l2 - oligopolystennek.se/onewebmedia/l2 - oligopoly.pdf · oligopoly • example: zocord –...

1

Oligopoly

Varian Ch. 16

Johan Stennek

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Oligopoly

•  Example:Zocord– Reducescholesterol– ProducedbyMerck&Co

•  Patentexpired– April2003(inSweden)– Othercompaniesstartedtosellperfectcopies

(=containingexactlythesameacIveingredientSimvastaIn)

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0

1

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6

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10

okt./95 mars/97 juli/98 dec./99 apr./01 sep./02 jan./04 maj/05 okt./06 feb./08 juli/09

PriceofZocordinSwedenNominalpriceperdailydose(SEK)

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Agenda•  WhatiscompeIIon?

– MonopolyvsBertrandtrap [Varian 16.4]

•  Sourcesofmarketpower–  ProductdifferenIaIon(Hotelling) [Slides, Tirole]–  ConsumerinformaIon [Varian 16.4, example]–  QuanItycompeIIon(Cournot) [Varian 16.1-3]

•  Cartels[Varian 16.10-11]

WhatispricecompeIIon?

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WhatispricecompeIIon?

•  Comparemonopolyandduopoly

–  Givenmarket(technology,demand)

–  Differentnumberoffirms

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DWL

Monopoly

QuanIty

Price

qm

pm

Profit

Consumersurplus

qwelfare-max

8

Duopoly

•  Timing

1.  Firmssetpricessimultaneously

2.  Consumersdecidehowmuchtobuyandfromwhom

NB:FirmshavenoImetoreact!

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Duopoly

•  Technology–  Constantmarginalcost–  Firmshavesamemarginalcost

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

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Duopoly

•  Consumerbehavior

–  Allbuyfromcheapestfirm

–  Ifsameprice:50-50split

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Duopoly

•  DefiniIon:A’sresidualdemand

–  Trade-offbetweenpriceandsalesforfirmA

•  giventhepricechargedbyB,

•  givenmarketdemand

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Duopoly

Competitors price

Marketdemand:D(p)

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Duopoly

Competitors price

Marketdemand:D(p)

●

Residualdemand:Di(p1,p2)

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Duopoly

Competitors price ●

ResidualdemandisperfectlyelasIcatcompeItor’sprice

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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

#

$

%%

&

%%

16

Duopoly

•  Interdependence

–  Firm1’sprofitdependsonfirm2’spriceandviceversa

–  Formulateasnormalformgame

–  Nashequilibrium

17

Duopoly

•  Claim

–  UniqueNashequilibrium:p1=p2=c

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Duopoly

•  TwoalternaIveproofs1.  Tryallpossiblestrategyprofiles

2.  Best-replyanalysis

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Duopoly

Candidate Profitable deviation

p1 > p2 > c Firm? DeviaIon?

p1 = p2 > c

p1 > p2 = c

p1 = p2 = c

Proof1

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Duopoly


p1 > p2 > c Firm 1 p1 = p2 – ε (max pm)

p1 = p2 > c ? ?

p1 > p2 = c

p1 = p2 = c

Proof1

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Duopoly



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

p1 > p2 = c ? ?

p1 = p2 = c

Proof1

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Duopoly




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

p1 = p2 = c ? ?

Proof1

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Duopoly




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

p1 = p2 = c - -

Proof1

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Duopoly

•  Proof2:Bestreplyanalysis

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Duopoly


BestreplyTofindbestprice,givencompeItor’sprice,i.e.bestreply,simplysolve“monopoly”problem,butgivenresidualdemand

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Duopoly


TechnicalproblemdisconInuityindemand=>disconInuityintotalrevenue=>marginalrevenuenotdefined

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Duopoly


Solu8onAnalyzedifferentcases

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BertrandBest-replyanalysis

p2

p1

p2=p1

c

c

pm

pm

Whatifp1>pm

Firm2“owns”marketdemanduptoandincludingpm.

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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

Whatifc<p1≤pm

Sincep1isbelowpm,set“highest”possiblepricebelowp1

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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

Whatifp1=c

Allp2≥p1=>zeroprofit

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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

Whatifp1<c

Allp2≥p1=>zeroprofit

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p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

Bestreplycorrespondence

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p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

SelecIon

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Bertrand

p2

p1

p2=p1

c

c

pm

pm

Firm1’sbestreply

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Bertrand

p2

p1

p2=p1

c

c

pm

pm

Firm2’sbestreply

Firm1’sbestreply

SolepointofintersecIon

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Duopoly


Intui8on:

•  SmallreducIoninprice=>Massiveexpansionofsales

•  AlwaysprofitabletoreducepricebelowcompeItor

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Consumersurplus

Duopoly

p=c

q*

NoprofitNodeadweightloss–allocaIveefficiency

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WhatispricecompeIIon?•  PredicIon(comparemonopoly&duopoly)

–  MorefirmsèLowerprices

•  Q:IsthispredicIontrue?–  TheoreIcally:Robust

•  Extreme•  Existscounterexamples

–  Empirically:Robust•  OverImeInstrument=whenpatentsexpire

•  AcrossgeographicalmarketsInstrument=differentmarketsize

•  Existscounterexamples

42

“BertrandTrap”

•  ExtremesituaIon–  2firms: p=c&π=0

–  Reason:Reducepriceonecent,getallcustomers

•  Moreoven

– Morefirms:p>c&π>0

–  Reason:Don’tgetallcustomers

–  Examples: ProductdifferenIaIon;consumerpriceinfo

SourcesofMarketPower

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Sourcesofmarketpower1.  Fewfirms/Entrybarriers(necessarybutnotsufficient)2.  ProductdifferenIaIon:horizontal&verIcal

3.  QuanItycompeIIon/Capacityconstraints

4.  Costadvantage5.  Uninformedcustomers

6.  Customerswitchingcosts

7.  PricediscriminaIon:informaIon&arbitrage

8.  CartelizaIon

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Sourcesofmarketpower1.  Fewfirms/Entrybarriers2.  ProductdifferenIaIon:horizontal&verIcal

3.  QuanItycompeIIon/capacityconstraints

4.  Costadvantage5.  Uninformedcustomers

6.  Customerswitchingcosts

7.  PricediscriminaIon:informaIon&arbitrage

8.  CartelizaIon

ProductDifferenIaIon(Hotellingmodel)

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ProductDifferenIaIon•  Twostores

–  Constantmarginalcost

–  Homogenousgoods

–  Locatedatendpointsofastreetoflength1

•  Unitmassofconsumers

–  IdenIcal;unitdemand;wtp=v

–  Uniformlydistributedoverstreet

–  TransportaIoncost=t

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ProductDifferenIaIon

Firm1 Firm2Consumeratx

0 x 1

Distancetofirm1=x Distancetofirm2=1–x

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Unitmassofconsumers

0 1

f(x)=1

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•  Timing–  Firmssetprices

–  Consumerschoosestore

•  ConsumeruIlity

–  u1(x)=v–p1–tx–  u2(x)=v–p2–t(1-x)

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Firm1

u1(x)=(v–p1)–tx

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Firm1 Firm2

u1(x)=v–p1–tx u2(x)=v–p2–t(1-x)

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Firm1 Firm2z

Ifp1andp2arenottoohigh,thereexistsamarginalconsumeru1(z)=u2(z)>0

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Firm1 Firm2z

Allconsumersx<zbuyfromfirm1Allconsumersx>zbuyfromfirm2

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Firm1 Firm2z

f(x)

!!

D1= f x( )dx

0

z

∫ = dx0

z

∫ = z

D2= f x( )dx

z

1

∫ = dxz

1

∫ = 1− z

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Firm1 Firm2zz’

DemandsdependonpricesIffirm1increasespricetop1’

Firm1’sdemandisreducedtoz’

Firm2’sdemandisincreasedto1-z’

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•  Derivedemand–thealgebra:

–  Consumeratxbuysfromfirm1,if•  v–p1–tx≥v–p2–t(1-x)•  p2–p1≥tx–t(1-x)•  p2–p1≥2tx–t•  t+p2–p1≥2tx

•  !!x ≤ z ≡

12+p2− p

1

2t

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•  Demand:

–  Technicality•  0≤D1≤1

•  AbovesoluIononlyifp2–t≤p1≤p2+t

!!D1p1,p

2( ) = 12 +p2− p

1

2t

!!

D1p1,p

2( ) =1 p

1≤ p

2−t

12+p2− p

1

2tif p

1∈ p

2−t ,p

2+t$

%&'

0 p1≥ p

2+t

)

*

++

,

++

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Firmprofit(Assumingp1 ∈ p2 − t ,p2 + t⎡⎣ ⎤⎦ inequilibrium)

π1 p1 ,p2( ) = p1 − c( )⋅D1 p1 ,p2( ) = p1 − c( )⋅ 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟

Firstordercondition

∂π1 p1 ,p2( )∂p1

=D1 p1 ,p2( ) +∂D1 p1 ,p2( )

∂p1⋅ p1 − c( ) = 0

∂π1 p1 ,p2( )∂p1

= 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟− 12t

⋅ p1 − c( ) = 0Bestreply

p1 =c+ t2

+ 12p2

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π1 p1 ,p2( ) = p1 − c( )⋅D1 p1 ,p2( ) = p1 − c( )⋅ 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟

Firstordercondition

∂π1 p1 ,p2( )∂p1

=D1 p1 ,p2( ) +∂D1 p1 ,p2( )

∂p1⋅ p1 − c( ) = 0

∂π1 p1 ,p2( )∂p1

= 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟− 12t


p1 =c+ t2

+ 12p2

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π1 p1 ,p2( ) = p1 − c( )⋅D1 p1 ,p2( ) = p1 − c( )⋅ 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟

Firstordercondition

∂π1 p1 ,p2( )∂p1

=D1 p1 ,p2( ) +∂D1 p1 ,p2( )

∂p1⋅ p1 − c( ) = 0

∂π1 p1 ,p2( )∂p1

= 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟− 12t


p1 =c+ t2

+ 12p2

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π1 p1 ,p2( ) = p1 − c( )⋅D1 p1 ,p2( ) = p1 − c( )⋅ 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟

Firstordercondition

∂π1 p1 ,p2( )∂p1

=D1 p1 ,p2( ) +∂D1 p1 ,p2( )

∂p1⋅ p1 − c( ) = 0

∂π1 p1 ,p2( )∂p1

= 12+p2 − p12t

⎛

⎝⎜⎞

⎠⎟− 12t


p1 =c+ t2

+ 12p2

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ProductDifferenIaIonp1

p2

p2+tp2-t

t

v Bestreply

!!p1=c + t2

+12p2

Exercise:Explainother3segmentsofbest-reply

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p2

t

v Bestreply

Bestreply

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p2

t

v

c+t

c+t

p1(p2)

p2(p1)

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!!!

Equilibrium

p1=c + t2

+12p2

p2=c + t2

+12p1

Solve!for!p1

p1=c + t2

+12

c + t2

+12p1

⎛

⎝⎜⎞

⎠⎟

p1−14p1=c + t2

+c + t4

34p1=3 c + t( )

4p1= c + t

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•  Equilibriumpriceis

–  Increasinginc(asBertrand)– Unaffectedbyv(asBertrand,valueofcommonqualitycompetedaway)

–  Increasingint(MarkupdeterminedbydifferenIaIon)

!!p* = c + t

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•  TransportaIoncost=horizontaldifferenIaIon– Physicaldistance– Sweetnessoffood– Colorofcloths– …

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•  Whathappensiftislow?

Firm1

u1(x)=v–p1–tx

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Firm1 Firm2zz’

SmallreducIoninprice,giveslargeincreaseinsales(=elasIcresidualdemand)Thus,pricereducIonsmoreprofitable

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•  Voluntaryexercises– Whathappensifv2>v1?Interpret!

– Whathappensifc2<c1?Interpret!

– Whathappensiftbecomeslarge?

ConsumerInformaIon

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ConsumerInformaIon

•  Twotypesofconsumers•  unitdemand;wtp=v

–  Informed•  Know: p1andp2•  Behavior: gotocheapest•  Share: 1-2αwhereα<½(thinkofαassmall)

– Uninformed•  Know: noprices•  Behavior: selectstoreatrandom•  Share: 2α(αgotoeachstore)

74

ConsumerInformaIon

•  Residualdemand

–  Ifα=0,thenBertrand–  Ifα>0,thenalwayskeepsomecustomers

!!

D1p1,p

2( ) =α p

1> p

2

12

p1= p

2

1−α p1< p

2

#

$

%%

&

%%

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ConsumerInformaIon

•  Claim– Nosymmetricequilibriuminpurestrategies

•  Proof– Assumep1=p2>0(=mc)

•  SIck: π1=p2(1/2)

•  Undercut: π1=(p2-ε)(1-α)whichisbe~er

– Assumep1=p2=0•  SIck: π1=0

•  Increase: π1=vα>0

76

ConsumerInformaIon

•  Claim– Noasymmetricequilibriuminpurestrategies

•  Proof(assumecontrary:p1>p2)

–  Thenitmustbethatp1=v(bestp1abovep2)

–  Thenitmustbethatp2=v–ε(bestp2,givenp1)

–  Thenp1=p2be~ersincep2½>v αó(v–ε)½>vα

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ConsumerInformaIon

•  Claim–  Existssymmetricequilibriuminmixedstrategies

•  NotaIon–  Firmi’sstrategy=probabilitydensityfi(p)

•  Proof– ByconstrucIon

p

fi(p)

78

ConsumerInformaIon

•  EquilibriumprobabilitydensiIes–  f1(p)=f2(p)=f(p)

–  Strictlyposi6veinsomeinterval

•  EquilibriumCDF(=probabilityp2<r)

– 

•  BydefiniIon:–  Pr{p2<p1}=F2(p1)foranygivenp1

!!F2 r( ) = f2 z( )dz

0

r

∫

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ConsumerInformaIon

Firm2'sexpectedprofitifchoosingp2

Eπ2 p2( ) = prob p1 > p2{ }⋅p2 ⋅ 1−α( )+ prob p1 < p2{ }⋅p2 ⋅α

Withrandomization,allp2 intheintervalmustgivesameprofit

1−F1 p2( )⎡⎣ ⎤⎦⋅p2 ⋅ 1−α( )+F1 p2( )⋅p2 ⋅α = const

Rewritep2 1−α( )−F1 p2( )⋅p2 ⋅ 1−2α( ) = const

F1 p2( ) = 1−α1−2α

⎛⎝⎜

⎞⎠⎟− const

p2

11−2α

Thisishowfirm1mustbehavetomakefirm2indifferentbetweendifferentpricesintheinterval

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ConsumerInformaIon

Symetricequilibrium

F p( ) = 1−α1−2α

⎛⎝⎜

⎞⎠⎟− const

p1

1−2α

DetermineconstantF v( ) =1 (IfIchargep=v,mypriceishigherwithprob=1)

1−α1−2α

⎛⎝⎜

⎞⎠⎟− const

v1

1−2α=1

const =αv

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ConsumerInformaIon

!!!

Equilibrium!CDF

F p( ) = 1−α1−2α

⎛⎝⎜

⎞⎠⎟− αv

p1

1−2α

Note:!Lowest!price!with!positive!probability

F p( ) = 0⇔ p = α1−α

v > 0

82

ConsumerInformaIon

1 F(p)

v!!

α

1−αv p

83

ConsumerInformaIon

•  Conclusions– Marketpower

•  p>c=0•  Eπ=α·v(Proof:p=v=>π=α·v;Eπsameforallp)

–  PricediscriminaIon•  Uninformedpaymore

–  InformaIonexternality•  lowerα=>lowerprices•  ConsumershaveinsufficientincenIvestobecomeinformed

QuanItyCompeIIon(Cournotmodel)

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QuanItyCompeIIon

•  AlternaIvemarketstructure

–  First,firmsproduce

–  Then,firmsbringproducetoaucIon(wheremarketclearingpriceisdetermined)

•  Note

–  Pricingdecisionisdelegated

–  Butequilibriumpriceaffectedbyamountproduced

86

CournotDuopoly

•  Timing

–  Firmsproducesimultaneously:q1andq2

–  JointaucIonwithmarket-clearingprice:p=P(q1+q2)

–  NB:FirmshavenoImetoreact!

87

CournotDuopoly

•  Technology–  Constantmarginalcost–  Firmshavesamemarginalcost

•  Demand–  Firms’goodshomogenous– Marketdemand:Linear

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CournotDuopoly

•  Profits–  πi(q1,q2)=P(q1+q2)·qi-c·qi

89

Duopoly

•  DefiniIon:Residualdemand

–  Showsthetrade-offbetweenpriceandsalesforfirmA

•  giventhequanItyproducedbyB,

•  givenmarketdemand

90

Duopoly

•  Deriveresidualdemand

–  Usedirectdemandratherthanindirectdemand

– Marketdemand:q=Q(p)orq1+q2=Q(p)

–  Residualdemand:q1=Q1(p;q2)=Q(p)-q2

91

CournotDuopolyResidualDemand

Marketclearingprice

q1D

92

CournotDuopolyResidualDemand

Marketclearingprice

D q1D1

D1isaparallelshivofDbyq2units

93

CournotDuopolyBestReply

Marketclearingprice

QuanIty

Assumefirm2willproduceq2.Howmuchwillfirm1produce?

D1 D

c

94

CournotDuopolyBestReply

Marketclearingprice

QuanIty

Assumefirm2willproduceq2.Howmuchwillfirm1produce?

q*1

P(q2+q*1)

D1 D

c

Firmismonopolistunderresidualdemand

q2+q*1

95

CournotDuopoly

•  Linearexample

Profitπ1 q1 ,q2( ) = P q1 +q2( )⋅q1 −C q1( )π1 q1 ,q2( ) = α −q1 −q2( )⋅q1 − c ⋅q1

FOC∂π1 q1 ,q2( )

∂q1= P q1 +q2( )+ ∂P q1 +q2( )

∂q1⋅q1 −C ' q1( ) =0

∂π1 q1 ,q2( )∂q1

= α −q1 −q2( )−q1 − c =0

Bestreply

q1 =α − c( )2 − 12 ⋅q2

Equilibrium

q1 = q2 =α − c( )3

p= 13 ⋅α + 2

3 ⋅c > c

p< pm = 12 ⋅α + 1

2 ⋅c

96

CournotDuopoly



FOC∂π1 q1 ,q2( )

∂q1= P q1 +q2( )+ ∂P q1 +q2( )

∂q1⋅q1 −C ' q1( ) =0

∂π1 q1 ,q2( )∂q1

= α −q1 −q2( )−q1 − c =0

Bestreply

q1 =α − c( )2 − 12 ⋅q2

Equilibrium

q1 = q2 =α − c( )3

p= 13 ⋅α + 2

3 ⋅c > c

p< pm = 12 ⋅α + 1

2 ⋅c

97

CournotDuopoly



FOC∂π1 q1 ,q2( )

∂q1= P q1 +q2( )+ ∂P q1 +q2( )

∂q1⋅q1 −C ' q1( ) =0

∂π1 q1 ,q2( )∂q1

= α −q1 −q2( )−q1 − c =0

Bestreply

q1 =α − c( )2 − 12 ⋅q2

Equilibrium

q1 = q2 =α − c( )3

p= 13 ⋅α + 2

3 ⋅c > c

p< pm = 12 ⋅α + 1

2 ⋅c

98

CournotDuopoly

•  Conclusions– Marketpower

•  pd>c

– EffectofconcentraIononprice•  pd<pm

99

CournotDuopoly

•  QuanItycompeIIonvspricecompeIIon– CournotpricehigherthanBertrandprice– Detailsma~er

●

Cournot Bertrand

100

CournotDuopoly

•  ProblemsetincludesaddiIonaldeterminantsofmarketpower– Whatabouttriopoly,quadropolyandsoon?[Varian 16.3]–  ComparaIvestaIcs[Varian 16.2]

101

CournotDuopoly•  AlternaIveinterpretaIon:Cournot=PricecompeIIonundercapacityconstraints–  Timing

1.  FirmsproducequanIIesq1andq2

2.  Firmssetpricesp1andp2

–  Inequilibrium•  Period2:Bothfirmschargemarketclearingpricepi=P(q1+q2)

•  Period1:BothfirmsproduceCournotquanIIes

102

CournotDuopoly•  Sketchofproof

–  SubgameperfecIon=>Startwithperiod2

–  Period2•  AssumebothfirmshaveproducedquanIIesq1andq2•  Whatpricesdotheywishtocharge?

•  Tocutthestoryshort,assumeq1=q2=qCournot

103

CournotDuopoly

Competitors price

Marketdemand:D(p)

●

Residualdemand:Di(p1,p2)

RECALLPRICESETTINGWITHHOMOGENOUSGOODS

104

CournotDuopoly

●

Assumefirm2setsp2=P(2qCournot)

2qCournot

p2=P(2qCournot)

105

CournotDuopoly

●

Then,Iffirm1setsp1=p2,consumerswishtobuyatmostqCournot

qCournot

p2=P(2qCournot)

106

CournotDuopoly

●

Noreasontoundercut,thefirmcannotsellmorethanithasproducedanyway=capacityconstraint

qCournot

p2=P(2qCournot)

c

107

CournotDuopoly•  Moregenerally

–  Period2•  AssumebothfirmshaveproducedquanIIesq1andq2•  Then,itisanequilibriumforbothfirmstosetthemarketclearingprice,i.e.p1=p2=P(q1+q2)

–  Period1•  Thetruncatedgameinperiod1issimplytheCournotgame

108

CournotDuopoly

•  Caveat–  ThisworksifmarginalcostsrelaIvelyhigh

–  Ifmarginalcoststoolow,thereisnoequilibriuminpurestrategies

Cartels

109

Cartels

•  OligopolisIccompeIIon–  Lowerpricesandprofits

•  Whydon’tfirmsagreeonpricesinstead?–  IncenIvetocheat–  Notenforcedbycourts

110

Cartels

•  But,cartelsdoexist–  Sweden:asphalt,petrol–  Europe:SothebyandChrisIes

•  Whatdowemiss?– Marketsarelonglived–  FirmscanreactoncompeItors’pastbehavior–  ChangesthesituaIondramaIcally

111

CartelsAModel

•  Setup

–  Players:Twofirms

–  AcIons:Setpricesineachperiod(Bertrand)

–  Time:t=1,2,3,…(infinite)

–  InformaIon:Completeand“almostperfect”

–  Payoff:Πi=Σtδt-1πi(pt1,pt2)[δ<1isdiscountfactor]

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CartelsAModel

•  Note

– Wehavedefinedextensiveformgame

–  LookforSPE

–  Strategyspaceextremelycomplicated–CannotlookforallSPE

–  FocusoninteresIngcases

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CartelsTriggerStrategy

•  DefiniIon

–  Startoutchargingthemonopolyprice

–  Ifnofirmhascheatedinthepast,chargemonopolyprice

–  Ifsomeonehascheatedinthepast,setpriceequaltomarginalcost

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•  Claim

–  IfAbehavesaccordingtoTS,itisinB’sinteresttoalsofollowTSineverysubgame,andviceversa.

•  Note

–  NoincenIvestodeviateè[TS,TS]=SPE– Monopolypricewillprevail–  CooperaIonhingesonthreatofpricewar

•  Outofequilibrium•  Butcredible

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•  Proof–Generalremarks

–  NeedonlystudyincenIvestodeviateintwotypesofsubgames

•  Noonehasdeviatedsofar•  Someonehasdeviated

–  One-stagedeviaIonprinciple•  AlmostperfectinformaIon=>Needonlystudyone-period-deviaIons

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•  Proof–Punishmentphase–  Assumesomeonehasdeviatedinthepast

–  AssumeBsIckstoTS

–  IfAsIckstoTS•  Πno-dev=0+δ0+δ20+…=0

–  IfAdeviatesoneperiod•  MaximumprofitincurrentperiodissIll0

•  WarsIllconInuesinfuture

•  Πdev=0+δ0+δ20+…=0

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•  Proof–CooperaIvephase–  Assumenoonehasdeviatedinthepast

–  AssumeBsIckstoTS

–  IfAsIckstoTS•  Πno-dev=πm/2+δπm/2+δ2πm/2+…=πm/[2(1-δ)]

–  IfAdeviatesoneperiod•  Maximumprofitduringtheperiodisπm

•  Warstarts

•  Πdev=πm+δ0+δ20+…=πm

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•  Proof–CooperaIvephase–  NoincenIvetodeviateif

•  Πno-dev<Πdev

•  πm/[2(1-δ)]<πm

•  δ>1/2

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•  Conclusion–  Cartelsself-enforcing–  IffirmssufficientlypaIent

•  PolicyimplicaIons

–  Notsufficienttodenyfirmslegalenforcement–  Necessarytomakecollusionillegalandpunish

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Cartels

•  CompeIIonisalsopossible–  CompeIIveStrategy:Alwayssetpriceequaltocost

–  IfAfollowsCS,BhasincenIvetofollowCS–  CSisalsoSPE

•  Whatshouldwepredict?–  Economicshasnoanswertoday

•  EconomicssIlluseful–  DelineatenecessarycondiIonsforcollusion(e.g.interestrate).

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Cartels

•  FactorsfacilitaIngcollusion–  Discountfactor(interestrate)–  ConcentraIon–  Entrybarriers–  FrequencyofinteracIon–  Transparency–  BusinesscyclesandfluctuaIons–  Firmdifferences

•  Howtousethelist–  IdenIfypotenIallyproblemaIcindustries–  Incases,analyzeifallegaIonsplausible

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CartelsConcentraIon

•  Ifaduopolyfirmcheats»  Gain(firstperiod): πm/2=πm–πm/2»  Loss(subsequently): -πm/2=0–πm/2

•  Ifatriopolyfirmcheats»  Gain(firstperiod): 2πm/3=πm–πm/3»  Loss(subsequently): -πm/3=0–πm/3

•  PredicIon–  LowerconcentraIon→moretempIngtocheat→cartelslessstable

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l2 - oligopolystennek.se/onewebmedia/l2 - oligopoly.pdf · oligopoly • example: zocord –...

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