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Solutions Homework Assignment 2
4.1
a. Set up Lagrangian
£
(1.00
.10
.25 )
ts
t
s .
!
=
+
"
"
0.5
0.5
£
(
/ )
.10
£
( /
)
.25
s
t
t
t
s
s
"
=
#
"
"
=
#
"
£
1.00
.10
.25
0
t
s
"
=
#
#
=
"
Ratio of first two equations implies
2.5
2.5
t
t
s
s
=
=
Hence
1.00 = .10
t
+ .25
s
= .50
s
.
s
= 2
t
= 5
Utility =
10
b. New utility
10
or
ts
= 10
and
.25
5
.40
8
t
s
=
=
5
8
s
t
=
Substituting into indifference curve:
2
5
10
8
s
=
s
2
= 16
s
= 4
t
= 2.5
Cost of this bundle is 2.00, so Paul needs another dollar.
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View Full Document4.2
Use a simpler notation for this solution:
U
(
f
,
c
)
=
2/3
f
1/3
c
I
=
600
a.
£
=
f
c
+
!
(600
"
40
f
"
8
c
)
!
£
!
f
=
2 / 3(
c
/
f
)
"
40
#
!
£
!
c
=
1/ 3(
f
/
c
)
"
8
Hence,
5
2
, 2
5
c
c
f
f
=
=
Substitution into budget constraint yields
f
= 10,
c
= 25.
b. With the new constraint:
f
= 20,
c
= 25
Note: This person always spends 2/3 of income on
f
and 1/3 on
c
.
Consumption of California wine does not change when price of French wine
changes.
c. In part a,
2 3
1 3
2 3
1 3
(
,
)
10
25
13.5
U
f c
f
c
=
=
=
. In part b,
2 3
1 3
(
,
)
20
25
21.5
U
f c
=
=
. To achieve the part b utility with part a prices, this
person will need more income. Indirect utility is
21.5
=
(2 3)
2 3
(1 3)
Ip
f
!
p
c
!
=
(2 3)
I
(40)
!
(8)
!
1 3
. Solving this equation
for the required income gives
I
= 964. With such an income, this person
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This note was uploaded on 11/22/2010 for the course ECON 411 taught by Professor Ann during the Fall '10 term at University of Oregon.
 Fall '10
 ann
 Microeconomics

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