Transcript Document

Firm Supply
厂商供给

How does a firm decide how much product to
supply? This depends upon the firm’s
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
technology
market environment
goals
competitors’ behaviors

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Are there many other firms, or just a few?
Do other firms’ decisions affect our firm’s payoffs?
Is trading anonymous, in a market? Or are trades
arranged with separate buyers by middlemen?
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Monopoly (垄断）: Just one seller that
determines the quantity supplied and the marketclearing price.
Oligopoly （寡头垄断）: A few firms, the
decisions of each influencing the payoffs of the
others.

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.


Monopolistic Competition （垄断竞争）: Many
firms each making a slightly different product.
Each firm’s output level is small relative to the
total.
Pure Competition (完全竞争): Many firms, all
making the same product. Each firm’s output level
is small relative to the total.
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Later chapters examine monopoly, oligopoly, and
the dominant firm.
This chapter explores only pure competition.
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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.
The firm is free to vary its own price.

If own price above the market price
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then the quantity demanded is zero.
If own price below the market price
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then the quantity demanded is the entire
market quantity-demanded.

So what is the demand curve faced by the
individual firm?
$/output unit
Market Supply
pe
Market Demand
Y
$/output unit
Market Supply
p’
pe
At a price of p’, zero is
demanded from the firm.
Market Demand
y
$/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.

So the demand curve faced by the individual firm
is ...
$/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.
$/output unit
p’
pe
p”
Market Demand
Y
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What does it mean to say that an individual firm is
“small relative to the industry”?
$/output unit
Firm’s MC
pe
Firm’s demand
curve
y
The individual firm’s technology causes it
always to supply only a small part of the
total quantity demanded at the market price.
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Each firm is a profit-maximizer in a short-run.
Q: How does each firm choose its output level?
A: By solving
max  s ( y )  py  cs ( y ).
y 0
max  s ( y )  py  cs ( y ).
y 0
What can the solution ys* look like?
d s ( y )
(a) ys* > 0:
(i)
(y)
dy
2
 p  MCs ( y )  0
d  s ( y)
*
( ii )
 0 at y  y s .
dy 2
ys*
y
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
For the interior case of ys* > 0, the firstorder maximum profit condition is
d s ( y )
 p  MC s ( y )  0.
dy
*
That is, 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*.
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p = MC is a necessary condition(必要条件) for
profit maximization, but
It is not a sufficient condition（充分条件）.
For the interior case of ys* > 0, the secondorder maximum profit condition is
2
d  s ( y) d
dMCs ( y )

p  MCs ( y )  
 0.

dy
dy
dy 2
dMCs ( y*s )
That is,
 0.
dy
So at a profit maximum with ys* > 0, the
firm’s MC curve must be upward-sloping.
$/output unit
At y = ys*, p = MC and MC
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.
$/output unit
pe
y’
At y = ys*, p = MC and MC
slopes upwards. y = ys* is
profit-maximizing.
So a profit-max.
supply level
can lie only on
MCs(y)
the upwards
sloping part
ys*
y of the firm’s
MC curve.

but……
not every point on the upward-sloping part of the
firm’s MC curve represents a profit-maximum.
The Firm’s Short-Run Shut-Down
Condition
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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.
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So the firm will choose an output level y > 0 only if
 s ( y )  py  F  c v ( y )   F.
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So the firm will choose an output level y > 0 only if
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I.e., only
 sif( y )  py  F  c v ( y )   F.
pyif c v ( y )  0
Equivalently, only
cv ( y)
p
 AVCs ( y ).
y
$/output unit
MCs(y)
ACs(y)
AVCs(y)
y
$/output unit
MCs(y)
ACs(y)
AVCs(y)
y
$/output unit
p  AVCs(y)
MCs(y)
ACs(y)
AVCs(y)
y
$/output unit
p  AVCs(y)
ys* > 0.
MCs(y)
ACs(y)
AVCs(y)
y
$/output unit
p  AVCs(y)
ys* > 0.
MCs(y)
ACs(y)
AVCs(y)
p  AVCs(y)
y
ys* = 0.
$/output unit
p  AVCs(y)
ys* > 0.
MCs(y)
ACs(y)
AVCs(y)
p  AVCs(y)
The firm’s short-run
supply curve
y
ys* = 0.
$/output unit
Shutdown
MC
(y)
s
point
ACs(y)
AVCs(y)
The firm’s short-run
supply curve
y
Shut-down (关门) is not the same as exit （退出）.
 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 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?
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A competitive firm’s long-run profit function is
( y )  py  c( y ).
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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.
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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
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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
$/output unit
MC(y)
AC(y)
y
$/output unit
MC(y)
p > AC(y)
AC(y)
y
$/output unit
MC(y)
p > AC(y)
AC(y)
y
$/output unit
The firm’s long-run
supply curve
MC(y)
AC(y)
y
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Firm‘s long-run supply curve is the portion of
the long-run marginal cost curve that lies
above the average cost curve.
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In this case, the firm’s long-run supply curve is a
horizontal line.
Why?
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Average Total Production Costs
(平均总生产成本)
c( w 1 , w 2 , y )
AC( w 1 , w 2 , y ) 
.
y
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If a firm’s technology exhibits constant returns-toscale then doubling its output level from y’ to 2y’
requires doubling all input levels.
Total production cost doubles.
Average production cost does not change.
$/output unit
AC(y)
decreasing r.t.s.
constant r.t.s.
increasing r.t.s.
y
$/output unit
LMC=long-run supply
Cmin
When p=Cmin
When p<Cmin
When p>Cmin
Y
Willing to supply any amount Y
Y=0
Arbitrarily large amount

How is the firm’s long-run supply curve related to
all of its short-run supply curves?
$/output unit
ACs(y)
MCs(y)
MC(y)
AC(y)
y
$/output unit
ACs(y)
MC(y)
MCs(y)
AC(y)
p’
ys*
y*
y
ys* is profit-maximizing in this short-run.
$/output unit
ACs(y)
MC(y)
MCs(y)
p’
AC(y)
s
ys*
y*
y
ys* is profit-maximizing in this short-run.
$/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.
$/output unit
ACs(y)
MCs(y)
MC(y)
AC(y)
p”
ys*
y
ys* is loss-minimizing (减损) in this short-run.
$/output unit
ACs(y)
MCs(y)
MC(y)
AC(y)
p” Loss
ys*
y
ys* is loss-minimizing (减损) in this short-run.
Loss <-F
$/output unit
ACs(y)
MCs(y)
MC(y)
AC(y)
p” Loss
ys*
y
This loss can be eliminated in the longrun by the firm exiting the industry.
$/output unit
MC(y)
AC(y)
y
$/output unit
MC(y)
p’
AC(y)
ys*
y
ys* is profit-maximizing in this short-run.
$/output unit
MC(y)
p’
AC(y)
s
ys*
y
ys* is profit-maximizing in this short-run.
$/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.
$/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.
$/output unit
MC(y)
p’

AC(y)
s
y* ys*
y
The firm can increase profit by producing
y* units of output.
$/output unit
MC(y)
AC(y)
y
$/output unit
MC(y)
AC(y)
y
$/output unit
MC(y)
AC(y)
y
$/output unit
Long-run supply curve
MC(y)
AC(y)
y
Short-run supply curves
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The long-run supply curve is more elastic (and is
more sensitive to price) than the short-run supply
curve.
Because the firm has more leeway in adjusting
supply in the long-run than in the short run.
The firm’s producer’s surplus (生产者剩余) is the
accumulation of
extra revenue - extra production cost.
by producing extra unit of output
 How is producer’s surplus related to profit?

$/output unit
MCs(y)
ACs(y)
AVCs(y)
y
$/output unit
MCs(y)
ACs(y)
AVCs(y)
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
y*(p)
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
PS
y*(p)
y
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.
$/output unit
MCs(y)
p
c v ( y * (p )) 
ACs(y)
AVCs(y)
y*(p)
 MCs ( z)d( z)
y*( p )
0
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
Revenue
= py*(p)
y*(p)
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
Revenue
= py*(p)
cv(y*(p))
y*(p)
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
PS
y*(p)
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
y*(p)
y
$/output unit
MCs(y)
p
ACs(y)
AVCs(y)
Y‘
y*(p)
y

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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.
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Market environments
Market demand for a competitive firm
Short-run supply decision
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Upward sloping MC curve
Shut-down condition
Long-run supply decision
Comparing long-run and short-run decisions.
Producer’s surplus and profits