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Chapter 9 23
Chapter 9
Buying and Selling
The idea of an endowment is an important one, and I wanted to devote a whole
chapter to it rather than give it the cursory treatment it gets in most books. It
is somewhat unnatural in a two-good context, so it is worth pointing out to
students that artificiality and emphasizing that the concept of an endowment
does make perfectly good sense in a more general context.
Emphasize the statement in Section 9.3 that an increase in the value of the
endowment allows for greater consumption possibilities of both goods. You’ll be
happy you did this when you discuss present value! Be sure to explain why a
consumer would necessarily prefer an endowment with higher value, while she
may or may not prefer a consumption bundle with higher value.
The section on price changes is a very nice application of revealed preference
arguments. Students often appreciate this idea a lot more after seeing these
applications.
The Slutsky equation treatment in this chapter is quite neat, but a trifle
involved. Point out that in the original treatment of the Slutsky equation money
income didn’t change when prices changed—only the purchasing power of the
money changed. In this chapter, where consumers get their money from selling
their endowments, money income does change when purchasing power changes,
and this effect has to be accounted for.
I have found that blowing up Figure 9.7 and carefully stepping through the
movements is a big help in seeing this point. Point out that if we take away
the budget line through point C, we have the standard diagram of the previous
chapter. The movement from Dto Cis the only new thing that has been added
in this chapter.
If you’ve got a group that is pretty comfortable with abstraction, the
treatment in the appendix to this chapter will be of interest. It gives an exact
derivation of the Slutsky equation in this case.
Section 9.7 gives a very short example of the Slutsky equation when an endow-
ment is present. Point out how the result comes solely from the maximization
hypothesis, and how hard it would be to figure this out without some analytic
tools. That’s the point of analytic tools like the Slutsky equation: they make this
kind of calculation mechanical so that you don’t have to reproduce a complicated
path of reasoning in each particular case.
24 Chapter Highlights
The last topic in the chapter is the analysis of labor supply. The first thing
we do is manipulate the budget constraint so it fits into the framework studied
earlier. Emphasize that this is a common strategy for analysis: arrange the
problem at hand so that it looks like something we’ve seen before. Also, it is
useful to emphasize the interpretation of the endowment in this context: the
endowment is what you end up consuming if you don’t engage in any market
transactions.
Once the labor supply problem has been put in the standard framework, we
can apply all the tools that we have at our disposal. The first one is the Slutsky
equation. In Section 9.9 I go through a mistaken analysis, and then correct it to
give the right analysis. I think that this is appropriate in this case, since so many
people get the labor supply analysis wrong. A backward-bending labor supply
curve is not a Giffen phenomenon. The supply curve of labor slopes backward
because the endowment of leisure is worth more when the wage rate rises, and
this can lead to an increased consumption of leisure due to the income effect.
The overtime example is really a dandy illustration of substitution effects.
I sometimes introduce the idea by considering the following paradox: if an
employer increases a flat wage by some amount, and pays a higher wage for all
hours worked, his employees could easily end up choosing to work less. But if the
employer pays the same increased wage as an overtime wage, the employees will
never choose to work less, and will likely choose to work more. Isn’t it paradoxical
that giving the workers more money (via the flat wage increase) results in less
labor forthcoming? Seen in terms of substitution effects and revealed preference,
it all makes very good sense, but without those ideas, this common phenomenon
can seem very confusing.
Buying and Selling
A. Up until now, people have only had money to exchange for goods. But in
reality, people sell things they own (e.g., labor) to acquire goods. Want to
model this idea.
B. Net and gross demands
sell (negative).
C. Budget constraint
1. value of what you consume = value of what you sell.
2. p1x1+p2x2=p1ω1+p2ω2
D. Comparative statics
1. changing the endowment
a) normal and inferior
b) increasing the value of the endowment makes the consumer better off.
2. changing prices
Chapter 9 25
a) if the price of a good the consumer is selling goes down, and the
b) if the consumer is a net buyer of a good and the price decreases, then
c) etc.
3. offer curves and demand curves
a) offer curves — what consumer “offers” to buy or sell
E. Slutsky equation
1. when prices change, we now have three effects
a) ordinary substitution effect
2. three effects shown in Figure 9.7.
3. the income effect depends on the net demand.
4. Slutsky equation now takes the form
5. read through proof in appendix.
F. Labor supply
G. Two goods
1. consumption (C)
H. Budget constraint for labor supply
1. pC =M+wL
2. define ¯
C=M/p
3. pC +w(¯
L−L)=p¯
C+w¯
L
I. Comparative statics
1. apply Slutsky equation to demand for leisure to get
∂w = substitution effect + ( ¯
2. increase in the wage rate has an ambiguous effect on supply of labor.
Depends on how much labor is supplied already.
J. Overtime
1. offer workers a higher straight wage, they may work less.
