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Problem Set 2
Question 1.
a)
Budget constraint.
120
20
=
+
M
G
Where the budget line is given by:
G
M
20
120
−
=
b)
Substitution Method.
Get M from the budget constraint:
G
M
20
120
−
=
Plug it into the objective function:
2
/
1
2
/
1
)
20
120
(
max
G
G
G
−
F.O.C.
0
)
20
(
)
20
120
)(
2
/
1
(
)
20
120
(
)
2
/
1
(
2
/
1
2
/
1
2
/
1
2
/
1
=
−
−
+
−
−
−
G
G
G
G
)
20
(
)
20
120
(
G
G
=
−
120
40
=
G
3
*
=
G
and thus
60
*
=
M
c)
Marginal utility per dollar method
G
M
G
M
M
G
M
G
20
20
1
20
2
/
1
2
/
1
2
/
1
2
/
1
=
⇒
=
⇒
=
−
−
G
M
6
120
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View Full Document Substitute for M in the budget constraint:
3
*
120
20
20
=
⇒
=
+
G
G
G
and thus
60
*
=
M
d)
Lagrangian Method
)
20
120
(
)
;
,
(
2
/
1
2
/
1
M
G
M
G
M
G
L
−
−
+
=
λ
F.O.C.
0
20
2
1
)
;
,
(
2
/
1
2
/
1
=
−
=
∂
∂
−
M
G
G
M
G
L
0
2
1
)
;
,
(
2
/
1
2
/
1
=
−
=
∂
∂
−
M
G
M
M
G
L
0
20
120
)
;
,
(
=
−
−
=
∂
∂
M
G
M
G
L
From the first two equations:
G
M
G
M
M
G
M
G
20
20
1
20
2
/
1
2
/
1
2
/
1
2
/
1
=
⇒
=
⇒
=
−
−
Plug into the third equation:
3
*
120
20
20
=
⇒
=
+
G
G
G
and thus
60
*
=
M
Question 2.
a)
Budget constraint.
120
20
=
+
M
G
G
M
6
120
b)
Substitution Method.
Get M from the budget constraint:
G
M
20
120
−
=
Plug it into the objective function:
)
20
120
log(
2
log
max
G
G
G
−
+
F.O.C.
0
20
120
40
1
=
−
−
+
G
G
)
40
(
)
20
120
(
G
G
=
−
120
60
=
G
2
*
=
G
and thus
80
*
=
M
c)
Marginal utility per dollar method
G
M
G
M
M
G
40
20
2
1
20
2
1
=
⇒
=
⇒
=
Substitute for M in the budget constraint:
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This note was uploaded on 04/01/2010 for the course ECON 180052110 taught by Professor Mcdevitt during the Winter '09 term at UCLA.
 Winter '09
 McDevitt

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