Transcription
Lecture Notes1Microeconomic TheoryGuoqiang TIANDepartment of EconomicsTexas A&M UniversityCollege Station, Texas 77843(gtian@tamu.edu)August, 2002/Revised: February 20131This lecture notes are only for the purpose of my teaching and convenience of my students in class,but not for any other purpose.
Contents1 Preliminaries on Modern Economics and Mathematics1.11Nature of Modern Economics . . . . . . . . . . . . . . . . . . . . . . . . .11.1.1Modern Economics and Economic Theory . . . . . . . . . . . . . .11.1.2Key Assumptions and Desired Properties Commonly Used Economics31.1.3The Basic Analytical Framework of Modern Economics . . . . . . .41.1.4Methodologies for Studying Modern Economics . . . . . . . . . . .61.1.5Roles, Generality, and Limitation of Economic Theory . . . . . . .81.1.6Roles of Mathematics in Modern Economics . . . . . . . . . . . . . 101.1.7Conversion between Economic and Mathematical Languages . . . . 111.1.8Distinguish between Necessary and Sufficient Conditions as wellNormative and Positive Statements . . . . . . . . . . . . . . . . . . 111.2ILanguage and Methods of Mathematics . . . . . . . . . . . . . . . . . . . . 121.2.1Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.2Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 141.2.3Concave and Convex Functions . . . . . . . . . . . . . . . . . . . . 141.2.4Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.5The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 191.2.6Point-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 211.2.7Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 251.2.8Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 26Individual Decision Making302 Consumer Theory32i
2.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2Consumption Set and Budget Constraint . . . . . . . . . . . . . . . . . . . 332.32.42.52.2.1Consumption Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.2.2Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Preferences and Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.1Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.2The Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . 40Utility Maximization and Optimal Choice . . . . . . . . . . . . . . . . . . 452.4.1Consumer Behavior: Utility Maximization . . . . . . . . . . . . . . 452.4.2Consumer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . 452.4.3Consumer’s First Order-Conditions . . . . . . . . . . . . . . . . . . 462.4.4Sufficiency of Consumer’s First-Order Conditions . . . . . . . . . . 49Indirect Utility, and Expenditure, and Money Metric Utility Functions . . 522.5.1The Indirect Utility Function . . . . . . . . . . . . . . . . . . . . . 522.5.2The Expenditure Function and Hicksian Demand . . . . . . . . . . 542.5.3The Money Metric Utility Functions . . . . . . . . . . . . . . . . . 572.5.4Some Important Identities . . . . . . . . . . . . . . . . . . . . . . . 602.6Duality Between Direct and Indirect Utility . . . . . . . . . . . . . . . . . 642.7Properties of Consumer Demand. . . . . . . . . . . . . . . . . . . . . . . 662.7.1Income Changes and Consumption Choice . . . . . . . . . . . . . . 662.7.2Price Changes and Consumption Choice . . . . . . . . . . . . . . . 662.7.3Income-Substitution Effect: The Slutsky Equation . . . . . . . . . . 672.7.4Continuity and Differentiability of Demand Functions . . . . . . . . 702.7.5Inverse Demand Functions . . . . . . . . . . . . . . . . . . . . . . . 722.8The Integrability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 732.9Revealed Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762.9.1Axioms of Revealed Preferences . . . . . . . . . . . . . . . . . . . . 762.9.2Characterization of Revealed Preference Maximization . . . . . . . 782.10 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.11 Topics in Demand Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 822.11.1 Endowments in the Budget Constraint . . . . . . . . . . . . . . . . 82ii
2.11.2 Income-Leisure Choice Model . . . . . . . . . . . . . . . . . . . . . 832.11.3 Homothetic Utility Functions . . . . . . . . . . . . . . . . . . . . . 842.11.4 Aggregating Across Goods . . . . . . . . . . . . . . . . . . . . . . . 842.11.5 Aggregating Across Consumers . . . . . . . . . . . . . . . . . . . . 903 Production Theory953.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.2Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963.33.43.53.63.2.1Measurement of Inputs and Outputs . . . . . . . . . . . . . . . . . 963.2.2Specification of Technology . . . . . . . . . . . . . . . . . . . . . . . 963.2.3Common Properties of Production Sets . . . . . . . . . . . . . . . . 1003.2.4Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.2.5The Marginal Rate of Technical Substitution . . . . . . . . . . . . . 1033.2.6The Elasticity of Substitution . . . . . . . . . . . . . . . . . . . . . 104Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.3.1Producer Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.3.2Producer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . . 1073.3.3Producer’s First-Order Conditions . . . . . . . . . . . . . . . . . . . 1083.3.4Sufficiency of Producer’s First-Order Condition . . . . . . . . . . . 1093.3.5Properties of Net Supply Functions . . . . . . . . . . . . . . . . . . 1113.3.6Weak Axiom of Profit Maximization . . . . . . . . . . . . . . . . . 1123.3.7Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Profit Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153.4.1Properties of the Profit Function . . . . . . . . . . . . . . . . . . . 1163.4.2Deriving Net Supply Functions from Profit Function. . . . . . . . 117Cost Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1183.5.1First-Order Conditions of Cost Minimization . . . . . . . . . . . . . 1193.5.2Sufficiency of First-Order Conditions for Cost Minimization . . . . 120Cost Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.6.1Properties of Cost Functions . . . . . . . . . . . . . . . . . . . . . . 1243.6.2Properties of Conditional Input Demand . . . . . . . . . . . . . . . 1253.6.3Average and Marginal Costs . . . . . . . . . . . . . . . . . . . . . . 126iii
3.73.6.4The Geometry of Costs . . . . . . . . . . . . . . . . . . . . . . . . . 1283.6.5Long-Run and Short-Run Cost Curves . . . . . . . . . . . . . . . . 129Duality in Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1303.7.1Recovering a Production Set from a Cost Function . . . . . . . . . 1313.7.2Characterization of Cost Functions . . . . . . . . . . . . . . . . . . 1353.7.3The Integrability for Cost Functions4 Choice Under Uncertainty1394.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1394.2Expected Utility Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.3II. . . . . . . . . . . . . . . . . 1364.2.1Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.2.2Expected Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.2.3Uniqueness of the Expected Utility Function . . . . . . . . . . . . . 1444.2.4Other Notations for Expected Utility . . . . . . . . . . . . . . . . . 145Risk aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454.3.1Absolute Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 1454.3.2Global Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . 1484.3.3Relative Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . 1524.4State Dependent Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1534.5Subjective Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . 154Strategic Behavior and Markets5 Game Theory1591615.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.2Description of a game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.2.15.35.4Strategic Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1665.3.1Mixed Strategies and Pure Strategies . . . . . . . . . . . . . . . . . 1665.3.2Nash equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1675.3.3Dominant strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 171Repeated games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171iv
5.55.6Refinements of Nash equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 1745.5.1Elimination of dominated strategies . . . . . . . . . . . . . . . . . . 1745.5.2Sequential Games and Subgame Perfect Equilibrium . . . . . . . . . 1755.5.3Repeated games and subgame perfection . . . . . . . . . . . . . . . 180Games with incomplete information . . . . . . . . . . . . . . . . . . . . . . 1815.6.1Bayes-Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 1815.6.2Discussion of Bayesian-Nash equilibrium . . . . . . . . . . . . . . . 1846 Theory of the Market1866.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1866.2The Role of Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1876.3Perfect Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1876.46.3.1Assumptions on Competitive Market . . . . . . . . . . . . . . . . . 1886.3.2The Competitive Firm . . . . . . . . . . . . . . . . . . . . . . . . . 1886.3.3The Competitive Firm’s Short-Run Supply Function . . . . . . . . 1886.3.4Partial Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . 1906.3.5Competitive in the Long Run . . . . . . . . . . . . . . . . . . . . . 192Pure Monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1936.4.1Profit Maximization Problem of Monopolist . . . . . . . . . . . . . 1936.4.2Inefficiency of Monopoly . . . . . . . . . . . . . . . . . . . . . . . . 1956.4.3Monopoly in the Long Run. . . . . . . . . . . . . . . . . . . . . . 1966.5Monopolistic Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . 1976.6Oligopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1996.7III6.6.1Cournot Oligopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . 2006.6.2Stackelberg Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2016.6.3Bertrand Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2026.6.4Collusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204Monopsony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205General Equilibrium Theory and Social Welfare2077 Positive Theory of Equilibrium: Existence, Uniqueness, and Stability 209v
7.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2097.2The Structure of General Equilibrium Model . . . . . . . . . . . . . . . . . 2117.37.47.2.1Economic Environments . . . . . . . . . . . . . . . . . . . . . . . . 2117.2.2Institutional Arrangement: Private Market Mechanism . . . . . . . 2137.2.3Individual Behavior Assumptions: . . . . . . . . . . . . . . . . . . . 2147.2.4Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 214Some Examples of GE Models: Graphical Treatment . . . . . . . . . . . . 2167.3.1Pure Exchange Economies . . . . . . . . . . . . . . . . . . . . . . . 2167.3.2The One-Consumer and One Producer Economy . . . . . . . . . . . 222The Existence of Competitive Equilibrium . . . . . . . . . . . . . . . . . . 2257.4.1The Existence of CE for Aggregate Excess Demand Functions . . . 2267.4.2The Existence of CE for Aggregate Excess Demand Correspondences2457.4.3The Existence of CE for General Production Economies . . . . . . . 2477.5The Uniqueness of Competitive Equilibria . . . . . . . . . . . . . . . . . . 2477.6Stability of Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 2517.7Abstract Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2567.7.1Equilibrium in Abstract Economy . . . . . . . . . . . . . . . . . . . 2577.7.2The Existence of Equilibrium for General Preferences . . . . . . . . 2598 Normative Theory of Equilibrium: Its Welfare Properties2648.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2648.2Pareto Efficiency of Allocation . . . . . . . . . . . . . . . . . . . . . . . . . 2658.3The First Fundamental Theorem of Welfare Economics . . . . . . . . . . . 2718.4Calculations of Pareto Optimum by First-Order Conditions . . . . . . . . . 2738.4.1Exchange Economies . . . . . . . . . . . . . . . . . . . . . . . . . . 2748.4.2Production Economies . . . . . . . . . . . . . . . . . . . . . . . . . 2758.5The Second Fundamental Theorem of Welfare Economics . . . . . . . . . . 2768.6Non-Convex Production Technologies and Marginal Cost Pricing . . . . . . 2828.7Pareto Optimality and Social Welfare Maximization . . . . . . . . . . . . . 2858.88.7.1Social Welfare Maximization for Exchange Economies . . . . . . . . 2868.7.2Welfare Maximization in Production Economy . . . . . . . . . . . . 287Political Overtones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289vi
9 Economic Core, Fair Allocations, and Social Choice Theory2929.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2929.2The Core of Exchange Economies . . . . . . . . . . . . . . . . . . . . . . . 2939.3Fairness of Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2989.4Social Choice Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3039.4.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3039.4.2Basic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3049.4.3Arrow’s Impossibility Theorem . . . . . . . . . . . . . . . . . . . . 3069.4.4Some Positive Result: Restricted Domain . . . . . . . . . . . . . . . 3099.4.5Gibbard-Satterthwaite Impossibility Theorem . . . . . . . . . . . . 31110 General Equilibrium Under Uncertainty31810.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31810.2 A Market Economy with Contingent Commodities . . . . . . . . . . . . . . 31910.3 Arrow-Debreu Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 32310.4 Sequential Trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32510.5 Incomplete Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331IVExternalities and Public Goods11 Externalities33633911.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33911.2 Consumption Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 34011.3 Production Externality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34711.4 Solutions to Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34911.4.1 Pigovian Tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35011.4.2 Coase’ Voluntary Negotiation and Enforceable Property Rights Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35111.4.3 Missing Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36111.4.4 The Compensation Mechanism . . . . . . . . . . . . . . . . . . . . 36212 Public Goods36712.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367vii
12.2 Notations and Basic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 36712.3 Discrete Public Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36912.3.1 Efficient Provision of Public Goods . . . . . . . . . . . . . . . . . . 36912.3.2 Free-Rider Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 37012.3.3 Voting for a Discrete Public Good . . . . . . . . . . . . . . . . . . . 37112.4 Continuous Public Goods. . . . . . . . . . . . . . . . . . . . . . . . . . . 37212.4.1 Efficient Provision of Public Goods . . . . . . . . . . . . . . . . . . 37212.4.2 Lindahl Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 37412.4.3 Free-Rider Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 378VInformation, Incentives, Mechanism Design, and ContractTheory38213 Optimal Mechanism Design: Contracts with One-Agent and HiddenInformation38713.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38713.2 Basic Settings of Principal-Agent Model with Adverse Selection . . . . . . 38913.2.1 Economic Environment (Technology, Preferences, and Information) 38913.2.2 Contracting Variables: Outcomes . . . . . . . . . . . . . . . . . . . 38913.2.3 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38913.3 The Complete Information Optimal Contract(Benchmark Case) . . . . . . 39013.3.1 First-Best Production Levels . . . . . . . . . . . . . . . . . . . . . . 39013.3.2 Implementation of the First-Best . . . . . . . . . . . . . . . . . . . 39113.3.3 A Graphical Representation of the Complete Information OptimalContract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39213.4 Incentive Feasible Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . 39313.4.1 Incentive Compatibility and Participation . . . . . . . . . . . . . . 39313.4.2 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39413.4.3 Monotonicity Constraints . . . . . . . . . . . . . . . . . . . . . . . 39513.5 Information Rents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39513.6 The Optimization Program of the Principal . . . . . . . . . . . . . . . . . 39613.7 The Rent Extraction-Efficiency Trade-Off . . . . . . . . . . . . . . . . . . . 397viii
13.7.1 The Optimal Contract Under Asymmetric Information . . . . . . . 39713.7.2 A Graphical Representation of the Second-Best Outcome . . . . . . 40013.7.3 Shutdown Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40013.8 The Theory of the Firm Under Asymmetric Information . . . . . . . . . . 40213.9 Asymmetric Information and Marginal Cost Pricing . . . . . . . . . . . . . 40213.10The Revelation Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40313.11A More General Utility Function for the Agent . . . . . . . . . . . . . . . . 40513.11.1 The Optimal Contract . . . . . . . . . . . . . . . . . . . . . . . . . 40513.11.2 More than One Good . . . . . . . . . . . . . . . . . . . . . . . . . . 40713.12Ex Ante versus Ex Post Participation Constraints . . . . . . . . . . . . . . 40813.12.1 Risk Neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40813.12.2 Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41013.13Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41413.13.1 Renegotiating a Contract . . . . . . . . . . . . . . . . . . . . . . . . 41413.13.2 Reneging on a Contract . . . . . . . . . . . . . . . . . . . . . . . . 41513.14Informative Signals to Improve Contracting . . . . . . . . . . . . . . . . . 41513.14.1 Ex Post Verifiable Signal . . . . . . . . . . . . . . . . . . . . . . . . 41613.14.2 Ex Ante Nonverifiable Signal . . . . . . . . . . . . . . . . . . . . . . 41713.15Contract Theory at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 41713.15.1 Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41813.15.2 Nonlinear Pricing by a Monopoly . . . . . . . . . . . . . . . . . . . 41813.15.3 Quality and Price Discrimination . . . . . . . . . . . . . . . . . . . 41913.15.4 Financial Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . 42013.15.5 Labor Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42113.16The Optimal Contract with a Continuum of Types . . . . . . . . . . . . . 42213.17Further Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42614 Optimal Mechanism Design: Contracts with One-Agent and HiddenAction42914.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42914.2 Basic Settings of Principal-Agent Model with Moral Hazard . . . . . . . . 43014.2.1 Effort and Production . . . . . . . . . . . . . . . . . . . . . . . . . 430ix
14.2.2 Incentive Feasible Contracts . . . . . . . . . . . . . . . . . . . . . . 43114.2.3 The Complete Information Optimal Contract . . . . . . . . . . . . 43214.3 Risk Neutrality and First-Best Implementation . . . . . . . . . . . . . . . . 43314.4 The Trade-Off Between Limited Liability Rent Extraction and Efficiency . 43514.5 The Trade-Off Between Insurance and Efficiency . . . . . . . . . . . . . . . 43714.5.1 Optimal Transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43714.5.2 The Optimal Second-Best Effort . . . . . . . . . . . . . . . . . . . . 43914.6 More than Two Levels of Performance . . . . . . . . . . . . . . . . . . . . 44014.6.1 Limited Liability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44014.6.2 Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44214.7 Contract Theory at Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 44314.7.1 Efficiency Wage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44314.7.2 Sharecropping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44414.7.3 Wholesale Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . 44614.7.4 Financial Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . 44614.8 A Continuum of Performances . . . . . . . . . . . . . . . . . . . . . . . . . 44814.9 Further Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44915 General Mechanism Design: Contracts with Multi-Agents45215.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45215.2 Basic Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45415.2.1 Economic Environments . . . . . . . . . . . . . . . . . . . . . . . . 45415.2.2 Social Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45515.2.3 Economic Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 45615.2.4 Solution Concept of Self-Interested Behavior . . . . . . . . . . . . . 45715.2.5 Implementation and Incentive Compatibility . . . . . . . . . . . . . 45815.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46015.4 Dominant Strategy and Truthful Revelation Mechanisms . . . . . . . . . . 46115.5 Gibbard-Satterthwaite Impossibility Theorem . . . . . . . . . . . . . . . . 46415.6 Hurwicz Impossibility Theorem . . . . . . . . . . . . . . . . . . . . . . . . 46515.7 Vickrey-Clark-Groves Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 46815.7.1 Vickrey-Clark-Groves Mechanisms for Discrete Public Good . . . . 468x
15.7.2 The Vickrey-Clark-Groves Mechanisms with Continuous Public Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47215.7.3 Balanced VCG Mechanisms . . . . . . . . . . . . . . . . . . . . . . 47715.8 Nash Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47915.8.1 Nash Equilibrium and General Mechanism Design . . . . . . . . . . 47915.8.2 Characterization of Nash Implementation . . . . . . . . . . . . . . . 48115.9 Better Mechanism Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 48715.9.1 Groves-Ledyard Mechanism . . . . . . . . . . . . . . . . . . . . . . 48715.9.2 Walker’s Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 48915.9.3 Tian’s Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49115.10Incomplete Information and Bayesian-Nash Implementation . . . . . . . . 49415.10.1 Bayesian-Nash Implementation Problem . . . . . . . . . . . . . . . 49415.10.2 Ex-Post Efficient Implementation by the Expected Externality Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49715.10.3 Participation Constraints . . . . . . . . . . . . . . . . . . . . . . . . 50115.10.4 The Revenue Equivalence Theorem in Auctions . . . . . . . . . . . 50615.10.5 Correlated Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51015.10.6 Ex Post Implementation . . . . . . . . . . . . . . . . . . . . . . . . 51315.10.7 Ex post Implementation with Common Values . . . . . . . . . . . . 51416 Dynamic Mechanism Design52316.1 Dynamic Contracts with Commitment . . . . . . . . . . . . . . . . . . . . 52316.1.1 Dynamic P-A Model with Constant Type . . . . . . . . . . . . . . . 52416.1.2 Dynamic P-A Model with Markov Types . . . . . . . . . . . . . . . 52516.2 Dynamic Contracts without Full Commitment . . . . . . . . . . . . . . . . 52716.2.1 Basic Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52716.2.2 Full Analysis of A Simple Model . . . . . . . . . . . . . . . . . . . . 530xi
Chapter 1Preliminaries on Modern Economicsand MathematicsIn this chapter, we first set out some basic terminologies and key assumptions imposedin modern economics in general and in the lecture notes in particular. We will discuss the standard analytical framework usually used in modern economics. We will alsodiscuss methodologies for studying modern economics as well as some key points oneshould pay attention. The methodologies for studying modern economics and key pointsinclude: providing studying platforms, establishing reference/benchmark systems, developing analytical tools, noting generality and limitation of an economic theory, the role ofmathematics, distinguishing necessary and sufficient conditions for a statement, and conversion between economic and mathematical language. We will then discuss some basicmathematics results that we will use in the lecture notes.1.1Nature of Modern Economics1.1.1 Modern Economics and Economic TheoryWhat is economics about?Economics is a social science that studies individuals’ economic behavior, economicphenomena, as well as how individual agents, such as consumers, firms, and governmentagencies, make trade-off choices that allocate limited resources among competing uses.1
People’s desires are unlimited, but resources are limited, therefore individuals mustmake trade-offs. We need economics to study this fundamental conflict and how thesetrade-offs are best made. Four basic questions must be answered by any economic institution:(1) What goods and services should be produced and in what quantity?(2) How should the product be produced?(3) For whom should it be produced and how should it be distributed?(4) Who makes the decision?The answers depend on the use of economic institutions. There are two basic economicinstitutions that have been so far used in the real world:(1) Market economic institution (the price mechanism): Most decisions oneconomic activities are made by individuals. This primarily decentralizeddecision system is the most important economic institution discovered forreaching cooperation amongst individuals and solving the conflicts thatoccur between them. The market economy has been proven to be onlyeconomic institution, so far, that can keep sustainable development andgrowth within an economy.(2) Planed economic institution: Most decisions on economic activities aremade by governments, which are mainly centralized decision systems. What is Modern Economics?Modern economics, mainly developed in last sixty years, systematically studies individuals’ economic behavior and economic phenomena by a scientific studying method – observation theory observation – and through the use of various analytical approaches. What is Economic Theory?2
An economic theory, which can be considered an axiomatic approach, consists of a setof assumptions and conditions, an analytical framework, and conclusions (explanationsand/or predications) that are derived from the assumptions and the analytical framework.Like any science, economics is concerned with the explanation of observed phenomena and also makes economic predictions and assessments based on economic theories.Economic theories are developed to explain the observed phenomena in terms of a set ofbasic assumptions and rules. Microeconomic theoryMicroeconomic theory aims to model economic activities as the interaction of individualeconomic agents pursuing their private interests.1.1.2Key Assumptions and Desired Properties Commonly UsedEconomicsEconomists usually make all or some of the following key assumptions and conditionswhen they study economic problems:(1) Individuals are (bounded) rational: self-interested behavior assumption;(2) Scarcity of resources: individuals confront scarce resources;(3) Information about individuals’s economic characteristics and actions isincomplete or asymmetric to a decision marker. As such decentralizeddecision makings is desired.(4) Economic freedom: voluntary cooperation and voluntary exchange;(5) Incentive compatibility of parties: the system or economic mechanismshould solve the problem of interest conflicts among individuals or economic units;(6) Well-defined property rights;(7) Equity in opportunity;(8) Allocative efficiency of resources;Relaxing any of these assumptions may result in different conclusions.3
1.1.3The Basic Analytical Framework of Modern EconomicsThe basic analytical framework for an economic theory consists of five aspects or steps:(1) specification of economic environments, (2) imposition of behavioral assumptions,(3) adoption of economic institutional arrangements, (4) determination of equilibria, and(5) evaluation of outcomes resulting from a undertaken institution.
Lecture Notes 1 Microeconomic Theory Guoqiang TIAN Department of Economics Texas A&M University College Station, Texas 7
