Unit 5
Lecture notes: Microeconomic Theory Econ 629 Department of Economics, Texas A&M University
Rodrigo A. Velez∗ b Department of Economics, Texas A&M University, College Station, TX 77843 USA

September 9, 2014

Contents
1 Consumer’s Revealed Preference 1.1 Preference maximization . . . . . . . . 1.2 Utility maximization . . . . . . . . . . 1.3 Properties of demand correspondence . 1.4 Continuity of choice . . . . . . . . . . 1.5 Problems . . . . . . . . . . . . . . . . 1.6 Expenditure minimization problem . . 1.7 Problems . . . . . . . . . . . . . . . . 2 Homework assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 2 3 3 5 9 10

1

Consumer’s Revealed Preference

What are the testable implications of consumers’ preference maximization? For simplicity, we assume throughout this section that prices are strictly positive. We denote the set of Walrasian budget sets with strictly positive W prices B++ . We assume throughout that X ≡ RL . +
∗

All errors are my own. rvelezca@econmail.tamu.edu

1

1.1

Preference maximization

Let be a preference relation on X. Recall from our abstract study of choice that the choices of the agent represented by in a budget set B(p, w) ∈ B W are given by: C (p, w) ≡ {x ∈ B(p, w) : for each y ∈ B(p, w), x y}.

1.2

Utility maximization

Suppose that preference is represented by utility function u. Then x∗ ∈ C (p, w) if and only if for each y ∈ B(p, w), u(x) ≥ u(y). So x∗ is chosen by agent if and only if it solves the Utility Maximization Problem (UMP): max u(x) subject to x ∈ RL and p · x ≤ w + Definition 1. Let A be a set and f : A → R a real valued function defined on A. An element x ∈ A is a maximizer of f on A if for each y ∈ A, f (x) ≥ f (y). The set of