Lecture Notes 1
Microeconomic Theory
Guoqiang TIAN
Department of Economics
Texas A&M University
College Station, Texas 77843
()
August, 2002/Revised: September 2015
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.
,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 Modern Economics and Modern Market System Governance . . . . 4
1.1.3 Modern Economics and Ancient Chinese Economic Thought . . . . 13
1.1.4 The Most Basic Assumption in Modern Economics . . . . . . . . . 17
1.1.5 Other Assumptions Usually adopted in Economics . . . . . . . . . . 19
1.1.6 A Proper Understanding of Modern Economics . . . . . . . . . . . 27
1.1.7 Basic Analytical Framework of Modern Economics . . . . . . . . . . 28
1.1.8 Basic Research Methodologies in Modern Economics . . . . . . . . 37
1.1.9 Basic Requirements for Understanding Modern Economic Theory . 43
1.1.10 Roles of Modern Economic Theory . . . . . . . . . . . . . . . . . . 44
1.1.11 Some Remarks on Modern Economic Theory . . . . . . . . . . . . . 45
1.1.12 Distinguishing Sufficient and Necessary Conditions . . . . . . . . . 50
1.1.13 The Role of Mathematics in Modern Economics . . . . . . . . . . . 50
1.1.14 Conversion between Economic and Mathematical Language . . . . . 53
1.2 Language and Methods of Mathematics . . . . . . . . . . . . . . . . . . . . 54
1.2.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.2.2 Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 56
1.2.3 Concave and Convex Functions . . . . . . . . . . . . . . . . . . . . 57
1.2.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
1.2.5 The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 62
1.2.6 Point-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 63
1.2.7 Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 68
i
, 1.2.8 Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 68
I Individual Decision Making 75
2 Consumer Theory 77
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.2 Consumption Set and Budget Constraint . . . . . . . . . . . . . . . . . . . 78
2.2.1 Consumption Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.2.2 Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.3 Preferences and Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.3.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.3.2 The Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.4 Utility Maximization and Optimal Choice . . . . . . . . . . . . . . . . . . 90
2.4.1 Consumer Behavior: Utility Maximization . . . . . . . . . . . . . . 90
2.4.2 Consumer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . 90
2.4.3 Consumer’s First Order-Conditions . . . . . . . . . . . . . . . . . . 91
2.4.4 Sufficiency of Consumer’s First-Order Conditions . . . . . . . . . . 94
2.5 Indirect Utility, and Expenditure, and Money Metric Utility Functions . . 98
2.5.1 The Indirect Utility Function . . . . . . . . . . . . . . . . . . . . . 98
2.5.2 The Expenditure Function and Hicksian Demand . . . . . . . . . . 100
2.5.3 The Money Metric Utility Functions . . . . . . . . . . . . . . . . . 103
2.5.4 Some Important Identities . . . . . . . . . . . . . . . . . . . . . . . 105
2.6 Duality Between Direct and Indirect Utility . . . . . . . . . . . . . . . . . 109
2.7 Properties of Consumer Demand . . . . . . . . . . . . . . . . . . . . . . . 111
2.7.1 Income Changes and Consumption Choice . . . . . . . . . . . . . . 111
2.7.2 Price Changes and Consumption Choice . . . . . . . . . . . . . . . 112
2.7.3 Income-Substitution Effect: The Slutsky Equation . . . . . . . . . . 113
2.7.4 Continuity and Differentiability of Demand Functions . . . . . . . . 116
2.7.5 Inverse Demand Functions . . . . . . . . . . . . . . . . . . . . . . . 117
2.8 The Integrability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.9 Revealed Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
2.9.1 Axioms of Revealed Preferences . . . . . . . . . . . . . . . . . . . . 121
ii
, 2.9.2 Characterization of Revealed Preference Maximization . . . . . . . 123
2.10 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.11 Topics in Demand Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2.11.1 Endowments in the Budget Constraint . . . . . . . . . . . . . . . . 128
2.11.2 Income-Leisure Choice Model . . . . . . . . . . . . . . . . . . . . . 129
2.11.3 Homothetic Utility Functions . . . . . . . . . . . . . . . . . . . . . 129
2.11.4 Aggregating Across Goods . . . . . . . . . . . . . . . . . . . . . . . 130
2.11.5 Aggregating Across Consumers . . . . . . . . . . . . . . . . . . . . 135
3 Production Theory 142
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
3.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
3.2.1 Measurement of Inputs and Outputs . . . . . . . . . . . . . . . . . 143
3.2.2 Specification of Technology . . . . . . . . . . . . . . . . . . . . . . . 143
3.2.3 Common Properties of Production Sets . . . . . . . . . . . . . . . . 147
3.2.4 Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.2.5 The Marginal Rate of Technical Substitution . . . . . . . . . . . . . 150
3.2.6 The Elasticity of Substitution . . . . . . . . . . . . . . . . . . . . . 151
3.3 Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
3.3.1 Producer Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
3.3.2 Producer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . . 154
3.3.3 Producer’s First-Order Conditions . . . . . . . . . . . . . . . . . . . 155
3.3.4 Sufficiency of Producer’s First-Order Condition . . . . . . . . . . . 156
3.3.5 Properties of Net Supply Functions . . . . . . . . . . . . . . . . . . 158
3.3.6 Weak Axiom of Profit Maximization . . . . . . . . . . . . . . . . . 159
3.3.7 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
3.4 Profit Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
3.4.1 Properties of the Profit Function . . . . . . . . . . . . . . . . . . . 163
3.4.2 Deriving Net Supply Functions from Profit Function . . . . . . . . 164
3.5 Cost Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
3.5.1 First-Order Conditions of Cost Minimization . . . . . . . . . . . . . 166
3.5.2 Sufficiency of First-Order Conditions for Cost Minimization . . . . 167
iii
Microeconomic Theory
Guoqiang TIAN
Department of Economics
Texas A&M University
College Station, Texas 77843
()
August, 2002/Revised: September 2015
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.
,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 Modern Economics and Modern Market System Governance . . . . 4
1.1.3 Modern Economics and Ancient Chinese Economic Thought . . . . 13
1.1.4 The Most Basic Assumption in Modern Economics . . . . . . . . . 17
1.1.5 Other Assumptions Usually adopted in Economics . . . . . . . . . . 19
1.1.6 A Proper Understanding of Modern Economics . . . . . . . . . . . 27
1.1.7 Basic Analytical Framework of Modern Economics . . . . . . . . . . 28
1.1.8 Basic Research Methodologies in Modern Economics . . . . . . . . 37
1.1.9 Basic Requirements for Understanding Modern Economic Theory . 43
1.1.10 Roles of Modern Economic Theory . . . . . . . . . . . . . . . . . . 44
1.1.11 Some Remarks on Modern Economic Theory . . . . . . . . . . . . . 45
1.1.12 Distinguishing Sufficient and Necessary Conditions . . . . . . . . . 50
1.1.13 The Role of Mathematics in Modern Economics . . . . . . . . . . . 50
1.1.14 Conversion between Economic and Mathematical Language . . . . . 53
1.2 Language and Methods of Mathematics . . . . . . . . . . . . . . . . . . . . 54
1.2.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.2.2 Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 56
1.2.3 Concave and Convex Functions . . . . . . . . . . . . . . . . . . . . 57
1.2.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
1.2.5 The Envelope Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 62
1.2.6 Point-to-Set Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 63
1.2.7 Continuity of a Maximum . . . . . . . . . . . . . . . . . . . . . . . 68
i
, 1.2.8 Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . 68
I Individual Decision Making 75
2 Consumer Theory 77
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.2 Consumption Set and Budget Constraint . . . . . . . . . . . . . . . . . . . 78
2.2.1 Consumption Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.2.2 Budget Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.3 Preferences and Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.3.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.3.2 The Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.4 Utility Maximization and Optimal Choice . . . . . . . . . . . . . . . . . . 90
2.4.1 Consumer Behavior: Utility Maximization . . . . . . . . . . . . . . 90
2.4.2 Consumer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . 90
2.4.3 Consumer’s First Order-Conditions . . . . . . . . . . . . . . . . . . 91
2.4.4 Sufficiency of Consumer’s First-Order Conditions . . . . . . . . . . 94
2.5 Indirect Utility, and Expenditure, and Money Metric Utility Functions . . 98
2.5.1 The Indirect Utility Function . . . . . . . . . . . . . . . . . . . . . 98
2.5.2 The Expenditure Function and Hicksian Demand . . . . . . . . . . 100
2.5.3 The Money Metric Utility Functions . . . . . . . . . . . . . . . . . 103
2.5.4 Some Important Identities . . . . . . . . . . . . . . . . . . . . . . . 105
2.6 Duality Between Direct and Indirect Utility . . . . . . . . . . . . . . . . . 109
2.7 Properties of Consumer Demand . . . . . . . . . . . . . . . . . . . . . . . 111
2.7.1 Income Changes and Consumption Choice . . . . . . . . . . . . . . 111
2.7.2 Price Changes and Consumption Choice . . . . . . . . . . . . . . . 112
2.7.3 Income-Substitution Effect: The Slutsky Equation . . . . . . . . . . 113
2.7.4 Continuity and Differentiability of Demand Functions . . . . . . . . 116
2.7.5 Inverse Demand Functions . . . . . . . . . . . . . . . . . . . . . . . 117
2.8 The Integrability Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.9 Revealed Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
2.9.1 Axioms of Revealed Preferences . . . . . . . . . . . . . . . . . . . . 121
ii
, 2.9.2 Characterization of Revealed Preference Maximization . . . . . . . 123
2.10 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.11 Topics in Demand Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2.11.1 Endowments in the Budget Constraint . . . . . . . . . . . . . . . . 128
2.11.2 Income-Leisure Choice Model . . . . . . . . . . . . . . . . . . . . . 129
2.11.3 Homothetic Utility Functions . . . . . . . . . . . . . . . . . . . . . 129
2.11.4 Aggregating Across Goods . . . . . . . . . . . . . . . . . . . . . . . 130
2.11.5 Aggregating Across Consumers . . . . . . . . . . . . . . . . . . . . 135
3 Production Theory 142
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
3.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
3.2.1 Measurement of Inputs and Outputs . . . . . . . . . . . . . . . . . 143
3.2.2 Specification of Technology . . . . . . . . . . . . . . . . . . . . . . . 143
3.2.3 Common Properties of Production Sets . . . . . . . . . . . . . . . . 147
3.2.4 Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.2.5 The Marginal Rate of Technical Substitution . . . . . . . . . . . . . 150
3.2.6 The Elasticity of Substitution . . . . . . . . . . . . . . . . . . . . . 151
3.3 Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
3.3.1 Producer Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
3.3.2 Producer’s Optimal Choice . . . . . . . . . . . . . . . . . . . . . . . 154
3.3.3 Producer’s First-Order Conditions . . . . . . . . . . . . . . . . . . . 155
3.3.4 Sufficiency of Producer’s First-Order Condition . . . . . . . . . . . 156
3.3.5 Properties of Net Supply Functions . . . . . . . . . . . . . . . . . . 158
3.3.6 Weak Axiom of Profit Maximization . . . . . . . . . . . . . . . . . 159
3.3.7 Recoverability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
3.4 Profit Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
3.4.1 Properties of the Profit Function . . . . . . . . . . . . . . . . . . . 163
3.4.2 Deriving Net Supply Functions from Profit Function . . . . . . . . 164
3.5 Cost Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
3.5.1 First-Order Conditions of Cost Minimization . . . . . . . . . . . . . 166
3.5.2 Sufficiency of First-Order Conditions for Cost Minimization . . . . 167
iii
