Lecture Notes, January 7 & 12 , 2010
The Edgeworth Box
2 person, 2 good, pure exchange economy
Fixed positive quantities of
X and Y, and two households, 1 and 2.
Household 1 is endowed with
of good X and
of good Y, utility function
X
1
Y
1
U
1
(X
1
, Y
1
) .
Household 2 is endowed with
of good X and
of good Y, utility
X
2
Y
2
function U
2
(X
2
, Y
2
)
X
1
+ X
2
=
X
1
X
2
X
Y
1
+ Y
2
=
.
Y
1
Y
2
Y
Each point in the Edgeworth box represents an attainable choice of X
1
and X
2
, Y
1
and Y
2
.
1's origin is at the southwest corner; 1's consumption increases as the allocation
point moves in a northeast direction;
2's increases as the allocation point moves in
a southwest direction.
Superimpose indifference curves on the Edgeworth Box.
Competitive Equilibrium
(p
o
x
, p
o
y
) so that (X
o1
, Y
o1
) maximizes U
1
(X
1
, Y
1
)
subject to
(p
o
x
, p
o
y
)(X
1
, Y
1
) (p
o
x
, p
o
y
)
and
X
1
,
Y
1
(X
o2
, Y
o2
) maximizes U
2
(X
2
, Y
2
)
subject to
(p
o
x
, p
o
y
1
, Y
1
p
o
x
, p
o
y
)
, and
X
2
,
Y
2
(X
o1
, Y
o1
) + (X
o2
, Y
o2
) =
X
1
,
Y
1
X
2
,
Y
2
or
(X
o1
, Y
o1
) + (X
o2
, Y
o2
)
, where the inequality holds
X
1
,
Y
1
X
2
,
Y
2
co-ordinatewise and any good for which there is a strict inequality has a price of 0.
Pareto efficiency:
An allocation is Pareto efficient if all of the opportunities for mutually
desirable reallocation have been fully used.
The allocation is Pareto efficient if
there is no available reallocation that can improve the utility level of one household
while not reducing the utility of any household.
Tangency of 1 and 2's indifference curves :
Pareto efficient allocations.
Pareto efficient allocation:
Economics 113
Prof. R. Starr
Mr. Troy Kravitz, UCSD
Winter 2010
January 7 & 12, 2010
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