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Econ3131
Spring 2008
Talia Bar
Prelim 2 suggested solution
Part I  Questions 1 and 2.
Question 1
(20 minutes) (Consumer theory)
People on Gull island consume two goods
x
1
and
x
2
well behaved and homothetic*. These preferences are represented by a utility function
u
(
x
1
;x
2
)
(same utility for all consumers rich or poor). Initially, prices of the goods are
p
1
= 1
and
p
2
= 1
:
There are rich and poor people in the island. Rich islanders have an income
m
R
= 120
:
Poor
islanders (poor or low income) have income
m
L
= 100
:
Assume interior solutions throughout this
question.
(a) It is known that the optimal choice of rich islanders is
(
x
1
;x
2
)
R
= (60
;
60)
:
What is the
optimal choice of poor islanders?
(b) Provide one graph in the 2 goods space
x
1
x
2
showing the budget and the optimal choice
optimal point.
Recall that the income o/er curves of homothetic preferences are all straight lines
through the origin. When income is scaled up or down by any amount
t >
0
, the demanded
1
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View Full Documentbundle scales up or down by the same amount. In this question, since a poor consumer
has the same homothetic utility as a rich consumer and only a lower income, demand is
scaled down by the same proportion, hence
(
x
1
;x
2
)
L
= (50
;
50)
:
(c) A new king came to power. The king decides to promote equality for all islanders. He
imposes a tax of
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 Spring '06
 MASSON

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