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Lyon
Econ 7140
April 3, 2008
Third Exam
1.
For the utility functions
( )
x
x
U
ln
=
and
( )
x
x
V
=
a.
Show they are CRRA utility functions. Explain.
b.
TFU, At any level of
x
,
U
exhibits more risk aversion than does
V
.
Remember that the explanation is the important part.
2.
The profit function is
( )
wx
x
pq
−
=
π
where
q
is a strictly concave production
function and
x
, a scalar, is the only input. The hireprice of
x
is a stochastic
variable with density function
( )
w
φ
and mean
w
. Individual A maximizes
expected profits and Individual B maximizes expected utility.
a.
Identify the FONC for Individual A. Show your work and explain
everything.
b.
Now work with Individual B where
( )
u
is strictly concave.
i.
Identify the FONC. Show your work and explain everything.
ii.
Show that the FONC can be written
()
()
( )
() ( )
( ) ()
∫
∫
−
′
=
′
−
′
b
a
b
a
dw
w
w
wx
x
pq
u
dw
w
x
q
p
wx
x
pq
φ
*
*
*
*
*
iii.
Subtract from both sides
()
()
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 Spring '10
 Kutler
 Microeconomics, Utility

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