Name:
[Last],
[First]
EC 701
Microeconomics
Michael Manove
20 December 2004
Final Examination
Instructions:
Answer two of the three parts of Problem 1 (but do
not
answer all three parts).
Then answer Problems 2, 3, 4 and 5. Think before you write. Do not spend too much time on
any one problem. If you have to leave the room for any reason, please give the instructor your
examination on the way out. You will have 180 minutes to complete a 150minute exam. I suggest
that you do not exceed the recommended times for each question until you have answered all
questions. Then you can use the extra time to improve your answers. If you
fi
nish before 11:45
pm, you may leave, but be extremely quiet on the way out and in the hallway!
Problem 1.
[20 minutes, total]
Prove any two of the following three propositions:
a)
[10 minutes]
Proposition (Slutsky equation for Hicksian demand).
If
U
(
x
)
is a
strictly quasiconcave and wellbehaved utility function and
V
(
p, w
)
is the corresponding
indirect utility function, then
∂x
i
(
p, w
)
∂p
j
=
∂h
i
(
p, u
)
∂p
j
−
∂x
i
(
p, w
)
∂w
x
j
(
p, w
)
where
x
i
(
p, w
)
is ordinary demand and
h
i
(
p, u
)
is Hicksian demand and where
u
=
V
(
p, w
)
.
[You are free to cite theorems about the expenditure function
e
(
p, u
)
in your proof.]
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EC 701 Final Exam
December 20, 2004
page
2
b)
[10 minutes]
Proposition (Law of Supply).
Suppose
y
(
·
)
is a supply (derived demand)
function. Then for any two price vectors
p
0
and
p
À
0
,
we have
(
p
0
−
p
)(
y
(
p
0
)
−
y
(
p
))
≥
0
.
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 Spring '11
 CHAN
 Microeconomics, Game Theory, Utility, Mj, Pedro

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