Lecture Notes, March 28, 2011
General Equilibrium Theory
Marketclearing prices and allocation of several goods, taking into account
crossmarket interactions.
Existence of Equilibrium
(Pareto) Efficiency of Allocation
Decentralization of decisionmaking
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
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 Fall '08
 ZAMBRANO
 Economics, Microeconomics, Utility, Prof. R. Starr

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