AdvancedMicroeconomicTheory(3rdEdition)

CONTENTSPREFACExvPART I ECONOMIC AGENTS1CHAPTER 1CONSUMER THEORY31.1Primitive Notions31.2Preferences and Utility4 1.2.1Preference Relations5 1.2.2The Utility Function131.3The Consumers Problem191.4Indirect Utility and Expenditure28 1.4.1The Indirect Utility Function28 1.4.2The Expenditure Function33 1.4.3Relations Between the Two411.5Properties of Consumer Demand48 1.5.1Relative Prices and Real Income48 1.5.2Income and Substitution Effects50 1.5.3Some Elasticity Relations591.6Exercises63viiiCONTENTSCHAPTER 2TOPICS IN CONSUMER THEORY732.1Duality: A Closer Look73 2.1.1Expenditure and Consumer Preferences73 2.1.2Convexity and Monotonicity78 2.1.3Indirect Utility and Consumer Preferences812.2Integrability852.3Revealed Preference912.4Uncertainty97 2.4.1Preferences98 2.4.2Von Neumann-Morgenstern Utility102 2.4.3Risk Aversion1102.5Exercises118CHAPTER 3THEORY OF THE FIRM1253.1Primitive Notions1253.2Production126 3.2.1Returns to Scale and Varying Proportions1323.3Cost1353.4Duality in Production1433.5The Competitive Firm145 3.5.1Profit Maximisation145 3.5.2The Profit Function1473.6Exercises154PART II MARKETS AND WELFARE163CHAPTER 4PARTIAL EQUILIBRIUM1654.1Perfect Competition1654.2Imperfect Competition170 4.2.1Cournot Oligopoly174CONTENTSix4.2.2Bertrand Oligopoly175 4.2.3Monopolistic Competition1774.3Equilibrium and Welfare179 4.3.1Price and Individual Welfare179 4.3.2Efficiency of the Competitive Outcome183 4.3.3Efficiency and Total Surplus Maximisation1864.4Exercises188CHAPTER 5GENERAL EQUILIBRIUM1955.1Equilibrium in Exchange1965.2Equilibrium in Competitive Market Systems201 5.2.1Existence of Equilibrium203 5.2.2Efficiency2125.3Equilibrium in Production220 5.3.1Producers220 5.3.2Consumers223 5.3.3Equilibrium225 5.3.4Welfare2325.4Contingent Plans236 5.4.1Time236 5.4.2Uncertainty236 5.4.3Walrasian Equilibrium with Contingent Commodities2375.5Core and Equilibria239 5.5.1Replica Economies2405.6Exercises251CHAPTER 6SOCIAL CHOICE AND WELFARE2676.1The Nature of the Problem2676.2Social Choice and Arrows Theorem269 6.2.1A Diagrammatic Proof274xCONTENTS6.3Measurability, Comparability, and Some Possibilities279 6.3.1The Rawlsian Form282 6.3.2The Utilitarian Form284 6.3.3Flexible Forms2856.4Justice2886.5Social Choice and the Gibbard-Satterthwaite Theorem2906.6Exercises296PART III STRATEGIC BEHAVIOUR303CHAPTER 7GAME THEORY3057.1Strategic Decision Making3057.2Strategic Form Games307 7.2.1Dominant Strategies308 7.2.2Nash Equilibrium311 7.2.3Incomplete Information3197.3Extensive Form Games325 7.3.1Game Trees: A Diagrammatic Representation328 7.3.2An Informal Analysis of Take-Away330 7.3.3Extensive Form Game Strategies331 7.3.4Strategies and Payoffs332 7.3.5Games of Perfect Information and Backward Induction Strategies333 7.3.6Games of Imperfect Information and Subgame Perfect Equilibrium337 7.3.7Sequential Equilibrium3477.4Exercises364CHAPTER 8INFORMATION ECONOMICS3798.1Adverse Selection380 8.1.1Information and the Efficiency of Market Outcomes380CONTENTSxi8.1.2Signalling385 8.1.3Screening4048.2Moral Hazard and the PrincipalAgent Problem413 8.2.1Symmetric Information414 8.2.2Asymmetric Information4168.3Information and Market Performance4208.4Exercises421CHAPTER 9AUCTIONS AND MECHANISM DESIGN4279.1The Four Standard Auctions4279.2The Independent Private Values Model428 9.2.1Bidding Behaviour in a First-Price, Sealed-Bid Auction429 9.2.2Bidding Behaviour in a Dutch Auction432 9.2.3Bidding Behaviour in a Second-Price, Sealed-Bid Auction433 9.2.4Bidding Behaviour in an English Auction434 9.2.5Revenue Comparisons4359.3The Revenue Equivalence Theorem437 9.3.1Incentive-Compatible Direct Selling Mechanisms: A Characterisation441 9.3.2Efficiency4449.4Designing a Revenue Maximising Mechanism444 9.4.1The Revelation Principle444 9.4.2Individual Rationality445 9.4.3An Optimal Selling Mechanism446 9.4.4A Closer Look at the Optimal Selling Mechanism451 9.4.5Efficiency, Symmetry, and Comparison to the Four Standard Auctions4539.5Designing Allocatively Efficient Mechanisms455 9.5.1Quasi-Linear Utility and Private Values456 9.5.2Ex Post Pareto Efficiency458xiiCONTENTS9.5.3Direct Mechanisms, Incentive Compatibility and the Revelation Principle458 9.5.4The Vickrey-Clarke-Groves Mechanism461 9.5.5Achieving a Balanced Budget: Expected Externality Mechanisms466 9.5.6Property Rights, Outside Options, and Individual Rationality Constraints469 9.5.7The IR-VCG Mechanism: Sufficiency of Expected Surplus472 9.5.8The Necessity of IR-VCG Expected Surplus4789.6Exercises484MATHEMATICAL APPENDICES493CHAPTER A1SETS AND MAPPINGS495A1.1Elements of Logic495 A1.1.1Necessity and Sufficiency495 A1.1.2Theorems and Proofs496A1.2Elements of Set Theory497 A1.2.1Notation and Basic Concepts497 A1.2.2Convex Sets499 A1.2.3Relations and Functions503A1.3A Little Topology505 A1.3.1Continuity515 A1.3.2Some Existence Theorems521A1.4Real-Valued Functions529 A1.4.1Related Sets530 A1.4.2Concave Functions533 A1.4.3Quasiconcave Functions538 A1.4.4Convex and Quasiconvex Functions542A1.5E