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Chapter 8 21
Chapter 8
Slutsky Equation
Most books talk about income and substitution effects, but then they don’t
do anything with the ideas. My view is that you have to give the student enough
of an understanding of an idea to be able to compute with it; otherwise, why
bother?
The Slutsky decomposition is an analytical tool that allows us to understand
how demand changes when a price changes. It does this by breaking the total
change in demand up into smaller pieces. The sign of the overall effect depends
on the sign of the pieces, but the sign of the pieces is easier to determine.
I have used the Slutsky definition of substitution effect in this chapter. This is
because it is much easier to compute examples using this definition. The Hicksian
definition is theoretically more elegant, but students can’t compute with it until
they have more advanced mathematical tools.
A large part of getting this material across is just convincing the students to
read the book. The change in income necessary to compensate for a change in
price is neither a difficult concept nor a difficult calculation, but it has to be
repeated a few times before the students grasp it.
One way to describe income and substitution effects is to give an example
based on their own consumption patterns. Talk about a student who spends all
of her allowance on food and books. Suppose that the price of books drops in
half, but her parents find out about it and cut her allowance. How much do they
cut her allowance if they want her to keep her old consumption level affordable?
Once they grasp the idea of the substitution and income effect, it isn’t hard
to put them together in Section 8.4. The next real hurdle is expressing the
Slutsky equation in terms of rates of change, as is done in Section 8.5. This
is the way that we usually refer to the Slutsky equation in later chapters, so it
is worthwhile going through the algebra so they can see where it comes from.
However, if you don’t want to go through the algebraic computations, just make
sure that they get the basic point: the change in demand can be decomposed
into a substitution effect (always negative, i.e., opposite the direction of price
change) and an income effect (positive or negative depending on whether we
have a normal or inferior good).
I usually skip the Optional sections in this chapter, but they are there for
reference if needed. I like the tax rebate section, but it is a little sophisticated.
Emphasize the idea that even if you give the money from the tax back to the
22 Chapter Highlights
consumers, the demand for the good will go down and consumers will be left
worse off.
Slutsky Equation
A. We want a way to decompose the effect of a price change into “simpler” pieces.
1. these are hypothetical changes
1. this measures how demand changes when we change prices, keeping
purchasing power fixed
1. increase income, keep prices fixed
E. Total change in demand is substitution effect plus the income effect.
1. if good is normal good, the substitution effect and the income effect
F. Specific examples
1. perfect complements — Figure 8.4.
G. Application — rebating a tax
1. put a tax on gasoline and return the revenues
2. original budget constraint: px∗+y∗=m
H. Rates of change
1. can also express Slutsky effect in terms of rates of change
2. takes the form ∂x
3. can interpret each part just as before
