Lecture Notes, March 28, 2011
General Equilibrium Theory
Market-clearing prices and allocation of several goods, taking into account
cross-market interactions.
Existence of Equilibrium
(Pareto) Efficiency of Allocation
Decentralization of decision-making
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