Lecture Notes1 Microeconomic Theory Guoqiang TIAN Department of Economics Texas A&M University College Station, Texas 77843 ([email protected]) August, 2002/Revised: January 2018 1This lecture notes are for the purpose of my teaching and convenience of my students in class. Contents 1 Preliminaries on Modern Economics and Mathematics 1 1.1 Nature of Modern Economics . 2 1.1.1 Modern Economics and Economic Theory . 2 1.1.2 Modern Economics and Modern Market System Governance 5 1.1.3 Modern Economics and Ancient Chinese Economic Thought 16 1.1.4 The Most Basic Assumption in Modern Economics . 20 1.1.5 Other Assumptions Usually adopted in Economics . 23 1.1.6 A Proper Understanding of Modern Economics . 32 1.1.7 Basic Analytical Framework of Modern Economics . 34 1.1.8 Basic Research Methodologies in Modern Economics . 45 1.1.9 Basic Requirements for Understanding Modern Economic Theory . 53 1.1.10 Roles of Modern Economic Theory . 54 1.1.11 Some Remarks on Modern Economic Theory . 55 1.1.12 Distinguishing Sufficient and Necessary Conditions . 60 1.1.13 The Role of Mathematics in Modern Economics . 61 1.1.14 Conversion between Economic and Mathematical Language 65 1.2 Language and Methods of Mathematics . 66 1.2.1 Functions . 66 1.2.2 Separating Hyperplane Theorem . 68 i 1.2.3 Concave and Convex Functions . 69 1.2.4 Optimization . 71 1.2.5 The Envelope Theorem . 75 1.2.6 Point-to-Set Mappings . 76 1.2.7 Continuity of a Maximum . 82 1.2.8 Fixed Point Theorems . 82 1.2.9 Continuous Distributions . 84 1.2.10 Hazard Rates . 85 1.2.11 Stochastic Dominance . 86 1.2.12 Hazard Rate Dominance . 91 1.2.13 Reverse Hazard Rate Dominance . 91 1.2.14 Order Statistics . 92 1.2.15 Affiliation . 93 I Individual Decision Making 102 2 Consumer Theory 104 2.1 Introduction . 104 2.2 Consumption Set and Budget Constraint . 105 2.2.1 Consumption Set . 105 2.2.2 Budget Constraint . 106 2.3 Preferences and Utility . 107 2.3.1 Preferences . 107 2.3.2 The Utility Function . 113 2.4 Utility Maximization and Optimal Choice . 119 2.4.1 Consumer Behavior: Utility Maximization . 119 2.4.2 Consumer's Optimal Choice . 119 2.4.3 Consumer's First Order-Conditions . 121 ii 2.4.4 Sufficiency of Consumer's First-Order Conditions . 124 2.5 Indirect Utility, and Expenditure, and Money Metric Utility Func- tions . 129 2.5.1 The Indirect Utility Function . 129 2.5.2 The Expenditure Function and Hicksian Demand . 131 2.5.3 The Money Metric Utility Functions . 135 2.5.4 Some Important Identities . 138 2.6 Duality Between Direct and Indirect Utility . 142 2.7 Properties of Consumer Demand . 145 2.7.1 Income Changes and Consumption Choice . 145 2.7.2 Price Changes and Consumption Choice . 145 2.7.3 Income-Substitution Effect: The Slutsky Equation . 146 2.7.4 Continuity and Differentiability of Demand Functions . 150 2.7.5 Inverse Demand Functions . 151 2.8 The Integrability Problem . 153 2.9 Revealed Preference . 156 2.9.1 Axioms of Revealed Preferences . 156 2.9.2 Characterization of Revealed Preference Maximization . 159 2.10 Recoverability . 161 2.11 Topics in Demand Behavior . 164 2.11.1 Endowments in the Budget Constraint . 164 2.11.2 Income-Leisure Choice Model . 165 2.11.3 Homothetic Utility Functions . 166 2.11.4 Aggregating Across Goods . 167 2.11.5 Aggregating Across Consumers . 173 3 Production Theory 180 3.1 Introduction . 180 3.2 Production Technology . 181 iii 3.2.1 Measurement of Inputs and Outputs . 181 3.2.2 Specification of Technology . 182 3.2.3 Common Properties of Production Sets . 185 3.2.4 Returns to Scale . 188 3.2.5 The Marginal Rate of Technical Substitution . 190 3.2.6 The Elasticity of Substitution . 190 3.3 Profit Maximization . 192 3.3.1 Producer Behavior . 192 3.3.2 Producer's Optimal Choice . 194 3.3.3 Producer's First-Order Conditions . 195 3.3.4 Sufficiency of Producer's First-Order Condition . 197 3.3.5 Properties of Net Supply Functions . 199 3.3.6 Weak Axiom of Profit Maximization . 200 3.3.7 Recoverability . 202 3.4 Profit Function . 204 3.4.1 Properties of the Profit Function . 204 3.4.2 Deriving Net Supply Functions from Profit Function . 206 3.5 Cost Minimization . 207 3.5.1 First-Order Conditions of Cost Minimization . 208 3.5.2 Sufficiency of First-Order Conditions for Cost Minimization 210 3.6 Cost Functions . 214 3.6.1 Properties of Cost Functions . 215 3.6.2 Properties of Conditional Input Demand . 216 3.6.3 Average and Marginal Costs . 217 3.6.4 The Geometry of Costs . 219 3.6.5 Long-Run and Short-Run Cost Curves . 221 3.7 Duality in Production . 222 3.7.1 Recovering a Production Set from a Cost Function . 223 iv 3.7.2 Characterization of Cost Functions . 227 3.7.3 The Integrability for Cost Functions . 229 4 Choice Under Uncertainty 232 4.1 Introduction . 232 4.2 Expected Utility Theory . 233 4.2.1 Lotteries . 233 4.2.2 Expected Utility . 235 4.2.3 Uniqueness of the Expected Utility Function . 237 4.2.4 Other Notations for Expected Utility . 238 4.3 Risk aversion . 239 4.3.1 Absolute Risk Aversion . 239 4.3.2 Global Risk Aversion . 243 4.3.3 Relative Risk Aversion . 247 4.4 State Dependent Utility . 249 4.5 Subjective Probability Theory . 250 II Strategic Behavior and Markets 256 5 Game Theory 258 5.1 Introduction . 258 5.2 Description of a game . 259 5.2.1 Strategic Form . 259 5.3 Solution Concepts . 264 5.3.1 Mixed Strategies and Pure Strategies . 264 5.3.2 Nash equilibrium . 265 5.3.3 Dominant strategies . 269 5.4 Repeated games . 270 5.5 Refinements of Nash equilibrium . 273 v 5.5.1 Elimination of dominated strategies . 273 5.5.2 Sequential Games and Subgame Perfect Equilibrium . 274 5.5.3 Repeated games and subgame perfection . 280 5.6 Games with incomplete information . 282 5.6.1 Bayes-Nash Equilibrium . 282 5.6.2 Discussion of Bayesian-Nash equilibrium . 285 6 Theory of the Market 288 6.1 Introduction . 288 6.2 The Role of Prices . 289 6.3 Perfect Competition . 290 6.3.1 Assumptions on Competitive Market . 290 6.3.2 The Competitive Firm . 290 6.3.3 The Competitive Firm's Short-Run Supply Function . 291 6.3.4 Partial Market Equilibrium . 293 6.3.5 Competitive in the Long Run . 295 6.4 Pure Monopoly . 296 6.4.1 Profit Maximization Problem of Monopolist . 296 6.4.2 Inefficiency of Monopoly . 299 6.4.3 Monopoly in the Long Run . 300 6.5 Monopolistic Competition . 301 6.6 Oligopoly . 304 6.6.1 Cournot Oligopoly . 304 6.6.2 Stackelberg Model . 305 6.6.3 Bertrand Model . 307 6.6.4 Collusion . 309 6.7 Monopsony . 310 vi III General Equilibrium Theory and Social Welfare 312 7 Positive Theory of Equilibrium: Existence, Uniqueness, and Sta- bility 314 7.1 Introduction . 314 7.2 The Structure of General Equilibrium Model . 317 7.2.1 Economic Environments . 317 7.2.2 Institutional Arrangement: Private Market Mechanism . 321 7.2.3 Individual Behavior Assumptions: . 322 7.2.4 Competitive Equilibrium . 322 7.3 Some Examples of GE Models: Graphical Treatment . 326 7.3.1 Pure Exchange Economies . 326 7.3.2 The Economy With One Consumer And One Producer/Robinson Crusoe Economy . 334 7.4 Existence of Competitive Equilibrium . ..