Midterm 1 Answer Key
February 25, 2010
1.
a) X*=
:
4
&
100
p
X
=
40
p
x
dX
&
dp
X
=
&
40
p
2
x
:
Jack&s consumption of X
decreases with a price increase for X.
Z*=
(1
±
:
4)
&
100
p
Z
=
60
p
Y
dZ
&
dp
X
= 0
:
Jack&s consumption of Z doesn&t
change with a price increase for X.
b) While an increase in
p
x
leads to a decrease in the consumption of X,
there is no e/ect on either
p
Z
or the optimal consumption Z*. The share of the
budget spent on X is
p
X
&
X
Y
:
But it is also 1
p
Z
&
Z
Y
. Since the share of income
spent on Z hasn&t changed, the share of income spent on X must also remain
unchanged. Thus, the decrease in the units of X comsumed must exactly make
up for the increased price.
Thus, the change in consumption of X is entirely
due to the substitution e/ect, and not the income e/ect.
2.
a) Setting supply equal to demand, we ±nd:
20 + 5
p
=
140
&
5
p
(1)
10
p
=
120
(2)
p
&
=
12
(3)
Q
&
=
20 + 5
±
12 = 80
(4)
b) The new supply function with a tax is
Q
s
= 20+5(
p
&
t
) = 20+5
p
&
5
t
=
20
&
10 = 5
p
= 10 + 5
p:
Setting our new supply function equal to demand we get:
10 + 5
p
=
140
&
5
p
(5)
10
p
=
130
(6)
p
&
=
13
(7)
(
p
&
S
=
p
&
&
t
= 11)
(8)
Q
&
=
140
&
(5
±
13) = 75
(9)
1
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 Spring '10
 PERLOFF
 Utility, qs, optimal bundle, new optimal bundle

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