1
ECO 301: Intermediate Microeconomics
Marco A Castaneda
Homework 2: Answers
1.
ANSWER
The consumer has preferences represented by the utility function
U = min{X,Y}
a)
The commodities are perfect complements. Therefore, the optimal
consumption vector is determined by the conditions
X = Y
10X + 10Y = 300
Therefore, we have the optimal consumption vector X* = 15 and Y* = 15, as
illustrated in the graph.
b)
In this situation, the optimal consumption vector is determined by the
conditions
X = Y
20X + 10Y = 300
Therefore, we have the optimal consumption vector X* = 10 and Y* = 10, as
illustrated in the graph.
Y
20
15
10
5
X
25
30
5
10
15
20
25
30
Indifference
curve
Budget line
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ANSWER
A consumer has preferences represented by the utility function
U = 2X + 3Y
For this utility function, we have
MU
X
= 2
and
MU
Y
= 3
and
3
2
MU
MU
MRS
Y
X
XY
=
=
Therefore, the indifference curves are linear, and the optimal consumption vector
will involve the consumption of only one commodity.
a)
In this situation, we have
Y
Y
X
X
P
MU
5
3
5
2
P
MU
=
<
=
Therefore, the consumer should spend all of their income in commodity Y,
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 Spring '08
 Castaneda
 Utility, 50 dollars, MRS xy, optimal consumption vector

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