Answer to Practice Homework 4
5.5
a)
At the consumer’s optimum we must have
y
x
x
y
x
y
MU
MU
P
P
y
x
P
P
=
=
Substituting into the budget line,
x
y
P x
P y
I
+
=
, gives
2
2
y
x
y
x
y
y
P
P
y
P y
I
P
P y
I
I
y
P
+
=
=
=
b)
Yes, clothing is a normal good.
Holding
y
P
constant, if
I
increases
y
will also
increase.
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
0
5
10
15
20
25
Y
Price(Y)
D
1
D
2
c)
The crossprice elasticity of demand of food with respect to the price of clothing
must be zero.
Note in part a) that with this utility function the demand for
y
does
not depend on the price of
x
.
Similarly, you can show that the demand for food
is
x = I /
(2
P
x
), which does not depend on the price of
y
.
In fact, the consumer
divides her income equally between the two goods regardless of the price of
either.
Since the demands do not depend on the prices of the other goods, the
crossprice elasticities must be zero.
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 Spring '08
 Bryant
 py, 80.00 60.00 40.00 20.00 0.00 0 5 10, Px Py Substituting

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