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92 CHAPTER 3 CONSUMER PREFERENCES AND THE CONCEPT OF UTILITY
3.3 A consumer’s willingness to substitute one good for another will depend on the com-

SPECIAL modities in question. For example, one consumer may view Coke and Pepsi as perfect
PREFERENCES substitutes and always be willing to substitute a glass of one for a glass of the other. If
so, the marginal rate of substitution of Coke for Pepsi will be constant and equal to 1,
rather than diminishing. Sometimes a consumer may simply be unwilling to substitute
one commodity for another. For example, a consumer might always want exactly 1
ounce of peanut butter for each ounce of jelly on his sandwiches and be unwilling to
consume peanut butter and jelly in any other proportions. To cover cases such as these
and others, there are several special utility functions. Here we discuss four: utility func-
tions in the case of perfect substitutes and the case of perfect complements, the
Cobb–Douglas utility function, and quasilinear utility functions.

PERFECT SUBSTITUTES

perfect substitutes In some cases, a consumer might view two commodities as perfect substitutes for one
(in consumption) Two another. Two goods are perfect substitutes when the marginal rate of substitution of one
goods such that the mar- for the other is a constant. For example, suppose David likes both butter (B) and mar-
ginal rate of substitution garine (M) and that he is always willing to substitute a pound of either commodity for a
of one good for the other pound of the other. Then MRS MRS 1. We can use a utility function such as
B,M
M,B
is constant; therefore, the U aB aM, where a is any positive constant, to describe these preferences. (With this
indifference curves are
B
M
straight lines. utility function, MU a and MU a. It also follows that MRS B,M MU MU M
B
a a 1, and the slope of the indifference curves will be constant and equal to 1.)
More generally, indifference curves for perfect substitutes are straight lines, and
the marginal rate of substitution is constant, though not necessarily equal to 1. For
example, suppose a consumer likes both pancakes and waffles and is always willing
to substitute two pancakes for one waffle. A utility function that would describe
his preferences is U P 2W, where P is the number of pancakes and W the
number of waffles. With these preferences, MU 1 and MU W 2, so each waf-
P
fle yields twice the marginal utility of a single pancake. We also observe that
P
MRS P,W MU MU W 1 2. Two indifference curves for this utility function are
APPLICA TION 3.3

Taste Tests least under blindfold test conditions, most beer
drinkers cannot distinguish between brands of
If you listen to advertisements on television, you beer.” He also noted that brewers have devoted
might believe that most goods are highly differenti- “considerable talent and resources . . . to publiciz-
ated products and that most consumers have strong ing real or imagined differences in beers, with the
preferences for one brand over another. To be sure, hope of producing product differentiation.” In the
there are differences among brands, and brands vary end, Elzinga suggested, despite brewers’ efforts to
in price. But are brands so different that one producer differentiate their products from those of their
could raise the price of its product without losing a competitors, most consumers would be quite will-
significant portion of its sales? ing to substitute one brand of beer for another,
In looking at the U.S. beer industry, Kenneth especially if one brand were to raise its price signif-
Elzinga observed, “Several studies indicate that, at icantly. 7

7 K. Elzinga, “The Beer Industry,” in W. Adams, The Structure of American Industry, 8th ed. pp.142–143
(New York: Macmillan Publishing Company, 1990).