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Homework #2
due August 18 in class
University of California, Los Angeles
Each question is worth 5.25 points, for a total of 25 points.
1. Jessica spends all her income on books for school and cigarettes.
The
utility she derives from these goods is described by the function
U
(
b;c
) =
3 ln
b
+ ln
c
.
(a) Use the Lagrangian method to derive Jessica±s monthly demand func
tions for books and cigarettes.
If cigarettes cost $5 per pack and
books cost $50 each, while Jessica±s mother gives her $200 a month
for expenses, how many books and cigarettes will Jessica choose to
purchase?
Jessica±s Lagrangian is
L
= 3 ln
b
+ ln
c
+
(
M
p
b
b
p
c
c
)
which gives us ²rst order conditions
@L
@b
:
3
b
b
= 0
(1)
@L
@c
:
1
c
c
= 0
(2)
@L
:
M
p
b
b
p
c
c
= 0
(3)
We use
(1)
and
(2)
to ²nd the relationship
3
c
b
=
p
b
p
c
c
=
p
b
3
p
c
b
and plug this into
(3)
M
=
p
b
b
+
p
c
p
b
3
p
c
b
±
=
p
b
b
+
p
b
3
b
=
4
3
p
b
b
to ²nd the demand functions
b
(
p
b
;p
c
;M
)
=
3
M
4
p
b
c
(
p
b
;p
c
;M
)
=
M
4
p
c
1
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View Full Document This means that if cigarettes cost $5 per pack and books cost $50
each, while Jessica has $200 in income, Jessica will choose to purchase
b
(50
;
5
;
200)
=
3 (200)
4 (50)
=
3
c
(50
;
5
;
200)
=
200
4 (5)
=
10
cigarettes by half? How much should the government tax cigarettes?
5 packs of cigarettes
c
(50
;
5 +
t;
200)
=
200
4 (5 +
t
)
= 5
200
=
20 (5 +
t
)
t
=
5
The government needs to tax cigarettes by $5 per pack.
of cigarettes by half? By how much should her mother reduce her
income?
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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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