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THIRD EDITIONThe classic text in advanced microeconomic theory,revised and expanded.Advanced Microeconomic Theory remains a rigorous, up-to-date standard in microeconomics, givingall the core mathematics and modern theory the advanced student must master.Long known for careful development of complex theory, together with clear, patient explanation, thisstudent-friendly text, with its efficient theorem-proof organisation, and many examples and exercises,is uniquely effective in advanced courses.New in this edition General equilibrium with contingent commodities Expanded treatment of social choice, with a simplified proof of Arrow’s theorem andcomplete, step-by-step development of the Gibbard – Satterthwaite theoremADVANCED MICROECONOMIC THEORYADVANCEDMICROECONOMICTHEORYTHIRD EDITIONGEOFFREY A. JEHLEPHILIP J. RENYGEOFFREY A. JEHLEPHILIP J. RENY Extensive development of Bayesian games New section on efficient mechanism design in the quasi-linear utility, private valuesenvironment. The most complete and easy-to-follow presentation of any text. Over fifty new exercisesEssential reading for students at Masters level, those beginning a Ph.D and advanced undergraduates.A book every professional economist wants in their collection.GEOFFREY A. JEHLEPHILIP J. RENYADVANCEDMICROECONOMICTHEORYTHIRD EDITIONCover photograph Getty Imageswww.pearson-books.comCVR JEHL1917 03 SE CVR.indd 110/11/2010 16:08

AdvancedMicroeconomicTheory

We work with leading authors to develop thestrongest educational materials in economics,bringing cutting-edge thinking and bestlearning practice to a global market.Under a range of well-known imprints, includingFinancial Times Prentice Hall, we craft high qualityprint and electronic publications that help readersto understand and apply their content, whetherstudying or at work.To find out more about the complete range of ourpublishing, please visit us on the World Wide Web at:www.pearsoned.co.uk.

AdvancedMicroeconomicTheoryTHIRD EDITIONG E O F F R E Y A. J E H L EVassar CollegeP H I L I P J. R E N YUniversity of Chicago

Pearson Education LimitedEdinburgh GateHarlowEssex CM20 2JEEnglandand Associated Companies throughout the worldVisit us on the World Wide Web at:www.pearsoned.co.ukFirst published 2011c Geoffrey A. Jehle and Philip J. Reny 2011 The rights of Geoffrey A. Jehle and Philip J. Reny to be identified as author of this work have been asserted bythem in accordance with the Copyright, Designs and Patents Act 1988.All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted inany form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either theprior written permission of the publisher or a licence permitting restricted copying in the United Kingdomissued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS.ISBN: 978-0-273-73191-7British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British LibraryLibrary of Congress Cataloging-in-Publication DataA catalog record for this book is available from the Library of Congress10 9 8 7 6 5 4 3 2 114 13 12 11Typeset in 10/12 pt and Times-Roman by 75Printed and bound in Great Britain by Ashford Colour Press Ltd, Gosport, Hampshire

To Rana and KamranG.A.J.To Dianne, Lisa, and ElizabethP.J.R.

CO N T E N T SPREFACExvPART IECONOMIC AGENTS1CHAPTER 1CONSUMER THEORY3Primitive Notions3Preferences and 5.11.5.21.5.31.6Preference RelationsThe Utility Function513The Consumer’s Problem19Indirect Utility and Expenditure28The Indirect Utility FunctionThe Expenditure FunctionRelations Between the Two283341Properties of Consumer Demand48Relative Prices and Real IncomeIncome and Substitution EffectsSome Elasticity Relations485059Exercises63

viiiCONTENTSCHAPTER 22.1TOPICS IN CONSUMER THEORY73Duality: A Closer Look73Expenditure and Consumer PreferencesConvexity and MonotonicityIndirect Utility and Consumer Preferences7378812.2Integrability852.3Revealed Preference91Uncertainty97PreferencesVon Neumann-Morgenstern UtilityRisk .5CHAPTER 33.13.23.2.1Exercises118THEORY OF THE FIRM125Primitive Notions125Production126Returns to Scale and Varying Proportions1323.3Cost1353.4Duality in Production143The Competitive Firm1453.53.5.13.5.23.6Profit MaximisationThe Profit FunctionExercises145147154PART IIMARKETS AND WELFARE163CHAPTER 4PARTIAL EQUILIBRIUM165Perfect Competition165Imperfect Competition1704.14.24.2.1Cournot Oligopoly174

ixCONTENTS4.2.24.2.34.34.3.14.3.24.3.34.4Bertrand OligopolyMonopolistic CompetitionEquilibrium and WelfarePrice and Individual WelfareEfficiency of the Competitive OutcomeEfficiency and Total Surplus Maximisation175177179179183186Exercises188GENERAL EQUILIBRIUM1955.1Equilibrium in Exchange1965.2Equilibrium in Competitive MarketSystems201CHAPTER .35.55.5.15.6CHAPTER 66.16.26.2.1Existence of EquilibriumEfficiencyEquilibrium in ingent PlansTimeUncertaintyWalrasian Equilibrium with ContingentCommoditiesCore and EquilibriaReplica ercises251SOCIAL CHOICE AND WELFARE267The Nature of the Problem267Social Choice and Arrow’s Theorem269A Diagrammatic Proof274

xCONTENTS6.36.3.16.3.26.3.3Measurability, Comparability, and SomePossibilitiesThe Rawlsian FormThe Utilitarian FormFlexible Forms2792822842856.4Justice2886.5Social Choice and theGibbard-Satterthwaite Theorem290Exercises296PART IIISTRATEGIC BEHAVIOUR303CHAPTER 7GAME THEORY305Strategic Decision Making305Strategic Form 7.3.47.3.57.3.67.3.77.4CHAPTER 88.18.1.1Dominant StrategiesNash EquilibriumIncomplete InformationExtensive Form GamesGame Trees: A Diagrammatic RepresentationAn Informal Analysis of Take-AwayExtensive Form Game StrategiesStrategies and PayoffsGames of Perfect Information and BackwardInduction StrategiesGames of Imperfect Information and SubgamePerfect EquilibriumSequential ses364INFORMATION ECONOMICS379Adverse Selection380Information and the Efficiency of Market Outcomes380

ngMoral Hazard and the Principal–AgentProblemSymmetric InformationAsymmetric Information3854044134144168.3Information and Market Performance4208.4Exercises421AUCTIONS AND MECHANISM DESIGN4279.1The Four Standard Auctions4279.2The Independent Private ValuesModel428CHAPTER .29.4.39.4.49.4.59.59.5.19.5.2Bidding Behaviour in a First-Price, Sealed-BidAuctionBidding Behaviour in a Dutch AuctionBidding Behaviour in a Second-Price, Sealed-BidAuctionBidding Behaviour in an English AuctionRevenue ComparisonsThe Revenue Equivalence TheoremIncentive-Compatible Direct Selling Mechanisms:A CharacterisationEfficiencyDesigning a Revenue MaximisingMechanismThe Revelation PrincipleIndividual RationalityAn Optimal Selling MechanismA Closer Look at the Optimal Selling MechanismEfficiency, Symmetry, and Comparison to the FourStandard AuctionsDesigning Allocatively EfficientMechanismsQuasi-Linear Utility and Private ValuesEx Post Pareto 53455456458

xiiCONTENTS9.5.39.5.49.5.59.5.69.5.79.5.89.6Direct Mechanisms, Incentive Compatibilityand the Revelation PrincipleThe Vickrey-Clarke-Groves MechanismAchieving a Balanced Budget: ExpectedExternality MechanismsProperty Rights, Outside Options, and IndividualRationality ConstraintsThe IR-VCG Mechanism: Sufficiency ofExpected SurplusThe Necessity of IR-VCG Expected SurplusExercises458461466469472478484MATHEMATICAL APPENDICES493CHAPTER A1SETS AND MAPPINGS495Elements of R A2A2.1Necessity and SufficiencyTheorems and Proofs495496Elements of Set Theory497Notation and Basic ConceptsConvex SetsRelations and FunctionsA Little Topology497499503505ContinuitySome Existence Theorems515521Real-Valued Functions529Related SetsConcave FunctionsQuasiconcave FunctionsConvex and Quasiconvex Functions530533538542Exercises546CALCULUS AND OPTIMISATION551Calculus551

Functions of a Single VariableFunctions of Several VariablesHomogeneous FunctionsOptimisationReal-Valued Functions of Several VariablesSecond-Order ConditionsConstrained 3A2.3.4A2.3.5A2.3.6Equality ConstraintsLagrange’s MethodGeometric InterpretationSecond-Order ConditionsInequality ConstraintsKuhn-Tucker Conditions577579584588591595A2.4Optimality Theorems601A2.5Separation Theorems607A2.6Exercises611LIST OF THEOREMS619LIST OF DEFINITIONS625HINTS AND ANSWERS631REFERENCES641INDEX645

PR E FA C EIn preparing this third edition of our text, we wanted to provide long-timereaders with new and updated material in a familiar format, while offeringfirst-time readers an accessible, self-contained treatment of the essentialcore of modern microeconomic theory.To those ends, every chapter has been revised and updated. Themore significant changes include a new introduction to general equilibrium with contingent commodities in Chapter 5, along with a simplifiedproof of Arrow’s theorem and a new, careful development of the GibbardSatterthwaite theorem in Chapter 6. Chapter 7 includes many refinementsand extensions, especially in our presentation on Bayesian games. Thebiggest change – one we hope readers find interesting and useful – isan extensive, integrated presentation in Chapter 9 of many of the central results of mechanism design in the quasi-linear utility, private-valuesenvironment.We continue to believe that working through exercises is the surestway to master the material in this text. New exercises have been added tovirtually every chapter, and others have been updated and revised. Manyof the new exercises guide readers in developing for themselves extensions, refinements or alternative approaches to important material coveredin the text. Hints and answers for selected exercises are provided at the endof the book, along with lists of theorems and definitions appearing in thetext. We will continue to maintain a readers’ forum on the web, wherereaders can exchange solutions to exercises in the text. It can be reachedat http://alfred.vassar.edu.The two full chapters of the Mathematical Appendix still providestudents with a lengthy and largely self-contained development of the settheory, real analysis, topology, calculus, and modern optimisation theory

xviPREFACEwhich are indispensable in modern microeconomics. Readers of this edition will now find a fuller, self-contained development of Lagrangian andKuhn-Tucker methods, along with new material on the Theorem of theMaximum and two separation theorems. The exposition is formal but presumes nothing more than a good grounding in single-variable calculusand simple linear algebra as a starting point. We suggest that even students who are very well-prepared in mathematics browse both chapters ofthe appendix early on. That way, if and when some review or reference isneeded, the reader will have a sense of how that material is organised.Before we begin to develop the theory itself, we ought to say a wordto new readers about the role mathematics will play in this text. Often, youwill notice we make certain assumptions purely for the sake of mathematical expediency. The justification for proceeding this way is simple, andit is the same in every other branch of science. These abstractions from‘reality’ allow us to bring to bear powerful mathematical methods that, bythe rigour of the logical discipline they impose, help extend our insightsinto areas beyond the reach of our intuition and experience. In the physicalworld, there is ‘no such thing’ as a frictionless plane or a perfect vacuum.In economics, as in physics, allowing ourselves to accept assumptionslike these frees us to focus on more important aspects of the problem andthereby helps to establish benchmarks in theory against which to gaugeexperience and observation in the real world. This does not mean that youmust wholeheartedly embrace every ‘unrealistic’ or purely formal aspectof the theory. Far from it. It is always worthwhile to cast a critical eye onthese matters as they arise and to ask yourself what is gained, and what issacrificed, by the abstraction at hand. Thought and insight on these pointsare the stuff of which advances in theory and knowledge are made. Fromhere on, however, we will take the theory as it is and seek to understand iton its own terms, leaving much of its critical appraisal to your momentsaway from this book.Finally, we wish to acknowledge the many readers and colleagueswho have provided helpful comments and pointed out errors in previouseditions. Your keen eyes and good judgements have helped us make thisthird edition better and more complete than it otherwise would be. Whilewe cannot thank all of you personally, we must thank Eddie Dekel, RogerMyerson, Derek Neal, Motty Perry, Arthur Robson, Steve Williams, andJörgen Weibull for their thoughtful comments.

PART IECONOMIC AGENTS

CHAPTER 1CONSUMER THEORYIn the first two chapters of this volume, we will explore the essential features of modernconsumer theory – a bedrock foundation on which so many theoretical structures in economics are built. Some time later in your study of economics, you will begin to notice justhow central this theory is to the economist’s way of thinking. Time and time again youwill hear the echoes of consumer theory in virtually every branch of the discipline – howit is conceived, how it is constructed, and how it is applied.1.1 PRIMITIVE NOTIONSThere are four building blocks in any m