Advanced Microeconomic Theory ADVANCED - USP

1 ADVANCED Microeconomic THEORYTHIRD EDITIONADVANCED Microeconomic THEORYTHIRD EDITIONADVANCED Microeconomic THEORYTHIRD EDITIONGEOFFREY A. JEHLEPHILIP J. RENYGEOFFREY A. JEHLEPHILIP J. RENYGEOFFREY A. JEHLEPHILIP J. photograph Getty ImagesThe classic text in ADVANCED Microeconomic Theory , revised and expanded. ADVANCED Microeconomic Theory remains a rigorous, up-to-date standard in microeconomics , giving all the core mathematics and modern Theory the ADVANCED student must master. Long known for careful development of complex Theory , together with clear, patient explanation, this student-friendly text, with its effi cient theorem-proof organisation, and many examples and exercises, is uniquely effective in ADVANCED in this edition General equilibrium with contingent commodities Expanded treatment of social choice, with a simplifi ed proof of Arrow s theorem and complete, step-by-step development of the Gibbard Satterthwaite theorem Extensive development of Bayesian games New section on effi cient mechanism design in the quasi-linear utility, private values environment.

2 The most complete and easy-to-follow presentation of any text. Over fi fty new exercisesEssential reading for students at Masters level, those beginning a and ADVANCED undergraduates. A book every professional economist wants in their collection. 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 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 find out more about the complete range of ourpublishing, please visit us on the World Wide Web AdvancedMicroeconomicTheoryTHIRD EDITIONGEOFFREYA. JEHLEV assar CollegePHILIPJ.

3 RENYU niversity of Chicago Pearson Education LimitedEdinburgh GateHarlowEssex CM20 2 JEEnglandand Associated Companies throughout the worldVisit us on the World Wide Web 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 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.

4 978-0-273-73191-7 British 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 Congress1098765432114 13 12 11 Typeset in 10/12 pt and Times-Roman by 75 Printed and bound in Great Britain by Ashford Colour Press Ltd, Gosport, Hampshire To Rana and Dianne, Lisa, and CONTENTSPREFACExvPART IECONOMIC AGENTS1 CHAPTER 1 CONSUMER Primitive Preferences and Preference The Utility The Consumer s Indirect Utility and The Indirect Utility The Expenditure Relations Between the Properties of Consumer Relative Prices and Real Income and Substitution Some Elasticity Exercises63 viiiCONTENTSCHAPTER 2 TOPICS IN CONSUMER Duality.

5 A Closer Expenditure and Consumer Convexity and Indirect Utility and Consumer Revealed Von Neumann-Morgenstern Risk Exercises118 CHAPTER 3 Theory OF THE Primitive Returns to Scale and Varying Duality in The Competitive Profit The Profit Exercises154 PART IIMARKETS AND WELFARE163 CHAPTER 4 PARTIAL Perfect Imperfect Cournot Oligopoly174 Bertrand Monopolistic Equilibrium and Price and Individual Efficiency of the Competitive Efficiency and Total Surplus Exercises188 CHAPTER 5 GENERAL Equilibrium in Equilibrium in Competitive Existence of Equilibrium in Contingent Walrasian Equilibrium with Core and Replica Exercises251 CHAPTER 6 SOCIAL CHOICE AND The Nature of the Social Choice and Arrow s A Diagrammatic Proof274 Measurability, Comparability, and The Rawlsian The Utilitarian Flexible Social Choice and theGibbard-Satterthwaite Exercises296 PART IIISTRATEGIC BEHAVIOUR303 CHAPTER 7 GAME Strategic Decision Strategic Form Dominant Nash Incomplete Extensive Form Game Trees.

6 A Diagrammatic An Informal Analysis of Extensive Form Game Strategies and Games of Perfect Information and BackwardInduction Games of Imperfect Information and SubgamePerfect Sequential Exercises364 CHAPTER 8 INFORMATION Adverse Information and the Efficiency of Market Outcomes380 Moral Hazard and the Principal Symmetric Asymmetric Information and Market Exercises421 CHAPTER 9 AUCTIONS AND MECHANISM DESIGN The Four Standard The Independent Private Bidding Behaviour in a First-Price, Bidding Behaviour in a Dutch Bidding Behaviour in a Second-Price, Bidding Behaviour in an English Revenue The Revenue Equivalence Incentive-Compatible Direct Selling Mechanisms:A Designing a Revenue The Revelation Individual An Optimal Selling A Closer Look at the Optimal Selling Efficiency, Symmetry, and Comparison to the FourStandard Designing Allocatively Quasi-Linear Utility and Private Ex Post Pareto Efficiency458 Direct Mechanisms, Incentive Compatibilityand the Revelation The Vickrey-Clarke-Groves Achieving a Balanced Budget: ExpectedExternality Property Rights, Outside Options, and IndividualRationality The IR-VCG Mechanism.

7 Sufficiency ofExpected The Necessity of IR-VCG Expected Exercises484 MATHEMATICAL APPENDICES493 CHAPTER A1 SETS AND Elements of Necessity and Theorems and Elements of Set Notation and Basic Convex Relations and A Little Some Existence Real-Valued Related Concave Quasiconcave Convex and Quasiconvex Exercises546 CHAPTER A2 CALCULUS AND Calculus551 Functions of a Single Functions of Several Homogeneous Real-Valued Functions of Several Second-Order Constrained Equality Lagrange s Geometric Second-Order Inequality Kuhn-Tucker Optimality Separation Exercises611 LIST OF THEOREMS619 LIST OF DEFINITIONS625 HINTS AND ANSWERS631 REFERENCES641 INDEX645 PREFACEIn 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 those ends, every chapter has been revised and updated.

8 Themore significant changes include a new introduction to general equilib-rium with contingent commodities in Chapter 5, along with a simplifiedproof of Arrow s theorem and a new, careful development of the Gibbard-Satterthwaite 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 cen-tral results of mechanism design in the quasi-linear utility, 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 exten-sions, refinements or alternative approaches to important material coveredin the text.

9 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 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 xviPREFACE which are indispensable in modern microeconomics . Readers of this edi-tion 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 pre-sumes nothing more than a good grounding in single-variable calculusand simple linear algebra as a starting point.

10 We suggest that even stu-dents 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 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 mathemat-ical 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 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.