4 - Oligopoly (slides)
Transcript of 4 - Oligopoly (slides)
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Oligopoly
• Example:Zocord– Reducescholesterol– ProducedbyMerck&Co
– PatentexpiredinApril2003(inSweden)– Othercompaniesstartedtosellperfectcopies
(=containingexactlythesameacIveingredientSimvastaIn)
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Oligopoly
• QuesIon– HowdoescompeIIonwork?– Howstrongisit?– Howdoesthatdependonthemarket?
• Comparemonopolyandduopoly– Givenmarket(technology,demand)– Q:Howdoespricedependon#firms?
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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
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
#
$
%%
&
%%
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DuopolyGameTheory
• Inter-dependentdecisions– Firm1’sopImalpricedependsonfirm2’sprice
– Firm2’sopImalpricedependsonfirm1’sprice
• Howtoanalyze– Cannotsimplyassumeprofitmaximizingbehavior
– Gametheory
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DuopolyGameTheory
• Gameinnormalform– Q:Elementsofagameinnormalform?
• Players,Strategies,Payoffs– Players
• Firm1andFirm2
– Strategies• Eachfirmchoosesapricepi(arealnumber)• Recall:Strategyprofile=Apriceforeachplayer(p1,p2)
– Payoffs• Profits• Recall:PayofffuncIonassignsapayoffforeverypossiblestrategyprofile,πi(p1,p2)
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DuopolyGameTheory
• Nashequilibrium– “Acommonunderstandingamongallplayersofhowtheyareallgoingtobehave”
– Astrategyprofilesuchthatnoplayercanincreaseitspayoffgiventhatallotherplayersfollowtheirstrategies
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DuopolyGameTheory
• Nashequilibriuminduopolygame
– Apairofprices(p1,p2)suchthat
• π1(p1,p2)≥π1(p’1,p2)forallp’1
• π2(p1,p2)≥π2(p1,p’2)forallp’2
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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
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qm
pm
qm/2
DuopolyIntuiIveAnalysis
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Nounilateralchangeprofitable?-Higherprice→q=0,π=0- Lowerprice→q>0,p<c,π<0
p=c
q*q*/2
DuopolyIntuiIveAnalysis
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• Ifbothfirmschargep=c
– NoincenIvetochangebehavior
– ReasonablepredicIon
– Nashequilibrium
DuopolyIntuiIveAnalysis
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• Twoformalproofs
– Foreverypossibleoutcome,invesIgateifsomeonehasincenIvetodeviate
– Bestreplyanalysis
Duopoly
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Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c who? what?
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Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c Firm i pi = pj – ε (max pm)
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Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c Firm i pi = pj – ε (max pm)
p1 > p2 = c who? what?
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Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c Firm i pi = pj – ε (max pm)
p1 > p2 = c Firm 2 p2 = p1 – ε (max pm)
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Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c Firm i pi = pj – ε (max pm)
p1 > p2 = c Firm 2 p2 = p1 – ε (max pm)
p1 = p2 = c who? what?
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Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c Firm i pi = pj – ε (max pm)
p1 > p2 = c Firm 2 p2 = p1 – ε (max pm)
p1 = p2 = c - -
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DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Q:Whatdowemeanby“firm2’sbestreplyfuncIon”?A:Profitmaximizingp2foreverypossiblep1
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DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Q:Whatdowemeanby“firm2’sbestreplyfuncIon”?A:Profitmaximizingp2foreverypossiblep1
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Duopoly
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
Firm1’sbestreply
NashequilibriumA(p1,p2)thatliesonbothbestreplyfuncIons
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WhatispricecompeIIon?
• ExtremepredicIon(“Bertrandparadox”)– 2firms=>p=c&π=0
• Q:ReasonforextremepredicIon?– Reducepriceonecent,getallcustomers
– AlwaysprofitabletoreducepricebelowcompeItor,aslongasp>c.
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WhatispricecompeIIon?
• Moreooen
– Morefirms:p>c&π>0
– Reason:Don’tgetallcustomers
– Examples: ProductdifferenIaIon
WhatispricecompeIIon?
• EsImatedLernerindexes(mark-ups)inautomobiles
• Conclusion
• CompeIIondoesnoteliminateallmarkups• Also
• 3rddegreepricediscriminaIonalsowithcompeIIon• Highmarkupsinhomecountries
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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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WhatispricecompeIIon?
• TheoreIcallyrobust– ManyothermodelsofoligopolygivesamequalitaIvepredicIon
• Empirically“confirmed”– ManyempiricalstudiessuggestthatcompeIIonleadstolowerprices
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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?
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QuanItyCompeIIon
• Bertrandmodel– Firmssetprices– ConsumersdecidequanIIes(firmsmustdeliver)
• Cournotmodel– FirmschosequanIIes– Thenpriceissettoclearthemarket
• Note1:Differencemawers(contrasttomonopoly)
• Note2:TwodifferentinterpretaIons
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QuanItyCompeIIon• FirstinterpretaIon
– Stage1:Firmsproduce:q1,q2– Stage2:FirmsbringproducetoaucIon:p=P(q1+q2)
• Example– Fishingvillage
• Note– Pricingdecisionisdelegated– Butequilibriumpriceaffectedbyamountproduced– Weomittheissuewhyp=P(q1+q2)
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QuanItyCompeIIon
• SecondinterpretaIon:Two-stagegame– Stage1:FirmschosecapaciIes:k1,k2
– Stage2:Firmssetprices:p1,p2
• Note:– UndersomecondiIonsp1=p2=P(k1+k2)
– Thenstudychoiceofcapacity(=quanIty)
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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)
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ExogenouscondiIons
• Simplify1:Technology– Constantmarginalcost– Firmshavesamemarginalcost
• Simplify2:Demand– Firms’goodshomogenous– Marketdemand:Linear
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CournotDuopoly
• Technology– Constantmarginalcosts,c
• Demand(linear)– Individualdemand: q=a–p– Numberofconsumers: m– Marketdemand: Q=m*(a–p)
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CournotDuopoly
• Exercise:– Solvethemodel
• Steps:1. SetupprofitfuncIons2. Findbest-replyfuncIons3. FindequilibriumquanIIes4. Findequilibriumprice
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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( )
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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
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Derivebest-replyfuncIonsq1
q2
a − c( ) ⋅m2
Firm 1's best-reply function
q1 =a − c( ) ⋅m
2− 1
2⋅q2
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Derivebest-replyfuncIonsq1
q2
a − c( ) ⋅m2
Firm 1's best-reply function
q1 =a − c( ) ⋅m
2− 1
2q2
Firm 2's best-reply function
q2 =a − c( ) ⋅m
2− 1
2q1
a − c( ) ⋅m2
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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
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Computeequilibriumprice
Equilibrium price
p* = a − 1m⋅ q1
* + q2*( )
p* = a − 1m⋅
a − c( ) ⋅m3
+a − c( ) ⋅m
3⎛⎝⎜
⎞⎠⎟
p* = a + 2 ⋅c3
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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
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CompareCournot-Bertrand
• Bertrand:Cheaptostealcustomers– Lowerpricealiwle⇒Stealallconsumers
• Cournot:Expensivetostealcustomers– Tostealalotofconsumers,afirmneedstoincreaseitsproducIonalot⇒largereducIoninequilibriumprice
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CompareCournot-Bertrand
Competitors price
Marketdemand
●
Residualdemand
Competitors quantity
Marketdemand
Residualdemand
Bertrand Cournot
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CompareCournot-Bertrand
Competitors price
Marketdemand
●
Residualdemand
Competitors quantity
Marketdemand
Residualdemand
Bertrand Cournot
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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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CournotDuopolyResidualDemand
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)
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CournotDuopolyResidualDemand
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 = q’1, then p = P(q’1+q2)
q’1 q2+q’1
P(q’1+q2) *
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CournotDuopolyResidualDemand
Market clearing price Assume firm 2 will produce q2.
How will market price vary with q1?
q2
P(0+q2) *
D q1 0
Two point on firm 1’s residual demand
q’1 q2+q’1
P(q’1+q2) *
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CournotDuopolyResidualDemand
Market clearing price Assume firm 2 will produce q2.
How will market price vary with q1?
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
Market clearing price
Quantity
Assume firm 2 will produce q2. How much will firm 1 produce?
D1 D
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CournotDuopolyBestReply
Market clearing price
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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CournotDuopolyBestReply
Market clearing price
Quantity D +Δq2 -Δq1
If Firm 2 produces more, Firm 1 produces less
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CournotDuopolyBestReply
Market clearing price
Quantity D +Δq2 -Δq1
Note: P(q1 + q2) is reduced Hence: q1 + q2 is increased Hence: q1 reduced by less than q2 increased