Chapter 5 13
Chapter 5
Choice
This is the chapter where we bring it all together. Make sure that students
understand the method of maximization and don’t just memorize the various
special cases. The problems in the workbook are designed to show the futility of
memorizing special cases, but often students try it anyway.
The material in Section 5.4 is very important—I introduce it by saying “Why
should you care that the MRS equals the price ratio?” The answer is that this
allows economists to determine something about peoples’ trade-offs by observing
market prices. Thus it allows for the possibility of benefit-cost analysis.
The material in Section 5.5 on choosing taxes is the first big non-obvious
result from using consumer theory ideas. I go over it very carefully, to make
sure that students understand the result, and emphasize how this analysis
uses the techniques that we’ve developed. Pound home the idea that the
analytic techniques of microeconomics have a big payoff—they allow us to answer
questions that we wouldn’t have been able to answer without these techniques.
If you are doing a calculus-based course, be sure to spend some time on the
appendix to this chapter. Emphasize that to solve a constrained maximization
problem, you must have two equations. One equation is the constraint, and one
equation is the optimization condition. I usually work a Cobb-Douglas and a
perfect complements problem to illustrate this. In the Cobb-Douglas case, the
optimization condition is that the MRS equals the price ratio. In the perfect
complements case, the optimization condition is that the consumer chooses a
bundle at the corner.
Choice
A. Optimal choice
1. move along the budget line until preferred set doesn’t cross the budget set.
Figure 5.1.
2. note that tangency occurs at optimal point — necessary condition for
3. tangency is not suffcient. Figure 5.4.
a) unless indifference curves are convex.
14 Chapter Highlights
4. optimal choice is demanded bundle
a) as we vary prices and income, we get demand functions.
B. Examples
1. perfect substitutes: x1=m/p1if p1<p
2; 0 otherwise. Figure 5.5.
2. perfect complements: x1=m/(p1+p2). Figure 5.6.
5. concave preferences: similar to perfect substitutes. Note that tangency
6. Cobb-Douglas preferences: x1=am/p1. Note constant budget shares, a=
C. Estimating utility function
1. examine consumption data
4. can use the fitted utility function as guide to policy decisions
D. Implications of MRS condition
1. why do we care that MRS =−price ratio?
2. if everyone faces the same prices, then everyone has the same local trade-off
3. since everyone locally values the trade-off the same, we can make policy
E. Application — choosing a tax. Which is better, a commodity tax or an income
tax?
1. can show an income tax is always better in the sense that given any
2. outline of argument:
a) original budget constraint: p1x1+p2x2=m
e) income tax that raises same amount of revenue leads to budget con-
straint: p1x1+p2x2=m−tx∗
1
1) this line has same slope as original budget line
2) also passes through (x∗
1,x
∗
2)
3. caveats
a) only applies for one consumer — for each consumer there is an income
tax that is better
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F. Appendix — solving for the optimal choice
1. calculus problem — constrained maximization
2. max u(x1,x
2)s.t. p1x1+p2x2=m
3. method 1: write down MRS =p1/p2and budget constraint and solve.
6. example 1: Cobb-Douglas problem in book
7. example 2: quasilinear preferences