Ani Guerdjikova
Fall 2006
Department of Economics
Intermediate Microeconomics
Cornell University
ECON 313
Problem Set 6
Problem 24
∗
(Expenditure minimization, duality)
Farmer Frank has preferences for ham
(
x
1
)
and cheese
(
x
2
)
which are given by the utility func
tion
U
(
x
1
;
x
2
)=2
√
x
1
+
x
2
Thepricesare
p
1
=1
and
p
2
=2
.
a) Yesterday, farmer Frank wanted to obtain a utility level of
U
=5
. Represent his indifference
curve in a diagram and determine his optimal consumption bundle.
b) Today, farmer Frank is not as hungry. He wants to obtain a utility level of
U
=1
.D
rawh
isnew
indifference curve and determine the optimal consumption bundle. Does the marginal rate equal
the price ratio?
c) Determine farmer Frank’s Hicks’ demand functions,
h
i
¡
p
1
;
p
2
;
U
¢
for
i
=1
,
2
.D
e
r
i
v
eh
i
s
expenditure function
e
¡
p
1
;
p
2
;
U
¢
.
Problem 25
(Demand and duality, CobbDouglas utility function)
The utility function of a consumer is given by:
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 Fall '06
 MASSON
 Microeconomics

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