Bluebook – 21 out of 50 pts. (2 qns., 10 pts. each + 1)
Answer these questions in your bluebook. Show your work and intermediate steps for partial credit. Points
are split equally across parts. Your score will
only
be based on the marks in your bluebook. You will not
receive any credit for anything written on your exam paper. You will receive 1 extra point for correctly writing
your name, perm number, version (A,B,C, or D), and TA’s name on your bluebook.
1. Consider an exchange economy consisting of two people,
A
and
B
, endowed with two goods, 1 and 2.
Person
A
is initially endowed with
ω
A
= (4
,
8) and person
B
is initially endowed with
ω
B
= (4
,
0).
Their preferences are given by
U
A
(
x
1
, x
2
) =
x
1
x
2
and
U
B
(
x
1
, x
2
) =
x
2
1
x
2
2
.
(a) Write the equation of the contract curve (express
x
A
2
as a function of
x
A
1
).
Answer
:
x
A
2
=
x
A
1
(b) Let
p
2
= 1.
Find the competitive equilibrium price,
p
1
, and allocations,
x
A
= (
x
A
1
, x
A
2
) and
x
B
= (
x
B
1
, x
B
2
).
Answer
:
p
1
= 1,
x
A
= (6
,
6), and
x
B
= (2
,
2)
(c) Now suppose that person
B
’s preferences are instead given by
U
B
(
x
1
, x
2
) = min
{
x
1
, x
2
}
. Given
a price of
p
1
=
1
3
(and assuming
p
2
= 1), what Paretooptimal allocation will result from trade
between the two people?
Answer
:
x
A
= (7
,
7) and
x
B
= (1
,
1).
(d) Briefly explain why this price and allocation combination are not a competitive equilibrium.
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 Spring '08
 KILENTHONG
 Fisherman, total dollar value

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