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MunicipalDerivatives-OrderonMotiontoDismiss - Lecture Notes...

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Lecture Notes 1 Microeconomic Theory Guoqiang TIAN Department of Economics Texas A&M University College Station, Texas 77843 ([email protected]) August, 2002/Revised: December 2011 1 This lecture notes are only for the purpose of my teaching and convenience of my students in class, but not for any other purpose. It is greatly acknowledged that some materials are drawn from the references in the end of each charter.
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Contents 1 Preliminaries on Modern Economics and Mathematics 1 1.1 Nature of Modern Economics . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Modern Economics and Economic Theory . . . . . . . . . . . . . . 1 1.1.2 Key Assumptions and Desired Properties Commonly Used Economics 3 1.1.3 The Basic Analytical Framework of Modern Economics . . . . . . . 4 1.1.4 Methodologies for Studying Modern Economics . . . . . . . . . . . 6 1.1.5 Roles, Generality, and Limitation of Economic Theory . . . . . . . 8 1.1.6 Roles of Mathematics in Modern Economics . . . . . . . . . . . . . 10 1.1.7 Conversion between Economic and Mathematical Languages . . . . 11 1.1.8 Distinguish between Necessary and Sufficient Conditions as well Normative and Positive Statements . . . . . . . . . . . . . . . . . . 11 1.2 Language and Methods of Mathematics . . . . . . . . . . . . . . . . . . . . 12 1.2.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 14 1.2.3 Concave and Convex Functions . . . . . . . . . . . . . . . . . . . . 14 1.2.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.5 The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.6 Point-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.7 Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 25 1.2.8 Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 26 I Individual Decision Making 30 2 Consumer Theory 32 i
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2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Consumption Set and Budget Constraint . . . . . . . . . . . . . . . . . . . 33 2.2.1 Consumption Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2.2 Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Preferences and Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.2 The Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4 Utility Maximization and Optimal Choice . . . . . . . . . . . . . . . . . . 45 2.4.1 Consumer Behavior: Utility Maximization . . . . . . . . . . . . . . 45 2.4.2 Consumer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . 45 2.4.3 Consumer’s First Order-Conditions . . . . . . . . . . . . . . . . . . 46 2.4.4 Sufficiency of Consumer’s First-Order Conditions . . . . . . . . . . 49 2.5 Indirect Utility, and Expenditure, and Money Metric Utility Functions . . 52 2.5.1 The Indirect Utility Function . . . . . . . . . . . . . . . . . . . . . 52 2.5.2 The Expenditure Function and Hicksian Demand . . . . . . . . . . 54 2.5.3 The Money Metric Utility Functions . . . . . . . . . . . . . . . . . 57 2.5.4 Some Important Identities . . . . . . . . . . . . . . . . . . . . . . . 60 2.6 Duality Between Direct and Indirect Utility . . . . . . . . . . . . . . . . . 64 2.7 Properties of Consumer Demand . . . . . . . . . . . . . . . . . . . . . . . 66 2.7.1 Income Changes and Consumption Choice . . . . . . . . . . . . . . 66 2.7.2 Price Changes and Consumption Choice . . . . . . . . . . . . . . . 66 2.7.3 Income-Substitution Effect: The Slutsky Equation . . . . . . . . . . 67 2.7.4 Continuity and Differentiability of Demand Functions . . . . . . . . 70 2.7.5 Inverse Demand Functions . . . . . . . . . . . . . . . . . . . . . . . 72 2.8 The Integrability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.9 Revealed Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.9.1 Axioms of Revealed Preferences . . . . . . . . . . . . . . . . . . . . 76 2.9.2 Characterization of Revealed Preference Maximization . . . . . . . 78 2.10 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.11 Topics in Demand Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.11.1 Endowments in the Budget Constraint . . . . . . . . . . . . . . . . 82 ii
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2.11.2 Income-Leisure Choice Model . . . . . . . . . . . . . . . . . . . . . 83 2.11.3 Homothetic Utility Functions . . . . . . . . . . . . . . . . . . . . . 84 2.11.4 Aggregating Across Goods . . . . . . . . . . . . . . . . . . . . . . . 84 2.11.5 Aggregating Across Consumers . . . . . . . . . . . . . . . . . . . . 90 3 Production Theory 95 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.2.1 Measurement of Inputs and Outputs . . . . . . . . . . . . . . . . . 96 3.2.2 Specification of Technology . . . . . . . . . . . . . . . . . . . . . . . 96 3.2.3 Common Properties of Production Sets . . . . . . . . . . . . . . . . 100 3.2.4 Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.2.5 The Marginal Rate of Technical Substitution . . . . . . . . . . . . . 103 3.2.6 The Elasticity of Substitution . . . . . . . . . . . . . . . . . . . . . 104 3.3 Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.3.1 Producer Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.3.2 Producer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . . 107 3.3.3
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