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18 Chapter Highlights
Chapter 7
Revealed Preference
This is a big change of pace, and usually a welcome one. The basic idea of
revealed preference, as described in Section 7.1, is a very intuitive one. All I
want to do in this chapter is give the students the tools to express that intuition
algebraically.
I think that the material in Section 7.3, on recovering preferences, is very
exciting. Start out with the idea of indirect revealed preference, as depicted in
Figure 7.2. Point out that the optimization model allows us to predict how this
person would behave when faced with a choice between (x1,x
2)and(z1,z
2), even
though we have never observed the person when faced with this choice! This is a
big idea, and a very important one. Again, drive home how the economic model
of optimization allows us to make strong predictions about behavior.
Figure 7.3 is the natural extension of this line of reasoning. Given the
idea of revealed preference, and more importantly the idea of indirect revealed
preference, we can determine the shape of underlying indifference curves from
looking at choice data. I motivate this in terms of benefit-cost issues, but you
could also choose to think about forecasting demand for products in a marketing
survey, or similar applications.
Once students understand the idea of revealed preference, they can usually
understand the Weak Axiom right away. However, they generally have difficulty
in actually checking whether the Weak Axiom is satisfied by some real numbers.
I added Section 7.5 for this reason; it just outlines one systematic way to check
WARP. The students can omit this in their first reading, but they might want
to come back to it when they start to do the exercises. If your students know a
little computer programming, you might ask them to think about how to write
a computer program to check WARP.
The same comments go for the treatment of the Strong Axiom and checking
SARP. This is probably overkill, but I found that students couldn’t really handle
problem 7.5 in the workbook without some guidance about how to systematically
check SARP. Speaking of the workbook, the problems in this section are really
fun. I am especially fond of 7.6 and 7.7. Problem 7.9 had some wrong numbers
in it in early printings of Workouts, so people with old books should be warned.
Finally, the material on index numbers is very worthwhile. Students here
about price indices and cost-of-living indices all the time, so it’s nice to describe
the theory that lies behind these ideas.
Chapter 7 19
Revealed Preference
A. Motivation
1. up until now we’ve started with preference and then described behavior
2. revealed preference is “working backwards” — start with behavior and
B. Basic idea
1. if (x1,x
2) is chosen when (y1,y
2) is affordable, then we know that (x1,x
2)
2. in equations: if (x1,x
2) is chosen when prices are (p1,p
2)andp1x1+p2x2≥
3. see Figure 7.1.
5. if Xis directly revealed preferred to Y,andYis directly revealed preferred
See Figure 7.2.
6. the “chains” of revealed preference can give us a lot of information about
7. the information revealed about tastes by choices can be used in formulating
C. Weak Axiom of Revealed Preference
1. recovering preferences makes sense only if consumer is actually maximizing
4. in symbols, we have (x1,x
2) purchased at prices (p1,p
2)and(y1,y
2)
5. this kind of behavior is inconsistent with the optimizing model of consumer
choice
7.WARP:if(x1,x
2) is directly revealed preferred to (y1,y
2), then (y1,y
2)
9. this condition can be checked by hand or by computer
D. Strong Axiom of Revealed Preference
1. WARP is only a necessary condition for behavior to be consistent with
2. Strong Axiom of Revealed Preference (SARP): if (x1,x
2) is directly or
3. SARP is a necessary and sufficient condition for utility maximization
4. this means that if the consumer is maximizing utility, then his behavior
5. furthermore if his observed behavior is consistent with SARP, then we can
20 Chapter Highlights
6. can also be tested by a computer
E. Index numbers
1. given consumption and prices in 2 years, base year band some other year
t
2. how does consumption in year tcompare with base year consumption?
3. general form of a consumption index:
4. natural to use prices as weights
5. get two indices depending on whether you use period tor period bprices
7. Laspeyres index uses period b(base period) weights:
8. note connection with revealed preference: if Paasche index is greater than
1, then period tmust be better than period b:
a)
b)
t
9. same sort of thing can be done with Laspeyres index — if Laspeyres index
