Perfect Competition
Perfect Competition
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Outline
• Competition
– Short run
Short run
– Implications for firms
– Implication for supply curves
• Perfect competition
– Long run – Implications for firms
– Implication for supply curves
• Broader implications
Broader implications
– Implications for tax policy.
– Implication for R&D
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Competition vs Perfect Competition
Competition vs
Perfect Competition
• Competition
– Each firm takes price as given.
• As we saw => Price equals marginal cost
• Perfect competition
P f t
titi
– Each firm takes price as given.
– Profits are zero
P fit
– As we will see
• P=MC=Min(Average Cost)
P=MC=Min(Average Cost)
• Production efficiency is maximized • Supply is flat
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Competitive industries
Competitive industries
• One way to think about this is market share
y
• Any industry where the largest firm produces less than 1% of output is going to be competitive
• Agriculture?
– For sure
• Services?
– Restaurants?
• What about local consumers and local suppliers
• manufacturing
– Most often not so.
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Competition
• Here
Here only assume that each firm takes price as only assume that each firm takes price as
given.
– It want to maximize profits
It want to maximize profits
•
•
•
•
•
Two decisions. ( )
(1) if it produces how much
П(q) =pq‐C(q) => p‐C’(q)=0
(2) should it produce at all П(q*)>0 produce, if П(q
)>0 produce if П(q*)<0 shut down
)<0 shut down
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Competitive equilibrium
Competitive equilibrium
• Given
Given n, firms each with cost C(q) and D(p) it n firms each with cost C(q) and D(p) it
is a pair (p*,q*) such that • 1. D(p
1 D(p *) =n
) =n q*
• 2. MC(q*) =p *
• 3. П(p *,q*)>0 1. Says demand equals supply, 2. firm maximize y
q
pp y,
profits, 3. profits are non negative.
If we fix the number of firms This may not exist
If we fix the number of firms. This may not exist.
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Step 1 Max П
Step 1 Max П
p
Marginal Cost
Average Costs
Profits
Short Run Average Cost
Or
Average Variable Cost
Costs
q
7
Step 1 Max П,
Step 1 Max П, p
Marginal Cost
Average Costs
Losses
Price
Costs
Costs
Short Run Average Cost
Or
Average Variable Cost
q
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So entry exit matters
So entry exit matters
• Individual firm decision
Individual firm decision
– If P=MC(q*) => q*(P)
• Suppose there are n firms each with cost C(q)
Suppose there are n firms each with cost C(q)
– Each takes price as given sets q so that P=MC(q*)
– Total supply is nq*
• Is that consistent with demand?
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• n firms, • demand for good is p=a‐bQ
d
df
di
bQ
Example
p
– Let C(q) = F+(0.5q2/c)
– MC=q so if P=MC => S
MC
if P MC Si(P) =P/c => S(P)=Pn/c
(P) P/
S(P) P /
• Market equilibrium
– P=a‐bQ
b and Q=Pn/c d
/
– a‐bQ=Qc/n => Q=a/(b+c/n) =>P=a/n(b+c/n), q=a/n(b+c/n)
• Firm rationality
П=pq‐C(q) => (a/n(b+c/n))
П=pq
C(q) => (a/n(b+c/n))2 –F‐0.5
F 0 5 (a/n(b+c/n)) (a/n(b+c/n)) 2
П= 0.5(a/n(b+c/n))2–F.
• If F large enough not be an equlibirum
If F large enough not be an equlibirum
10
12000
10000
8000
D
N=1
N=2
N=3
N=5
N=10
6000
4000
2000
0
0
5000
10000
15000
20000
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Suppose П= 0.5(a/n(b+c/n))2–F<0
Example
p
• Still what happens
ll h h
• Can ask given F what is the largest n (n*) such that П= 0.5(a/n(b+c/n))2–F>0
• n* is the largest number of firms that can be in g
the market and make a profit
• If n>n
If n>n* there are too many firms and some there are too many firms and some
one will have to exit
• If n<n
If n<n* there are too few firms. It would pay there are too few firms It would pay
for at least one firm to invest and enter. Because it would make profits
Because it would make profits
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12000
19500000
10000
14500000
8000
dollars
Profits
Revenues
9500000
6000
Costs
Price
Quantity
4000
4500000
2000
‐500000
1
3
5
7
9
11
0
Firms
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Competitive equilibrium in production
with endogenous entry
h d
• Given
Given C(q) and D(p) it is a triplet (p
C(q) and D(p) it is a triplet (p*,n*,q*) )
such that • 1. D(p
1. D(p *) ) =n
n* q*
• 2. MC(q*) =p *
• 3. П(p
3 П(p *(n*),q
) q*(n*)>0 )>0
• 4. П(p *(n*+1), q*(n*+1))<0
1 S
1. Says demand equals supply, 2. firm d
d
l
l 2 fi
maximimize profits, 3. profits are non negative 4 cant squeeze any more firms
negative, 4, cant squeeze any more firms
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Perfect competition
Perfect competition
• Perfect competition
e ect co pet t o
– Each firm takes price as given.
– Profits are zero
– As we will see
• P=MC=Min(Average Cost)
• Production efficiency is maximized Production efficiency is maximized
• Supply is flat
• Perfect competition is a competitive equilibrium p
p
q
with endogenous entry neglecting the discrete number of firms
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Why perfect
Why perfect
• Competition is:
Competition is:
– Price taking behavior
• Competition is
Competition is
– More firms reduce profits
• But profits are non negative
– So optimality must imply they are zero. • Its perfect because producers are maximizing p
profits but they are not having any
y
g y
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Zero profit
Zero profit
Zero profit implies cost =revenue
If I divide both sides by q => price = average cost
But recall price=marginal cost
So perfect competition =>p=AC=MC
That leads to efficiency because
MC=AC <=> Min AC
d C (q) C (q) C (q)
C (q)
0


 C (q) 
2
dq q
q
q
q
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Shut down
Shut down
• Firm
Firm shuts down when price < average cost
shuts down when price < average cost
• Firm shuts down in short run when price < short run average cost = min average variable
short run average cost = min average variable cost
• Firm exits in long run when price < long run Fi
i i l
h
i
l
average cost = min average total cost
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Firm Costs
Firm Costs
p
Marginal Cost
Average CostsLRATC
Short Run Average Cost
O
Or
Average Variable Cost
Price if
Competition
is perfect
q
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Firm Reaction to Price Changes
Firm Reaction to Price Changes
p
Short run
supply
MC
ATC
AVC
q
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Long‐run
Long
run Equilibrium
Equilibrium
SRS
p
P0
LRATC=LRS
D
Q
Q0
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• Under
Under perfect competition
perfect competition
• Supply curve is flat and dictated by the long run (total) average cost curve
run (total) average cost curve.
• Changes in demand are completely compensated by changes in quantities (thus db h
i
ii (h
by entry or exit)
• Implication, any change in taxes or regulation is completely passed through to consumers
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Increase in Demand
Increase in Demand
SRS0
P
SRS2
P1
P0
LRATC=LRS
D1
D0
Q
Q0
Q1
Q2
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Large Decrease in Demand
Large Decrease in Demand
SRS1
P
SRS0
SRS2
2
LRS
1
SR
adjustment
D1
D0
Q
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Competitive producers Key points
Competitive producers Key points
•
•
•
•
Competitive equilibrium
Competitive
equilibrium
Perfect competition
Role of entry and exit
l f
d i
Short run vs long run adjustment
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