Economics 104A
Solution for Midterm Exam
Winter 2008
1.
(a) (5pt) Let
u
(
x
1
,x
2
) =
√
x
1
+
x
2
be a utility function for a consumer. Are the two
goods perfect substitutes for the consumer? Explain why or why not. Draw the
IC with utility level 1.
Answer:
Notice
MU
1
(
x
) =
MU
2
(
x
) =
1
2
√
x
1
+
x
2
.
It follows
MRS
(
x
) = 1 which in turn implies that the consumer is always willing
to substitute one good for another at a 11 ration. The IC with utility level 1 is
the straight line
x
1
+
x
2
= 1 (see Figure 1).
(b) (5pt) Andy purchases only two goods, kumquats (K) and oranges (O). He has
an income of $40 and can buy kumquats at $4 per pound and oranges at $2 per
pound. His utility function is
u
(
K,O
) = 5
K
+ 3
O
. What bundle of kumquats
and oranges should he purchase to maximize utility? Why?
Answer:
The given utility function implies
MU
K
(
x
) = 5 and
MU
O
(
x
) = 3.
Hence,
MRS
(
x
) =
5
3
which implies that kumquats and oranges are perfect substitutes for Andy. Since
p
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 Winter '10
 Staff
 Utility, Substitute good

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