Perfect CompetitionPerfect Competition

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OutlineOutline• 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 CompetitionCompetition vs Perfect Competition

• Competition– Each firm takes price as given.

• As we saw => Price equals marginal cost

P f t titi• Perfect competition– Each firm takes price as given.P fit– Profits are zero

– 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 industriesCompetitive industries

• One way to think about this is market sharey• Any industry where the largest firm produces less than 1% of output is going to be competitive

• Agriculture?– For sure

• Services?• Services?– Restaurants?

• What about local consumers and local suppliers

• manufacturing– Most often not so.

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CompetitionCompetition

• Here only assume that each firm takes price asHere 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 shut downП(q )>0 produce,  if П(q )<0 shut down

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Competitive equilibriumCompetitive equilibrium

• Given n firms each with cost C(q) and D(p) itGiven n, firms each with cost C(q) and D(p) it is a pair (p*,q*) such that 

• 1 D(p *) =n q*• 1. D(p ) =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 existIf we fix the number of firms. This may not exist.

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Step 1 Max ПStep 1 Max Пp

Marginal Cost

Average CostsAverage Costs

Short Run Average Cost

Profits

Short Run Average CostOr

Average Variable Cost

Costsq

Costs

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Step 1 Max П,Step 1 Max П, p

Marginal Cost

Average CostsAverage Costs

Losses

Price

Short Run Average CostOr

Average Variable CostCosts Average Variable CostqCosts

Costs

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So entry exit mattersSo entry exit matters

• Individual firm decisionIndividual 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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Example• n firms, d d f d i bQ

p• demand for good is p=a‐bQ– Let C(q) = F+(0.5q2/c)MC if P MC S (P) P/ S(P) P /– MC=q so if P=MC => Si(P) =P/c => S(P)=Pn/c

• Market equilibriumb d /– P=a‐bQ and Q=Pn/c  

– a‐bQ=Qc/n => Q=a/(b+c/n) =>P=a/n(b+c/n), q=a/n(b+c/n)q=a/n(b+c/n)

• Firm rationalityП=pq C(q) => (a/n(b+c/n))2 F 0 5 (a/n(b+c/n)) 2П=pq‐C(q) => (a/n(b+c/n))2 –F‐0.5 (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

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12000

8000

10000 D N=1 N=2

N=3 N=5 N=10

6000

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0

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0 5000 10000 15000 200000 5000 10000 15000 20000

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ExampleSuppose П= 0.5(a/n(b+c/n))2–F<0

ll h hp

• Still what happens

• 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 gthe market and make a profit

• If n>n* there are too many firms and someIf n>n there are too many firms and some one will have to exit

• If n<n* there are too few firms It would pay• If n<n there are too few firms. It would pay for at least one firm to invest and enter. Because it would make profitsBecause it would make profits

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1200019500000

10000

14500000

6000

8000

9500000

dollars

Profits

Revenues

Costs

2000

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4500000

Price

Quantity

0

2000

‐5000001 3 5 7 9 11

Firms

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Competitive equilibrium in productionh dwith endogenous entry

• Given C(q) and D(p) it is a triplet (p*,n*,q*)Given C(q) and D(p) it is a triplet (p ,n ,q ) such that 

• 1. D(p *) =n* q*1. D(p )  n q• 2. MC(q*) =p *

• 3 П(p *(n*) q*(n*)>0• 3. П(p (n ),q (n )>0 • 4. П(p *(n*+1), q*(n*+1))<01 S d d l l 2 fi1. Says demand equals supply, 2. firm maximimize profits, 3. profits are non negative 4 cant squeeze any more firmsnegative, 4, cant squeeze any more firms

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Perfect competitionPerfect competition

• Perfect competitione 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 qwith endogenous entry neglecting the discrete number of firms

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Why perfectWhy 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 profits but they are not having anyp y g y

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Zero profitZero profitZero profit implies cost =revenueIf I divide both sides by q => price = average costIf I divide both sides by q => price = average costBut recall price=marginal costSo perfect competition =>p=AC=MCThat leads to efficiency because

MC=AC <=> Min AC

qCC

qCqCqCd )()(

)()()(0

qq

qCq

qqq

qq

dq)(

)()()()(

02

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Shut downShut down

• Firm shuts down when price < average costFirm shuts down when price < average cost

• Firm shuts down in short run when price < short run average cost = min average variableshort run average cost = min average variable cost

Fi i i l h i l• Firm exits in long run when price < long run average cost = min average total cost

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Firm CostsFirm Costsp

Marginal Cost

Average CostsLRATCAverage Costs

Price if

Short Run Average CostO

Price if Competition is perfect

OrAverage Variable Cost

q19

Firm Reaction to Price ChangesFirm Reaction to Price Changesp

MC

ATC

Short run supply

AVC

q

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Long‐run EquilibriumLong run Equilibriump SRS

LRATC=LRSP0

Q

D

Q0

Q

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• Under perfect competitionUnder perfect competition

• Supply curve is flat and dictated by the long run (total) average cost curverun (total) average cost curve.

• Changes in demand are completely d b h i i i ( hcompensated by changes in quantities (thus 

by entry or exit)

• Implication, any change in taxes or regulation is completely passed through to consumers

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Increase in DemandIncrease in Demand

P SRS0

P1SRS2

LRATC=LRSP0

D

Q

D0

D1

Q0 Q1 Q2

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Large Decrease in DemandLarge Decrease in Demand

P SRS0SRS1P SRS01

SRS2

LRS2

1

D0D1

SR adjustment

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Competitive producers Key pointsCompetitive producers Key points

• Competitive equilibriumCompetitive equilibrium

• Perfect competition

l f d i• Role of entry and exit

• Short run vs long run adjustment

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