Page 115 - Microeconomics, Fourth Edition

c03consumerpreferencesandtheconceptofutility.qxd 6/14/10 2:54 PM Page 89

3.2 UTILITY FUNCTIONS 89
Diminishing Marginal Rate of Substitution
For many (but not all) goods, MRS x,y diminishes as the amount of x increases along an
indifference curve. To see why, refer to Figure 3.9. At basket A, to get 1 more hamburger,
Eric would be willing to forgo as many as 5 glasses of lemonade. And this makes sense
because at basket A Eric is drinking much lemonade and eating only a few hamburgers.
So we might expect MRS x,y to be large. However, if Eric were to move to basket D, where
he is consuming more hamburgers and less lemonade, he might not be willing to give up
as many glasses of lemonade to get still another hamburger. Thus, his MRS x,y will be
lower at D than at A. We have already shown that Eric’s MRS x,y at basket D is 2, which
is lower than his MRS x,y at basket A. In this case Eric’s preferences exhibit a diminishing diminishing marginal
marginal rate of substitution of x for y. In other words, the marginal rate of substitu- rate of substitution
tion of x for y declines as Eric increases his consumption of x along an indifference curve. A feature of consumer pref-
What does a diminishing marginal rate of substitution of x for y imply about the erences for which the mar-
shape of the indifference curves? Remember that the marginal rate of substitution of ginal rate of substitution of
one good for another good
x for y is just the negative of the slope of the indifference curve on a graph with x on diminishes as the consump-
the horizontal axis and y on the vertical axis. If MRS x,y diminishes as the consumer in- tion of the first good in-
creases x along an indifference curve, then the slope of the indifference curve must be creases along an indiffer-
getting flatter (less negative) as x increases. Therefore, indifference curves with di- ence curve.
minishing MRS x,y must be bowed in toward the origin, as in Figure 3.9.

APPLICA TION 3.2

How People Buy Cars: The
when companies attempt to forecast the potential
Importance of Attributes market for a new product.
Nestor Arguea, Cheng Hsiao, and Grant Taylor
We began this chapter by discussing one of the choices (AHT) used data on prices in the U.S. automobile mar-
you would face as you decide whether to buy an auto- ket to estimate what are known as hedonic prices for
5
mobile, the level of fuel efficiency. But you will proba- automobile attributes. A discussion of hedonic prices
bly also care about other attributes of the car you is the stuff of an advanced econometrics course, so
might buy. Should it be big or small? Should it have a we won’t go into the details of AHT’s methods here.
big engine and lots of horsepower, or should it have a Roughly speaking, a hedonic price is a measure of the
smaller engine and thus get better gas mileage? marginal utility of a particular attribute. Given this,
In other words, when you buy a car you are really the ratio of hedonic prices for two different automo-
buying a bundle of attributes. Just as we can build a bile attributes, such as horsepower and gas mileage,
theory of consumer choice among different goods by represents the marginal rate of substitution between
means of a utility function defined over those goods, these attributes for the typical automobile consumer.
we can also build a model of consumer choice among Based on AHT’s estimates, the marginal rate of
different varieties of the same good (such as automo- substitution of gas mileage for horsepower for a typ-
biles) by means of a utility function defined over the ical U.S. auto consumer in 1969 was 3.79. This means
attributes of this good. For example, the satisfaction that the typical consumer would be willing to forgo
that consumers would derive from different brands of 3.79 horsepower to get an additional one mile per
cars could be described by a utility function over horse- gallon in gas mileage. Between 1969 and 1986 the
power, gas mileage, luggage space, and so forth. Market marginal rate of substitution of gas mileage for horse-
researchers often use this attribute-based approach power gradually fell, reaching 0.71 by 1986.

5 N. M. Arguea, C. Hsiao, and G. A. Taylor, “Estimating Consumer Preferences Using Market Data—An
Application to U.S. Automobile Demand,” Journal of Applied Econometrics 9 (1994): 1–18.