Shomu Banerjee
ECON 201
ANSWERS TO EXCHANGE WITH MORE THAN 2 PERSONS
An economy consists of two types of consumers,
males
and
females
. There are 4
males and 8 females
. There are two consumption goods,
x
1
and
x
2
, that can be
traded. There is no production. Each male is initially endowed with 4 units of
x
1
and 0 units of
x
2
; each female is endowed with 0 units of
x
1
and 12 units of
x
2
.
Each male has identical utility functions given by
u
(
x
1
,
x
2
) =
x
1
x
2
and his marginal
rate of substitution equals 
x
2
/
x
1
. Each female has identical utility functions given
by
u
(
x
1
,
x
2
) =
x
1
(
x
2
)
3
and her marginal rate of substitution equals 
x
2
/(3
x
1
). The
good
x
2
is the numéraire good (
p
2
= $1); for simplicity write
p
1
as just
p
.
Then males’ demand for good
x
1
is
x
1
=
m
M
/2
p
and for good
x
2
is
x
2
=
m
M
/2,
where
m
M
refers to the income of males. Similarly, for females, the demand for
good
x
1
is
x
1
=
m
F
/4
p
and for good
x
2
is
x
2
= 3
m
F
/4, where
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This note was uploaded on 10/26/2010 for the course ECONOMICS ECON 201 taught by Professor Dr.shomubanerjee during the Summer '07 term at Emory.
 Summer '07
 Dr.ShomuBanerjee
 Microeconomics

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