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Practice Problem from Lecture 3
A consumer has the following utility function:
U
=
x
1
4
y
3
4
1. Find the uncompensated demand functions for
x
and
y
.
ANSWER: The constrained utility maximization problem
L
=
x
1
4
y
3
4
+
(
M
p
x
x
p
y
y
)
@L
@x
:
1
4
x
3
4
y
3
4
x
= 0
@L
@y
:
3
4
x
1
4
y
1
4
y
= 0
@L
:
M
p
x
x
±
p
y
y
±
= 0
which in turn provide two conditions that must hold at the optimum:
(a) the MRS must equal the price ratio:
1
4
x
3
4
y
3
4
3
4
x
1
4
y
1
4
=
p
x
p
y
y
±
3
x
±
=
p
x
p
y
y
±
=
3
p
x
p
y
x
±
(b) the budget constraint must hold with equality:
M
=
p
x
x
±
+
p
y
y
±
functions:
M
=
p
x
x
±
+
p
y
3
p
x
p
y
x
±
±
=
4
p
x
x
±
x
(
p
x
;p
y
;M
)
=
M
4
p
x
y
(
p
x
;p
y
;M
)
=
3
p
x
p
y
M
4
p
x
±
=
3
M
4
p
y
1
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View Full Document 2. Find the indirect utility function.
ANSWER: The indirect utility function is found by plugging our uncom
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This note was uploaded on 09/23/2008 for the course ECON 11 taught by Professor Cunningham during the Summer '08 term at UCLA.
 Summer '08
 cunningham
 Utility

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