4 - Oligopoly (slides) - stennek.sestennek.se/onewebmedia/4 - Oligopoly (slides).pdf · 4 Oligopoly...

1

Oligopoly

Johan Stennek

2

Oligopoly

•  Example:Zocord– Reducescholesterol– ProducedbyMerck&Co

– PatentexpiredinApril2003(inSweden)– Othercompaniesstartedtosellperfectcopies

(=containingexactlythesameacIveingredientSimvastaIn)

Examples

3

PriceofZocordinSweden

Nominalpriceperdailydose(SEK)

4

Oligopoly

•  QuesIon– HowdoescompeIIonwork?– Howstrongisit?– Howdoesthatdependonthemarket?

•  Comparemonopolyandduopoly– Givenmarket(technology,demand)– Q:Howdoespricedependon#firms?

Aduopolymodel(Bertrand)

6

Duopoly

•  Timing

1.  Firmssetpricessimultaneously

2.  Consumersdecidehowmuchtobuyandfromwhom

NB:FirmshavenoImetoreact!

7

Duopoly

•  Technology–  Constantmarginalcost–  Firmshavesamemarginalcost

•  Demand– Marketdemand:Linear(example)–  Firms’goodshomogenous

8

Duopoly

•  Consumerbehavior

–  Allbuyfromcheapestfirm

–  Ifsameprice:50-50split

9

DuopolyResidualdemand

Marketdemand:D(p)

10


Competitors price

Marketdemand:D(p)

11


Competitors price

Marketdemand:D(p)

●

Residualdemand:Di(p1,p2)

12

Duopoly

Profits

π i p1, p2( ) = pi − c( )Di p1, p2( )

where

D1 p1, p2( ) =

D p1( ) p1 < p212D p1( ) if p1 = p2

0 p1 > p2

#

$

%%

&

%%

13

DuopolyGameTheory

•  Inter-dependentdecisions–  Firm1’sopImalpricedependsonfirm2’sprice

–  Firm2’sopImalpricedependsonfirm1’sprice

•  Howtoanalyze–  Cannotsimplyassumeprofitmaximizingbehavior

–  Gametheory

14

DuopolyGameTheory

•  Gameinnormalform–  Q:Elementsofagameinnormalform?

•  Players,Strategies,Payoffs–  Players

•  Firm1andFirm2

–  Strategies•  Eachfirmchoosesapricepi(arealnumber)•  Recall:Strategyprofile=Apriceforeachplayer(p1,p2)

–  Payoffs•  Profits•  Recall:PayofffuncIonassignsapayoffforeverypossiblestrategyprofile,πi(p1,p2)

15

DuopolyGameTheory

•  Nashequilibrium– “Acommonunderstandingamongallplayersofhowtheyareallgoingtobehave”

– Astrategyprofilesuchthatnoplayercanincreaseitspayoffgiventhatallotherplayersfollowtheirstrategies

16

DuopolyGameTheory

•  Nashequilibriuminduopolygame

–  Apairofprices(p1,p2)suchthat

•  π1(p1,p2)≥π1(p’1,p2)forallp’1

•  π2(p1,p2)≥π2(p1,p’2)forallp’2

17

DuopolyIntuiIveAnalysis

qm

pm

qm/2

•  Q: Will the two firms charge pm?

–  Eachwouldsellqm/2

–  Eachwouldearnπm/2

•  What if a firm undercuts to pm – ε?

–  Itwouldsell≈qm

–  Itwouldearn≈πm

•  Conclusion

–  Small reduction in price è Massiveexpansionofsales

–  pm not reasonable prediction

18

qm

pm

qm/2


19

Q:Whatifbothchargep=c?- qi=q*/2- πi=0

p=c

q*q*/2


20

Nounilateralchangeprofitable?-Higherprice→q=0,π=0- Lowerprice→q>0,p<c,π<0

p=c

q*q*/2


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•  Ifbothfirmschargep=c

– NoincenIvetochangebehavior

– ReasonablepredicIon

– Nashequilibrium


22

•  Twoformalproofs

– Foreverypossibleoutcome,invesIgateifsomeonehasincenIvetodeviate

– Bestreplyanalysis

Duopoly

23

Duopoly

Candidate Profitable deviation

p1 > p2 > c who? what?

24

Duopoly


p1 > p2 > c Firm i pi = pj – ε (max pm)

25

Duopoly



p1 = p2 > c who? what?

26

Duopoly



p1 = p2 > c Firm i pi = pj – ε (max pm)

27

Duopoly




p1 > p2 = c who? what?

28

Duopoly




p1 > p2 = c Firm 2 p2 = p1 – ε (max pm)

29

Duopoly





p1 = p2 = c who? what?

30

Duopoly





p1 = p2 = c - -

31

DuopolyBest-replyanalysis

32


p2

p1

p2=p1

c

c

pm

pm

Setofallstrategyprofiles

33


p2

p1

p2=p1

c

c

pm

pm

Q:Whatdowemeanby“firm2’sbestreplyfuncIon”?A:Profitmaximizingp2foreverypossiblep1

34


p2

p1

p2=p1

c

c

pm

pm

Q:Whatdowemeanby“firm2’sbestreplyfuncIon”?A:Profitmaximizingp2foreverypossiblep1

35


p2

p1

p2=p1

c

c

pm

pm

Whatifp1>pm

36


p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

37


p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

Whatifc<p1≤pm

38


p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

39


p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

Whatifp1=c

40


p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

41


p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

Whatifp1<c

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p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

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p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

SelecIon

44

Duopoly

p2

p1

p2=p1

c

c

pm

pm

Firm1’sbestreply

45

Duopoly

p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

Firm1’sbestreply

NashequilibriumA(p1,p2)thatliesonbothbestreplyfuncIons

WhatispricecompeIIon?Comparemonopolyandduopoly

47

WhatispricecompeIIon?

•  PredicIon– MorefirmsèLowerprices

•  IsthispredicIontrue?

48


•  ExtremepredicIon(“Bertrandparadox”)–  2firms=>p=c&π=0

•  Q:ReasonforextremepredicIon?–  Reducepriceonecent,getallcustomers

–  AlwaysprofitabletoreducepricebelowcompeItor,aslongasp>c.

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•  Moreooen

– Morefirms:p>c&π>0

–  Reason:Don’tgetallcustomers

–  Examples: ProductdifferenIaIon


•  EsImatedLernerindexes(mark-ups)inautomobiles

•  Conclusion

•  CompeIIondoesnoteliminateallmarkups•  Also

•  3rddegreepricediscriminaIonalsowithcompeIIon•  Highmarkupsinhomecountries

50

Model Belgium France Germany Italy UK

FiatUno 7.6 8.7 9.8 21.7 8.7

FordEscort 8.5 9.5 8.9 8.9 11.5

Peugeot 9.9 13.4 10.2 9.9 11.6

Mercedes 14.3 14.4 17.2 15.6 12.3

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•  TheoreIcallyrobust– ManyothermodelsofoligopolygivesamequalitaIvepredicIon

•  Empirically“confirmed”– ManyempiricalstudiessuggestthatcompeIIonleadstolowerprices

52

DoesCompeIIonMawer?

Consumersurplus

p=c

q*

DWL

qm

pm

Profit

Consumersurplus

Duopoly Monopoly

53

Sourcesofmarketpower1.  Fewfirms&Entrybarriers2.  ProductdifferenIaIon:horizontal&verIcal

3.  QuanItycompeIIon/Capacityconstraints

4.  Costadvantage5.  Uninformedcustomers

6.  Customerswitchingcosts

7.  PricediscriminaIon:informaIon&arbitrage

8.  CartelizaIon

EconomicMethodology•  Economicmodel=Animaginaryeconomy

–  Includekeyfeaturesforissuesathand–  RemoveallcomplicaIons(egcompeIIon)–  AddfeaturessequenIally(egcompeIIon)

•  Pros–  Easytoseeprinciples–  Candoexperiments(egWhatistheeffectofcompeIIon)

•  Cons–  Notthefullpicture–  AreconclusionstrueorarIfacts?

54

CournotModel(AlternaIvetoBertrand)

56

QuanItyCompeIIon

•  Bertrandmodel– Firmssetprices– ConsumersdecidequanIIes(firmsmustdeliver)

•  Cournotmodel– FirmschosequanIIes– Thenpriceissettoclearthemarket

•  Note1:Differencemawers(contrasttomonopoly)

•  Note2:TwodifferentinterpretaIons

57

QuanItyCompeIIon•  FirstinterpretaIon

–  Stage1:Firmsproduce:q1,q2–  Stage2:FirmsbringproducetoaucIon:p=P(q1+q2)

•  Example–  Fishingvillage

•  Note–  Pricingdecisionisdelegated–  Butequilibriumpriceaffectedbyamountproduced–  Weomittheissuewhyp=P(q1+q2)

58

QuanItyCompeIIon

•  SecondinterpretaIon:Two-stagegame–  Stage1:FirmschosecapaciIes:k1,k2

–  Stage2:Firmssetprices:p1,p2

•  Note:– UndersomecondiIonsp1=p2=P(k1+k2)

– Thenstudychoiceofcapacity(=quanIty)

59

DuopolyGameTheory

•  Gameinnormalform–  Q:Elementsofagameinnormalform?

•  Players,Strategies,Payoffs–  Players

•  Firm1andFirm2

–  Strategies•  EachfirmchoosesaquanItyqi(arealnumber)•  Recall:Strategyprofile=AquanItyforeachplayer(q1,q2)

–  Payoffs•  Profits:πi(q1,q2)=P(q1+q2)・qi–C(qi)

•  Recall:PayofffuncIonassignsapayoffforeverypossiblestrategyprofile,πi(p1,p2)

60

ExogenouscondiIons

•  Simplify1:Technology– Constantmarginalcost– Firmshavesamemarginalcost

•  Simplify2:Demand– Firms’goodshomogenous– Marketdemand:Linear

61

CournotDuopoly

•  Technology–  Constantmarginalcosts,c

•  Demand(linear)–  Individualdemand: q=a–p–  Numberofconsumers: m– Marketdemand: Q=m*(a–p)

62

CournotDuopoly

•  Exercise:–  Solvethemodel

•  Steps:1. SetupprofitfuncIons2. Findbest-replyfuncIons3. FindequilibriumquanIIes4. Findequilibriumprice

63

Definethegame

Profitπ1 q1,q2( ) = P q1 + q2( ) ⋅q1 −C q1( )

Rewrite

π1 q1,q2( ) = a − 1m ⋅ q1 + q2( )− c( ) ⋅q1

DemandQ p( ) = m ⋅ a − p( )

Indirect demandp = a − 1

m ⋅ q1 + q2( )

64

Derivebest-replyfuncIonsProfitπ1 q1,q2( ) = P q1 + q2( ) ⋅q1 −C q1( )

Rewrite

π1 q1,q2( ) = a − 1m ⋅ q1 + q2( )− c( ) ⋅q1

FOC∂π1 q1,q2( )

∂q1

= a − 1m ⋅ q1 + q2( )− c( )− 1

m ⋅q1 = 0

Solve for best reply function

q1 =m ⋅ a − c( )

2− 1

2⋅q2

65

Derivebest-replyfuncIonsq1

q2

a − c( ) ⋅m2

Firm 1's best-reply function

q1 =a − c( ) ⋅m

2− 1

2⋅q2

66

Derivebest-replyfuncIonsq1

q2

a − c( ) ⋅m2


q1 =a − c( ) ⋅m

2− 1

2q2


q2 =a − c( ) ⋅m

2− 1

2q1

a − c( ) ⋅m2

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ComputeequilibriumquanIIesq1

q2

q1*

q2*

68

ComputeequilibriumquanIIesEquilibrium

q1 =a − c( ) ⋅m

2− 1

2⋅q2

q2 =a − c( ) ⋅m

2− 1

2⋅q1

Find q1*

q1* =

a − c( ) ⋅m2

− 12⋅

a − c( ) ⋅m2

− 12⋅q1

*⎛⎝⎜

⎞⎠⎟

Solve for q1*

q1* =

a − c( ) ⋅m3

69

ComputeequilibriumquanIIesq1

q2

q1*

q2*

Equilibrium

q1* =

a − c( ) ⋅m3

q2* =

a − c( ) ⋅m3

70

Computeequilibriumprice

Equilibrium price

p* = a − 1m⋅ q1

* + q2*( )

p* = a − 1m⋅

a − c( ) ⋅m3

+a − c( ) ⋅m

3⎛⎝⎜

⎞⎠⎟

p* = a + 2 ⋅c3

71

Comparewithmonopoly

Question: Effect of competition on price?

p* = a + 2 ⋅c3

pm = a + c2

Answer: Duopoly price lower

p* < pm

a + 2 ⋅c3

< a + c2

c < a

Conclusion:Morefirmsimplieslowerprices

72

CompareCournot-Bertrand

Bertrand

p* = c

Cournot

p* = a + 2 ⋅c3

> c

73


•  Bertrand:Cheaptostealcustomers– Lowerpricealiwle⇒Stealallconsumers

•  Cournot:Expensivetostealcustomers– Tostealalotofconsumers,afirmneedstoincreaseitsproducIonalot⇒largereducIoninequilibriumprice

74


Competitors price

Marketdemand

●

Residualdemand

Competitors quantity

Marketdemand

Residualdemand

Bertrand Cournot

75


Competitors price

Marketdemand

●

Residualdemand

Competitors quantity

Marketdemand

Residualdemand

Bertrand Cournot

CournotDuopoly:GraphicalSoluIon

76

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CournotDuopolyResidualDemand

Market clearing price

q1

Assume firm 2 will produce q2. How will market price vary with q1?

q2 D

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Market clearing price Assume firm 2 will produce q2.

How will market price vary with q1?

q2

P(0+q2) *

D q1 0

If q1 = 0, then p = P(0+q2)

79




q2

P(0+q2) *

D q1 0

If q1 = q’1, then p = P(q’1+q2)

q’1 q2+q’1

P(q’1+q2) *

80




q2

P(0+q2) *

D q1 0

Two point on firm 1’s residual demand

q’1 q2+q’1

P(q’1+q2) *

81




q2

P(0+q2)

D q1 0 q’1 q2+q’1

P(q’1+q2)

D1

D1 is a parallel shift of D by q2 units

*

*

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CournotDuopolyBestReply


Quantity

Assume firm 2 will produce q2. How much will firm 1 produce?

D1 D

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Quantity

Assume firm 2 will produce q2. How much will firm 1 produce?

q*1

P(q2+ q*1)

D1 D

c

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Assume firm 2 will increases production. How will firm 1 react?

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Quantity D +Δq2 -Δq1

If Firm 2 produces more, Firm 1 produces less

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Quantity D +Δq2 -Δq1

Note: P(q1 + q2) is reduced Hence: q1 + q2 is increased Hence: q1 reduced by less than q2 increased

87



Quantity

If q2 = 0 Then q1 = qm

D qm

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Quantity

If q2 = qc Then q1 = 0

D qc D1

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q1

q2

qm

qc

q*1(0) = qm

q*1(qc) = 0

Negative slope

Less than -1

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CournotDuopolyEquilibrium

q1

q2

qm

qc qm

qc

* qn

qn

Firm 2’s best reply

Equilibrium: Both a doing their best, given what the other does

2qn

qm < 2qn < qc

q1+q2=qc

4 - Oligopoly (slides) - stennek.sestennek.se/onewebmedia/4 - Oligopoly (slides).pdf · 4 Oligopoly...

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