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W3211 Spring 2009
Suggested Solution for Homework #3
.
V
(
x; y
) =
x
y
1
(1
)
1
, since
0
1
. Hence, the demand funtion for
x
and
y
of
U
(
x; y
)
and
V
(
x; y
)
are same. Since
V
(
x; y
)
is a CobbDouglas function,
x
=
p
x
and
y
=
(1
)
w
p
y
.
You can solve these through Lagrangian.
2.
U
(
w
) =
1
(
(1
)
1
)
±
(
p
x
)
±
(1
)
w
p
y
²
1
³
±
=
w
±
±
1
p
x
p
1
y
²
±
U
"(
w
) =
(
1)
w
±
2
±
1
p
x
p
1
y
²
±
<
0
since
1
<
0
. So, he is riskaverse.
Note that once we assume that both prices are equal to one, we have
U
(
w
) =
w
±
.
3. Let
z
be the probability that the widget is a success. EV(contract 1)
= 100
;
000 =
z
±
10
;
000
;
000 + (1
z
)
±
0 =
EV(contract 2) when
z
= 0
:
01
(a) EU(contract 1)
=
U
(100
;
000) = (100
;
000)
±
(b) EU(contract 2)
=
z
±
U
(10
;
000
;
000) + (1
z
)
±
U
(0) =
z
(10
;
000
;
000)
±
(c) Both contracts are indi/rent to him if EU(contract 1)
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.
 Spring '08
 Govel
 Utility

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