Homework Assignment # 6
Econ 121b. Intermediate Microeconomics
due March 30, 2011
Please put your
discussionsection time
on your answer.
1. Consider a pureexchange economy with two consumers,
A
and
B
, and two goods,
1
and
2
. For each
`
D
1
or 2 and
i
D
A
or
B
, write
x
i
`
for consumer
i
’s consumption of
good
`
. The utility functions are of CobbDouglas type:
u
A
.x
A
1
; x
A
2
/
D
.x
A
1
/
˛
.x
A
2
/
1
˛
and
u
B
.x
B
1
; x
B
2
/
D
q
x
B
1
x
B
2
;
where
1
2
< ˛ < 1
is a taste parameter. The endowments of consumers
A
and
B
are
!
A
D
.!
A
1
; !
A
2
/
and
!
B
D
.!
B
1
; !
B
2
/;
respectively. Finally, to ease the notation, write
N
!
1
D
!
A
1
C
!
B
1
and
N
!
2
D
!
A
2
C
!
B
2
:
(a) What is the set of
feasible allocations
in this economy?
(b) Draw the
Edgeworth box
for this economy. Label the axis appropriately, indicate
the size of each edge and locate the endowment point. Draw a couple of indiffer
ence curves for each consumer.
(c) What is a
Pareto efficient
allocation?
(d) Explain why, in general, a feasible allocation
.x
A
; x
B
/
is Pareto efficient if and
only if the marginal rate of substitution (MRS) of consumer
A
at
x
A
equals the
MRS of consumer
B
at
x
B
.
(e) Solve for the
contract curve
, i.e. the set of all Pareto efficient allocations. (Hint:
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 Spring '09
 SAMUELSON
 Economics, Microeconomics, Utility, #, competitive equilibrium

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