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Department of Economics
Econ 501.02
Winter 2007
Prof. James Peck
Midterm Questions and Answers
Part I: Short Answer.
1.
(10 points)
True or False, and explain. If a consumer’s preferences
for goods
x
and
y
can be represented by the utility function,
u
(
x, y
)=
xy
,then
the preferences can also be represented by the utility function,
u
(
x, y
)=10
xy
.
Answer:
There are many ways to see that the answer is True. The coe
ﬃ

cient of 10 does not a
f
ect the underlying preferences, because the indi
f
erence
curves are the same, only the labelling is di
f
erent. For example, the indi
f
er
ence curve corresponding to utility of 2 with the
f
rst utility function is the
indi
f
erence curve corresponding to utility of 20 with the second utility func
tion. Another way to see that the preferences are the same is to notice that
the marginal rate of substitution at any point
(
x, y
)
is
y/x
with either utility
function.
Finally, whenever
(
x
A
,y
A
)
is preferred to
(
x
B
,y
B
)
with the
f
rst utility func
tion, so
x
A
y
A
>x
B
y
B
holds, then
(
x
A
,y
A
)
is preferred to
(
x
B
,y
B
)
with the
second utility function, because
10
x
A
y
A
>
10
x
B
y
B
holds, and vice versa.
2.
(10 points)
True or False, and explain.
If the price elasticity of
demand for Honda Accords in the eastern half of the U.S. is
−
2
,andifthepr
ice
elasticity of demand for Honda Accords in the western half of the U.S. is also
−
2
, then the price elasticity of demand for the entire U.S. market must be
−
2
.
Answer:
The answer I had in mind was True. Intuitively, if a 1% increase
in price causes demand to fall by 2% in the East and 2% in the West, then
overall demand must fall by exactly 2%. To show this formally, we know
dX
E
dp
x
p
x
X
E
=
−
2=
dX
W
dp
x
p
x
X
W
,
so we can write
dX
E
dp
x
=
−
2
X
E
p
x
(1)
dX
W
dp
x
=
−
2
X
W
p
x
.
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This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Spring '08 term at Ohio State.
 Spring '08
 YANG
 Economics, Microeconomics

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