1
Microeconomic Theory
Cuneyt Orman
Econ 3101
Fall 2005
Notes on General Equilibrium Models
A Pure Exchange Economy
A pure exchange economy is an abstract economy where there is only one type of
economic agent, namely, consumers. Each consumer is endowed with some amount of
each good. We are interested in whether agents would find it desirable to trade these
goods among themselves; and if they do, then what would the outcome of this trade look
like. For the ease of exposition we will consider a two-consumer, two-good economy.
This is because many interesting phenomena can be described using only two consumers
and two goods. All of issues studied in such an environment generalize to an economy
with many consumers and many goods.
Now, consider such an economy. Suppose the initial endowments of consumers 1 and 2
are given by
)
4
,
3
(
)
,
(
1
1
1
=
=
y
x
ω
and
)
3
,
4
(
)
,
(
2
2
2
=
=
y
x
, respectively. That is
consumer 1 has 3 units of good
x
and 4 units of good
y
; and similarly for consumer 2. The
consumers have identical preferences, given by
3
/
2
3
/
1
)
,
(
y
x
y
x
U
=
.
A
feasible allocation
in this economy is an allocation
{ }
)
,
(
),
,
(
2
2
1
1
y
x
y
x
a
=
that satisfies
the
resource constraints
:
7
2
1
=
+
x
x
(Resource Constraint 1)
7
2
1
=
+
y
y
(Resource Constraint 2)
That is, for each of the goods, the total demand of two consumers must not exceed the
total supply of that good.
A
Pareto Optimal (or, Pareto Efficient) allocation
is a
feasible
allocation
{}
)
ˆ
,
ˆ
(
),
ˆ
,
ˆ
(
ˆ
2
2
1
1
y
x
y
x
a
=
such that
there exists no other feasible allocation
{}
)
,
(
),
,
(
2
2
1
1
y
x
y
x
a
=
such that
)
ˆ
,
ˆ
(
ˆ
ˆ
)
,
(
1
1
3
/
2
1
3
/
1
1
3
/
2
1
3
/
1
1
1
1
y
x
U
y
x
y
x
y
x
U
=
≥
=
,
and
)
ˆ
,
ˆ
(
ˆ
ˆ
)
,
(
2
2
3
/
2
2
3
/
1
2
3
/
2
2
3
/
1
2
2
2
y
x
U
y
x
y
x
y
x
U
=
≥
=
,
with at least one with strict inequality.
In English, this means something like: an allocation of the two goods to each of the
consumers is Pareto Optimal if it is not possible to find another allocation that makes
both consumers at least as well off as before and makes either consumer1 or consumer 2
strictly better off. If there is an allocation that makes one person better off without