Download Chapter Twenty-One

Chapter 22
Firm Supply
Firm Supply

How does a firm decide how much product to
supply? This depends upon the firm’s
technology
 market environment
 goals
 competitors’ behaviors

2
Market Environments
Are there many other firms, or just a few?
 Do other firms’ decisions affect our firm’s
payoffs?

3
Market Environments
Monopoly: Just one seller that determines the
quantity supplied and the market-clearing price.
 Oligopoly: A few firms, the decisions of each
influencing the payoffs of the others.
 Pure Competition: Many firms, all making the
same product. Each firm’s output level is small
relative to the total.

4
Market Environments

Dominant Firm: Many firms, but one much
larger than the rest. The large firm’s decisions
affect the payoffs of each small firm. Decisions
by any one small firm do not noticeably affect
the payoffs of any other firm.
5
Pure Competition

A firm in a perfectly competitive market knows
it has no influence over the market price for its
product. The firm is a market price-taker.
6
Pure Competition
If the firm sets its own price above the market
price then the quantity demanded from the
firm is zero.
 If the firm sets its own price below the market
price then the quantity demanded from the
firm is the entire market quantity-demanded.

7
Pure Competition

So what is the demand curve faced by the
individual firm?
8
Pure Competition
$/output unit
Market Supply
pe
Market Demand
Y
9
Pure
Competition
$/output unit
Market Supply
p’
pe
At a price of p’, zero is
demanded from the firm.
Market Demand
y
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Pure
Competition
$/output unit
Market Supply
p’
pe
p”
At a price of p’, zero is
demanded from the firm.
Market Demand
y
At a price of p” the firm faces the entire market
demand.
11
Pure Competition

So the demand curve faced by the individual
firm is ...
12
Pure
Competition
$/output unit
Market Supply
p’
pe
p”
At a price of p’, zero is
demanded from the firm.
Market Demand
y
At a price of p” the firm faces the entire market
demand.
13
Pure
Competition
$/output unit
p’
pe
p”
Market Demand
Y
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Smallness
What does it mean to say that an individual
firm is “small relative to the industry”?
 The individual firm’s technology causes it
always to supply only a small part of the total
quantity demanded at the market price.

15
The Firm’s Short-Run Supply
Decision
Each firm is a profit-maximizer and in a shortrun.
 Q: How does each firm choose its output level?
 A: By solving

max  s ( y )  py  cs ( y ).
y 0
16
The Firm’s Short-Run Supply
Decision
max  s ( y )  py  cs ( y ).
y 0
What can the solution ys* look like?
d s ( y )
(a) ys* > 0:
(i)
(y)
dy
 p  MCs ( y )  0
2
d  s ( y)
*
( ii )
 0 at y  y s .
dy 2
ys*
y
17
The Firm’s Short-Run Supply
Decision
max  s ( y )  py  cs ( y ).
y 0
What can the solution y* look like?
(b) ys* = 0:
d s ( y )
 p  MCs ( y )  0
(y)
dy
*
at y  y s  0.
y
ys* = 0
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The Firm’s Short-Run Supply
Decision
For the interior case of ys* > 0, the first-order
maximum profit condition is
That is,
d s ( y )
 p  MCs ( y )  0.
dy
*
p  MCs ( y s ).
So at a profit maximum with ys* > 0, the
market price p equals the marginal
cost of production at y = ys*.
19
The Firm’s Short-Run Supply
Decision
For the interior case of ys* > 0, the secondorder maximum profit condition is
d 2 s ( y )
dy 2
That is,
d
dMCs ( y )

 0.
p  MCs ( y )  
dy
dy
dMCs ( y*s )
 0.
dy
So at a profit maximum with ys* > 0, the
firm’s MC curve must be upward-sloping.
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The Firm’s Short-Run Supply
Decision
At y = ys*, p = MC and MC
$/output unit
slopes upwards. y = ys* is
profit-maximizing.
pe
MCs(y)
y’
ys*
y
At y = y’, p = MC and MC slopes downwards.
y = y’ is profit-minimizing.
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The Firm’s Short-Run Supply
Decision
At y = ys*, p = MC and MC
$/output unit
pe
y’
slopes upwards. y = ys* is
profit-maximizing.
So a profit-max.
supply level
can lie only on
MCs(y)
the upwardsloping part
ys*
y of the firm’s
MC curve.
22
The Firm’s Short-Run Supply
Decision

But not every point on the upward-sloping part
of the firm’s MC curve represents a profitmaximum.
23
The Firm’s Short-Run Supply
Decision
But not every point on the upward-sloping part
of the firm’s MC curve represents a profitmaximum.
 The firm’s profit function is
 s ( y )  py  cs ( y )  py  F  c v ( y ).
 If the firm chooses y = 0 then its profit is
 s ( y )  0  F  c v ( 0 )   F.

24
The Firm’s Short-Run Supply
Decision

So the firm will choose an output level y > 0
only if
 s ( y )  py  F  c v ( y )   F.

i.e., only if
py  c v ( y )  0
Equivalently, only if
cv ( y)
p
 AVCs ( y ).
y
25
The Firm’s SR Supply Decision
$/output unit
MCs(y)
ACs(y)
AVCs(y)
y
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The Firm’s SR Supply Decision
$/output unit
MCs(y)
ACs(y)
AVCs(y)
y
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The Firm’s SR Supply Decision
$/output unit
p  AVCs(y)
MCs(y)
ACs(y)
ys* > 0.
AVCs(y)
y
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The Firm’s SR Supply Decision
$/output unit
p  AVCs(y)
MCs(y)
ACs(y)
ys* > 0.
AVCs(y)
p  AVCs(y)
y
ys* = 0.
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The Firm’s SR Supply Decision
$/output unit
p  AVCs(y)
MCs(y)
ACs(y)
ys* > 0.
AVCs(y)
p  AVCs(y)
The firm’s short-run
supply curve
y
ys* = 0.
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The Firm’s SR Supply Decision
$/output unit
Shutdown
point
MCs(y)
ACs(y)
AVCs(y)
The firm’s short-run
supply curve
y
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The Firm’s Short-Run Supply
Decision
Shut-down is not the same as exit.
 Shutting-down means producing no output
(but the firm is still in the industry and suffers
its fixed cost).
 Exiting means leaving the industry, which the
firm can do only in the long-run.

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The Firm’s Long-Run Supply
Decision
The long-run is the circumstance in which the
firm can choose amongst all of its short-run
circumstances.
 How does the firm’s long-run supply decision
compare to its short-run supply decisions?

33
The Firm’s Long-Run Supply
Decision

A competitive firm’s long-run profit function is

The long-run cost c(y) of producing y units of
output consists only of variable costs since all
inputs are variable in the long-run.
( y )  py  c( y ).
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The Firm’s Long-Run Supply
Decision

The firm’s long-run supply level decision is to
max  ( y )  py  c( y ).
y 0

The 1st and 2nd-order maximization conditions
are, for y* > 0,
p  MC( y ) and
dMC( y )
 0.
dy
35
The Firm’s Long-Run Supply
Decision

Additionally, the firm’s economic profit level
must not be negative since then the firm would
exit the industry. So,
( y )  py  c( y )  0
c( y )
 p
 AC( y ).
y
36
The Firm’s LR Supply Decision
$/output unit
MC(y)
AC(y)
y
37
The Firm’s LR Supply Decision
$/output unit
MC(y)
p > AC(y)
AC(y)
y
38
The Firm’s LR Supply Decision
$/output unit
MC(y)
p > AC(y)
AC(y)
y
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The Firm’s LR Supply Decision
$/output unit
The firm’s long-run
supply curve
MC(y)
AC(y)
y
40
Constant RTS and LR Supply
If the long run technology exhibits constant
returns to scale, the long run MC curve
coincides with the long run AC curve, which is
a horizontal line.
 Therefore, the long run supply curve is a
horizontal line.

41
Constant RTS and LR Supply
$/output unit
LMC=long-run supply
Cmin
When p=Cmin, willing to supply any amount;
 When p<Cmin, supply zero;
 When p>Cmin, arbitrarily large amount.

42
The Firm’s Long-Run Supply
Decision

How is the firm’s long-run supply curve related
to all of its short-run supply curves?
43
LR & SR Supply Decisions
$/output unit
MCs(y)
ACs(y)
MC(y)
AC(y)
y
44
LR & SR Supply Decisions
$/output unit
ACs(y)
MC(y)
MCs(y)
AC(y)
p’
ys*
y*
y
ys* is profit-maximizing in this short-run.
45
LR & SR Supply Decisions
$/output unit
ACs(y)
MC(y)
MCs(y)
p’
AC(y)
s
ys*
y*
y
ys* is profit-maximizing in this short-run.
46
LR & SR Supply Decisions
$/output unit
ACs(y)
MC(y)
MCs(y)
p’
s
AC(y)

ys*
y*
y
The firm can increase profit by increasing x2
and producing y* output units.
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LR & SR Supply Decisions
$/output unit
ACs(y)
MC(y)
MCs(y)
AC(y)
p”
ys*
y
ys* is loss-minimizing in this short-run.
48
LR & SR Supply Decisions
$/output unit
ACs(y)
MC(y)
MCs(y)
AC(y)
p” Loss
ys*
y
ys* is loss-minimizing in this short-run.
49
LR & SR Supply Decisions
$/output unit
ACs(y)
MCs(y)
MC(y)
AC(y)
p” Loss
ys*
y
This loss can be eliminated in the long-run by
the firm exiting the industry.
50
LR & SR Supply Decisions
$/output unit
MC(y)
AC(y)
y
51
LR & SR Supply Decisions
$/output unit
MC(y)
AC(y)
p’
ys*
y
ys* is profit-maximizing in this short-run.
52
LR & SR Supply Decisions
$/output unit
MC(y)
p’
AC(y)
s
ys*
y
ys* is profit-maximizing in this short-run.
53
LR & SR Supply Decisions
$/output unit
MC(y)
AC(y)
p’
y* ys*
y
ys* is profit-maximizing in this short-run.
y* is profit-maximizing in the long-run.
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LR & SR Supply Decisions
$/output unit
MC(y)
p’
AC(y)

y* ys*
y
ys* is profit-maximizing in this short-run.
y* is profit-maximizing in the long-run.
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LR & SR Supply Decisions
$/output unit
MC(y)
p’

AC(y)
s
y* ys*
y
The firm can increase profit by reducing
x2 and producing y* units of output.
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LR & SR Supply Decisions
$/output unit
MC(y)
AC(y)
y
57
LR & SR Supply Decisions
$/output unit
MC(y)
AC(y)
y
58
LR & SR Supply Decisions
$/output unit
MC(y)
AC(y)
y
59
LR & SR Supply Decisions
$/output unit
Long-run supply curve
MC(y)
AC(y)
y
Short-run supply curves
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LR and SR Supply Decisions
When the price of output changes, the firm has
more choices to adjust in the long run than in
the short run.
 Therefore, the long run supply curve will be
more responsive to price – more elastic – than
the short run supply curve.

61
Producer’s Surplus Revisited
The firm’s producer’s surplus is the
accumulation of extra revenue less extra
production cost by producing extra unit of
output.
 How is producer’s surplus related to profit?

62
Producer’s Surplus Revisited
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
y*(p)
y
63
Producer’s Surplus Revisited
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
PS
y*(p)
y
64
Producer’s Surplus Revisited
So the firm’s producer’s surplus is
PS(p ) 
y*( p )
 p  MCs ( z)d( z)
0
 py * (p ) 
y*( p )
 MCs ( z)d( z)
0
 py * (p )  c v  y * (p ).
That is, PS = Revenue - Variable Cost.
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Producer’s Surplus Revisited
$/output unit
MCs(y)
p
c v ( y * (p )) 
ACs(y)
AVCs(y)
y*(p)
 MCs ( z)d( z)
y*( p )
0
y
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Producer’s Surplus Revisited
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
Revenue
= py*(p)
y*(p)
y
67
Producer’s Surplus Revisited
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
Revenue
= py*(p)
cv(y*(p))
y*(p)
y
68
Producer’s Surplus Revisited
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
PS
y*(p)
y
69
Producer’s Surplus Revisited
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
y*(p)
y
70
Producer’s Surplus Revisited
PS = Revenue - Variable Cost.
 Profit = Revenue - Total Cost
= Revenue - Fixed Cost
- Variable Cost.
 So, PS = Profit + Fixed Cost.
 Only if fixed cost is zero (the long-run) are PS
and profit the same.

71