Economics 111: Intermediate Microeconomics
Spring 2008
Homework 2 Answer Key
Professor: Pedro Dal Bó
1. Consider the following utility function:
U
=
x
1
2
1
x
1
2
2
.
a. Draw the indi
ff
erence curve that yields
U
= 5
(
fi
nd
x
2
as a function of
x
1
with
U
= 5
).
x
2
=
25
x
1
15
12.5
10
7.5
5
2.5
0
15
12.5
10
7.5
5
2.5
0
X1
X2
b. Find the MRS for every consumption bundle. Is the MRS decreasing in
x
1
?
MRS
=
MU
1
MU
2
=
x
2
x
1
It is decreasing in
x
1
.
c. In a new
fi
gure graph her budget set if
p
1
= 1
,
p
2
= 1
and
m
= 10
.
1
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15
12.5
10
7.5
5
2.5
0
15
12.5
10
7.5
5
2.5
0
X1
X2
d. Find her optimal consumption bundle (
x
∗
1
,
x
∗
2
) and draw it in the
fi
gure.
The optimal consumption value satis
fi
es the following two conditions:
x
1
x
2
= 1
(MRS=
p
1
p
2
)
x
1
+
x
2
= 10
(budget constraint).
Solving we get:
(
x
∗
1
, x
∗
2
) = (5
,
5)
.
15
12.5
10
7.5
5
2.5
0
15
12.5
10
7.5
5
2.5
0
X1
X2
e. Find her optimal consumption bundle (
x
∗
0
1
,
x
∗
0
2
) if
p
1
= 2
,
p
2
= 1
and
m
= 10
and
draw it in the
fi
gure.
Solving with the new prices we get:
(
x
∗
1
, x
∗
2
) = (2
.
5
,
5)
.
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 Spring '08
 DALBO
 Economics, Utility, X1

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