Nolan Miller
Notes on Microeconomic Theory
Nolan H. Miller September 5, 2003
Contents
1 The Economic Approach 2 Consumer Theory Basics 2.1 2.2 2.3 2.4 Commodities and Budget Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Demand Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Restrictions on Consumer Choices . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 8 9
A First Analysis of Consumer Choices . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5
Requirement 1 Revisited: Walras’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 2.5.7 2.5.8 What’s the Funny Equals Sign All About? . . . . . . . . . . . . . . . . . . . . 12 Back to Walras’ Law: Choice Response to a Change in Wealth . . . . . . . . 13 Testable Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Summary: How Did We Get Where We Are? . . . . . . . . . . . . . . . . . . 15 Walras’ Law: Choice Response to a Change in Price . . . . . . . . . . . . . . 15 Comparative Statics in Terms of Elasticities . . . . . . . . . . . . . . . . . . . 16 Why Bother? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Walras’ Law and Changes in Wealth: Elasticity Form . . . . . . . . . . . . . 18
2.6
Requirement 2 Revisited: Demand is Homogeneous of Degree Zero. . . . . . . . . . . 18 2.6.1 Comparative Statics of Homogeneity of Degree Zero . . . . . . . . . . . . . . 19
2.7
Requirement 3 Revisited: The Weak Axiom of Revealed Preference . . . . . . . . . . 20 2.7.1 2.7.2 Compensated Changes and the Slutsky Equation . . . . . . . . . . . . . . . . 21 Other Properties of the Substitution Matrix . . . . . . . . . . . . . . . . . . . 25 26
3 The Traditional Approach to Consumer Theory 3.1
Basics of Preference Relations . . . . . . . . . . . . . . .
Nolan H. Miller September 5, 2003
Contents
1 The Economic Approach 2 Consumer Theory Basics 2.1 2.2 2.3 2.4 Commodities and Budget Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Demand Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Restrictions on Consumer Choices . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 8 9
A First Analysis of Consumer Choices . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5
Requirement 1 Revisited: Walras’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 2.5.7 2.5.8 What’s the Funny Equals Sign All About? . . . . . . . . . . . . . . . . . . . . 12 Back to Walras’ Law: Choice Response to a Change in Wealth . . . . . . . . 13 Testable Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Summary: How Did We Get Where We Are? . . . . . . . . . . . . . . . . . . 15 Walras’ Law: Choice Response to a Change in Price . . . . . . . . . . . . . . 15 Comparative Statics in Terms of Elasticities . . . . . . . . . . . . . . . . . . . 16 Why Bother? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Walras’ Law and Changes in Wealth: Elasticity Form . . . . . . . . . . . . . 18
2.6
Requirement 2 Revisited: Demand is Homogeneous of Degree Zero. . . . . . . . . . . 18 2.6.1 Comparative Statics of Homogeneity of Degree Zero . . . . . . . . . . . . . . 19
2.7
Requirement 3 Revisited: The Weak Axiom of Revealed Preference . . . . . . . . . . 20 2.7.1 2.7.2 Compensated Changes and the Slutsky Equation . . . . . . . . . . . . . . . . 21 Other Properties of the Substitution Matrix . . . . . . . . . . . . . . . . . . . 25 26
3 The Traditional Approach to Consumer Theory 3.1
Basics of Preference Relations . . . . . . . . . . . . . . .
References: ver: Aug. 29, 2003 P0 ver: Aug. 29, 2003 P* ver: Aug. 29, 2003 P* DWL