Market Microstructure: Intermediaries and the Theory of the Firm

Market microstructure: intermediaries and the theory of the firm

This book presents a theory of the firm based on its economic role as an intermediary between customers and suppliers. Professor Spulber demonstrates how the intermediation theory of the firm explains firm formation by showing why firms arise in a market equilibrium with costly transactions. In addition, the theory helps explain how markets work by showing how firms select market-clearing prices. Models of intermediation and market microstructure from microeconomics and finance shed considerable light on the formation and market-making activities of firms. The intermediation theory of the firm is compared with existing economic theories of the firm, including neoclassical, industrial-organization, transaction-cost, and principal-agent models. Daniel F. Spulber is the Thomas G. Ayers Professor of Energy Resource Management and Professor of Management Strategy at the J. L. Kellogg Graduate School of Management, Northwestern University, where he has taught since 1990. He has also taught at Brown University, the University of Southern California, and the California Institute of Technology. Professor Spulber is the author of The Market Makers (McGrawHill/Business Week Books, 1998) and Regulation and Markets (MIT Press, 1989) and coauthor with J. Gregory Sidak of Deregulatory Takings and the Regulatory Contract (Cambridge University Press, 1997) and Protecting Competition from the Postal Monopoly (AEI Press, 1996). He is founding editor of the Journal of Economics & Management Strategy, published by MIT Press, and is the recipient of eight U.S. National Science Foundation grants for economic research.

Market microstructure: intermediaries and the theory of the firm Daniel F. Spulber

CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE

The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK http://www.cup.cam.ac.uk 40 West 20th Street, New York, NY 10011-4211, USA http://www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia © Daniel F. Spulber 1999 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1999 Typeset in Times Roman ll/13pt. in L£TEX2 £ [TB] A catalog record for this book is available from the British Library Library of Congress Cataloging in Publication Data Spulber, Daniel F. Market microstructure: intermediaries and the theory of the firm / Daniel F. Spulber. p. cm. Includes bibliographical references. ISBN 0-521-65025-9 (hardcover). - ISBN 0-521-65978-7 (pbk.) 1. Industrial organization (Economic theory) 2. Securities. 3. Stock exchanges. 4. Microeconomics. I. Title. HD2326.S72 1998 98-34680 CIP ISBN 0 52165025 9 ISBN 0 52165978 7

hardback paperback

Transferred to digital printing 2004

Contents

Preface and acknowledgments page ix Introduction xiii The intermediation theory of the firm xiii Market microstructure xvii Intermediated exchange versus matching and searching xix Alleviating adverse selection xxii Mitigating moral hazard and opportunism xxv Delegation to intermediaries xxvii Outline of the book xxix Part I: Market microstructure and the intermediation theory of the firm 1 Market microstructure and intermediation 1.1 Who decides? 1.2 The circular flow of economic activity 1.3 Comparison with other economic theories of the firm 1.4 Intermediation in the U.S. economy 1.5 Conclusion 2 Price setting and intermediation by firms 2.1 Price setting by intermediaries 2.2 Allocation under uncertainty and over time 2.3 Price adjustment by intermediaries 2.4 Inventories and market clearing by intermediaries 2.5 Conclusion Part II: Competition and market equilibrium 3 Competition between intermediaries 3.1 Bertrand competition for inputs with homogeneous products 3.2 Bertrand price competition with differentiated products and purchases 3.3 Bertrand competition with switching costs

3 4 7 13 21 26 27 28 34 40 48 57 61 64 68 71

vi

Contents

3.4 Bertrand competition when costs differ 3.5 Conclusion

74 79

Intermediation and general equilibrium 4.1 The neoclassical theory of the firm 4.2 Transaction costs and Walrasian equilibrium 4.3 Monopoly intermediation in general equilibrium 4.4 Monopolistic competition 4.5 Conclusion Appendix

81 83 94 96 104 106 108

III:: Intermediation versus decentralized trade Matching and intermediation by firms 5.1 Intermediation versus a matching market 5.2 Costly intermediation 5.3 Intermediation with random matching 5.4 Intermediation and matching with production 5.5 Conclusion

117 118 126 130 134 137

Search and intermediation by firms 6.1 The market model 6.2 Market equilibrium 6.3 Comparison with Walrasian equilibrium and with monopoly 6.4 Market equilibrium with continual entry of consumers and suppliers 6.5 Conclusion Appendix

159 162 164

Part IV: Intermediation under asymmetric information 7 Adverse selection in product markets 7.1 Intermediated trade 7.2 Intermediated trade with production 7.3 Market clearing by intermediaries 7.4 Product quality and guaranties by experts 7.5 Conclusion Appendix

171 173 179 182 193 197 198

8 Adverse selection in financial markets 8.1 Insiders, liquidity traders, and specialists 8.2 Competition between specialists 8.3 Informed intermediaries 8.4 Credit rationing by financial intermediaries 8.5 Conclusion

140 144 150 154

203 205 211 215 219 224

Contents

Part V: Intermediation and transaction-cost theory 9 Transaction costs and the contractual theory of the firm 9.1 Transaction costs versus management costs 9.2 Transaction costs, uncertainty, and bounded rationality 9.3 Transaction costs and opportunism 9.4 Transaction costs and ownership 9.5 Conclusion

vii

229 232 236 245 251 254

10 Transaction costs and the intermediation theory of the firm 256 10.1 Transaction costs and market microstructure 259 10.2 Intermediation and vertical integration 266 10.3 Intermediation and opportunism 276 10.4 Intermediation and ownership 281 10.5 Conclusion 285 Part VI: Intermediation and agency theory 11 Agency and the organizational-incentive theory of the firm 11.1 Vertical integration and the boundaries of the firm 11.2 Coordination of agents by the firm 11.3 Delegation of authority by owners to managers 11.4 Delegation of authority by managers to employees 11.5 Conclusion

289 291 299 306 314 317

12 Agency and the intermediation theory of the 12.1 What is an agent? 12.2 Delegated bargaining 12.3 Delegated competition 12.4 Delegated monitoring 12.5 Conclusion

319 321 329 332 335 342

firm

Conclusion The intermediation theory of the firm Market microstructure and intermediation Management implications Public policy implications

344 345 348 350 351

References Index

353 369

Preface and acknowledgments

Two fundamental and closely related questions raised by microeconomics are "Why are there firms?" and "How do markets work?" In this book, I set out an intermediation theory of the firm that addresses these two important questions. The intermediation theory of the firm provides explanations for the formation of firms by showing how firms arise in a market equilibrium. In addition, the theory helps explain how markets work by showing how firms select market-clearing prices. Models of intermediation and market microstructure from microeconomics and finance shed considerable light on the formation and market-making activities of firms. The analysis of firms begins with the observation that firms act as intermediaries between their customers and their suppliers. Without firms, consumers acting as buyers and sellers would engage in direct exchange, searching for each other and bargaining over the terms of trade. The intermediation theory of the firm can then be summarized: Firms are formed when the gains from intermediated exchange exceed the gainsfrom direct exchange. Intermediated exchange can have advantages over direct exchange for many reasons, which are set forth in this book. These include lowering the costs of transacting through centralization of exchange, reducing costs of searching and bargaining, reducing moral hazard and opportunism, alleviating the effects of adverse selection, allowing buyers and sellers to make credible commitments, and reducing the costs of monitoring performance through delegation. Resources are allocated through decentralized processes of direct exchange, through centralized exchange managed by intermediaries, or through some combination of the two. The institutions of exchange are referred to as market microstructure. The analysis suggests an intermediation theory of markets that explains how markets work. With intermediated exchange, firms select prices, clear markets, allocate resources, and coordinate transactions. Thus firms establish and operate markets. IX

x

Preface and acknowledgments

I confine my analysis to economic issues pertaining to the economic theory of the firm and market mechanisms. The book does not cover a number of related topics. I do not consider the vast and rapidly growing literature on empirical analysis of financial markets. See Campbell, Lo, and MacKinlay (1997) for an outstanding integrative survey of the econometrics of financial markets. I do not consider research on the sensitivity of market outcomes to changes in the rules for price setting, matching orders, time priority, market versus limit orders, size precedence, trade class (specialist, market maker, or dealer quotes), and so on. Some of these issues are specific to financial markets in which market performance can depend significantly on small variations in trading rules.1 Financial studies of market microstructure raise important theoretical and empirical questions about how prices are adjusted and communicated and how changes in demand and supply are reflected in the allocation of goods and services over time. I also do not address theoretical issues bearing on the detailed theory of financial institutions. For excellent treatments of the theory of financial market microstructure and financial institutions see O'Hara (1995) and Frankel, Galli, and Giovannini (1996). I consider only briefly issues pertaining to the theory and institutions of banking; see the excellent recent text of Freixas and Rochet (1997) on the microeconomics of banking. I draw on the following previously published papers. Spulber, Daniel R, 1996, "Market Making by Price-Setting Firms," Review of Economic Studies 63, 559-80. Spulber, Daniel P., 1996, "Market Microstructure and Intermediation," Journal of Economic Perspectives 10, 135-52. Spulber, Daniel R, 1995, "Bertrand Competition when Rivals' Costs are Unknown," Journal of Industrial Economics 43, 1-12. Spulber, Daniel R, 1994, "Economic Analysis and Management Strategy: A Survey Continued," Journal of Economics & Management Strategy 3, 355—406. Spulber, Daniel R, 1992, "Economic Analysis and Management Strategy: A Survey," Journal of Economics & Management Strategy 1, 535-74. Spulber, Daniel R, 1993, "Monopoly Pricing," Journal of Economic Theory 59,222-34. Spulber, Daniel R, 1993, "Monopoly Pricing of Capacity Usage Under Asymmetric Information," Journal of Industrial Economics 41, 1-17.

The present work is the product of two decades of teaching economics to students of economics, law, and business. I thank my many students whose stimulating questions helped me to reevaluate neoclassical economics and especially my business students, whose concerns required addressing the economic theory of the firm. 1

See Domowitz (1992,1993) for taxonomies of automated trade execution systems that consider these and other aspects of market microstructure.

Preface and acknowledgments

xi

I particularly thank Dean Donald P. Jacobs of the J. L. Kellogg Graduate School of Management for his great encouragement and generous support for my research. I also thank Academic Dean Dipak Jain for his extraordinary understanding and consideration for my work. I thank my editor at Cambridge University Press, Scott Parris, for his great interest and belief in the value of the project and his expert guidance in bringing it to fruition. I also express my gratitude to my wife Susan and to my children Rachelle, Aaron, and Benjamin for their wonderful enthusiasm and delightful company. The book is dedicated to my children for future reference.

Introduction

The intermediation theory of the firm provides an explanation for why firms exist. Firms are formed when intermediated exchange provides greater gains from trade than direct exchange between consumers and suppliers. The theory also helps to explain how markets work. Markets reach equilibrium through strategic pricing and contracting by intermediaries. Under some circumstances, intermediaries may have advantages over direct exchange in a number of activities: 1. 2. 3. 4. 5. 6.

Reducing transaction costs. Pooling and diversifying risk. Lowering costs of matching and searching. Alleviating adverse selection. Mitigating moral hazard and opportunism. Supporting commitment through delegation.

In this introductory chapter, I illustrate the intermediation theory of the firm with a series of basic examples. Later chapters present a more complete analysis of the models that underlie these examples. Some advantages derive from coordination economies: the firm is recognized as a central place of exchange, thus reducing costs of search. Other advantages derive from economies of scale and scope in subtle ways. For example, because an intermediary can handle a higher volume of transactions than individual buyers and sellers, the intermediary is able to reduce risk through pooling and diversification. Other advantages stem from longevity and economic incentives to build a reputation. In particular, intermediaries who are able to make credible commitments bring advantages over contracts between buyers and sellers that are subject to renegotiation.

The intermediation theory of the firm In this section, I illustrate the intermediation theory of the firm by means of a simple example. The example is consistent with a pure exchange economy but applies to production economies as well.

xiv

Introduction

Consider a simple economy with one consumer and one supplier (who may be another consumer). The supplier has one unit of a good available for purchase by the consumer. The supplier has an opportunity cost C of supplying the good. The consumer has a willingness to pay V for a unit of the good. I use the term direct exchange to refer to the consumer's purchase of a unit of a good from the supplier. The consumer and the supplier meet and bargain over the terms of exchange. I start with a simplistic notion of transaction costs as a lump sum. Later on, I will be much more specific about the nature of transaction costs. Suppose that the consumer and the supplier encounter total transaction costs equal to T. Assume for now that there are positive net gains from trade: V - C - T > 0. The process of decentralized exchange can involve noncooperative bargaining processes such as first-and-final offers and exchanging alternating price offers. Assume for simplicity that the consumer and the supplier evenly divide the net gains from trade:

(V -C - T)/2. All the results in this chapter generalize easily to uneven splits in gains from trade.1 Suppose that an intermediary can purchase the good from the supplier at some price w and resell it to the consumer at some price p. Assume that the intermediary can commit to price offers. With intermediated exchange, suppose that the intermediary bears all the transaction costs, which equal K. The intermediary competes with direct exchange. Suppose for now that the consumer and the supplier have the same willingness to pay and the same opportunity cost in intermediated exchange and in direct exchange. Then it is apparent that intermediated trade will occur if and only if intermediation lowers transaction costs: K < T. This is the main building block of the intermediation theory of the firm. In general, the introduction of intermediaries can change the equilibrium levels of gains from trade and even the transaction costs of direct exchange, as later examples will demonstrate. The entry of an intermediary can be illustrated by means of a basic noncooperative game. The consumer and the supplier must choose individually whether to trade directly or through an intermediary. If the 1

An even division of the net gains from trade corresponds to the Nash bargaining solution.

Introduction

xv

buyer and the seller decide to trade directly, they can make side payments to each other before negotiating the terms of trade. The sequence of events is as follows. Period 1. The intermediary makes a binding offer of an ask price p and a bid price w. Period 2. After observing p and w, the consumer and the supplier decide whether to try to trade directly with the other agent or to accept the intermediary's offer. If they do not agree to transact with each other, they both transact with the intermediary. Period 3. If the consumer and the supplier both choose to transact with the intermediary, trade takes place at p and w. If the consumer and the supplier both choose to transact with each other, they negotiate over the allocation of gains from trade. The game among intermediaries, consumers, and suppliers assumes that intermediaries are able to make binding commitments to prices. Individual consumers and suppliers are able to commit to trade with each other, but they are not able to make price commitments. The ability of the intermediary to make price commitments reflects the idea that the intermediary wishes to uphold a reputation for trading at posted prices. An intermediary trades a larger volume of goods than individual buyers and sellers. Moreover, an intermediary is in the market for more periods of time than individual buyers and sellers. Firms often are said to be bearers of reputation that outlasts the individuals who comprise the firm at any particular time. The volume of trades and the longevity of the intermediary create returns to building a reputation. Consider first the case of a monopoly intermediary. The monopoly ask price pM and bid price wM leave the buyer and the seller indifferent between transacting with the intermediary and direct exchange: V - pM = (V - C - T)/2 = wM

-C.

The monopolist's markup exactly equals the transaction cost of direct exchange, pM — wM = 7\ so the monopolist's profit equals pM -wM

-K

= T -

K.

Thus the monopoly intermediary is economically viable if and only if K < T. Consider the case of Bertrand price competition between intermediaries. Competition drives the profits of the intermediaries to zero so that the markup just equals their transaction costs:

pc - wc = K.

xvi

Introduction

The consumer and the supplier who deal with competitive intermediaries obtain total gains from trade equal to V — C — K. Suppose that these gains are split evenly by the competitive prices:

V - pc = (V - C - K)/2 = wc - C. Consumers and suppliers will be attracted by the prices pc and wc if and only if transaction costs of intermediated exchange do not exceed those under direct exchange. As in the monopoly case, the competitive intermediaries are economically viable if and only if K < T. Transaction costs under intermediated and direct exchange can arise because of many different factors. Suppose for example that intermediated exchange occurs immediately while direct exchange requires a delay for search and bargaining. After the delay, gains from trade V — C are realized and divided evenly between the consumer and the supplier. If the consumer and the supplier discount future benefits at rate 8, then the present value of returns from direct exchange equal S (V — C)/2. This is equivalent to assuming that the transaction costs of direct exchange are T = (1 - S)(V - C). An intermediary is viable if and only if K < (1 — S)(V — C). The intermediary is more likely to be viable if the discount factor is low, the consumer's willingness to pay is high, and the supplier's opportunity cost is low. Because there are time costs of search and bargaining, higher gains from trade increase the chance that an intermediary will be economically viable. The process of search can be imperfect so that the consumer and the supplier meet only with some probability /J. Suppose that the intermediary has a well-known address. Then the transaction costs of direct exchange are T = (1 - P)(V - C). If the matching process is inefficient so that ft is small, intermediated exchange will have an advantage over direct exchange. These examples introduce the intermediation theory of the firm. The existence of firms can be justified even in a pure-exchange economy, since the comparison between modes of exchange does not depend on production of goods. Firms arise as a means of economizing on transaction costs, not by internalizing transactions but by carrying them out more efficiently. I now turn to other ways in which intermediated exchange can lower transaction costs.

Introduction

xvii

Market microstructure Neoclassical economics leaves open the question of how markets attain equilibrium prices. In contrast, intermediation theory identifies price setting by firms as the mechanism by which the economy attains marketclearing prices. I address these issues in Chapters 1-4, which look at market microstructure in a number of settings including monopoly, oligopoly, Bertrand competition with entry, and general equilibrium. Firms select prices to balance their purchases and sales. They select ask prices to earn revenues and ration consumer demand. They select bid prices to stimulate suppliers and keep down purchase costs of inventories. Buy and sell prices are adjusted to equate marginal revenues and marginal cost subject to sales not exceeding purchases and inventories. Market microstructure theory requires that some firms have a measure of local market power, that is, there must be some price makers in the economy. In balancing their purchases and sales over time, firms allocate resources and clear markets. Intermediaries provide other important market-making services as well. They hold inventories of goods on hand and stand ready to sell to customers. They further have cash on hand and stand ready to buy from suppliers. This avoids the problem of the coincidence of wants, in which a buyer and a seller need to want to transact with each other at the same time. This function is familiar in securities markets, in which financial intermediaries provide liquidity by standing ready to buy and sell stocks. In retail and wholesale markets, intermediaries provide similar immediacy services by standing ready to buy and sell commodities. The cost of carrying inventories serves to create a bid-ask spread. The dynamic path of prices responds to the intermediary's inventory level and associated risks. The inventories of firms help to clear markets, smooth the patterns of demand and supply fluctuations, and reduce the risks of exchange. Quantity rationing of buyers and sellers is complementary to the firm's price-setting activities. As market makers, firms allocate goods and services across buyers and adjust purchases from suppliers to reduce the costs of carrying inventories while providing availability to customers. In securities markets, intermediaries like stock specialists smooth the pattern of exchange, creating market liquidity by holding inventories.2 Demsetz (1968) investigates the effects of trading volume on transaction 2

Baumol (1965) examines market makers and stability in the stock market. Stoll (1985) surveys alternative views of financial market making, examining the market maker as auctioneer, price stabilizer, information processor, and supplier of immediacy. He observes that only the latter two roles are based on maximizing behavior by the market maker.

xviii

Introduction

costs at the New York Stock Exchange and observes that "the ask-bid spread is the markup that is paid for predictable immediacy of exchange in organized markets; in other markets it is the inventory markup of retailer and wholesaler." Specialists on the New York Stock Exchange are compensated for managing orders and for assuming risk by standing ready to carry out trades on their own account. In an early model of market structure due to Garman (1976), buy and sell orders arrive randomly.3 The rates at which orders arrive can be interpreted as stationary demand and supply functions that depend on the ask and bid prices. A risk-neutral dealer with market power maximizes expected profit per unit of time, subject to the restriction that the stock inventory does not drift upward or downward, which means that the market clears at each date.4 Ho and Stoll (1980,1981) and Stoll (1978b) assume that the securities dealer is risk averse. The bid-ask spread reflects the elasticity of demand and supply and the dealer's degree of risk aversion. In addition, the bid-ask spread tends to increase the longer the dealer's planning horizon. Adding more periods provides the dealer with more opportunities for price adjustment, but increases the dealer's risk, thus requiring greater compensation and widening the bid-ask spread. Firms in product markets provide analogous market-making services. Clower and Leijonhufvud (1975) observe that intermediaries provide availability of products. They note that since consumers and firms face fixed transaction costs, they produce or sell at discrete time intervals, which can create problems of the double coincidence of timing. Intermediaries hold inventories to provide immediacy or availability to buyers and sellers. This happens both when retailers and wholesalers purchase goods from suppliers and hold the inventories needed to serve buyers and when manufacturers keep inventories of parts on hand and create product inventories. Just-in-time inventory management is a means of providing immediacy while lowering inventory costs. By holding inventories, firms acting as intermediaries reduce the risk of market transactions when demand fluctuates randomly. Retail and wholesale intermediaries diversify by purchasing and reselling a variety of products, thus pooling supplier risk; see Lim (1981). Spulber (1985) shows that manufacturers and wholesalers enter into financial 3

4

On the determinants of the bid-ask spread, the interested reader might begin with West and Tinic (1971), Tinic (1972), Benston and Hagerman (1974), Logue (1975), Stoll (1978a, 1978b), Ho and Stoll (1980, 1981), and Cohen et al. (1981). Since profits and inventories of the stock follow random walks, the intermediary with finite inventories will almost certainly go bankrupt at some point. However, Garman (1976) avoids this issue by considering the case in which the intermediary has infinite inventories of both cash and stock.

Introduction

xix

risk-sharing arrangements with retailers and pool inventories in central warehouses to smooth out differences in demand across stores. Large retail chains achieve important advantages through diversification of demand risk across individual stores. Intermediaries have an advantage over direct exchange between buyers and sellers because the increased volume of transactions reduces the variance of sales and of purchases. In direct exchange, buyers and sellers face the possibility of being rationed because of demand and supply side shocks. By standard law of large numbers arguments, the variance of expected purchases and sales falls with scale. Moreover, by serving multiple markets or by handling a broader range of products, intermediaries reduce risk through diversification.

Intermediated exchange versus matching and searching Market intermediaries coordinate the actions of buyers and sellers. Firms carry out transactions, operating the system of payments, inventory control, and record keeping that is essential for markets to function. In addition, firms provide a central place of exchange, thus reducing the search costs of buyers and sellers. Chapters 5 and 6 compare the costs of intermediation with those of direct exchange in markets with matching of buyers and sellers or costly search. Marketers - including retailers, wholesalers, used-car dealers, and energy dealers - purchase and resell goods. Brokers - including travel agents, real estate agents, insurance agents, and stockbrokers-provide coordination services without buying and selling goods.5 These intermediaries improve the welfare of consumers and suppliers by reducing or eliminating the uncertainty associated with making a satisfactory match. Intermediaries also add to the number of potential trading partners, thereby increasing the likelihood of encountering a trading partner and reducing search costs. Intermediaries must compete with decentralized exchange, in which consumers and suppliers seek each other out and negotiate prices directly.6 Sometimes both forms of exchange exist side by side. For example, an organized used-car market operated by automobile dealers coexists with a decentralized market in which buyers and sellers meet informally, often 5

6

In Yinger (1981), real estate brokers set housing prices, fix commissions, and invest in search for buyers and sellers of houses. His model explains the value of shared listings such as the Multiple Listings Service. See Rubinstein and Wolinsky (1987), Bhattacharya and Hagerty (1987), Yavas (1992), Yanelle (1989), and Gehrig (1993).

xx

Introduction

through newspaper advertising. What are the advantages of transacting with an intermediary? Consider first the matching market. Consumers have diverse levels of willingness to pay and suppliers have different opportunity costs. If consumers and suppliers are matched randomly, in a highly decentralized fashion, the terms of the exchange become uncertain and the risk of not completing a trade rises. After all, when consumers and suppliers bargain directly, the buyer has an incentive to understate willingness to pay and the seller to overstate opportunity costs. Asymmetric information about willingness to pay and opportunity costs causes efficiency distortions in the amount traded or even results in the breakdown of trade. An intermediary can eliminate this uncertainty by posting bid and ask prices and thus offer an advantage over a decentralized matching market. Buyers and sellers can choose between using intermediaries to trade at a known price and the risky option of the decentralized market. Gehrig (1993) models this choice and shows the profitability of intermediation. Suppose that each consumer purchases at most one unit of the good and suppliers sell at most one unit. Then the market demand and supply functions represent the distribution of buyer willingness-to-pay levels and supplier opportunity costs, respectively. The intermediary chooses a profit-maximizing bid-ask spread, given the value to buyers and sellers of the matching-market option. At the market equilibrium, consumers with a willingness to pay above a critical level (greater than the ask price) purchase from the intermediary. Suppliers with opportunity costs below a critical level (less than the bid price) sell to the intermediary. Consumers and suppliers with values between these two critical levels enter the matching market. The advantage of intermediated exchange can be illustrated by means of a simple example. Suppose that the consumer's willingness to pay can take one of two values with equal probability, VL and VH> Assume that VL < VH- Denote the expected value of the consumer's willingness to pay by Also suppose that the supplier's opportunity cost can take one of two values with equal probability, CL and c#. Assume that CL Denote the expected value of the supplier's opportunity cost by

c = (l/2)cL + (l/2)cH. Before entering the matching market, the consumer and the supplier do not know the type of their trading partner. Assume that after a consumer and a supplier decide to trade, they learn each other's type. At

Introduction

xxi

that point, trade occurs if and only if they have gains from trade. The consumer and the supplier split the gains from trade evenly. A high-willingness-to-pay consumer can trade with both types of suppliers: t># > c # . A low-opportunity-cost supplier can trade with both types of consumers: vi> CL- The market outcome will depend on whether a high-opportunity-cost supplier can trade with a lowwillingness-to-pay consumer, that is, VL may be greater than or less thanc#. Suppose first that VL > c#, so that all types will trade in the directexchange market. Then, since they are uninformed about the type of their trading partner, the expected gains from trade of a type / consumer and a type j supplier from the direct-exchange market are, respectively, (vt - c)/2,

i = 1, 2,

(v - CJ)/2,

j = 1, 2.

It is easy to demonstrate that there are no prices at which a monopoly intermediary is profitable, (even with zero transaction cost K). For example, suppose that the intermediary chooses the highest ask price and the lowest bid price that will attract the high-willingness-to-pay consumer and the low-opportunity-cost supplier. These prices are PM = VH ~ (vH - c)/2,

wM = cL + (v -

cL)/2,

It follows that pM -wM = (cH - vL)/2 < 0. Now suppose that vi < CH, SO that a high-opportunity-cost supplier cannot trade with a low-willingness-to-pay consumer. The expected gains from trade for a high-willingness-to-pay consumer and a low-opportunity-cost supplier do not change. However, because a lowwillingness-to-pay consumer has only one other potential trading partner, the low-willingness-to-pay consumer expects gains from trade in the direct exchange market equal to (VL — CL)/A. A high-opportunity-cost supplier expects gains from trade equal to (VH — CH)/4. The intermediary offers prices pM and wM and is profitable if (CH — VL)/2 > K. The prices attract the high-willingness-to-pay consumer and a low-opportunity-cost supplier. The low-willingness-to-pay consumer and the high-opportunity-cost-supplier are inactive since they do not gain from direct exchange with each other. Thus, when there is a chance of trade breaking down under direct exchange, vL < CH, an intermediary will enter the market and a separating market equilibrium will result. When consumers search for a product, they face costs of travel and costs of learning about prices and comparing product features. When suppliers search for a willing buyer, they incur costs of travel and

xxii

Introduction

of communicating information about their products. As noted earlier, intermediaries reduce transaction costs by centralizing exchange. However, in a world with multiple intermediaries, consumers and suppliers continue to incur search costs from visiting multiple intermediaries. Spulber (1996a) models a search market with many intermediaries. Consumers and suppliers discount future net benefits, so that the time spent searching is costly. As before, consumers have diverse willingness to pay levels, and suppliers have different opportunity costs. Moreover, firms that intermediate have different transaction costs. Firms set both bid and ask prices. Consumers search across firms to obtain a lower ask price, and suppliers search across firms to obtain a higher bid price. As a result of heterogeneity and costly search, the market equilibrium is a distribution of bid prices and a distribution of ask prices. The equilibrium depends on the discount rate of consumers and suppliers, for which a higher rate of discount lowers the number of active consumers and suppliers and raises the number of active firms. The intuition behind this result is that a higher discount rate increases the cost of time-consuming search for consumers and suppliers. This allows firms to raise ask prices and lower bid prices since consumers and suppliers are willing to pay a premium to avoid further search, thus raising the returns to intermediation by firms. The number of intermediary firms that are active in equilibrium increases. The discount rate determines the costs of search. As the discount rate falls to zero, the costs of search are eliminated, which shows the relationship between the size of the bid-ask spread and transaction costs. In such a model, the Walrasian equilibrium is the limiting case of an intermediated market as transaction costs diminish. The supply-and-demand model can thus be viewed as an ideal case that is consistent with an underlying market with search costs and price-setting firms.

Alleviating adverse selection Chapters 7 and 8 examine models in which intermediaries address problems of adverse selection. In Chapter 7,1 consider allocation by intermediaries under asymmetric information about buyer willingness-to-pay levels and seller opportunity costs and certification of product quality. In Chapter 8,1 turn to adverse selection problems in financial markets, including pricing by informed and uninformed market makers and credit rationing by financial intermediaries. Brokered exchange differs from trade between a buyer and seller in a subtle way. In direct trade, the buyer's payment must equal the seller's receipt, which constrains the possibilities for bargaining. A

Introduction

xxiii

broker introduces many other possibilities for bargaining since the broker can effectively tax or subsidize the transaction. By taxing the transaction, a broker can capture some of the gains from trade by improving the chance that trade takes place.7 The broker designs a trading rule that elicits offers from the buyer and the seller and earns a return by creating a spread between the buyer payments and the seller receipts. In many markets buyers and sellers are asymmetrically informed. Sellers often do not know customer characteristics that underlie market demand. Buyers frequently do not know the quality, durability, or safety of products they seek to purchase. Intermediaries help to fill this gap by collecting and supplying information to their customers and suppliers, often bundled with products and other services. Retailers can test products and describe their characteristics to their customers. Wholesalers report on market demand and customer requirements to their suppliers. Consolidating transactions through intermediaries can yield returns to scale in producing and distributing this information. Intermediaries can capture gains from trade that would be lost because of information asymmetries. Not only do intermediaries have advantages in gathering and reporting information, they can guarantee that the information they provide is accurate, backing up the guarantee with reputation and binding contracts. Product characteristics frequently are difficult for consumers to observe. Consumers are uncertain about the efficacy of Pharmaceuticals, the durability of appliances, or the quality of automobiles. If consumers are less informed than suppliers about product quality, the market can fail to exist as bad suppliers drive out good. In Akerlof's (1970) well-known market-for-lemons model, low-quality used cars drive out high-quality used cars, since consumers are willing to pay only an average price for cars of unknown quality, and only sellers of low-quality cars can trade at that price. The market for lemons fails to realize potential gains from trade. Customers would be willing to pay for a good car if they could observe its quality. An intermediary can capture some of these foregone returns by certifying the quality of the product. Biglaiser (1993) shows that introducing a monopoly intermediary into a market with adverse selection enhances efficiency. The intermediary has a greater incentive to invest in monitoring quality than does an individual buyer, since the intermediary buys more goods. Thus intermediaries are better able to distinguish higher-quality suppliers from those with lower quality. 7

See Myerson and Satterthwaite (1983), Spulber (1989b), and Mookherjee and Reichelstein (1992).

xxiv

Introduction

In addition, the intermediary's incentive to report accurately the quality of goods stems from the returns to building a good reputation. These returns can be greater for intermediaries since they carry out more transactions than individual suppliers. Buyers and sellers decide whether to transact directly with each other or to buy and sell through the intermediary. In equilibrium, all high-quality goods are sold through the intermediary and most low-quality goods are sold directly to buyers. As a result of this separation, the lemons problem is alleviated at the intermediated market equilibrium. A retail or wholesale intermediary can offer many different products for sale, and consumers can rely on the reputation of the intermediary without having to investigate the many product suppliers. In particular, intermediaries can serve as guarantors of the product quality of their suppliers through warranties and contract terms. A manufacturer's brand name often conveys information to customers who then do not need to know the quality of components purchased by the manufacturer. Since intermediaries handle the products of two or more suppliers, their incentives to sell a lower-quality good differ from those of individual suppliers. The intermediary that sells a low-quality product suffers a loss of reputation and thus loses customers for all other products. Intermediation lowers the threshold prices that are required for sustaining high-quality production. To illustrate the basic problem, consider an example with a single consumer and supplier. The supplier's product can be of high or low quality. Supplying a product of quality j entails an opportunity cost of CJ, j = L, //, where the opportunity cost increases with quality: CL A > (vH -

vL)/2.

Assume that in direct exchange the consumer and the supplier cannot commit to a price before the consumer's investment decision. After the consumer decides whether or not to invest A, the consumer and the supplier bargain over the division of the gains from trade. Surplus is evenly divided. If the consumer does not make investment A, then both the consumer and the supplier receive (VL — C)/2. If the consumer invests, then the consumer and the supplier each receive (VH — C)/2. This leads to the classic underinvestment result. The consumer will not

Introduction

xxvii

find it worthwhile to make the relationship-specific investment since the buyer must split the returns to investment with the supplier: (vH ~ C)/2 -A 0. I consider first the case in which the firm is a merchant, that is, the firm resells the goods that it purchases. For simplicity, assume that the firm incurs no transaction costs and does not transform the good through productive activities. I assume that the firm is constrained to set prices such that it sells no more than it buys: (1)

D(p) < S(w).

This assumes that the firm can purchase to stock and can freely dispose of its excess inventory.1 The firm's profit function is (2)

n(/7, w) = pD(p) - wS(w).

The firm chooses the ask price p and the bid price w to maximize profit 1

An alternative assumption would let the firm purchase to order and constrain the firm to purchase no more than its demand: D(p) > S(w). Another approach should allow the firm to be rationed by the short side of the market with sales equaling the minimum of demand and supply: min{D(p), S(w)}.

Price setting and intermediation by firms

31

subject to the supply-side constraint (1), D(p) < S(w). It can be shown that the firm will always choose ask and bid prices such that the supply constraint is strictly binding. Therefore, at the profit maximum, the firm chooses ask and bid prices (/?*, w*) that clear the market. The first-order conditions for the firm's profit-maximization problem imply the fundamental equation (3) and market-clearing condition (4): (3)

p*-w*

= p*/ri(p*) + w*/Kw*)9

(4)

2* = D(P*) = S(w%

where Q* is the amount traded. The profit-maximizing prices are set such that the bid-ask spread p* — w* is both positive and finite. The finiteness of the spread is significant since it shows that a monopolist earns arbitrage profits but does not increase the spread without bound. The positive spread is important since the intermediary's market-clearing prices depart from the Walrasian law of one price. The monopoly intermediary's arbitrage profits can be written as (5)

n ( / A w*) = <j>* - w*)Q\

that is, profits equal the bid-ask spread times sales. The monopoly intermediary's ask price and bid price are respectively above and below the Walrasian price: (6)

p* > pw > w*.

The monopoly intermediary's output is below the Walrasian input: (7)

0* < Qw.

The intermediary's optimal bid and ask prices are shown in Figure 2.1. The basic analysis can be extended easily to incorporate such exogenous effects as an excise tax. The intermediation diagram makes clear that thefirmhandling the tax does not fully pass it on to its customers nor does it fully reflect the tax in a price reduction to its suppliers. Instead, the ask price rises and the bid price falls as the firm adjusts to the tax, leading the equilibrium quantity that is sold to customers and bought from suppliers to decline as well. Moreover, the change in the spread does not fully reflect the amount of the tax as a consequence of both the elasticity of demand and the elasticity of supply. Garman (1976), who defined the concept of market microstructure, introduces a monopolist intermediary to represent centralized price setting in a dealership market for securities.2 Buy and sell orders arrive randomly 2

On the determinants of the bid-ask spread, see also West and Tinic (1971), Tinic (1972), Benston andHagerman(1974),Logue(1975),Stoll (1978a, 1978b), Ho and Stoll (1980,1981), and Cohen etal. (1981).

32

Market microstructure and the intermediation theory of the firm

p,w

S(w)

p*

/

Pw

D(p)

! Q*

Qw

Q

Figure 2.1. The basic intermediation model.

with stationary Poisson arrival rates of q and x. The order arrival rates can be interpreted as stationary demand and supply functions that depend on the ask and the bid prices q = D(p) and x = S(w). The monopolist maximizes expected profit per unit of time subject to the restriction that the stock inventory does not drift upward or downward, D(p) = S(w). Garman considers the case in which the intermediary has infinite inventories of both cash and stock. Otherwise, since profits and inventories of the good follow random walks, the intermediary with finite inventories will almost certainly go bankrupt by standard gambler's ruin arguments. Garman (1976) shows that the bid-ask spread chosen by the monopolist follows the solution of the static problem, as shown in Figure 2.1. Price setting by a manufacturer Suppose that the firm is a manufacturer rather than a merchant and transforms an input X into output Q by using the concave technology Q = H(X). The firm maximizes profit as given in Eq. (2) subject to the production constraint D(p) = H(S(w)). The firm's bid and ask prices solve (8)

p*Hf(S(w*)) -w* =

w*/t;(w%

Price setting and intermediation by

firms

33

Therefore, as a consequence of the firm's setting input and output prices, the marginal revenue product of the input exceeds the input price: p*H'(S(w*)) > w*. The firm's profit can be written as the sum of two components. Add and subtract the marginal revenue product of the input pH'(S(w)) to obtain (9)

n(/?*, w*) = [p*Hf(S(w*)) - w*]S(w*) +p*[H(S(w))/S(w*)

-

H'(S(w*))]S(w*).

The first bracketed term represents the firm's return due to the difference between the marginal revenue product of the input and the price of the input. This term is positive by the firm's optimization problem. The second bracketed term is the difference between the average and the marginal products of the input, which is positive given the concavity of the production function. Production technology is readily incorporated into the basic diagram by replacing the input supply function with the intermediary's average factor cost function. The monopsony cost function does not depend parametrically on prices because they are set by the intermediary. The cost function is defined by minimizing factor payments subject to the production constraint at each output level. The firm sets input prices to minimize factor costs. Let H be the firm's production function. Then the factor cost function is derived in the following manner: (10)

C(Q) = subject to Q = H(XU X2, •.., Xm) and Xt = S(wt), i = 1,2, . . . , r a .

Let c(Q) = C(Q)/Q represent the average factor cost. Then the firm chooses the profit-maximizing spread between the ask price and average factor cost, p — c. With one input, the average factor cost function is simply where u;* = W(Q*) = S~l(Q*) is the inverse of the supply function, Q* = D(p*) = H(S(w*)). Profit equals the markup over average factor

cost: [p*-c(Q*)]Q*.

The choice of the average factor cost determines the output produced by the firm since it specifies the prices paid to suppliers for inputs, which in turn determine the output through the production function. The graphical representation resembles the supply and demand diagram in

34

Market microstructure and the intermediation theory of the firm

Figure 2.1, with S(w) replaced with c(Q) and w* replaced with c(Q*). This analysis helps to illustrate why businesses often speak of pricing based on setting markups over unit cost.

2.2

Allocation under uncertainty and over time

In this section, I apply the basic intermediation pricing model to allocation under uncertainty and over time. To illustrate how firms allocate risk, I consider a simple example of an insurance firm that acts as an intermediary between two consumers, setting a bid-ask spread in insurance premiums. To show how firms allocate financial assets over time, I consider the case of a firm that intermediates between a borrower and a lender, setting a bid-ask spread in interest rates. Insurance pricing by an intermediary Consider an insurance company that insures one consumer and receives funding from another consumer. The consumer that purchases insurance from the firm faces a risk of loss. The other consumer, who does not face a risk of loss, acts as an investor, essentially by selling insurance to the firm. Each consumer has wealth co and utility function u(co) that is twice differentiable, increasing, and concave. The consumer's Arrow-Pratt index of absolute risk aversion, pA{co) = —uf/(a))/uf(co), does not increase in wealth. The consumer that purchases insurance is subject to a loss of L with probability /?. The consumer purchases coverage that is equal to y < L and pays a premium of py. The consumer's demand for coverage, y = y{p), is chosen to maximize (11)

V(y, p) = Pu(co -L + y-py)

+ {\- P)u(co - py).

The consumer's demand for insurance solves (12)

/3uf(a) -L + y- py)(l - p) - (1 - P)u'{co - py)p = 0.

The consumer that invests in thefirmsupplies coverage equal to x < co in the event of a loss and receives a premium of wx. The consumer's supply of coverage to the firm, x = x(w), is chosen to maximize (13)

U{x, w) = Pu(co -x + wx) + (l-

P)u(co + w x ) .

The consumer's supply of insurance solves (14)

-Pu\(o -x + wx){\ - w) + (1 - P)u\(o + wx)w = 0.

The consumer's supply function x(w) is upward sloping.

Price setting and intermediation by

firms

35

The insurance firm chooses prices p and w to maximize profit:

(15)

n(/?, w) = py(p) — wx(w) + 0(x(w) — y(p)),

subject to the coverage constraint y(p) < x(w).3 The insurance intermediary sets prices that clear the market, so that the coverage supplied to the firm exactly equals the coverage demanded: x(w*) = y(p*) = y*. Let (/?*, w*) be the optimal ask and bid prices for the insurance firm. The equilibrium of the insurance model has a number of interesting properties. The payment to the investor per unit of coverage is greater than the expected coverage supplied and less than the coverage:

0x < w*x < x. The insurance contract is not actuarily fair: p*y > PyThe consumer does not purchase full coverage y(p*) < L. The insurance intermediary chooses an ask price of insurance p* that is strictly greater than the bid price w*. From the consumer's first-order conditions, the marginal rate of substitution for the consumer purchasing insurance and for the consumer supplying insurance will not be equal: -L + y- p*y) _ 1 - 0 p* 1-0 w* u'((o — p*y) 0 1 — p* 0 1 — w* u'(co — x + w*x) u'(co + w*x) The insurance firm earns positive profit equal to the price spread times the level of coverage: U'(G>

n(/A w*) = (p* - w*)y*. In this example, the insurance firm bears no risk. All risk is shared between the consumer and the investor, with the insurance firm playing an intermediary role. The reason for this is that the insurancefirmwill not obtain coverage from the investor in excess of the demand for insurance coverage. Otherwise the marginal cost of increased investment would exceed the marginal revenue from additional sales, thus lowering the firm's profit. 3

The first-order conditions for the firm's profit-maximization problem are as follows:

y(p) + {p-P-

X)y'{p) = 0,

-x{w) + (-w + fi + k)x'(w) = 0, k(x(w) - y{p)) = 0,

A. > 0.

Then, k > 0 since w > fi, x'(w) > 0, and k = w — fi+ x{w)/x'{w).

36

Market microstructure and the intermediation theory of the firm

Pricing loans by an intermediary To illustrate how markets allocate resources over time, consider a firm that intermediates between a borrower and a lender. The borrower and the lender are assumed to have different rates of time preference. Similar results would be obtained if the borrower and the lender have different income patterns over time. Suppose for simplicity that there are only two time periods. Suppose further that the two consumers have additively separable utility functions, (16)

U(c,C) = u(c) + pju(C),

where c is first-period consumption, C is second-period consumption, and & is the discount factor applied to future benefits by consumer j , j = Z), S. Let fiD represent the discount factor of the consumer who demands a loan, and let /3s represent the discount factor of the consumer who supplies savings, where fiD must be less than /3s because of the greater impatience of the borrower compared with that of the lender. Suppose that each consumer earns income equal to 1 in each period. Let s represent the amount of saving, and let b represent the amount of borrowing. Then, if r is the interest rate on savings, the consumer who saves has a budget constraint in the first period given by (17)

c=l-s,

and a budget constraint in the second period of (18)

C= !+

(!+r)s.

Using budget constraints (17) and (18), it follows that the consumer who saves thus chooses s to maximize (19)

Us = w(l - s) + Psu(l + (1 + r)s),

which yields a supply of savings s = S(r) that solves

The borrowing consumer has a budget constraint in the first period given by (21)

c=l+b.

If i is the cost of borrowing, the borrowing consumer's second-period budget constraint is (22)

C = 1 - (1 + i)b.

Price setting and intermediation by firms

1

37

1 + 1/(1 + i)

Figure 2.2. Borrowing and lending with an intermediary.

Given budget constraints (21) and (22), the consumer chooses b to maximize

(23)

UD = u{\ + b) + pDu{\ - (1 + i)b).

The demand for credit b = D(i) solves (24)

The case of saving is shown in Figure 2.2. The budget line is kinked since the firm's ask price of loans i is greater than its bid price for savings r. Suppose that the intermediary discounts future profit with a factor S. The firm's profit then is a function of the ask price for loans and the bid price for savings: (25)

(i, r) = S(r)

-

r)].

The firm chooses prices i and r to maximize profit n(i, r) subject to two restrictions. First, the amount of credit cannot exceed the supply of savings:

(26)

Sir) > D(i).

38

Market microstructure and the intermediation theory of the firm

Second, the repayment to the lender cannot exceed the repayment by the borrower: (27) Assign shadow prices X and y on the first-period and the second-period inequality constraints and maximize profit subject to the two inequality constraints.4 Combining the first-order conditions for interest rates i and r and canceling terms show that the optimal interest rate spread chosen by the firm again satisfies the fundamental equation,

Suppose that the firm earns positive profit in each period, so that constraints (26) and (27) are not binding. Then the firm's bid and ask prices must be chosen such that the market discount factors are bounded by the discount factor of the consumer that borrows from the firm and the discount factor of the consumer that lends to the firm:

PD < —^— < 8 < < /3s. P (1+/*) (1+r*) P The inequalities 1/(1 + i*) < 8 < 1/(1 + r*) follow from the first-order conditions for i and r.5 The inequalities f)D < 1/(1 + i*) and 1/(1 + r*) < fis follow from the optimization problems of the saving and the borrowing consumers since utility is concave.6 It must be the case that the firm's discount factor lies between the borrowing and the saving consumers' discount factors, fiD < 8 < /3s. Consider what happens if the intermediary's discount factor lies outside of this range. If the intermediary's discount factor is large, 8 > fis, the firm will set interest rates so that it earns income in only the second period.7 The firm will set interest rates such that first-period profit is zero, S(r) = £>(/), so that, from the definition of profit,

n(i\ r) = 8{i - r)S(r). If the intermediary's discount factor is small, 8 < fiD, the firm will set 4

The first-order conditions for the intermediary's maximization problem are as follows: - 1 + 8(\ + i) - A. + y(l + i) = -(8 + 1 - 8(1 + r) + A. - y(l + r) = (8 +

5 6

7

y)D(i)/D'{i),

y)S(r)/S'(r),

A. > 0,

k[S(r) - D(i)] = 0,

Y > 0,

y[D(i)(l + i) - S(r)(l + r)] = 0.

Set A, and y equal to zero in the first-order conditions; see footnote 4. Note that for the saving consumer c=\— s < C = l + ( l + r)s, so fiD < 1/(1 + i *) follows from Eq. (20). Note that for the borrowing consumer c = 1 + b > C = 1 - (1+ i)b, so 1/(1 + r*) < 0s follows from Eq. (24). This follows from pD < l/(l+/*)and l / ( l + r * ) < Ps and thefirst-orderconditions in footnote 4.

Price setting and intermediation by

firms

39

interest rates such that it earns income in only the first period. Since second-period profit is zero, the definition of profit implies that

n(i\ r) = S(r) - D(i) = iD(i) - rS(r). At the intermediated outcome, consumer marginal rates of substitution are not equal. For example, when the intermediary earns positive profit in both periods, K'(1

(29)

+ b)

• = (1 + 0 > 1/5;

u'(l-s) Moreover, b = D(i*) > s = S(r*). Compare the monopoly outcome with the Walrasian outcome, which is depicted in Figure 2.3 at point c 1 , C 1 . The contract curve is represented in an Edgeworth box with two units on each axis representing the total income in each period. With consumer two saving and consumer one borrowing, a Walrasian equilibrium rate of interest r equates marginal rates of substitution:

u\\+b) P u\\ - (1 + r)b) l

r

u\\-s) fiV(l + (1 + r)s)'

Moreover, the amount borrowed equals the amount saved. Consumer 2

Consumer 1

1

c1

2

Figure 2.3. The contract curve with exchange between a borrower and a lender.

40

Market microstructure and the intermediation theory of the firm

The preceding applications of the basic intermediation pricing model show its generality and applicability to the study of market allocation in diverse settings. I have considered production models, allocation under uncertainty and allocation overtime. The intermediation model is fundamentally different from the traditional framework because it places the firm at the center of the action, providing an explicit mechanism for price adjustment. The intermediated equilibrium is a market-clearing equilibrium since demand at the equilibrium ask price equals supply at the equilibrium bid price. In Section 2.3,1 consider the question of how intermediaries adjust prices to changes in supply and demand so as to clear the market.

2.3

Price adjustment by intermediaries

How does thefirmrespond to demand shifts? In the traditional monopoly model, a price-setting firm with a rapidly increasing marginal cost curve will respond with smaller output adjustments and greater price adjustments relative to a firm whose marginal cost curve rises more slowly.8 This analysis must be modified for a price-setting intermediary who can also respond to a shift in demand by changing the price offered to suppliers. This will also modify the firm's output price and quantity decisions. The basic diagram showing the firm's bid-ask spread can be used to illustrate the adjustment of prices to fundamental changes in market conditions. Suppose for example that technological change or favorable production conditions shift out the supply function faced by the intermediary; see Figure 2.4. Then, at the initial ask price, Q\ units are sold, but at the initial bid price, a larger amount equal to X units is offered by suppliers. If the firm acting as an intermediary were to purchase the offered supplies, excess inventories would accumulate. The firm is able to reduce its costs without reducing its purchases by lowering the bid price offered to suppliers. However, the bid price will not be lowered until the original equilibrium output is reestablished, since profits are also increased when the ask price is lowered to consumers. Thus the new equilibrium is reached at a lower bid and a lower ask price as well and a higher equilibrium output, 02A similar analysis can be given for a shift in market demand. If demand increases, for example, the amount demanded Q\ exceeds the amount 8

See Gordon (1981) for further discussion and a literature survey.

Price setting and intermediation by

firms

41

p,w Si(w)

Pi

S2(w)

P2

w2 D(p)

Qi

Q2

X

Q

Figure 2.4. Adjustment of bid and ask prices to an increase in supply.

that the intermediary is able to purchase at the equilibrium ask price; see Figure 2.5. The profit-maximizing firm will raise the ask price to reduce demand but not to the full amount that would reduce demand to its initial level. Instead, the firm will also raise the bid price to bring forth more supplies, resulting in a new equilibrium with higher ask and bid prices and a higher equilibrium output, Q2. The price elasticity of the firm's suppliers thus will enter into the firm's output-pricing decision. Conversely, the output-price decision will be affected by shifts in the firm's supply curve, and the elasticity of demand will affect the firm's input-pricing decisions. To illustrate these issues, consider constant elasticity demand and supply curves:

where r] is the elasticity of demand, § is the elasticity of supply, and y is the market demand shock. The firm's ex post profit-maximizing ask price p(y) and bid price w(y) solve the fundamental equation and clear

42

Market microstructure and the intermediation theory of the firm

p,w

S(w)

D2(p)

D,(p)

I

I

Qi

Qi

I Q*1

Q

Figure 2.5. Adjustment of bid and ask prices to an increase in demand.

the market:

p — w = (p/rj) + (tu/f),

P~v(l +y) = w*.

Solving these two equations gives the equilibrium prices p* and w*:

w

J

P*=

L

J

Define ep = (y/p)dp/dy and ew = (y/w)dw/dy as the respon-

siveness of the ask and the bid prices with respect to the shock y, and eq = (y/q)dq/dy as the responsiveness of output with respect to y: y

i

y

$

An increase in either demand elasticity r] or supply elasticity § reduces the responsiveness of both ask and bid prices to demand shocks. Greater demand elasticity lowers the output response while greater supply elasticity raises the output response. Thus a firm facing a relatively more elastic supply function will respond to a demand shock with smaller adjustments of both bid and ask prices and relatively greater output adjustments. This need not indicate that the prices set by a profit-maximizing

Price setting and intermediation by firms

43

intermediary are sticky as a consequence of market power. The values of ep and eq in the intermediation model are identical with those for the Walrasian equilibrium price and quantity, given the demand and supply functions in the example. Inflationary expectations and menu costs ofprice adjustment In the neoclassical economic framework, market prices adjust costlessly, accurately, and instantaneously to economic fluctuations, as the Walrasian auctioneer takes account of all relevant demand and supply information. In contrast, recognizing thatfirmsselect prices to maximize profit and to balance purchases and sales, implies that price adjustment is a costly, and of necessity, an imperfect process. The debate over whether prices are flexible or sticky has significant implications for both microeconomics and macroeconomics. In microeconomics, the phenomenon of price stickiness should not suggest market failure, but instead should be viewed as evidence that price setting is a costly activity for firms. Price stickiness holds a central place in The General Theory of John Maynard Keynes and in the New Keynesian Economics. Price and wage inflexibility poses a fundamental challenge to the neoclassical model of market equilibrium, which implicitly assumes exogenous price adjustment. There is substantial evidence on price inflexibility in many markets.9 There are a host of explanations for price stickiness including the following: (1) It is costly to adjust prices and communicate price changes to customers, (2) long-term contracts cause some prices to be adjusted with less frequency, (3) imperfect competition reduces pricing flexibility relative to Walrasian price adjustment, (4) coordination failures between competing firms reduce the frequency of price adjustment, and (5) information asymmetries affect contracts in a manner that reduces reliance on price rationing of buyers or sellers.10 All these explanations share one feature in common: Firms are responsible for price adjustment. Some aspect of the firm's choice problem, either a cost of adjusting prices or a trade-off with some other action, underlies practically all explanations for pricing inflexibility. The inflexibility of prices forces one to consider the microstructure of markets to explain the price-adjustment mechanism. According to the administered pricing hypothesis of Means (1935, 1972) and others, industry concentration increases price rigidity because 9 10

See, for example, Carlton (1986), Cecchetti (1986), Danziger (1987), Blinder (1991), and Lach and Tsiddon (1992). See Mankiw and Romer (1991).

44

Market microstructure and the intermediation theory of the firm

the market power of firms represents market failure. The emphasis on market share and industry concentration misses the mark.11 Price stickiness is not necessarily a consequence of imperfect competition. Carlton (1986) suggests that such an effect, where it exists, may be due to large firms' having multiple instruments at their disposal for alleviating transaction costs without exclusive reliance on pricing. Blinder (1991) carries out a survey of managers to evaluate the alternative explanations for price stickiness. He finds support for firms that adjust delivery lags or service quality rather than prices and keep prices constant to honor implicit contracts with customers. Managers also report that lack of coordination with competitors delays price adjustment, as does stability of input costs. He finds evidence for the existence of price adjustment costs but his observations give less weight to the effects of these costs. His survey data seem to reject inventories as pricesmoothing devices. He further finds little support for bureaucratic inertia within firms delaying price adjustments, for constancy of marginal costs holding markups constant, or for prices being held constant to serve as indicators of product quality. Price rigidity is central to the new Keynesian Economics. Mankiw and Romer (1991) define the new Keynesian economics by posing two questions: "Does the theory violate the classical dichotomy?" and "Does the theory assume that real market imperfections in the economy are crucial for understanding economic fluctuations?" According to the new Keynesian economics, sticky prices cause nominal fluctuations, such as changes in the money supply to influence output and employment. Moreover, as they note, imperfect competition, imperfect information, and relative price rigidity are keys to explaining sticky prices. Intermediation by firms poses a challenge to the neoclassical market model that is consistent with and indeed extends the new Keynesian economics. Examining market microstructure yields additional insights into the causes and the consequences of price rigidity. Theories that explain the rigidity of output prices set by firms under imperfect competition are enhanced by consideration of market-making intermediaries that choose both output and input prices. The relationship between changes in product and factor prices can be better understood by examining the decisions of firms that select or at least influence their ask and bid prices. Inflation affects the selling, purchasing, and inventory-holding decisions of the intermediary when there are costs of price adjustment. For simplicity suppose that the expected rate of inflation is constant. Then, given costs of price adjustment, the firm's real prices fall continuously 11

See also Burns (1936) and Galbraith (1952). Stigler and Kindahl (1970) presented contrary evidence that prices used in actual transactions, as opposed to posted prices, were more flexible.

Price setting and intermediation by

firms

45

until its nominal prices are adjusted upward. The fall in real prices increases the amount demanded by the firm's customers while simultaneously reducing the amount offered by the firm's suppliers. If prices cannot be continuously adjusted, the firm can either quantity ration its customers and suppliers or use inventories to adjust to the inflationary cycle. Suppose that the firm adjusts its output and input prices synchronously rather than staggering its price adjustment.12 The relationship between the firm's input and output prices over time has important macroeconomic implications. Consider the single-price-adjustment model of Sheshinski and Weiss (1977).13 In their framework, a firm faces a lump-sum real cost of price adjustment fi. The real rate of interest is r. They show that the firm follows a dynamic price-adjustment rule similar to that of inventory adjustment. Under this rule, referred to as an (s, S) pricing policy, the firm sets its nominal price such that its initial real price equals S. As a result of inflation and the fact that the firm's nominal price is held constant, the real price drifts downward continuously. When the real price hits the critical level s, the firm incurs the cost of price adjustment and adjusts the nominal price upward to the desired initial real price 5, and the cycle is repeated. Sheshinski and Weiss show that the (s, S) prices straddle the profit-maximizing price s*. The optimal solution is depicted in Figure 2.6, where Tl(p) is profit as a function of the real price p.u Initially, the firm operates with negative marginal profit and finishes the cycle with positive marginal profit. The difference in real profits at the beginning and the end of the cycle equals the real rate of interest times the real cost of price adjustment. Sheshinski and Weiss demonstrate that an increase in the rate of inflation increases the initial price and decreases the terminal price, thereby increasing the magnitude of each nominal price change. The rate of inflation generally has an ambiguous effect on the frequency of price changes. An increase in the level of price-adjustment costs leads to larger and less frequent price adjustments. An increase in the real rate of interest decreases both the initial and terminal real prices. Derivation of an optimal dynamic two-price policy is relatively complicated. For purposes of illustration, suppose that the intermediary 12

13

14

Sheshinski and Weiss (1992) present conditions under which a two-product monopolist chooses to adjust both prices simultaneously. This type of analysis could be applied to examine the decision of an intermediary as to whether to synchonize or stagger pricing changes. With many small firms and initial price dispersion, the rigidity of price adjustment at the level of individual firms may cancel out in the aggregate; see Caplin and Spulber (1987). However, the aggregate neutrality of money or demand shocks is unlikely to occur in markets with monopolistic competition between intermediaries; see Spulber (1998b). Let g be the rate of inflation. The prices s and S solve U(S) — U(s) = r/S and n'(z)zr/8 dz = 0.

46

Market microstructure and the intermediation theory of the firm

$

Figure 2.6. The optimal (s, S) pricing policy under inflation with priceadjustment costs p.

follows simultaneous 0 , S) pricing policies in both its input and output prices. The firm sets initial real prices (pi, w\) and readjusts its nominal prices when prices fall to the critical levels (po, wo) at the end of their cycle.15 Let D(p) and S(w) represent demand and supply, respectively, as functions of real prices. Let (/?*, w*) represent the profit-maximizing prices in the absence of inflation, that is, the prices satisfy the fundamental equation and clear the market: q* — D(p*) = S(w*). Assume that, as in the single-price case, prices straddle the profit-maximizing price, po the firm experiences excess supply because q\ < q* < x\\ see Figure 2.7. The firm also experiences excess demand at the end of the cycle because JCO < q* < q\\ see Figure 2.8. The firm can address this imbalance by initially rationing its suppliers toward the start of the cycle and then rationing customers toward the end of the cycle. Alternatively, the firm can accumulate inventories early in the cycle and draw them 15

See Spulber (1998b) for a discussion of simultaneous and staggered price adjustment.

Price setting and intermediation by

firms

47

p,w

Pi

P*

D(p)

qi

q*

«!

q,x

Figure 2.7. The firm has excess supply at the beginning of the cycle. p,w S(w)

P*

Po

D(p)

Xo

q*

qo

Figure 2.8. The firm has excess demand at the end of the cycle.

48

Market microstructure and the intermediation theory of the firm

down later in the cycle, balancing demand and supply over the cycle. Note that when prices are adjusted synchronously, the ratio of the nominal output price to the nominal input price remains constant. For the individual firm, price stickiness due to adjustment costs creates imbalances in its supply and demand and creates cyclical oversupply and excess demand. If rationing of customers and suppliers is feasible, the firm will choose to adjust its prices such that there is excess supply at the time of price adjustment. If the input is labor, the difference between the amount of labor services offered and the amount hired represents involuntary unemployment at the recently increased wages. This excess supply is relieved as real wages fall, until the firm is eventually supply constrained. Interestingly, actual employment by the firm may not vary much over the cycle, even though there is a significant decline in labor services offered, because the initial labor demand is dampened by the demand-side constraint. If the input is a raw material or some intermediate manufactured good, the amount purchased may also remain more stable than the underlying amount offered by suppliers at the real bid price. As inflation continues, the firm will experience supply shortages and excess demand, before readjusting both prices upward. If the firm relies less on rationing and more on inventories as a buffer, price increases will be followed by a buildup in inventories. As the firm's real prices fall, the combination of increased sales and supply reductions will draw down inventories. With inventories, the firm will experience greater fluctuations in both sales and purchases than with demand and supply rationing, although total purchases and sales over the cycle will be much greater. This suggests that less reliance on inventory holding and more reliance on rationing will lower overall output and employment. Thus just-in-time inventory holding and downsizing might be expected to coincide. Reliance on inventories rather than on rationing depends on the costs of holding inventories and the associated costs of adjusting purchases and sales versus the cost and feasibility of rationing. If employment and supply purchases are quasi-fixed and prices are costly to adjust, the firm will depend on inventory buildups and depletion over the cycle rather than on rationing customers and suppliers.

2.4

Inventories and market clearing by intermediaries

How are supply and demand brought into balance? In the traditional Walrasian framework equilibrium, prices appear that not only ration consumers and stimulate suppliers, but that also equate supply and demand. As I emphasized in Section 2.3, the prices set by firms intermediating between buyers and sellers balance purchases and sales and thus

Price setting and intermediation by

firms

49

continue to serve a market-clearing role. However, firms have a number of other market-clearing instruments in their arsenal, most notably by holding inventories and by quantity rationing buyers and sellers. The inventories held by firms serve to smooth the patterns of demand and supply fluctuations and also reduce the risks of exchange. Firms stand ready to buy and sell. Holding inventories allows the firm to make sales and purchases at different times and provides a buffer that allows the firm to better match its sales and purchase flows. Quantity rationing means that the firm controls the level of its purchases and sales directly. Thus thefirmhas policy instruments in addition to price incentives for its customers and suppliers. The firm may choose to avoid adjusting prices because of the menu costs of changing prices or a desire for stable prices based on marketing considerations or competitive concerns. Even if prices are not adjusted, the firm need not ration if it can meet demand through purchases, production, or inventory depletion. However, these output changes also are costly. Thus allocating scarce stocks among its customers provides another way to balance the firm's demand and supply. Similarly, a firm with multiple suppliers can choose to distribute its purchases among the suppliers rather than change its purchase prices or amount purchased. Through inventory holding and quantity rationing, firms perform market-clearing activities generally thought to take place outside the firm. By balancing its purchases and sales over time, the firm supplements the market-clearing function of prices. Economic analysis generally stresses that firms allocate goods and services internally, for example by allocating labor services to various tasks, by allocating capital investment across its divisions, or by allocating products across its retail outlets. While these activities are certainly an essential aspect of the allocation of scarce resources, the firm does much more in terms of allocating goods and services. What I am emphasizing is the firm's actions that bring market demand and supply into balance. Excess inventories and stockouts Intermediaries are likely to face both supply and demand shocks. This uncertainty complicates the firm's pricing problem and increases the difficulty of balancing supply and demand to clear the market. Imbalances in purchases and sales are costly for the firm. Excess inventories entail carrying costs while stockouts mean sales earnings foregone. The basic issues can be illustrated with a simple model with a single buyer and a single seller, each buying or selling a single unit. The seller's cost c is uniformly distributed on the unit interval, so that the supply function S(w) = w denotes the probability that a unit will be

50

Market microstructure and the intermediation theory of the firm

supplied at price w. The buyer's valuation v is uniformly distributed on the unit interval, so that the demand function D(p) = 1 — p denotes the probability that a unit will be supplied at price p. Suppose first that the firm's sales equal the minimum of its supply and demand:

Q =min{x,q}. So the firm's expected sales equal E Q = (1 — p)w. The firm's expected profit is thus FI = pEQ — wS(w): n = p{\ — p)w — w .

The firm sets the ask and bid prices to maximize expected profit: p* = 1/2, w* = 1/8, n* = 1/64. In this example, which corresponds to purchasing to stock, the firm trades off the risk of lost sales, if the supply is not obtained, against the risk of excess inventories, if the buyer does not make a purchase. How does the preceding purchasing-to-stock case compare with purchasing to order? With purchasing to order, thefirmmust solve for the bid price to be offered to the seller given that the consumer has already placed an order at price p. Thus, given that a unit at price p has been ordered, the firm chooses w to maximize expected earnings (p — w)w. Contingent on having received an order at price /?, the offer to the seller thus is w = p/2. The firm chooses the ask price p to maximize expected profit, which equals expected earnings times the likelihood of making a sale: FI = (p — w)w{\ — p).

Substituting for w — p/2 and solving the maximization problem yields the firm's bid and ask prices and expected profit: p* = 2/3,

w* = 1/3,

n* = 1/27.

In this simple example, purchasing to order yields a higher profit since there is no penalty from stock outs as in the purchase-to-stock case. Of course, purchasing to order usually is not feasible if the firm is to provide immediacy. The lower profit for the merchant purchasing to stock is due to the cost of providing immediacy. The efforts of firms, whether retailers, wholesalers, or manufacturers, to reduce inventories by such methods as just-in-time ordering and delivery are intended to lower the carrying cost of inventories while taking advantage of more current market demand information. In contrast to merchants, who purchase goods for resale, brokers do not purchase goods or hold inventories.16 Brokers in such markets as 16

See Hackett (1992) for a comparison of intermediation by merchants and brokers.

Price setting and intermediation by

firms

51

securities, insurance, real estate, travel, and some commodities fix a commission rate but not bid and ask prices. Suppose that the broker brings together the buyer and the seller and earns a commission equal to sp, where s < 1 is a share of the purchase price. After the buyer and the seller meet, the buyer observes the seller's cost and the seller observes the buyer's valuation. If the buyer's valuation is sufficiently greater than the seller's cost, they divide the surplus according to the Nash bargaining solution. Otherwise, no trade occurs. For trade to take place, there must be a price such that the buyer's willingness to pay is greater than or equal to the price, and the price net of the broker's commission is greater than or equal to the seller's cost: v > P,

p(\ -

s)>c.

This implies that trade takes place only if

v > c/{\ - s). Clearly, firms with costs above (1 — s) will not be able to trade. The price that satisfies the Nash bargaining solution maximizes (v — p)

- s) - c\. P =

+

2 2(1 -s)' The expected price is thus

= (1 - s)/4. The profit of the broker thus is n = (1 — s)s/4, so that the profitmaximizing commission rate is s * = 1/2 and the broker's expected profit is n* = 1/16. In this simple example, brokers earn more than merchants, whether merchants order to stock or purchase to order, because the broker shares the gains from trade without the costs of providing immediacy. The broker also benefits from the buyer and seller bargaining, which in this example reveals buyer willingness to pay and seller cost. With greater transaction costs between buyers and sellers, merchants then would have the advantage over brokers. Pricing and inventories I now examine the basic issues of inventory holding by a marketmaking firm by using a two-period model. To illustrate the effects of uncertainty on the pattern of prices and sales, let the firm's demand and supply functions be subject to random shocks y and z, respectively,

52

Market microstructure and the intermediation theory of the firm

which are uniformly distributed on the interval [0, a], with expected values a/2. Suppose that the shocks are additively separable, so that at time period t, sales and purchases are given as follows:

qt = D(pt,yt)= 1 - pt+yt, xt = S(wt,zt) = wt +zt. The firm's inventory ht is observable at the start of the period, while the inventory left at the end of the period is not known until the demand and supply shocks have been observed. The end-of-period inventory obeys the transition equation,

ht+\ =ht+xt

-qt.

I assume that thefirmcannot stock out, which requires that end-of-period inventory cannot be less than zero, ht+\ > 0. Because the stock-out constraint must hold for any realization of demand and supply shocks, it is sufficient that it hold for the highest realization of the demand shock and the lowest realization of the supply shock:

ht +

S(wt,0)-D(pt9a)>0.

Prices are chosen before current demand and supply shocks are observed. Suppose that unit inventory costs c are paid on inventory held at the start of the period, where 0 < c < 1 + a/2. Also, future earnings are discounted by a factor S = 1/(1 + r), where r is the rate of interest. To analyze the effects of inventory holding on the firm's pricing policies, it is useful to consider a two-period setting. The firm chooses prices pt, wt to maximize the present discounted value of expected profit: 2

V = E J2S'^lPtDipt, yt) - wtS(wt, zt)l subject to the inventory-transition constraint and the stock-out constraint. The firm solves its optimization problem by backward induction, beginning with the second-period maximization: V(h2) = max E[p2D(p2, y2) - w2S(w2, z2) - ch2], subject to h2 + S(w2, 0) - D(p2, a) > 0.17 17

Thefirst-ordernecessary conditions for the firm's problem are as follows: £[/>2£>i(P2, yi) + D(P2, y2)] = A2/>i0>2,«), E[w2Si(w2, zi) + S(u;2, Z2)] = ^iS\{w2, 0), X2[h2 + S(w2, 0) - D(p2, a)] = 0, X2 > 0.

Price setting and intermediation by

firms

53

If realized inventories are low, h2 < (l+a)/2, the stock-out constraint is binding, and prices solve p2 - w2 = (1 + a)/2,

h2 + W2-l + P2-aSecond-period prices are thus p\ = (3 + 3a - 2/z2)/4,

w\ = (1 + a - 2/z2)/4,

and the shadow price is X2 = (1 + 2a — 2/z2)/2. If inventories are moderate, (1 + a)/2 < /*2 < (2 + 3a)/4 then no purchases are made, w2 = 0, and the ask price is constrained by available inventories through the stock-out constraint, h2 = D(p2, a):

p2 =

l+a-h2,

and the shadow price is X2 = (2 + 3a — 4h2)/2. Finally, with large inventories, h2 > (2 + 3a)/4, the shadow price is zero, no purchases are made, and the ask price falls to the unconstrained monopoly price:

p5 = (2 + fl)/4. Consider next the firm's first-period pricing problem. For simplicity, suppose that there is no initial inventory, h\ = 0. Then the firm solves max

Pl,W\

subject to S(wu 0) - D(pua) > 0.18 Note the additive separability of the demand and the supply shocks; the equations yield the fundamental markup equation,

where rj\ — —p\ED\/ED

and §1 = w\ES\/ES. The markup equals

p * - u ; * = (l+fl)/2, which is the same as in the second period. If the stock-out constraint is binding, then w\ + p\ = 1 + a, and the firm's prices are p\ = 3(1 + 2a)/A and w\ = (1 + a)/A. These are benchmark prices for a monopolist maximizing single-period profit subject only to a stock-out constraint. If the stock-out constraint is nonbinding because of the value of holding inventories, the firm increases both the ask and the bid prices to raise expected inventories. 18

The first-order conditions for the firm's problem are as follows:

E[wiSi(wuzi) + S(wu zi)] = 8EV'(h2)Si(wuzi) + ^\Si(wu 0), A-i [S(wi, 0) - D(pi, a)] = 0,

A-i > 0.

54

Market microstructure and the intermediation theory of the firm

(l+2t)/2

(2+3a)/4

h2

Figure 2.9. The marginal value of inventory in the second period.

By the envelope theorem, the marginal value of inventories in the second period is the shadow price on the inventory constraint net of the carrying cost of inventories: V\h2) = X*(/i2) - c. Figure 2.9 illustrates the marginal value of inventory. Note that the marginal value is most responsive to changes in inventory for moderate inventory levels since the firm does not make purchases and simply sells its inventory in that range. The second-period ask price is also most responsive to changes in inventory in the moderate range for the same reason, while the bid price is responsive only with low inventories. The ask price is most responsive in the moderate range since there it is the sole instrument for building up or drawing down inventories.19 If the constraint is nonbinding, the marginal value of inventories in the second period affects first-period prices. For the case in which the firm holds inventories at the end of the first period and both buys and sells output in the second period, the expected shadow price is20 EX2 = 1/2 +a19

20

Eh2 = 3/2 + a - wx - px.

Reagan (1982) obtains a different result for a monopolist; she shows that when the firm drives its stock of inventories to zero, in periods of high demand, price becomes more responsive to demand disturbances. The difference with the model presented here is that the firm builds inventories by producing at a constant unit cost, rather than by purchasing as in the present model. A sufficient condition for inventories to be low in the second period is

Price setting and intermediation by firms

55

Therefore the first-period prices are 1 Pi = W,

=

2(1+8) 1

•0

2(1+8)

HI-

Compare the prices for the inventory-holding firm with the Walrasian equilibrium. The expected value of the Walrasian spot price that equates supply and demand, D(pw, y) = S(pw, JC), is Epw = 1/2. The expected market-clearing output is Eq w — (1 + a) 12. The prices set by the inventory-holding intermediary straddle the Walrasian price; w

w < Ep < p* fort = 1,2. In the second period, the lowest ask price is p\ = (2 + a)/A > 1/2. The highest bid price is w\ = (1 + a - 2h2)/4 < 1/2. As a result of the stock-out constraint, the expected sales and purchases are less than the expected Walrasian market-clearing output:

Eq* < Ex* < Eqw. These relationships are illustrated in Figure 2.10. p,w

ES(w,z) p

Ep w =l/2

Eqt

Ex,

Figure 2.10. The bid-ask spread with inventories.

56

Market microstructure and the intermediation theory of the firm

Quantity rationing Firms adjust prices to balance supply and demand. Inventories allow the firm to smooth out its purchasing and sales patterns. Consequently the firm will modify its pricing patterns when it can hold inventories so as to reduce the carrying costs of inventories as well as foregone revenue from stockouts. Another approach to market clearing and inventory cost reduction is quantity rationing. A growing literature on optimal quantity rationing can be applied to discern the role of firms in allocating goods and services. Rationing can be accomplished through state-contingent contracts. For example, with priority pricing, customers bid more for a higher priority, and rationing occurs if realized customer demand exceeds productive capacity.21 Carlton (1991) observes that, with random demand, there are costs to using the price system since a price that is too high will reduce sales and result in excess inventories, while a price that is too low will require rationing customers and foregoing sales. He suggests that many firms use nonprice-rationing methods, and that "firms and organized markets are competitors in production 'allocations'" (p. 257). Carlton observes that rationing the firm's customers essentially allocates products across those customers. He concludes that "one reason for a firm's existence is to facilitate trade among its customers" (p. 258). Thus consideration of rationing demonstrates how the firm is an intermediary between its customers. Suppose that the firm experiences demand shocks and that it is costly to adjust both bid and ask prices. As a result of demand uncertainty, customer demand and supplier offers will generally not be in balance. The firm can respond by building or depleting inventories or by producing or disposing of output. In addition to adjusting prices, production, and inventories, the firm can quantity ration customers or suppliers. Consider the case of excess demand; the case of excess supply is similar. Suppose that the firm has two customers and that at the firm's prices demand exceeds the firm's purchases: where x = S(w) is the firm's level of purchases. The firm must somehow distribute its stock between the two customers. Without changing the price, at least one consumer will be disappointed. Generally there would be gains from further trade between 21

Priority pricing with demand uncertainty is examined by Harris and Raviv (1981) and Spulber (1992a, 1992b, 1993a, 1993b), and with supply uncertainty by Chao and Wilson (1987), Wilson (1989a, 1989b), Viswanathan and Tse (1989), and Spulber (1992a, 1992b).

Price setting and intermediation by

firms

57

customers. Optimal rationing would require replicating the effects of a market-clearing price, p°, that solves Dl(p°) + D2(p°) = x. Simply distribute the optimal outputs to each consumer, q1 = Dl(p°) and q2 = D2(p°). The problem with this approach is that the firm is not likely to know the demand functions of its customers. I consider allocation by intermediaries under asymmetric information in Chapter 7. The firm can anticipate situations of excess demand by assigning priorities to consumers through a system of contingent contracts. Customers with a high marginal willingness to pay for the good will pay to have a higher priority. Priority pricing is considered in Chapter 7 as well. The output could be allocated randomly across the two consumers, or equivalently, on a first-come-first-served basis if the firm's customers arrive at random. This generally is not optimal since consumer marginal benefits will not be equal. Dividing the pie equally between the two customers suffers from the same problems. The firm can ration the two customers proportionally on the basis of past consumption; see Spulber (1992a, 1992b). The firm can respond to demand and supply imbalances through delivery lags (Zarnowitz 1962; Edlefsen 1981; Carlton 1983). Carlton observes that percentage fluctuations of delivery lags are usually much larger than price changes in many industries, including textile mill products, paper and allied products, steel, fabricated metals, nonelectrical machinery, and electrical machinery. Delivery lags make the qualities of the good endogenous, thus lowering demand. Then, by increasing the delivery lag 7\ the firm can clear the market in the short run, without adjusting the price: Delivery lags may also serve to increase the amount offered by suppliers since delayed production can lower costs. Thus, in the short run, the lag can be adjusted to increase supply and reduce demand: Retailers typically give discounts and rain checks for sale items that have stocked out. The firm can address customer and supplier desire for immediacy through the sale or the purchase of substitute products and services.

2.5

Conclusion

Markets clear through the intermediation activities of firms seeking to balance their purchases and sales. Pricing is the primary means of market

58

Market microstructure and the intermediation theory of the firm

clearing. This chapter presents the basic model of pricing by an intermediary. The intermediary sets a bid-ask spread to maximize profit while equating supply and demand. The intermediation pricing model provides an answer to a central question of microeconomics: How does the market attain its equilibrium? Moreover, the basic intermediation framework begins to provide an explanation for the economic purpose of firms beyond possessing technology and producing goods and services. Acting as intermediaries, firms take on tasks traditionally ascribed to an exogenous market mechanism. Instead, firms adjust prices to clear markets, rationing customers and stimulating suppliers. Market-making firms manage transactions for their customers and suppliers, allocating goods and services across customers, across states of the world, and over time. Managing transactions is an important and costly activity. There can be menu costs of adjusting prices in response to supply and demand shocks. This means that the firm's prices may not adjust perfectly to economic contractions and expansions. The macroeconomic implications of price rigidities are well understood. Price adjustment by intermediaries implies that price rigidity can increase when thefirmmust adjust multiple prices (Spulber, 1998b). For example, rigidities in input prices can contribute to the rigidity of output prices, even if the firm's output prices could be costlessly adjusted. The firm has alternative instruments for market clearing. Inventories can smooth the patterns of purchases and sales. In turn, inventory holding alters the firm's pricing strategies. The firm can further alter its supply and demand patterns by adjusting the features of its products and services, through marketing and sales efforts, delivery lags, and the provision of substitute and complementary goods and services. In Chapter 7, I examine contracting under asymmetric information as a means of market clearing.

Part II

Competition and market equilibrium

3

Competition between intermediaries

Industrial organization presents a theory of thefirmbased on two key elements that represent significant differences with the neoclassical firm: market power and competitive strategy. The firm in industrial organization exercises its market power by being a price maker rather than a price taker, selecting prices for its products and services. Moreover, the firm in industrial organization formulates a competitive strategy in anticipation of, or in reaction to, the strategic actions of rival firms. The presence of market power has several important ramifications for the theory of the firm. First, the focus of attention shifts from technology to market demand. The firm continues to act as a producer as in the neoclassical framework. Its production activities are presumed to be efficient and are represented by a cost function. In addition to its cost function, the firm is described in terms of its market demand, which reflects the willingness to pay of the firm's actual and potential customers. Therefore the industrial-organization model represents the firm by its demand and cost functions. The firm with market power is concerned primarily with how to set profit-maximizing prices. As a price setter, the firm provides the mechanism by which markets clear. The firm changes prices to reflect exogenous shifts in demand and to balance sales with production and inventories. The firm in industrial organization does not have a supply function in the neoclassical sense, although the firm may choose to offer a schedule of prices and quantities to prospective buyers. Therefore the firm in industrial organization plays a greatly expanded economic role, replacing the Walrasian auctioneer, by assessing consumer demands and setting prices to clear markets. Thefirmthus operates markets in addition to operating its productive technology. The intermediation theory of the firm draws heavily on industrialorganization models by assuming that the firm has market power in both product and factor markets. The firm has neither a supply function in the output markets nor a demand function in the input markets. 61

62

Competition and market equilibrium

The intermediaryfirmdoes not have a standard neoclassical cost function since it does not take as given some of its factor prices. The intermediary framework adds a new perspective to many traditional industrialorganization models because it examines the relationship between the firm's purchasing and sales strategies. The discussion of price setting and intermediation in Chapter 2 emphasized the firm's market power in output and input markets, without addressing competitive strategy. Yet intermediated markets often are quite competitive, as discussed in Chapter 1. This chapter examines how competition affect the results of the basic intermediation model. The qualitative results of the monopoly-monopsony case generally carry over to monopolistic competition between intermediaries. Firms offer a bidask spread and select prices by equating marginal revenue to marginal expenditure. Industrial organization recognizes that market-clearing prices are established by firms, while emphasizing the central place of pricing as a competitive strategy. The Bertrand model of price competition is the basic building block of industrial organization. Given homogeneous products, constant marginal costs, and full information, the traditional Bertrand price-competition model implies that firms price at marginal cost, earning zero profit. Stahl (1988) presents a two-period intermediation model with homogeneous products that extends the Bertrand model to competition between intermediaries in input markets, followed by price competition in output markets. The intermediation equilibrium results either in monopoly or in a competitive Walrasian equilibrium, depending on how inputs are allocated between the rival firms. The intermediation model has the appealing feature in that Edgeworth-type capacity constraints are derived endogenously as a consequence of bidding for productive inputs. The traditional Bertrand model results in a price war that eliminates monopoly rents. Various analyses of competitive price setting have extended the Bertrand model to see under what conditions the zero-profit outcome no longer holds. These extensions share a common theme: the derivation of downward-sloping residual demand functions. With downward-sloping demand, the firm retains market power, yet is nonetheless sensitive to the extent of competition. Demand is shown to be downward sloping under a variety of conditions, including differentiated products, consumer switching costs, unknown rival costs, and consumer search costs. These extensions of the Bertrand model carry over into intermediation models with Bertrand-type price competition.

Competition between intermediaries

63

Product differentiation is particularly significant as a consequence and a source of market power. Unlike the neoclassical firm, which chooses from a given menu of products on the basis of technological efficiency, thefirmin industrial-organization chooses the characteristics of its products. This has implications that range far beyond the technological aspects of product design. The firm can alter its demand by altering its products. Product differentiation in industrial organization models, beginning with Hotelling (1929), essentially serves to restore downwardsloping demand to the firm. When products of the firm and its rivals are differentiated, firms retain local monopoly power in the product space or at a geographic location. I extend the basic product-differentiation framework to competition between intermediaries by assuming that the firm's purchases are differentiated from those of its competitors. Because intermediaries have different geographic locations, suppliers may incur different transport costs in serving them. Also, intermediaries may purchase products with different specifications or they may impose different administrative requirements on transactions. Therefore, when purchases are differentiated, intermediaries will have monopsony power in input markets. Their purchases will be substitutes for suppliers. Thus, in bidding for inputs, competingfirmswill face upward-sloping supply curves rather than fixed input prices. I next consider the implications of switching costs for intermediation.l If its customers have switching costs, the firm also will face downwardsloping demand. Similarly, if the firm's suppliers have switching costs, the firm will face upward-sloping supply. I present a duopoly intermediation model in which both customers and suppliers have switching costs. I examine the effects of the distribution of switching costs on the market-equilibrium bid-ask spread and output level. As switching costs becomes small, the equilibrium approaches the Walrasian equilibrium. As switching costs become large, the equilibrium approaches the monopoly intermediation solution. The conclusions of the Bertrand model depend in a crucial way on the assumption that firms have full information about their rival's costs. In light of the significant amount of uncertainty that firms typically encounter about the efficiency and the costs of their rivals, the fullinformation assumption seems unrealistic. The possibility thatfirmscannot perfectly observe their rivals' costs is sufficient to yield positive expected profits for all firms and pricing above marginal cost. Asymmetry 1

Customer switching costs are introduced in Klemperer (1987), and Farrell and Shapiro (1988).

64

Competition and market equilibrium

of information about rivals' costs resolves the discontinuity in the effect of the pricing strategy on profit. Sincefirmshave positive expected profits at equilibrium with asymmetric information, firms have an incentive to enter the market and engage in price competition, which resolves the inconsistency in the Bertrand model. This chapter is organized as follows. I begin with Bertrand competition between intermediaries with homogeneous inputs and outputs. Then I consider a basic model of differentiated-product Bertrand competition between intermediaries. Next, I examine competition between intermediaries when both customers and suppliers must incur costs if they wish to switch intermediaries. Finally, I consider price competition between intermediaries that have private information about their own transaction costs.

3.1

Bertrand competition for inputs with homogeneous products

Stahl (1988) examines the effects of winner-take-all competition for inputs. Firms may choose prices sequentially, competing first for supplies and then for customers or competing first for sales and then for supplies. Inputs are homogeneous, as are outputs. In this section, I consider Stahl's model of purchasing to stock. The analysis of purchasing to order is similar. If two firms offer identical prices, then each firm obtains half of the available supplies at that offer price: x = S(w)/2. If the firms offer different prices, the highest-priced firm obtains all the available supplies at that price: x = S(w), and the other firm leaves the market. Because of the equal-sharing and winner-take-all assumptions and the symmetry of the model, it is sufficient to consider the outcome in which both firms offer the same price in the first stage and have the same stocks x. Next, consider the second-stage output-pricing competition with capacity constraints given by input stocks. There are three possible outcomes. If firm one has a lower price than firm two, its sales are qx = min{x, D(pi)}. If the two firms offer the same price, then firm one's sales are qx = min{x, D(Pl)/2). If firm one has a higher price than firm two, then the firm obtains some share of sales given by the residual demand function RD(p\, p2, x): qx = min{x, RD(px, pi, x)}. The residual demand function is sufficiently general to include both

Competition between intermediaries

65

uniform and random rationing (and any convex combination of the two rationing rules).2 Firm one's residual demand RD(p\, /?2, x) is jointly continuous in both prices and decreasing in p\. As the firm's price approaches that of its rival, the firm obtains the excess demand of the rival: lim RD(p\, p2, x) = max{D(/?2) — x, 0}.

PI-+P2

Finally, the residual demand of the high-priced firm is less than or equal to half of market demand at the high price:

RD(pi,p2,x)

D'1

p2>

(2JC).

In the first stage, the high-priced firm purchases all the inputs supplied: x\ = S(w\) if w\ > W2 and x\ = 0 if w\ < wi. If the two firms offer the same price, they each obtain half of the input that is supplied:

x\ = S(w\)/2 if w\ = W2.

If there is not a tie, the winning bidder earns

n*(w) = R*(S(w)) - wS(w), where R*(x) is defined as the maximum revenue that the stock-constrained firm can obtain:

R*(x) =

max{pD(p)\D(p)<x}.

Assume that pD(p) is strictly concave. Define w° as the zero-monopoly-rent bid, which is the highest price such that

n*(w°) = 0. Clearly no firm will bid higher than the zero-monopoly-rent bid, w°. Moreover, if bothfirmswere to bid w°, their profits could not be positive. Yet thefirmshave an incentive to outbid each other up to the bid price, w°. Let pR be the ask price that maximizes sales revenue, that is, Suppose that the sales-revenue-maximizing price is greater than the Walrasian price, pR > p w; see Figure 3.1. Then no (subgame-perfect) Nash 2

Uniform rationing (Levitan and Shubik 1972) is a parallel inward shift of demand: RD(pi,p2,

x) = max{D(Pl) - x, 0}.

Random rationing (Beckman 1965; Allen and Hellwig 1986) is an inward rotation of the demand curve: 2,x)

= (l-

where a = min{x/D{pi), 1}.

a)D(pi),

66

Competition and market equilibrium

p,w

q*

q

q,x

Figure 3.1. The revenue-maximizing price, pR, exceeds the Walrasian price, P W.

equilibrium exists. If pR > pw, it follows that the zero-monopoly-rent bid must exceed the Walrasian equilibrium price: w° > pw. This is because the firm could earn a positive profit by setting its bid price at pw, setting the ask price at pR, and discarding the excess capacity (qw —q R). The equilibrium fails to exist because both firms will bid the zero-monopoly-rent price w°. To make nonnegative profit in the second stage, they must both set their price at the revenue-maximizing level p R. This cannot be a Nash equilibrium, since then they have excess capacity, so that each firm has an incentive to shade its price below that of the competitor. If the revenue-maximizing price is not greater than the Walrasian price, pR pw, the elasticity of demand at the Walrasian price is less than 1. The bid price and the ask price both exceed

68

Competition and market equilibrium

the Walrasian price,

pR>w°>

pw,

and the output sold is less than the amount purchased, which is less than the Walrasian output,

qR < x < qw. In the case in which pR 1. Then the outcome is Walrasian: p = w° = p w and q = x = q w. In either case, Bertrand competition with homogeneous products eliminates all monopoly rents.

3.2

Bertrand price competition with differentiated products and purchases

The Bertrand model of price competition leads to the dramatic conclusion that, with two or more firms, the market price always will equal marginal cost and that firms will earn zero profit. Many have interpreted this result as implying that a market with two identical firms is perfectly competitive or, if costs are similar, approximately competitive. The Bertrand model provides important insights by focusing exclusively on the firm's price-setting role. The highly simplified structure of market demand, production costs, and product characteristics provide an ideal case in which firms have no market power in equilibrium. This conclusion is troubling because in practice firms generally appear to have some power to set prices in the presence of competition. The Bertrand model of competition is subject to a fundamental discontinuity. If two firms offer the same price, they share the market in some manner. However, if one firm slightly undercuts its rival, it captures the entire market. The discontinuity observed in the Bertrand model suggests that the model fails to describe the process of competition and market allocation in some crucial way. Moreover, the behavioral assumptions are open to question. Since firms always earn zero profit in equilibrium, they lack the incentive to enter the market and to engage in vigorous price competition. Thus, while the basic price-competition model provides a mechanism for establishing the market price, the model neglects the complex ways in which firms compete to set prices. Various models of price competition in industrial organization extend the Bertrand-Nash model of competition by introducing more general descriptions of the firm that serve to eliminate the fundamental discontinuity. Differentiating a product from one's competitors is a means of altering the firm's market power. The firm determines the effects on demand of

Competition between intermediaries

69

distinguishing its product from those of its rivals and selects the product characteristic to increase consumer willingness to pay for its products. Therefore product differentiation by firms is the inevitable counterpart to price setting. Markets operate through the price-setting and the productdesign activities of firms. As a counterpart to product differentiation, firms can gain monopsony power with suppliers by offering attractive working relationships and providing differentiated services to suppliers. Manufacturers and large retailers provide suppliers with technical expertise, logistical and accounting support, and information processing. They supply design specifications to parts suppliers. These activities can lower the cost to suppliers of providing service relative to the cost of serving other firms. Industrial-organization models draw a useful (but somewhat artificial) distinction between horizontal and vertical product differentiation. Horizontal product differentiation refers to product characteristics such as color, style, or flavor, for which one cannot argue individual tastes. Vertical differentiation refers to product features, such as quality and durability, for which consumer preferences agree. In practice, firms distinguish their products in many ways, and the two types of product differentiation are not easily distinguished. Moreover, firms generally offer multiple products arranged in several product lines that combine horizontal and vertical differences. If a product has two vertical features on which consumers agree, they will generally disagree on the best combination of these features. The horizontal product-differentiation model was introduced by Hotelling (1929) as a means of restoring market power to the Bertrand model of price competition. Since products differ, firms have captive customers as well as other customers who are more sensitive to price differences. Firms can set different prices while retaining those customers who prefer the types of products they offer. In this way, the Hotelling model eliminates the fundamental discontinuity of the Bertrand model.3 Consider a simple duopoly intermediation model in which firms offer customers differentiated products. Moreover, suppose that the input purchases of the firms are differentiated as well. This can arise if the firms require customized products from suppliers or if the costs of serving the intermediaries differ because of travel costs or transaction costs. For ease of presentation, consider a symmetric model in which each firm 3

The Hotelling model is itself subject to a discontinuity if products are not sufficiently differentiated since then the firm with the lowest price captures the entire captive market by slightly lowering its price. D'Aspremont, Gabszewicz, and Thisse (1979) show that there is no pure strategy equilibrium if firms are located too near to each other.

70

Competition and market equilibrium

faces the following demand and supply functions: qt = Di(pu

P2)

Xi = St(Wu

W2) = Wi -

= l - pi + tpj9 TWj,

where i, j = 1,2,/ / j . The constant t, 0 < t < 1, represents the degree of interaction in the output market, while r, 0 < t < 1, is the degree of interaction in the input market.4 The two firms choose the output and the input prices simultaneously. Let (/?*, p^w*, w2) be a Bertrand-Nash equilibrium. Then firm one chooses prices (/?*, w\) to maximize profit,

n(pi, wu p\, wl) = p\Di(pi, P2) - wiSi(u;i, wl), subject to S\(w\, W2) > D\(p\, p^). Firm two's problem is similar. In equilibrium, each firm equates its marginal revenue to its marginal factor cost, taking the other firm's equilibrium prices as given. The equilibrium prices solve the fundamental equation for the duopoly case and the stock constraint:

The own-price elasticities 77* and £* are defined by

w* The Bertrand-Nash equilibrium prices are represented in Figure 3.3. At symmetric equilibrium, given the linear demand and supply functions, the prices set by the two firms are

1

4 - 30 + T) + 2tr. Thus, the bid-ask spread is positive and both firms earn positive profits. The output of each firm is 4 - 3(f + r) + 2tx 4

Thefirmscompete by choosing prices. The problem cannot be recast as a Cournot quantity-choice game without changing the equilibrium outcome; see Singh and Vives (1984).

Competition between intermediaries

71

S(w,,w2*)

Pi

Figure 3.3. Competitive equilibrium ask and bid prices with differentiated products and purchases.

A higher value of the demand interaction parameter increases the output prices, the input prices, the bid-ask spreads, and the output of each firm. A higher value of the supply interaction parameter, r, increases the output and the input prices and lowers the bid-ask spreads, and the output of each firm.

33

Bertrand competition with switching costs

Paul Klemperer (1995, p. 517) points out that a "switching cost results from a consumer's desire for compatibility between his current purchase and a previous investment." He lists the following types of investment made by customers: (1) need for compatibility with existing equipment, (2) transaction costs of switching suppliers; (3) costs of learning to use new brands; (4) uncertainty about the quality of contested brands; (5) discount coupons and similar devices (such as "frequent flyer" and other "loyalty contracts"), and (6) psychological costs of switching or noneconomic brand loyalty. Klemperer (1995, p. 518) further observes that "[m]any of consumers' costs of switching to new suppliers have parallels in firms' costs of serving new customers." These can include transaction costs from opening new accounts, learning to work with new customers, and uncertainty about the characteristics of the new customers.

72

Competition and market equilibrium

As a consequence of switching costs, therefore, intermediaries may have both loyal customers and loyal suppliers, each of whom have made relationship-specific investments. Thus the current sales and purchases of the intermediary depend on past sales and purchases. In this section, I recast the basic intermediation model by considering a duopoly that competes for customers and suppliers in the presence of switching costs. I show that when the range of switching costs approaches zero, the competitive equilibrium approaches the Walrasian equilibrium. Conversely, when the range of switching costs becomes large, the competitive equilibrium approaches the monopoly intermediary outcome. Let market demand and supply be linear: D(p) = 1 — p and S(w) = w. The intermediaries' production and transaction costs are assumed to be zero to simplify the example further. Market shares have been determined in a previous period. For purposes of illustration, these are taken as given. The model is easily extended to allow the shares to be determined by price competition in the previous period; see Klemperer (1995) for the one-sided output-pricing case. Let o\ and oi be the initial customermarket shares of firms one and two, respectively. Let f i and & be the firms' initial supplier-market share. Note that o\ + 02 = fi + £2 = 1The customers and the suppliers have switching costs that are the same, without loss of generality. Switching costs k are uniformly distributed on the interval [0, K], A consumer of type k will switch purchases from firm two to firm one only if Pi - P\ > k. A supplier of type k will switch sales from firm two to firm one only if W\ — W2 > k.

Suppose that firm one is the lower-priced firm. Firm one sells to (1) its customers with reservation prices greater than or equal to p\, (2) to the rival firm's customers with reservation prices greater than or equal to P2 and switching costs less than or equal to pi — p\, and (3) to the rival firm's customers with reservation prices in the range (p\, pi) and a reservation price less switching cost greater than or equal to p\. Therefore, if firm one is the low-priced firm, p\ < pi, the quantity sold by firm one equals n

P2

n

_

K Firm two thus sells

w2, IS w

(w\ - w2)

"?2

I

**'1 —

/ ~F

Firm two purchases -w2) The marginal own-price effects are 9