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601
1
Final Examination Answers
Answer seven (7) of the following nine (9) questions in the exam booklets provided.
Number each question carefully so that the instructor can
f
nd your answer to any
question easily. All questions are of equal weight.
1. Textbooks introduce various kinds of systems of demand equations for con
sumers (e.g. Walrasian and Hicksian demands) and
f
rms (e.g. inputs demands based
on pro
f
t maximization or on cost minimization). How are the various consumer
demand systems related to the various producer demand systems? If a particular
consumer (producer) demand system has no counterpart in producer (consumer) the
ory can you design a “new” demand system that would
f
ll this gap? Explain your
answer carefully. In the context of consumers assume two goods; in the context of
producers assume one output and two inputs.
ANSWER
Marshallian demands derive from the problem
Max
x
1
,x
2
u
(
x
1
2
)
such that
w
−
p
1
x
1
−
p
2
x
2
=0
which yields
x
i
(
p
1
,p
2
,w
)
.
(1)
Hicksian demands derive from the problem
Min
h
1
,h
2
p
1
h
1
+
p
2
h
2
such that
u
(
h
1
2
)
−
u
0
which yields
h
i
(
p
1
2
,u
0
)
.
(2)
Input demands of a pro
f
tmaximizing price taking
f
rm arise from the problem
x
1
2
pf
(
x
1
2
)
−
w
1
x
1
−
w
2
x
2
(3)
which yields
x
i
(
w
1
2
)
.
Input demands of a costminimizing
f
rm derive from the problem
x
1
2
w
1
x
1
+
w
2
x
2
such that
f
(
x
1
2
)
−
y
0
which yields
x
i
(
w
1
2
,y
0
)
(4)
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Problems (2) and (4) are clearly the same and thus the associated demands func
tions
h
i
(
p
1
,p
2
,u
0
)
and
x
i
(
w
1
,w
2
,y
0
)
have much in common. The only di
f
erence is
that utility cannot be measured in the same sense as output.
Problems (1) and (3) are di
f
erent. The analogue of (1) in producer theory would
be a
f
rm that maximized sales subject to a constraint on the total costs of its inputs.
The problem faced by this kind of
f
rm would be
Max
x
1
,x
2
pf
(
x
1
2
)
such that
C
0
−
w
1
x
1
−
w
2
x
2
=0
which would yield
x
i
(
w
1
2
,C
0
)
,
which are much like the Marshallian demands of consumer theory. One could produce
the analogue of (3) in consumer theory by using the concept of the marginal utility
of money  the extra utility yielded by one more dollar of expenditure. Denote the
marginal utility of money by
λ
.
The inverse of
λ
is the “price” of utility  the number
of dollars it takes to buy one unit of utility.
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 Fall '08
 Burbidge,John

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