Production by a Competitive Firm
• Remember:
– A competitive firm takes all prices as given
– A production function F(x1, …, xn) …
– And Input Prices, (p1, …, pn) …
Supply
• Can summarized in
– Long-run cost function cL(y)
– Long-run cost function cs(y)
ECON 370: Microeconomic Theory
Summer 2004 – Rice University
• Then the firm produces at the point where
Stanley Gilbert
– py = c´(y) = MC(y)
Econ 370 - Supply
Mathematically
2
Supply Decision
• Second-Order Condition:
∂
MC ( y ) ≥ 0
∂y
• In particular, a firm seeks to maximize profit:
• First-Order Condition is:
∂Π ∂
∂
=
p y y − cs ( y ) = p y − cs′ ( y ) = 0
∂y ∂y
∂y
⇒ p y = MC s ( y )
• Second-Order Condition is:
∂ 2Π
≤0
∂y 2
or
Econ 370 - Supply
⇒
$/output unit
• Π = pyy – cs(y)
MC(y)
• Implies:
ATC(y) • Downward-sloping part
of marginal cost curve is
not part of supply curve
∂
∂
[
p y − c′s ( y )] = − MC s ( y ) ≤ 0
∂y
∂y
AVC(y)
∂
MC s ( y ) ≥ 0
∂y
Not Optimal
3
Econ 370 - Supply
y
4
1
An Exception
Short Run Shut-Down
• In some cases, the profit-maximizing production
level is zero
• Shut-down decision:
• MCs(y) < AVCs(y)
$/output unit
• That is, the firm is better off shutting down
• In those cases, p ≠ MCs
• Short Run
– This applies when py < AVC(y)
MCs(y)
ATCs(y)
• Long Run
AVCs(y)
– This applies when py < ATC(y)
y
Not Optimal
Econ 370 - Supply
• Implies no
production
5
Econ 370 - Supply
Short Run Firm Supply Curve
6
Short Run Firm Supply Curve
• The Supply curve is a function representing how
much a firm will supply for any given price
$/output unit
• That is, it is a function q = Ss(p)
• And, it is equal to the marginal cost curve above
the shutdown level
Short-Run
Supply Curve,
MCs(y)
ATCs(y)
AVCs(y)
y
Econ 370 - Supply
7
Econ 370 - Supply
8
2
Long Run Shut-Down
Long Run Firm Supply Curve
• Shut-down decision:
Long-Run
Supply Curve,
MCL(y)
• MCL(y) < ATCL(y)
Not Optimal
$/output unit
$/output unit
Supply Curve
• Implies no
MCs(y)
production
ATCL(y)
ATCL(y)
y
Econ 370 - Supply
y
9
Short Run v. Long Run
Econ 370 - Supply
10
LR and SR Supply Decisions: Graph
• The Short-Run and Long-Run supply curves in
general will not be equal
$/output unit
• Long Run Supply curve is more elastic
ATCs(y)
MCL(y)
• When short-run prices = long-run prices
– Then short-run supply = long-run supply
MCs(y)
p’
Πs
ΠL
ys*
Econ 370 - Supply
ATC(y)
y*
y
11
3
LR and SR Supply Decisions: Graph
$/output unit
ATCs(y)
LR and SR Supply Decisions: Graph
$/output unit
MCL(y)
ATCs(y)
MCL(y)
MCs(y)
MCs(y)
p’’
ATC(y)
Πs
p’
Loss
ΠL
ys*
y* ys*
y
Supply Curves
P
ATC(y)
y
Market Supply – No Entry
• We assume that in the short run, there is no entry
into the market
Short Run
Long Run
• When there is no entry into the market,
• The market supply curve is the sum of the supply
curves for individual firms
• That is
– If Si(p) is the supply curve for firm i
– The market supply curve SM(p) is:
– SM(p) = ΣSi(p)
Q
Econ 370 - Supply
15
Econ 370 - Supply
16
4
Long Run Market Supply
“Zero Profit” Condition
• In the long run, market entry is possible
• Economic Profit = Revenue – Economic Cost
• If I can earn $50,000 per year teaching economics,
• So Economic Profit represents the excess return to
a factor over its market return
• But I can earn $100,000 per year by starting a
consulting firm,
• If capital earns twice the market rate in the
computer industry,
• What am I likely to do?
– Then we expect a lot of people to invest in the
computer industry
– Thus (eventually) competing away the economic profits
– So in the long run, we expect economic profits to be
zero
• Note: Economic Profit ≠ Accounting Profit
Econ 370 - Supply
17
Econ 370 - Supply
“Zero Profit” Continued
18
Firm Demand
• If capital earns half the market rate in the
typewriter industry,
• The demand an individual firm faces is…
• The Market Demand Curve…
– Then we expect investors to disinvest from the industry
– And the industry to shrink
– Thus (eventually) restoring zero economic profits
• Minus the supply curves of all other firms in the
market
• So Economic profits (or losses) serve as a signal
that more (or less) investment is needed in an
industry
Econ 370 - Supply
19
Econ 370 - Supply
20
5
The Second Firm
Market
The Third Firm
Entering Firm
P
Market
P
Entering Firm
P
Q
P
Q
Econ 370 - Supply
21
Q
Econ 370 - Supply
“Small” Markets
Q
22
Long Run Market Supply
• “Small” Markets
P
–
–
–
–
Can be served by only a few firms
Profits for incumbent firms may be > 0
But, profits for any potential entrant will be < 0
Example: Large commercial jets
• For “Large” Markets
–
–
–
–
Q
Econ 370 - Supply
23
Econ 370 - Supply
No firm has more than a small piece of the market
Economic Profits for all firms are zero
Price is p ≈ min{ATC}
Example: the world market for wheat
24
6
Limiting Case – “Large” Markets
“Large” Markets: Individual Firm
P
P
Q
Econ 370 - Supply
Q
25
Econ 370 - Supply
26
7