Firm Supply
Demand Curve Facing
Competitive Firm
Supply Decision of a
Competitive Firm
Producer’s Surplus
and Profits
Long-Run
The Demand Curve Facing a
Competitive Firm
p
market
price
p
*
0
y
Supply Decision of a
Competitive Firm
Problem of a competitive firm:
max py − c( y )
y
Revenues, Costs, and Profits
py
p
Π( y )
c( y )
y
Maximum Profits
py
p
c( y )
y
*
y
Optimal Quantity Supplied
Firm maximizes:
max py − c( y )
y
Necessary condition for optimal choice:
∂c( y )
p=
= MC ( y )
∂y
An Example
Short-run cost function:
c( y ) = y + 1
2
Marginal cost function:
MC ( y ) = 2 y
An Example
Average variable costs:
2
y
AVC ( y ) =
=y
y
Average costs:
2
y
1
1
AC ( y ) =
+ = y+
y y
y
An Example
Profit maximization:
max py − ( y + 1)
2
y
Necessary condition:
p = 2y
An Example
p
AC
MC
AVC
2
0
1
y
An Example: Profits
p
AC
p
MC
AVC
*
AC ( y * )
AVC ( y * )
0
y
*
y
Producer’s Surplus
Producer’s surplus=Area below price above
supply curve
Alternatively:
*
py −
below supply curve
where area below supply curve (MC):
*
cv ( y )
An Example: Producer’s Surplus
p
AC
p
MC
AVC
*
0
y
*
y
An Example: Producer’s Surplus
p
AC
p
MC
AVC
*
AVC ( y * )
0
y
*
y
Producer’s Surplus and Profits
Producer’s surplus:
*
*
py − cv ( y )
Profits:
*
*
py − cv ( y ) − F
An Example: Producer’s Surplus
and Profits
p
AC
p
MC
AVC
*
AC ( y * )
AVC ( y * )
0
y
*
y
An Example
Output:
*
p
y =
2
*
Profits:
*
(
Π = py − y
*2
(
p )
+ 1) =
* 2
4
−1
An Example
Profits:
(
p )
Π=
* 2
4
Producer’s surplus:
−1
1 *  p  (p )
p   =
2  2 
4
*
* 2
One Exception: y1 or y2 ?
MC
AC , MC , AVC
AC
AVC
p*
y1
y2
y
A Second Exception: Shutdown!
Profits if firm produces:
*
*
Π = py − cv ( y ) − F
Profits if firm does not produce:
Π = −F
Producing is better if:
*
*
py − cv ( y ) > 0
A Second Exception: Shutdown!
Producing is better if:
*
*
py − cv ( y ) > 0
Rearrange. Produce only if:
*
cv ( y )
p>
*
y
Shutdown
MC
AC , MC , AVC
AC
AVC
p
*
y
*
y
The Firm’s Supply Curve
AC , MC , AVC
MC
AC
AVC
0
y
Long and Short Run Supply in
Consultant Firm Example
MC S ( y )
MC ( y )
p***
p
0
MC L ( y )
91
yL
**
yS
**
y
Shutdown in the Short-Run and
in the Long-Run
In the short-run, the shutdown condition is:
*
cv ( y )
*
p<
= AVC ( y )
*
y
In the long-run, the shutdown condition is:
*
c( y )
*
p<
= AC ( y )
*
y