ChOligopoly微观范里安上海交通大学赵旭实用

会计学1ChOligopoly微观范里安上海交通大学赵旭实用OligopolyHowdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplyingthesameproduct.第1页/共94页QuantityCompetitionAssumethatfirmscompetebychoosingoutputlevels.Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1+y2.Themarketpricewillbep(y1+y2).Thefirms’totalcostfunctionsarec1(y1)andc2(y2).第2页/共94页QuantityCompetitionSupposefirm1takesfirm2’soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunctionas

Giveny2,whatoutputlevely1maximizesfirm1’sprofit?第3页/共94页QuantityCompetition;AnExampleSupposethatthemarketinversedemandfunctionis

andthatthefirms’totalcostfunctionsareand第4页/共94页QuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionis第5页/共94页QuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizing

outputlevelsolves第6页/共94页QuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizing

outputlevelsolvesI.e.firm1’sbestresponsetoy2is第7页/共94页QuantityCompetition;AnExampley2y16015Firm1’s“reactioncurve”第8页/共94页QuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionis第9页/共94页QuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizing

outputlevelsolves第10页/共94页QuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizing

outputlevelsolvesI.e.firm1’sbestresponsetoy2is第11页/共94页QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”45/445第12页/共94页QuantityCompetition;AnExampleAnequilibriumiswheneachfirm’soutputlevelisabestresponsetotheotherfirm’soutputlevel,forthenneitherwantstodeviatefromitsoutputlevel.Apairofoutputlevels(y1*,y2*)isaCournot-Nashequilibriumifand第13页/共94页QuantityCompetition;AnExampleand第14页/共94页QuantityCompetition;AnExampleandSubstitutefory2*toget第15页/共94页QuantityCompetition;AnExampleandSubstitutefory2*toget第16页/共94页QuantityCompetition;AnExampleandSubstitutefory2*togetHence第17页/共94页QuantityCompetition;AnExampleandSubstitutefory2*togetHenceSotheCournot-Nashequilibriumis第18页/共94页QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”6015Firm1’s“reactioncurve”45/445第19页/共94页QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”4860Firm1’s“reactioncurve”813Cournot-Nashequilibrium第20页/共94页QuantityCompetitionGenerally,givenfirm2’schosenoutput

levely2,firm1’sprofitfunctionisandtheprofit-maximizingvalueofy1solvesThesolution,y1=R1(y2),isfirm1’sCournot-

Nashreactiontoy2.第21页/共94页QuantityCompetitionSimilarly,givenfirm1’schosenoutput

levely1,firm2’sprofitfunctionisandtheprofit-maximizingvalueofy2solvesThesolution,y2=R2(y1),isfirm2’sCournot-

Nashreactiontoy1.第22页/共94页QuantityCompetitiony2y1Firm1’s“reactioncurve”Firm1’s“reactioncurve”Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*)第23页/共94页Iso-ProfitCurvesForfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevelP1.Whatdoiso-profitcurveslooklike?第24页/共94页y2y1Iso-ProfitCurvesforFirm1Withy1fixed,firm1’sprofit

increasesasy2decreases.第25页/共94页y2y1Increasingprofit

forfirm1.Iso-ProfitCurvesforFirm1第26页/共94页y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?y2’第27页/共94页y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y2’y1’第28页/共94页y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y1’isfirm1’s

bestresponsetoy2=y2’.y2’y1’第29页/共94页y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y1’isfirm1’s

bestresponsetoy2=y2’.y2’R1(y2’)第30页/共94页y2y1y2’R1(y2’)y2”R1(y2”)Iso-ProfitCurvesforFirm1第31页/共94页y2y1y2’y2”R1(y2”)R1(y2’)Firm1’sreactioncurve

passesthroughthe“tops”offirm1’siso-profit

curves.Iso-ProfitCurvesforFirm1第32页/共94页y2y1Iso-ProfitCurvesforFirm2Increasingprofit

forfirm2.第33页/共94页y2y1Iso-ProfitCurvesforFirm2Firm2’sreactioncurve

passesthroughthe“tops”offirm2’siso-profit

curves.y2=R2(y1)第34页/共94页CollusionQ:AretheCournot-Nashequilibriumprofitsthelargestthatthefirmscanearnintotal?第35页/共94页Collusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

higherprofitstobothfirms?(y1*,y2*)istheCournot-Nash

equilibrium.第36页/共94页Collusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

higherprofitstobothfirms?(y1*,y2*)istheCournot-Nash

equilibrium.第37页/共94页Collusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

higherprofitstobothfirms?(y1*,y2*)istheCournot-Nash

equilibrium.第38页/共94页Collusiony2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP2HigherP1第39页/共94页Collusiony2y1y1*y2*HigherP2HigherP1y2’y1’第40页/共94页Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1第41页/共94页Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).第42页/共94页CollusionSothereareprofitincentivesforbothfirmsto“cooperate”byloweringtheiroutputlevels.Thisiscollusion.Firmsthatcolludearesaidtohaveformedacartel.Iffirmsformacartel,howshouldtheydoit?第43页/共94页CollusionSupposethetwofirmswanttomaximizetheirtotalprofitanddivideitbetweenthem.Theirgoalistochoosecooperativelyoutputlevelsy1andy2thatmaximize第44页/共94页CollusionThefirmscannotdoworsebycolludingsincetheycancooperativelychoosetheirCournot-NashequilibriumoutputlevelsandsoearntheirCournot-Nashequilibriumprofits.SocollusionmustprovideprofitsatleastaslargeastheirCournot-Nashequilibriumprofits.第45页/共94页Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).第46页/共94页Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).(y1”,y2”)earnsstill

higherprofitsfor

bothfirms.y2”y1”第47页/共94页Collusiony2y1y1*y2*y2~y1~(y1,y2)maximizesfirm1’sprofit

whileleavingfirm2’sprofitat

theCournot-Nashequilibrium

level.~~第48页/共94页Collusiony2y1y1*y2*y2~y1~(y1,y2)maximizesfirm1’sprofit

whileleavingfirm2’sprofitat

theCournot-Nashequilibrium

level.~~y2_y2_(y1,y2)maximizesfirm

2’sprofitwhileleaving

firm1’sprofitatthe

Cournot-Nash

equilibriumlevel.__第49页/共94页Collusiony2y1y1*y2*y2~y1~y2_y2_Thepathofoutputpairsthat

maximizeonefirm’sprofit

whilegivingtheotherfirmat

leastitsCNequilibrium

profit.第50页/共94页Collusiony2y1y1*y2*y2~y1~y2_y2_Thepathofoutputpairsthat

maximizeonefirm’sprofit

whilegivingtheotherfirmat

leastitsCNequilibrium

profit.Oneof

theseoutputpairsmustmaximizethe

cartel’sjointprofit.第51页/共94页Collusiony2y1y1*y2*y2my1m(y1m,y2m)denotes

theoutputlevels

thatmaximizethe

cartel’stotalprofit.第52页/共94页CollusionIssuchacartelstable?Doesonefirmhaveanincentivetocheatontheother?I.e.iffirm1continuestoproducey1munits,isitprofit-maximizingforfirm2tocontinuetoproducey2munits?第53页/共94页CollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m).第54页/共94页Collusiony2y1y2my1my2=R2(y1m)isfirm2’s

bestresponsetofirm1choosingy1=y1m.R2(y1m)y1=R1(y2),firm1’sreactioncurvey2=R2(y1),firm2’s

reactioncurve第55页/共94页CollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m)>y2m.Firm2’sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromy2mtoR2(y1m).第56页/共94页CollusionSimilarly,firm1’sprofitincreasesifitcheatsonfirm2byincreasingitsoutputlevelfromy1mtoR1(y2m).第57页/共94页Collusiony2y1y2my1my2=R2(y1m)isfirm2’s

bestresponsetofirm1choosingy1=y1m.R1(y2m)y1=R1(y2),firm1’sreactioncurvey2=R2(y1),firm2’s

reactioncurve第58页/共94页CollusionSoaprofit-seekingcartelinwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable.E.g.OPEC’sbrokenagreements.第59页/共94页TheOrderofPlaySofarithasbeenassumedthatfirmschoosetheiroutputlevelssimultaneously.Thecompetitionbetweenthefirmsisthenasimultaneousplaygameinwhichtheoutputlevelsarethestrategicvariables.第60页/共94页TheOrderofPlayWhatiffirm1choosesitsoutputlevelfirstandthenfirm2respondstothischoice?Firm1isthenaleader.Firm2isafollower.Thecompetitionisasequentialgameinwhichtheoutputlevelsarethestrategicvariables.第61页/共94页TheOrderofPlaySuchgamesarevonStackelberggames.Isitbettertobetheleader?Orisitbettertobethefollower?第62页/共94页StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?第63页/共94页StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).第64页/共94页StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).Firm1knowsthisandsoperfectlyanticipatesfirm2’sreactiontoanyy1chosenbyfirm1.第65页/共94页StackelbergGamesThismakestheleader’sprofitfunction第66页/共94页StackelbergGamesThismakestheleader’sprofitfunction

Theleaderthenchoosesy1tomaximizeitsprofitlevel.第67页/共94页StackelbergGamesThismakestheleader’sprofitfunction

Theleaderchoosesy1tomaximizeitsprofit.Q:WilltheleadermakeaprofitatleastaslargeasitsCournot-Nashequilibriumprofit?第68页/共94页StackelbergGamesA:Yes.TheleadercouldchooseitsCournot-Nashoutputlevel,knowingthatthefollowerwouldthenalsochooseitsC-Noutputlevel.Theleader’sprofitwouldthenbeitsC-Nprofit.Buttheleaderdoesnothavetodothis,soitsprofitmustbeatleastaslargeasitsC-Nprofit.第69页/共94页StackelbergGames;AnExampleThemarketinversedemandfunctionisp=60-yT.Thefirms’costfunctionsarec1(y1)=y12andc2(y2)=15y2+y22.Firm2isthefollower.Itsreactionfunctionis第70页/共94页StackelbergGames;AnExampleTheleader’sprofitfunctionistherefore第71页/共94页StackelbergGames;AnExampleTheleader’sprofitfunctionisthereforeForaprofit-maximum,第72页/共94页StackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoice第73页/共94页StackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceA:第74页/共94页StackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceA:TheC-Noutputlevelsare(y1*,y2*)=(13,8)sotheleaderproducesmorethanitsC-NoutputandthefollowerproduceslessthanitsC-Noutput.Thisistruegenerally.第75页/共94页StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP2HigherP1第76页/共94页StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP1Follower’sreactioncurve第77页/共94页StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.(y1S,y2S)istheStackelbergequilibrium.HigherP1y1SFollower’sreactioncurvey2S第78页/共94页StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.(y1S,y2S)istheStackelbergequilibrium.y1SFollower’sreactioncurvey2S第79页/共94页PriceCompetitionWhatiffirmscompeteusingonlyprice-settingstrategies,insteadofusingonlyquantity-settingstrategies?GamesinwhichfirmsuseonlypricestrategiesandplaysimultaneouslyareBertrandgames.第80页/共94页BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssettheirpricessimultaneously.Q:IsthereaNashequilibrium?第81页/共94页BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.第82页/共94页BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.Allfirmssettheirpricesequaltothemarginalcostc.Why?第83页/共94页BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.第84页/共94页BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.第85页/共94页BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.Hence,atanequilibrium,allfirmsmustsetthesameprice.第86页/共94页Bertrand