Page 109 - Microeconomics, Fourth Edition

c03consumerpreferencesandtheconceptofutility.qxd 6/14/10 2:54 PM Page 83

3.2 UTILITY FUNCTIONS 83
Solution This means the consumer’s utility always increases when
he purchases more food and/or clothing.
(a) By examining the utility function, we can see that U
increases whenever x or y increases. This means that the (b) In both marginal utility functions, as the value of the
consumer likes more of each good. Note that we can denominator increases (holding the numerator con-
also see that more is better for each good by looking at stant), the marginal utility diminishes. Thus, MU x and
the marginal utilities MU x and MU y , which must always MU y are both diminishing.
be positive because the square roots of x and y must
always be positive (all square roots are positive numbers). Similar Problem: 3.4

Learning-By-Doing Exercise 3.2 shows the two ways to determine whether the
marginal utility of a good is positive. First, you can look at the total utility function.
If it increases when more of the good is consumed, marginal utility is positive. Second,
you can look at the marginal utility of the good to see if it is a positive number. When
the marginal utility is a positive number, the total utility will increase when more of
the good is consumed.

LEARNING-BY-DOING EXERCISE 3.2
S
D
E
Marginal Utility That Is Not Diminishing
Some utility functions satisfy the assump- Solution
tion that more is better, but with a marginal utility that
is not diminishing. Suppose a consumer’s preferences for (a) U increases whenever H or R increases, so more
hamburgers and root beer can be represented by the must be better for each good. Also, MU H and MU R are
utility function U 2H R, where H measures the both positive, again indicating that more is better.
number of hamburgers consumed and R the number of ( b) As H increases, MU H falls, so the consumer’s mar-
root beers. The marginal utilities are ginal utility of hamburgers is diminishing. However,

1 MU R 1 (no matter what the value of R), so the con-
MU sumer has a constant (rather than a diminishing) marginal
H
22H utility of root beer (i.e., the consumer’s utility always in-
MU 1 creases by the same amount when he purchases another
R
root beer).
Problem
Similar Problem: 3.5
(a) Does the consumer believe that more is better for
each good?
(b) Does the consumer have a diminishing marginal
utility of hamburgers? Is the marginal utility of root beer
diminishing?

Indifference Curves
To illustrate the trade-offs involved in consumer choice, we can reduce the three- indifference curve
dimensional graph of Brandon’s utility function in Figure 3.4 to a two-dimensional curve connecting a set of A
graph like the one in Figure 3.5. Both graphs illustrate the same utility function consumption baskets that
U 1xy. In Figure 3.5 each curve represents baskets yielding the same level of utility yield the same level of sat-
to Brandon. Each curve is called an indifference curve because Brandon would be isfaction to the consumer.