Chapter 12 The Partial Equilibrium Competitive Model
What is a partial equilibrium?
Focus on the market for
one good
only.
Not a complete economy!
The market/aggregate demand for good
X
is the sum of
all individual demands for good
X
.
Market demand function:
X
(
p
X
) =
∑
n
i
=
1
x
i
(
p
X
,
p
Y
,
m
i
)
,
where
x
i
(
p
X
,
p
Y
,
m
i
)
is individual
i
°s demand for good
X
.
X
(
p
X
)
obviously depends
p
X
(
endogenous variable).
X
(
p
X
)
also depends on other prices and incomes (
exogenous)
.
It is the
horizontal
sum of all individual demand curves.
Market demand curve shifts when any
exogenous variable
changes.
For simplicity, denote the market demand as
Q
D
(
p
) =
X
(
p
X
)
.
Q. Wen
(UW)
Econ 400
University of Washington
1 / 54

Chapter 12 The Partial Equilibrium Competitive Model
Elasticities are de±ned similarly
Price elasticity:
e
Q
,
p
=
∂
Q
D
(
p
)
∂
p
p
Q
D
(
p
)
.
In general, market demand cannot be written as a function of
aggregate income.
In short run, the market supply is the sum of
all individual ±rm°s supply functions.
Short-run market supply:
Q
S
(
p
) =
∑
m
i
=
1
q
i
(
p
,
v
,
w
)
.
In short-run, the number of ±rms,
m
, is ±xed, and use SR supply
functions.
Example 12.2
A Short-run Supply Function
there are 100
identical
±rms, each has supply function
q
i
(
p
) =
10
3
p
.
The market supply function is
Q
S
(
p
) =
100
°
10
3
p
=
1
,
000
3
p
.
Q. Wen
(UW)
Econ 400
University of Washington
2 / 54

Chapter 12 The Partial Equilibrium Competitive Model
Equilibrium price determination:
Q
D
(
p
±
) =
Q
S
(
p
±
)
.
In long run, each ±rm
mostly
follows its long-run supply function.
If the number of ±rms is ±xed exogenously,
then the analysis is the same as in short run (non-negative pro±t).
If ±rms are
free to enter/exist
the market.
then the number of ±rms is determined
endogenously
!
When market price is higher than a ±rm°s min average cost,
then a typical ±rm will have positive pro±t,
and more ±rm will enter the market.
the market price decreases,
entry stops when it is no longer pro±table.
Additional to price and quantity, the number of ±rms varies!
Q. Wen
(UW)
Econ 400
University of Washington
3 / 54

Chapter 12 The Partial Equilibrium Competitive Model
Q
p
Market demand (Blue), MC (Red), 6 ±rms
Q. Wen
(UW)
Econ 400
University of Washington
4 / 54

Chapter 12 The Partial Equilibrium Competitive Model
Example 12.4
In±nitely Elastic Long-run Supply (simpli±ed)
Market demand:
Q
D
(
p
) =
25
,
000
²
3
p
.
A representative ±rm°s cost function:
C
(
q
) =
40
q
2
+
8
,
000.
Average cost function:
AC
(
q
) =
40
q
+
8
,
000
q
.
Marginal cost function:
MC
(
q
) =
80
q
.
To ±nd min AC, set
MC
(
q
) =
AC
(
q
)
:
80
q
=
40
q
+
8
,
000
q
)
q
=
20.
So the min of AC is
AC
(
20
) =
1
,
600.
A ±rm°s supply function is
q
(
p
) =
°
p
80
when
p
³
1
,
600
,
0
when
p
´
1
,
600
.
Q. Wen
(UW)
Econ 400
University of Washington
5 / 54

Chapter 12 The Partial Equilibrium Competitive Model
Example 12.4
In±nitely Elastic Long-run Supply
When there are
n
±rms, the market supply function is
Q
S
(
p
) =
n
°
q
(
p
)
.

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- Fall '08
- Ellis,G
- Microeconomics, Game Theory, Supply And Demand, Wen