Chapter 2 Solutions
1.(a) For this consumer, 6 0. Show that 0 ~ 6 if the transitivity assumption holds.
1.(b) Show that x y, y z, and z x.
2.(a) The indifference curve corresponding to u = 1 passes through the points (0.5, 2), (1, 1), and
(2, 0.5). The indifference curve corresponding to u = 2 passes through the points (0.5, 4),
(1, 2), (2, 1), and (4, 0.5).
2.(b) The MRS equals 1 along the ray from the origin x2 = x1, and it equals 2 along the ray
from the origin x2 = 2x1.
3.(a) The indifference curves are downward-sloping parallel lines with a slope of −1 and the
arrow pointing northeast.
3.(b) The indifference curves are upward-sloping with the arrow pointing northwest.
3.(c) The indifference curves are vertical with the arrow pointing to the right.
3.(d) The indifference curves are downward-sloping and convex with the arrow pointing northeast.
4.(a) The indifference curves are horizontal; the consumer is neutral about x1 and likes x2.
4.(b) The indifference curves are downward-sloping parallel lines with a slope of −1; the consumer
considers x1 and x2 to be perfect substitutes.
4.(c) The indifference curves are L-shaped, with kinks along the ray from the origin x2 = 12
x1;
the consumer considers x1 and x2 to be perfect complements.
4.(d) The indifference curves are upward-sloping and convex (shaped like the right side of a U);
the consumer likes x2, but dislikes x1, i.e., good 1 is a bad for the consumer.
Contents
Preface
1 Introduction
Part I Theory of the Consumer
2 Preferences and Utility
2.1 Introduction
2.2 The Consumer’s Preference Relation
2.3 The Marginal Rate of Substitution
2.4 The Consumer’s Utility Function
2.5 Utility Functions and the Marginal Rate of Substitution
2.6 A Solved Problem
Exercise
Appendix. Differentiation of Functions
3 The Budget Constraint and the Consumer’s Optimal Choice
3.1 Introduction
3.2 The Standard Budget Constraint, the Budget Set, and the Budget Line
3.3 Shifts of the Budget Line
3.4 Odd Budget Constraints
3.5 Income and Consumption over Time
3.6 The Consumer’s Optimal Choice: Graphical Analysis
3.7 The Consumer’s Optimal Choice: Utility Maximization Subject to the Budget Constraint
3.8 Two Solved Problems
Exercises
Appendix. Maximization Subject to a Constraint:
The Lagrange Function Method
4 Demand Functions
4.1 Introduction
4.2 Demand as a Function of Income
4.3 Demand as a Function of Price
4.4 Demand as a Function of Price of the Other Good
4.5 Substitution and Income Effects
4.6 The Compensated Demand Curve
4.7 Elasticity
4.8 The Market Demand Curve
4.9 A Solved Problem
Exercises
5 Supply Functions for Labor and Savings
5.1 Introduction to the Supply of Labor
5.2 Choice between Consumption and Leisure
5.3 Substitution and Income Effects in Labor Supply
5.4 Other Types of Budget Constraints
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