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Chapter 3
A Consumer’s Constrained Choice
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Chapter Outline
3.1
Preferences
Properties of Consumer Preferences
Preference Maps
Indifference Curves
3.2
Utility
Utility Function
Ordinal Preference
Utility and Indifference Curves
Willingness to Substitute Between Goods
Curvature of Indifference Curves
3.3
Budget Constraint
3.4
Constrained Consumer Choice
The Consumer’s Optimum Bundle
Maximizing Utility Subject to a Constraint Using Calculus
Minimizing Expenditure
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Teaching Tips
The material in this chapter represents a challenge to students for a number of reasons. Most will not have
learned constrained optimization before. Also, utility analysis may seem quite abstract to them. Some take
issue with the assumption of rational behavior on the part of individuals and it needs to be stressed that the
models require only rational behavior on average. Finally, this is the point where the calculus techniques
go beyond the methods they are likely to have learned in their calculus prerequisite.
To overcome these stumbling blocks, you may want to devote one class to presenting and discussing the
technical points of utility theory and budget lines using one or two running examples, and another class to
applications. Whether you decide to present applications as you go, or after presenting the technical material,
this is one area where the students have to see the theory applied in order for it to make sense. You might
also consider breaking the class into small groups to work on problems that test their understanding (additional
problems are provided below). This way, you can migrate among the groups to get a better idea of how
many are struggling and who needs help. The methods presented in this chapter will be needed in Chapter 4
for the derivation of demand curves. If they are not confident with the material in this chapter, they are
almost certain to struggle not only in Chapter 4, but also when it comes to production and cost, since the
methodology there is similar.
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Perloff •
Microeconomics: Theory and Applications with Calculus
The class should see that the notion of a measurable
util
is nonsense and will find the model more believable
given that only ordinal measurability is needed. Section 3.3 on budget lines should not require much class
time, though it is worth putting an equation and graph on the board and briefly discussing how parameter
changes affect the constraint. More difficult manipulations of the budget constraint can be introduced
using taxes, subsidies, and binding quotas with or without transferability.
For Section 3.4, Constrained Choice, the technical portion of the material should come fairly easily if the
class has a solid grasp of indifference curves. Using plenty of examples and applications will make the
process of utility maximization seem less abstract. There are several in the text as well as in the additional
applications below. You may want to spend some time contrasting interior solutions and corner solutions.
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 Spring '08
 CONSTANTINE

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