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90 CHAPTER 3 CONSUMER PREFERENCES AND THE CONCEPT OF UTILITY

This decline in the marginal rate of substitution ding indifference curve) to another, and at these bun-
of gas mileage for horsepower could reflect changes dles the marginal rates of substitution may differ.
in consumer tastes, or it could also reflect simultane- The key point of this example is that marginal
ous changes in automobile prices, gasoline prices, and rate of substitution is more than just a theoretical
consumer incomes. As we will see in the next chapter, concept. It can be estimated and used to help us un-
when changes in prices and income occur, consumers derstand the trade-offs that consumers are willing to
move from one consumption bundle (and correspon- make between products and product attributes.

LEARNING-BY-DOING EXERCISE 3.3
S
D
E
Indifference Curves with Diminishing MRS x,y
Suppose a consumer has preferences (b) On the same graph draw a second indifference curve,
between two goods that can be represented by the util- U 2 200. Show how MRS x, y depends on x and y, and
ity function U xy. For this utility function, MU x y use this information to determine if MRS x, y is diminish-
and MU y x. 6 ing for this utility function.

Problem Solution
(a) On a graph, draw the indifference curve associated (a) To draw the indifference curve U 1 128 for the utility
with the utility level U 1 128. Then answer the follow- function U xy, we plot points where xy 128—for
ing questions: example, point G(x 8, y 16), point H(x 16, y
1. Does the indifference curve intersect either axis? 8), and point I(x 32, y 4)—and then connect these
2. Does the shape of the indifference curve indicate points with a smooth line. Figure 3.11 shows this indif-
that MRS x, y is diminishing? ference curve.

20

15 G Preference
directions

y 10
H
5 I U = 200
2
U = 128
1
0
10 20 30 40
x
FIGURE 3.11 Indifference Curves with Diminishing MRS x,y
The indifference curves on this graph are for the utility function U xy, for which
MRS x,y y x . On curve U 1 , the MRS x,y at basket G is 16 8 2 ; therefore, the slope of the
indifference curve at G is 2. The MRS x,y at basket I is 4 32 1 8 ; therefore, the slope
of the indifference curve at I is 1 8 . Thus, for U 1 (and for U 2 ) MRS x,y diminishes as x
increases, and the indifference curves are bowed in toward the origin.

6 To see how these marginal utilities can be derived from the utility function, you would use the calculus
techniques illustrated in Learning-By-Doing Exercise A.7 in the Mathematical Appendix.