Chapter 3 Homework Key
Due: February 20, 2007
1. Consider the utility function
x
y
)
y
,
x
(
U
=
with
x
2
/
y
MU
x
=
and
x
MU
y
=
.
a.
Does the consumer believe more is better for each good? Explain.
Since
U
increases whenever
x
or
y
increases, more of each good is better.
This is
also confirmed by noting that
MU
x
and
MU
y
are both positive for any positive
values of
x
and
y
.
b.
Do the consumer’s preferences exhibit a diminishing marginal utility of x? Explain. Is the
marginal utility of y diminishing? Explain.
Since
2
y
x
x
MU
=
, as
x
increases (holding
y
constant),
x
MU
falls.
Therefore
the marginal utility of
x
is diminishing.
However,
y
MU
x
=
.
As
y
increases,
MU
y
does not change.
Therefore the preferences exhibit a constant, not
diminishing, marginal utility of
y
.
2. The utility that Julie receives by consuming food F and clothing C is given by
FC
)
C
,
F
(
U
=
.
For this utility function, the marginal utilities are
C
MU
F
=
and
F
MU
C
=
.
a.
On a graph with F on the horizontal axis and C on the vertical axis, draw indifference
curves for U = 12, U = 18 and U = 24.
0
2
4
6
8
10
12
14
0
5
10
15
Food
Clothing
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Do the shapes of these indifference curves suggest Julie has a diminishing marginal rate
of substitution of food for clothing? Explain.
Yes, since the indifference curves are convex toward the origin we know that
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 Spring '08
 Mcferrin
 Utility, Marginal rate of substitution

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