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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
DuopolyResidualdemand
Competitors price
Marketdemand:D(p)
11
DuopolyResidualdemand
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
DuopolyIntuiIveAnalysis
19
Q:Whatifbothchargep=c?- qi=q*/2- πi=0
p=c
q*q*/2
DuopolyIntuiIveAnalysis
20
Nounilateralchangeprofitable?-Higherprice→q=0,π=0- Lowerprice→q>0,p<c,π<0
p=c
q*q*/2
DuopolyIntuiIveAnalysis
21
• Ifbothfirmschargep=c
– NoincenIvetochangebehavior
– ReasonablepredicIon
– Nashequilibrium
DuopolyIntuiIveAnalysis
22
• Twoformalproofs
– Foreverypossibleoutcome,invesIgateifsomeonehasincenIvetodeviate
– Bestreplyanalysis
Duopoly
23
Duopoly
Candidate Profitable deviation
p1 > p2 > c who? what?
24
Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
25
Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c who? what?
26
Duopoly
Candidate Profitable deviation
p1 > p2 > c Firm i pi = pj – ε (max pm)
p1 = p2 > c Firm i pi = pj – ε (max pm)
27
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?
28
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)
29
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?
30
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 - -
31
DuopolyBest-replyanalysis
32
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Setofallstrategyprofiles
33
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Q:Whatdowemeanby“firm2’sbestreplyfuncIon”?A:Profitmaximizingp2foreverypossiblep1
34
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Q:Whatdowemeanby“firm2’sbestreplyfuncIon”?A:Profitmaximizingp2foreverypossiblep1
35
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Whatifp1>pm
36
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
37
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
Whatifc<p1≤pm
38
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
39
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
Whatifp1=c
40
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
41
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
Whatifp1<c
42
DuopolyBest-replyanalysis
p2
p1
p2=p1
c
c
pm
pm
Firm2’sbestreply
43
DuopolyBest-replyanalysis
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
WhatispricecompeIIon?
• ExtremepredicIon(“Bertrandparadox”)– 2firms=>p=c&π=0
• Q:ReasonforextremepredicIon?– Reducepriceonecent,getallcustomers
– AlwaysprofitabletoreducepricebelowcompeItor,aslongasp>c.
49
WhatispricecompeIIon?
• Moreooen
– Morefirms:p>c&π>0
– Reason:Don’tgetallcustomers
– Examples: ProductdifferenIaIon
WhatispricecompeIIon?
• 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
51
WhatispricecompeIIon?
• 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
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
67
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
CompareCournot-Bertrand
• Bertrand:Cheaptostealcustomers– Lowerpricealiwle⇒Stealallconsumers
• Cournot:Expensivetostealcustomers– Tostealalotofconsumers,afirmneedstoincreaseitsproducIonalot⇒largereducIoninequilibriumprice
74
CompareCournot-Bertrand
Competitors price
Marketdemand
●
Residualdemand
Competitors quantity
Marketdemand
Residualdemand
Bertrand Cournot
75
CompareCournot-Bertrand
Competitors price
Marketdemand
●
Residualdemand
Competitors quantity
Marketdemand
Residualdemand
Bertrand Cournot
CournotDuopoly:GraphicalSoluIon
76
77
CournotDuopolyResidualDemand
Market clearing price
q1
Assume firm 2 will produce q2. How will market price vary with q1?
q2 D
78
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)
79
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) *
80
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) *
81
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
*
*
82
CournotDuopolyBestReply
Market clearing price
Quantity
Assume firm 2 will produce q2. How much will firm 1 produce?
D1 D
83
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
84
CournotDuopolyBestReply
Assume firm 2 will increases production. How will firm 1 react?
85
CournotDuopolyBestReply
Market clearing price
Quantity D +Δq2 -Δq1
If Firm 2 produces more, Firm 1 produces less
86
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
87
CournotDuopolyBestReply
Market clearing price
Quantity
If q2 = 0 Then q1 = qm
D qm
88
CournotDuopolyBestReply
Market clearing price
Quantity
If q2 = qc Then q1 = 0
D qc D1
89
CournotDuopolyBestReply
q1
q2
qm
qc
q*1(0) = qm
q*1(qc) = 0
Negative slope
Less than -1
90
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
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