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Firm Supply

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Firm Supply
uHow does a firm decide how much product to supply?  This depends upon the firm’s
– technology
– market environment
– goals
– competitors’ behaviors

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Market Environments
uAre there many other firms, or just a few?
uDo other firms’ decisions affect our firm’s payoffs?
uIs trading anonymous, in a market?  Or are trades arranged with separate buyers by middlemen?

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Market Environments
uMonopoly:  Just one seller that determines the quantity supplied and the market-clearing price.
uOligopoly:  A few firms, the decisions of each influencing the payoffs of the others.

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Market Environments
uDominant 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.

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Market Environments
uMonopolistic Competition:  Many firms each making a slightly different product.  Each firm’s
output level is small relative to the total.
uPure Competition:  Many firms, all making the same product.  Each firm’s output level is small
relative to the total.

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Market Environments
uLater chapters examine monopoly, oligopoly, and the dominant firm.
uThis chapter explores only pure competition.

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Pure Competition
uA 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.
uThe firm is free to vary its own price.

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Pure Competition
uIf the firm sets its own price above the market price then the quantity demanded from the firm is
zero.
uIf the firm sets its own price below the market price  then the quantity demanded from the firm is
the entire market quantity-demanded.

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Pure Competition
uSo what is the demand curve faced by the individual firm?

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Pure Competition
Y
$/output unit
Market Supply
Market Demand
pe

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Pure Competition
y
$/output unit
Market Supply
pe
p’
At a price of p’, zero is demanded from the firm.
Market Demand

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Pure Competition
y
$/output unit
Market Supply
pe
p’
p”
At a price of p” the firm faces the entire market demand.
At a price of p’, zero is demanded from the firm.
Market Demand

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Pure Competition
uSo the demand curve faced by the individual firm is ...

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Pure Competition
y
$/output unit
Market Supply
pe
p’
p”
At a price of p” the firm faces the entire market demand.
At a price of p’, zero is demanded from the firm.
Market Demand

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Pure Competition
Y
$/output unit
pe
p’
p”
Market Demand

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Smallness
uWhat does it mean to say that an individual firm is “small relative to the industry”?

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Smallness
$/output unit
y
Firm’s MC
The individual firm’s technology causes it
always to supply only a small part of the
total quantity demanded at the market price.
Firm’s demand
          curve
pe

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The Firm’s Short-Run Supply Decision
uEach firm is a profit-maximizer and in a short-run.
uQ: How does each firm choose its output level?

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The Firm’s Short-Run Supply Decision
uEach firm is a profit-maximizer and in a short-run.
uQ: How does each firm choose its output level?
uA: By solving

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The Firm’s Short-Run Supply Decision
What can the solution ys* look like?

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The Firm’s Short-Run Supply Decision
What can the solution ys* look like?
(a) ys* > 0:
P(y)
y
ys*

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The Firm’s Short-Run Supply Decision
What can the solution y* look like?
(b) ys* = 0:
P(y)
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,
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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The Firm’s Short-Run Supply Decision
For the interior case of ys* > 0, the second-
order maximum profit condition is
That is,
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
$/output unit
y
pe
ys*
y’
MCs(y)

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The Firm’s Short-Run Supply Decision
$/output unit
y
pe
ys*
y’
At y = ys*, p = MC and MC
slopes upwards.  y = ys* is
                 profit-maximizing.
MCs(y)

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The Firm’s Short-Run Supply Decision
$/output unit
y
pe
ys*
y’
At y = ys*, p = MC and MC
slopes upwards.  y = ys* is
                 profit-maximizing.
At y = y’, p = MC and MC slopes downwards.
y = y’ is profit-minimizing.
MCs(y)

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The Firm’s Short-Run Supply Decision
$/output unit
y
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
                       the upwards
                          sloping part
                          of the firm’s
                          MC curve.
MCs(y)
ys*

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The Firm’s Short-Run Supply Decision
uBut not every point on the upward-sloping part of the firm’s MC curve represents a profit-maximum.

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The Firm’s Short-Run Supply Decision
uBut not every point on the upward-sloping part of the firm’s MC curve represents a profit-maximum.
uThe firm’s profit function is
uIf the firm chooses y = 0 then its profit is

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The Firm’s Short-Run Supply Decision
uSo the firm will choose an output level y > 0 only if

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The Firm’s Short-Run Supply Decision
uSo the firm will choose an output level y > 0 only if
uI.e., only if
Equivalently, only if

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
$/output unit
y

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
$/output unit
y

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
$/output unit
y
p > AVCs(y)

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
p > AVCs(y)                ys* > 0.
$/output unit
y

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
p < AVCs(y)                ys* = 0.
$/output unit
y
p > AVCs(y)                ys* > 0.

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
p < AVCs(y)                ys* = 0.
The firm’s short-run
supply curve
$/output unit
y
p > AVCs(y)                ys* > 0.

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The Firm’s Short-Run Supply Decision
AVCs(y)
ACs(y)
MCs(y)
The firm’s short-run
supply curve
Shutdown
    point
$/output unit
y

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The Firm’s Short-Run Supply Decision
uShut-down is not the same as exit.
uShutting-down means producing no output (but the firm is still in the industry and suffers its
fixed cost).
uExiting 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
uThe long-run is the circumstance in which the firm can choose amongst all of its short-run
circumstances.
uHow does the firm’s long-run supply decision compare to its short-run supply decisions?

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The Firm’s Long-Run Supply Decision
uA competitive firm’s long-run profit function is
uThe 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 Decision
uThe firm’s long-run supply level decision is to
uThe 1st and 2nd-order maximization conditions are, for y* > 0,

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The Firm’s Long-Run Supply Decision
uAdditionally, the firm’s economic profit level must not be negative since then the firm would exit
the industry.  So,

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The Firm’s Long-Run Supply Decision
MC(y)
AC(y)
y
$/output unit

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The Firm’s Long-Run Supply Decision
MC(y)
AC(y)
y
$/output unit
p > AC(y)

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The Firm’s Long-Run Supply Decision
MC(y)
AC(y)
y
$/output unit
p > AC(y)

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The Firm’s Long-Run Supply Decision
MC(y)
AC(y)
y
$/output unit
The firm’s long-run
supply curve

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The Firm’s Long-Run Supply Decision
uHow is the firm’s long-run supply curve related to all of its short-run supply curves?

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)
p’
ys*
y*
ys* is profit-maximizing in this short-run.

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)
p’
ys*
y*
ys* is profit-maximizing in this short-run.
Ps

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)
p’
ys*
y*
The firm can increase profit by increasing
x2 and producing y* output units.
Ps
P

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)
p”
ys*
ys* is loss-minimizing in this short-run.

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)
p”
ys*
ys* is loss-minimizing in this short-run.
Loss

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
ACs(y)
MCs(y)
p”
ys*
This loss can be eliminated in the long run by the firm exiting the industry.
Loss

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
p’
ys*
ys* is profit-maximizing in this short-run.

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
p’
ys*
ys* is profit-maximizing in this short-run.
Ps

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
p’
ys*
ys* is profit-maximizing in this short-run.
y* is profit-maximizing in the long-run.
y*

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
p’
ys*
ys* is profit-maximizing in this short-run.
y* is profit-maximizing in the long-run.
y*
P

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
p’
ys*
y*
Ps
P
The firm can increase profit by reducing
x2 and producing y* units of output.

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit

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The Firm’s Long & Short-Run Supply Decisions
MC(y)
AC(y)
y
$/output unit
Short-run supply curves
Long-run supply curve

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Producer’s Surplus Revisited
uThe firm’s producer’s surplus is the accumulation, unit by extra unit of output, of extra revenue
less extra production cost.
uHow is producer’s surplus related profit?

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
y*(p)

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
PS
y*(p)

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Producer’s Surplus Revisited
So the firm’s producer’s surplus is
That is, PS = Revenue - Variable Cost.

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
PS
y*(p)

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
y*(p)

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
y*(p)
Revenue
= py*(p)

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
y*(p)
Revenue
= py*(p)
cv(y*(p))

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Producer’s Surplus Revisited
y
$/output unit
AVCs(y)
ACs(y)
MCs(y)
p
PS
y*(p)

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Producer’s Surplus Revisited
uPS = Revenue - Variable Cost.
uProfit = Revenue - Total Cost
          = Revenue - Fixed Cost
                             - Variable Cost.
uSo,    PS = Profit + Fixed Cost.
uOnly if fixed cost is zero (the long-run) are PS and profit the same.