providing local goods in order to redress urban crises in developing nations. Local tax reforms and forces of competition are necessary to break the electoral equilibrium that taxes little and provides little of local goods.


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Index

bifurcation 322

accountability 224, 225, 228, 229, 232–235, 272, 283, 284, 333, 334 activism 225, 227, 228, 229 agglomeration 110 alliance formation 15–18, 20–22, 27, 169, 184, 313, 314, 326 anticipatory monetary policy 229, 230 Australian banking industry 19, 43, 45, 46, 314 autonomy 225, 235, 236, 271, 283, 330, 333, 234 autonomy and flexibility 271

117–119, 123, 125,

campaign contribution 87–97, 105, 318, 319 capital market threat 262 central bank bashing 234 central bank independence 215–217, 220, 221, 223, 224, 228, 229, 233, 235, 237, 230, 231 central banking 215, 217, 218, 228–233, 236, 330 central government 271, 272, 274, 275, 277, 282–284, 334 chaotic 46, 48–51, 55–61, 65, 82–84, 123–125, 155–158, 161, 165, 167, 315, 322, 325 chaotic discrimination 46, 48–51, 55, 56–61, 82–84, 155–158, 165, 315 chaotic dynamics 156, 157, 165 choice variable 273 coalition formation 17 collective goods 240

backward induction 69, 253, 296, 306 bankruptcy threat 262 bargaining game 129, 222, 295, 296 basing-point pricing 48, 157 best response function 34, 120, 121 bifurcate 161 359

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collusion 15, 17, 28, 33, 34, 45, 46, 48, 50, 59–61, 82, 193, 206, 207, 209, 313–315, 326, 329 collusive arrangement 46, 156, 208, 314 collusive device 193, 250 commitment linkage 57, 191, 193, 209, 329 common price 49, 157 competition policy 260–265, 270, 333 concentration ratio 28–30, 87, 171, 180, 184, 185, 326, 327 conflicts 1, 2, 4, 5, 7–11, 79, 81, 155, 169, 189, 209, 215, 234, 262, 266, 267, 271, 282, 285, 313, 314, 316, 317, 320, 325, 326, 328, 329, 331, 333, 334 conjectural variation 30–35, 37–42, 45–47, 65–67, 70, 71, 80, 314, 316, 325 conservative central banker 222 control and supervision 108, 321 cooperation 1–3, 10, 11, 13, 15, 17, 127, 189, 213, 239, 260, 267, 269, 270, 285, 313, 314, 319, 322, 326 cooperative game 16, 17, 295, 298, 335 cooperative investment 129, 130, 132–134, 136, 137, 144, 145, 147, 323 corruption 271, 272, 281–284, 334, 336

cost asymmetry 15, 27, 89, 105, 313, 319 cost structure 285 Cournot competition 20, 98, 190, 199 Cournot duopoly 250, 251 Cournot equilibrium 34, 52, 53, 60, 67, 92, 93 Cournot quantity competition 194 Cournot type quantity competition 252 Cournot-Nash equilibrium 17, 19, 20, 22, 97, 98, 100, 108, 195, 196, 199, 207, 252–255, 320 CPE 246–248 CPV 246–248 currency School 227 cycle 161, 162, 311 debt-GDP ratio 220 deductive equilibrium 156, 165, 325 deflationary bias 226 degree of competition 30,31, 41, 66, 71, 72, 75, 76, 78–81, 163, 316–318 demand elasticities 163 democratization 301 deregulation 249, 250, 260, 312, 337 developed world 8, 220, 237, 330, 331 development strategy 245, 246 direct democracy 304

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discrimination 46, 48–51, 55–61, 82–84, 128, 129, 155–158, 162, 163, 165, 315 disequalization 283, 333, 334 distorted price signal 53–55, 200 downstream 129, 189, 190, 193–198, 249–254, 256–260, 327, 328, 332, 333 downstream market 189, 190, 193–196, 249, 250, 252–254, 256–260, 327, 328, 332, 333 downward price distortion 58, 192 duopolist 31, 32, 34–39, 65, 68, 69, 71, 74, 87, 89, 92, 96, 105, 110, 194, 252, 318, 319, 325 duopoly 17, 19, 20, 23, 31–39, 41, 50, 87, 90–98, 101, 105, 127, 128, 138, 140, 142, 158, 178, 193–197, 250–254, 256, 314, 318, 319, 323 dynamic inconsistency 216, 221, 222, 225, 232 ecological footprints 244–246, 248 economic development 7, 11, 244, 245, 246, 298, 335 economic growth 223, 239, 240, 260, 262, 288, 301, 302 economic sustainability 246 educated guess 229, 230 efficiency 15, 17, 19, 27, 173, 174, 260, 262, 266, 285, 311, 313, 314, 336

361

electoral equilibrium 66, 68, 69, 72–74, 81, 305, 309, 312, 317, 318, 336, 337 electoral motives 80, 302, 305, 311, 317, 336 endogenous alliance formation 15, 17, 21, 22, 27, 313, 314 endogenous collusion 15, 28, 314 endogenous merger 17, 24–27, 88, 89, 97, 99–105, 169, 171–173, 175, 181, 184, 185, 314, 319, 326, 327 entrant 23–27, 50–53, 57, 58, 61, 83, 101–104, 127, 128, 138–140, 142, 150, 151, 190–193, 197–200, 206, 209, 323, 329 entry 15, 17, 20, 21, 24–27, 50, 51, 53, 55–59, 61, 62, 82, 88, 98, 99, 101–105, 132, 171, 172, 189–193, 196–200, 202, 204–207, 209, 286, 287, 298, 313–316, 319, 328, 329, 335 entry decision 58, 190, 191, 199, 328 entry deterrence 197, 209, 328 entry prevention 199 environmental assets 161, 167, 246 equilibria 3, 17, 26, 50, 51, 82, 104, 108, 109, 114–117, 119–122, 124, 125, 161, 167, 276–278, 280, 282, 284, 315, 321, 322, 325, 334

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equilibrium 1, 15, 87, 108, 131, 155, 171, 191, 221, 251, 272, 287, 302, 313 equilibrium outcome 123, 235, 281, 284, 334 equilibrium rate of inflation 221 ethics 239, 260, 262, 266, 269 evolution of central banking 217 exit decision 190, 328 exogenous merger 88, 98 extremal equilibrium 122 FDI 185, 242, 326 fine tuning 228 fiscal 220, 221, 226, 227, 271, 272, 279, 280, 282–284, 298, 299, 333–336 fiscal equilibrium 272, 279, 280 fiscal reform 279, 282–284, 334 flexible exchange rates 215 fly-paper effect 273 foreign firm 189, 190, 193–197, 207, 209, 286, 328, 329 fungibility 271 G7 countries 330 German economy 170, 178, 184, 185, 326 GIS 239 global market 245, 247, 258, 259, 286, 298, 331, 332, 335 global trade 6, 240, 285, 303, 327

globalization 1, 5–7, 124, 169–171, 185, 259, 301–304, 327, 332 grants 271, 272, 305, 308, 312, 337 group behavior 16 group size 16 growth rates 5, 215, 220 HHI 28–30, 173, 175, 177–179, 180, 182 high-effort equilibrium 108, 109, 321 high-social capital equilibrium 116, 124, 321, 322 hold up problem 133 ICT 239, 259, 332 imperfectly competitive model 285 incentive mechanism 234 incentive to merge 21, 98, 99 indeterminacy 33, 37, 112, 119, 121, 280 inflation 215, 216, 220–224, 227, 228, 230–232, 234, 237, 330, 331 inflation aversion 222 inflation blow-out 221 inflation tax 221 inflationary bias 216, 220, 221, 222, 225, 226 infrastructure 67–70, 72–77, 79–81, 85, 238, 316–318, 331 innovation 30, 32, 88, 240, 286, 292

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input price control 249–251 insiders and outsiders 267 integrated firm 189, 193–195, 208, 210, 211, 249–259, 327, 332, 333 intellectual monopoly 241 intellectual property rights 239–243, 332 interest smoothing 221, 233 IPR 240–243, 259 IPR protection 242 Keynesian 6, 215, 227, 303 knowledge-based products 241 labour union 285–288, 292, 295–297, 299, 334, 336 local firm 259, 332 local goods 273, 274, 284, 301, 302, 304–312, 334, 336, 337 local governance 271, 272, 283, 301, 302, 311, 333, 334, 336 local government 271–284, 301, 302, 304, 305, 307–309, 311, 312, 333, 334, 336, 337 local taxes 272, 283, 302, 305, 306, 311, 312, 333, 336, 337 localized competition 155, 158, 162, 167, 325, 326 locational choices 68 loss of stability 117, 119, 125, 322 low-effort equilibrium 108, 321 low-social capital equilibrium 116, 124, 321

363

managed money 215 managerial constraint 112 market distortions 257 market hostility 169 market segmentation 15, 19, 27, 155, 313, 315 merger formation 174 mergers 17, 18, 21, 25, 44, 88, 89, 97, 99–102, 105, 169–175, 178, 180–185, 260, 262, 265, 268, 314, 319, 326, 327 mergers in the Australian banking sector 44 mimicking 23, 101 mix of local goods 304 mixed equilibria 122 MNC 286–288, 290, 298 Monetarist 215, 216, 227 monetary 215–217, 220–222, 224–237, 329, 330 monetary rule 222, 225–227 monetary targeting 215 monopolization 89, 172, 243 monopolistic firms 249 monopolistic power 190, 194, 249, 252 monopoly outcome 34, 36, 43 morality 269 multinational investment 6, 287, 288, 296, 299, 303, 336 multinationals 285, 287, 289, 291–294, 299, 336 multiple equilibria 50, 51, 82, 276, 280, 284, 315, 334

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Nash equilibrium 1–4, 17, 19, 20, 22, 50, 56, 57, 60–62, 64, 65, 87, 90, 95, 97, 98, 100, 108–110, 112, 114, 115, 122, 125, 139, 156, 158, 160, 165, 191, 195, 196, 199, 207, 221, 251–255, 267–269, 272, 275–279, 284, 294, 296, 306, 315, 320, 322, 325, 334 Nash-Cournot 50, 52, 53, 55, 58, 60, 111, 192 Nash-Cournot price 50, 58, 192 national government 6, 9, 237, 277–281, 286–288, 292, 293, 295–299, 303, 330, 335, 336 natural rate 221 nature of competition 65–68, 70, 74, 80, 81, 316, 318 no distortion strategy 202, 206 non-cooperative game 16, 17, 298, 335 non-equilibrium behavior 156, 157 non-integrated firm 193, 208, 249–259, 332 oligopolistic 27, 31, 49, 81, 82, 169, 237, 315, 318, 330 open market operations 232, 233 optimal contract 224 optimal investment 127, 130, 136, 138, 141, 147–149, 287, 292, 297, 323 optimal royalty 252, 255, 256, 258, 259, 332 optimal taxes 306

overall Nash equilibrium

306

Pareto dominated Nash equilibrium 221 Pareto-improving reform 282 Pareto-inferior investment 133 partnership formation 15, 313 perfect Nash equilibrium 50, 57, 87, 191, 251, 255, 296, 315 political characteristics 80, 81, 305, 317, 318 pollution 73, 77, 245, 246 posted price 49, 50, 55, 56, 61, 62, 82, 158, 159, 315 potential competition 48, 190, 193, 207, 209, 328, 329 preference revelation 222 price capping 207 price discounts 49–51, 55, 56, 59, 61, 62, 65, 82, 155, 157, 158, 161, 162, 164, 165, 167, 315, 316, 325, 326 price discrimination 48, 49, 55–58, 61, 82, 128, 129, 156–158, 162, 163, 315 price distortion 53–55, 58, 59, 62, 82, 193, 199–210, 315, 316, 329 price stability 216–218, 225–228, 231 prisoner’s dilemma 135, 261, 262, 267–270 privatization 6, 132, 303 probabilistic voting 66, 72, 80, 81, 305, 309, 317

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probabilistic voting theorem 72, 81, 305, 309, 317 production-location decision 285, 286, 288, 292, 296 productivity growth 223 pure strategy 277, 284, 334 quantity competition 19, 24, 31, 50, 51, 90, 97, 101, 194, 197, 198, 252 reaction function 31, 32, 37–40, 42, 59, 64, 65, 71, 90, 114, 139, 151, 196, 198, 210, 254, 274–282, 284, 293, 294, 334 reciprocal 109, 169 re-election 68, 80, 81, 273, 305, 306, 309–311, 317, 318 regulatory framework 241, 260 regulatory issues 247 rent-seeking 65, 261, 268 repeated game 155, 235 retail duopoly 138 rivalry 1, 2, 11, 13, 15, 33, 46, 65, 79, 87, 107, 110, 163, 165, 169, 189, 213, 313, 314, 316, 319, 320, 322, 325, 326, 329, 331, 333, 334 rules and discretion 220 secrecy in central banking 232 Seigniorage 220, 221 separating equilibrium 24, 102 short run and long run dichotomy 231

365

signaling 23, 26, 50, 58, 101, 104, 191 signaling equilibrium 26, 104 signaling models 58, 191 sink 246 size asymmetry 173 small island developing states 239 social capital 107–125, 319–322 spatial competition 162 stability properties 117 stable equilibrium 117–119, 123, 125, 161, 276, 277, 280–284, 322, 334, stable voting equilibrium 66, 81, 305, 317 strategic entry deterrence 197 strategic mergers 260 successive markets 127, 133, 139 successive monopolies 127, 130, 132, 140, 323 supermodular game 119 supernormal profits 1, 52 surprise inflation 221, 232 sustainable growth 228 symmetric 43, 94, 105, 108, 114, 160, 175, 183, 185, 320, 321, 327 symmetric equilibrium 114 Tarski theorem 121 Tax 3, 68, 69, 72, 73, 128, 136, 138, 142, 149, 220, 221, 237, 271–274, 283, 285–290, 292–296, 298, 299, 302, 304, 305–312, 323, 330, 333, 335–337

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theory of limit pricing 190 Tiebout hypothesis 305 tied fund 273, 307 trade-off between growth and inflation 222 tragedy of the commons 127, 130, 135, 136, 141, 323 transaction costs 5 transfers 7, 271, 272, 274, 282–284, 334 triopoly 17, 20, 98, 314 TRIPs 242, 243 two-tier game 128, 138, 142, 288, 296, 297, 323 under-provision equilibrium 310, 311 unemployment 221 uniqueness 117 unstable equilibrium 276, 281, 282 untied fund 273 upstream 190, 193, 194, 247, 249, 252, 258

upstream market 190, 194, 249, 252, 258 upward price distortion 53, 55, 58, 59, 62, 82, 193, 199, 201, 203, 204, 206, 207, 315, 316 urban crises 301, 302, 312, 337 vertical foreclosure 189, 239, 258, 259, 327, 333 vertical market 189, 190, 192–194, 200, 209, 241, 247, 260, 327–329, 333 vicious cycle of urban poverty 311 voting equilibrium 66, 81, 305, 317 wage bargaining 286, 292, 295, 296 whole-sale retail game 127, 323 WIPO 241, 242 WTO 241–243

ECONOMICS OF RIVALRY, CONFLICT AND COOPERATION This book offers an extensive and original study of the dynamics of rivalry, evolution of costly and violent conflicts, and potential cooperation among powerful players. It unravels the special features of the global socio-economic system that can make it extremely fragile and vulnerable. It serves as a good reference source for anyone interested in some of the pressing and emerging problems of the global system, such as intranational and interethnic conflicts, climate change challenges, poverty and terrorism, and provides useful and rigorous insights into the collective bid to resolve some of these problems. Written in a simple and accessible manner, this book will help researchers and policy makers in understanding and abetting costly conflicts.

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Economics of Rivalry, Conflict and Cooperation

Conflict and Cooperation: Institutional and Behavioral Economics

Conflict and Cooperation

Principles of conflict economics

The Economics of Rights, Cooperation and Welfare

Japan and China: Cooperation, Competition and Conflict

Japan and China: Cooperation, Competition and Conflict

Religion and Development: Conflict or Cooperation?

Religion and Development: Conflict or Cooperation?

Religion and Development: Conflict or Cooperation?

Islam and the West: Conflict or Cooperation?

Mutual Accommodation: Ethnic Conflict and Cooperation

Islam and the West: Conflict or Cooperation?

Conflict and Cooperation in the Gulf Region

Conflict and Cooperation in the Gulf Region

The India-Pakistan Conflict: An Enduring Rivalry

Anglo-French Relations in the Twentieth Century: rivalry and cooperation

Birth Of Rivalry

Cooperation, Conflict and Consensus in the Organization of American States

Official Leadership in the City: Patterns of Conflict and Cooperation

Cooperation or Conflict in the Taiwan Strait?

Techno-nationalism and techno-globalism: conflict and cooperation

Birth Of Rivalry

The Jordan River and Dead Sea Basin: Cooperation Amid Conflict

Saudi-Iranian Relations Since the Fall of Saddam: Rivalry, Cooperation, and Implications for U.S. Policy

The Myth of “ethnic conflict”: politics, economics, and “cultural” violence

The Rivalry

The Rivalry

Origins of Altruism and Cooperation

Economics of Rivalry, Conflict and Cooperation

Conflict and Cooperation: Institutional and Behavioral Economics

Conflict and Cooperation

Principles of conflict economics

The Economics of Rights, Cooperation and Welfare

Japan and China: Cooperation, Competition and Conflict

Japan and China: Cooperation, Competition and Conflict

Religion and Development: Conflict or Cooperation?

Religion and Development: Conflict or Cooperation?

Religion and Development: Conflict or Cooperation?

Islam and the West: Conflict or Cooperation?

Mutual Accommodation: Ethnic Conflict and Cooperation

Islam and the West: Conflict or Cooperation?

Conflict and Cooperation in the Gulf Region

Conflict and Cooperation in the Gulf Region

The India-Pakistan Conflict: An Enduring Rivalry

Anglo-French Relations in the Twentieth Century: rivalry and cooperation

Birth Of Rivalry

Cooperation, Conflict and Consensus in the Organization of American States

Official Leadership in the City: Patterns of Conflict and Cooperation

Cooperation or Conflict in the Taiwan Strait?

Techno-nationalism and techno-globalism: conflict and cooperation

Birth Of Rivalry

The Jordan River and Dead Sea Basin: Cooperation Amid Conflict

Saudi-Iranian Relations Since the Fall of Saddam: Rivalry, Cooperation, and Implications for U.S. Policy

The Myth of “ethnic conflict”: politics, economics, and “cultural” violence

The Rivalry

The Rivalry

Origins of Altruism and Cooperation

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