Department of Economics
The Ohio State University
Final Exam Answers–Econ 805
Questions 2,3, and 4
Profs. Levin and Peck
March 19, 2002
2.
(20 points)
Suppose that an economy with two commodities has the excess demand
function given by
z
(
p
1
; p
2
) = (
¡
1
;
p
1
p
2
)
for
p
1
¸
0
and
p
2
>
0
.
[If we have
p
2
= 0
, then excess demand is not well
de…ned.]
(a)
Is this excess demand function consistent with Walras’ law?
That is,
does
p
¢
z
(
p
) = 0
for all prices for which excess demand is wellde…ned?
(b) Could this excess demand function have been derived from each consumer
maximizing utility subject to a budget constraint, where each utility function is
continuous, strictly monotonic, and strictly quasiconcave, and where all initial
endowments are strictly positive?
Explain carefully.
Answer:
(a)
Yes, this is consistent with Walras’ Law.
Evaluating
p
¢
z
(
p
)
, we have
p
1
(
¡
1) +
p
2
(
p
1
p
2
) = 0
:
(b)
This is impossible.
Under all these assumptions, our existence theo
rem guarantees that a CE exists.
Therefore, there is a price vector such that
z
(
p
)
·
0
.
However,
z
2
(
p
)
·
0
can only hold if
p
1
= 0
, which violates strict
monotonicity.
(If a price was zero, there would necessarily be excess demand
for that good.)
3.
(20 points)
Consider the following economy, with two consumers and two commodities.
The economy’s aggregate resources are given by the vector,
(1
;
1)
:
Consumer
1 has the utility function,
u
1
(
x
1
) = 2 log(
x
1
1
) + log(
x
2
1
)
;
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 Spring '08
 PECK
 Economics, excess demand, Walras, excess demand function

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