北京大学中级微观经济学Ch27-Oligopoly

.,ChapterTwenty-Seven,Oligopoly,.,Oligopoly,Amonopolyisanindustryconsistingasinglefirm.Aduopolyisanindustryconsistingoftwofirms.Anoligopolyisanindustryconsistingofafewfirms.Particularly,eachfirmsownpriceoroutputdecisionsaffectitscompetitorsprofits.,.,Oligopoly,Howdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplyingthesameproduct.,.,QuantityCompetition,Assumethatfirmscompetebychoosingoutputlevels.Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1+y2.Themarketpricewillbep(y1+y2).Thefirmstotalcostfunctionsarec1(y1)andc2(y2).,.,QuantityCompetition,Supposefirm1takesfirm2soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunctionasGiveny2,whatoutputlevely1maximizesfirm1sprofit?,.,QuantityCompetition;AnExample,Supposethatthemarketinversedemandfunctionisandthatthefirmstotalcostfunctionsare,and,.,QuantityCompetition;AnExample,Then,forgiveny2,firm1sprofitfunctionis,.,QuantityCompetition;AnExample,Then,forgiveny2,firm1sprofitfunctionis,So,giveny2,firm1sprofit-maximizingoutputlevelsolves,.,QuantityCompetition;AnExample,Then,forgiveny2,firm1sprofitfunctionis,So,giveny2,firm1sprofit-maximizingoutputlevelsolves,I.e.firm1sbestresponsetoy2is,.,QuantityCompetition;AnExample,y2,y1,60,15,Firm1s“reactioncurve”,.,QuantityCompetition;AnExample,Similarly,giveny1,firm2sprofitfunctionis,.,QuantityCompetition;AnExample,Similarly,giveny1,firm2sprofitfunctionis,So,giveny1,firm2sprofit-maximizingoutputlevelsolves,.,QuantityCompetition;AnExample,Similarly,giveny1,firm2sprofitfunctionis,So,giveny1,firm2sprofit-maximizingoutputlevelsolves,I.e.firm1sbestresponsetoy2is,.,QuantityCompetition;AnExample,y2,y1,Firm2s“reactioncurve”,45/4,45,.,QuantityCompetition;AnExample,Anequilibriumiswheneachfirmsoutputlevelisabestresponsetotheotherfirmsoutputlevel,forthenneitherwantstodeviatefromitsoutputlevel.Apairofoutputlevels(y1*,y2*)isaCournot-Nashequilibriumif,and,.,QuantityCompetition;AnExample,and,.,QuantityCompetition;AnExample,and,Substitutefory2*toget,.,QuantityCompetition;AnExample,and,Substitutefory2*toget,.,QuantityCompetition;AnExample,and,Substitutefory2*toget,Hence,.,QuantityCompetition;AnExample,and,Substitutefory2*toget,Hence,SotheCournot-Nashequilibriumis,.,QuantityCompetition;AnExample,y2,y1,Firm2s“reactioncurve”,60,15,Firm1s“reactioncurve”,45/4,45,.,QuantityCompetition;AnExample,y2,y1,Firm2s“reactioncurve”,48,60,Firm1s“reactioncurve”,8,13,Cournot-Nashequilibrium,.,QuantityCompetition,Generally,givenfirm2schosenoutputlevely2,firm1sprofitfunctionis,andtheprofit-maximizingvalueofy1solves,Thesolution,y1=R1(y2),isfirm1sCournot-Nashreactiontoy2.,.,QuantityCompetition,Similarly,givenfirm1schosenoutputlevely1,firm2sprofitfunctionis,andtheprofit-maximizingvalueofy2solves,Thesolution,y2=R2(y1),isfirm2sCournot-Nashreactiontoy1.,.,QuantityCompetition,y2,y1,Firm1s“reactioncurve”,Firm1s“reactioncurve”,Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*),.,Iso-ProfitCurves,Forfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevelP1.Whatdoiso-profitcurveslooklike?,.,y2,y1,Iso-ProfitCurvesforFirm1,Withy1fixed,firm1sprofitincreasesasy2decreases.,.,y2,y1,Increasingprofitforfirm1.,Iso-ProfitCurvesforFirm1,.,y2,y1,Iso-ProfitCurvesforFirm1,Q:Firm2choosesy2=y2.Wherealongtheliney2=y2istheoutputlevelthatmaximizesfirm1sprofit?,y2,.,y2,y1,Iso-ProfitCurvesforFirm1,Q:Firm2choosesy2=y2.Wherealongtheliney2=y2istheoutputlevelthatmaximizesfirm1sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.,y2,y1,.,y2,y1,Iso-ProfitCurvesforFirm1,Q:Firm2choosesy2=y2.Wherealongtheliney2=y2istheoutputlevelthatmaximizesfirm1sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1isfirm1sbestresponsetoy2=y2.,y2,y1,.,y2,y1,Iso-ProfitCurvesforFirm1,Q:Firm2choosesy2=y2.Wherealongtheliney2=y2istheoutputlevelthatmaximizesfirm1sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1isfirm1sbestresponsetoy2=y2.,y2,R1(y2),.,y2,y1,y2,R1(y2),y2”,R1(y2”),Iso-ProfitCurvesforFirm1,.,y2,y1,y2,y2”,R1(y2”),R1(y2),Firm1sreactioncurvepassesthroughthe“tops”offirm1siso-profitcurves.,Iso-ProfitCurvesforFirm1,.,y2,y1,Iso-ProfitCurvesforFirm2,Increasingprofitforfirm2.,.,y2,y1,Iso-ProfitCurvesforFirm2,Firm2sreactioncurvepassesthroughthe“tops”offirm2siso-profitcurves.,y2=R2(y1),.,Collusion,Q:AretheCournot-Nashequilibriumprofitsthelargestthatthefirmscanearnintotal?,.,Collusion,y2,y1,y1*,y2*,Arethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?,(y1*,y2*)istheCournot-Nashequilibrium.,.,Collusion,y2,y1,y1*,y2*,Arethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?,(y1*,y2*)istheCournot-Nashequilibrium.,.,Collusion,y2,y1,y1*,y2*,Arethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?,(y1*,y2*)istheCournot-Nashequilibrium.,.,Collusion,y2,y1,y1*,y2*,(y1*,y2*)istheCournot-Nashequilibrium.,HigherP2,HigherP1,.,Collusion,y2,y1,y1*,y2*,HigherP2,HigherP1,y2,y1,.,Collusion,y2,y1,y1*,y2*,y2,y1,HigherP2,HigherP1,.,Collusion,y2,y1,y1*,y2*,y2,y1,HigherP2,HigherP1,(y1,y2)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).,.,Collusion,Sothereareprofitincentivesforbothfirmsto“cooperate”byloweringtheiroutputlevels.Thisiscollusion.Firmsthatcolludearesaidtohaveformedacartel.Iffirmsformacartel,howshouldtheydoit?,.,Collusion,Supposethetwofirmswanttomaximizetheirtotalprofitanddivideitbetweenthem.Theirgoalistochoosecooperativelyoutputlevelsy1andy2thatmaximize,.,Collusion,ThefirmscannotdoworsebycolludingsincetheycancooperativelychoosetheirCournot-NashequilibriumoutputlevelsandsoearntheirCournot-Nashequilibriumprofits.SocollusionmustprovideprofitsatleastaslargeastheirCournot-Nashequilibriumprofits.,.,Collusion,y2,y1,y1*,y2*,y2,y1,HigherP2,HigherP1,(y1,y2)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).,.,Collusion,y2,y1,y1*,y2*,y2,y1,HigherP2,HigherP1,(y1,y2)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).,(y1”,y2”)earnsstillhigherprofitsforbothfirms.,y2”,y1”,.,Collusion,y2,y1,y1*,y2*,(y1,y2)maximizesfirm1sprofitwhileleavingfirm2sprofitattheCournot-Nashequilibriumlevel.,.,Collusion,y2,y1,y1*,y2*,(y1,y2)maximizesfirm1sprofitwhileleavingfirm2sprofitattheCournot-Nashequilibriumlevel.,(y1,y2)maximizesfirm2sprofitwhileleavingfirm1sprofitattheCournot-Nashequilibriumlevel.,_,_,.,Collusion,y2,y1,y1*,y2*,ThepathofoutputpairsthatmaximizeonefirmsprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit.,.,Collusion,y2,y1,y1*,y2*,ThepathofoutputpairsthatmaximizeonefirmsprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit.Oneoftheseoutputpairsmustmaximizethecartelsjointprofit.,.,Collusion,y2,y1,y1*,y2*,(y1m,y2m)denotestheoutputlevelsthatmaximizethecartelstotalprofit.,.,Collusion,Issuchacartelstable?Doesonefirmhaveanincentivetocheatontheother?I.e.iffirm1continuestoproducey1munits,isitprofit-maximizingforfirm2tocontinuetoproducey2munits?,.,Collusion,Firm2sprofit-maximizingresponsetoy1=y1misy2=R2(y1m).,.,Collusion,y2,y1,y2=R2(y1m)isfirm2sbestresponsetofirm1choosingy1=y1m.,R2(y1m),y1=R1(y2),firm1sreactioncurve,y2=R2(y1),firm2sreactioncurve,.,Collusion,Firm2sprofit-maximizingresponsetoy1=y1misy2=R2(y1m)y2m.Firm2sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromy2mtoR2(y1m).,.,Collusion,Similarly,firm1sprofitincreasesifitcheatsonfirm2byincreasingitsoutputlevelfromy1mtoR1(y2m).,.,Collusion,y2,y1,y2=R2(y1m)isfirm2sbestresponsetofirm1choosingy1=y1m.,R1(y2m),y1=R1(y2),firm1sreactioncurve,y2=R2(y1),firm2sreactioncurve,.,Collusion,Soaprofit-seekingcartelinwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable.E.g.OPECsbrokenagreements.,.,TheOrderofPlay,Sofarithasbeenassumedthatfirmschoosetheiroutputlevelssimultaneously.Thecompetitionbetweenthefirmsisthenasimultaneousplaygameinwhichtheoutputlevelsarethestrategicvariables.,.,TheOrderofPlay,Whatiffirm1choosesitsoutputlevelfirstandthenfirm2respondstothischoice?Firm1isthenaleader.Firm2isafollower.Thecompetitionisasequentialgameinwhichtheoutputlevelsarethestrategicvariables.,.,TheOrderofPlay,SuchgamesarevonStackelberggames.Isitbettertobetheleader?Orisitbettertobethefollower?,.,StackelbergGames,Q:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?,.,StackelbergGames,Q:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).,.,StackelbergGames,Q:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).Firm1knowsthisandsoperfectlyanticipatesfirm2sreactiontoanyy1chosenbyfirm1.,.,StackelbergGames,Thismakestheleadersprofitfunction,.,StackelbergGames,ThismakestheleadersprofitfunctionTheleaderthenchoosesy1tomaximizeitsprofitlevel.,.,StackelbergGames,ThismakestheleadersprofitfunctionTheleaderchoosesy1tomaximizeitsprofit.Q:WilltheleadermakeaprofitatleastaslargeasitsCournot-Nashequilibriumprofit?,.,StackelbergGames,A:Yes.TheleadercouldchooseitsCournot-Nashoutputlevel,knowingthatthefollowerwouldthenalsochooseitsC-Noutputlevel.TheleadersprofitwouldthenbeitsC-Nprofit.Buttheleaderdoesnothavetodothis,soitsprofitmustbeatleastaslargeasitsC-Nprofit.,.,StackelbergGames;AnExample,Themarketinversedemandfunctionisp=60-yT.Thefirmscostfunctionsarec1(y1)=y12andc2(y2)=15y2+y22.Firm2isthefollower.Itsreactionfunctionis,.,StackelbergGames;AnExample,Theleadersprofitfunctionistherefore,.,StackelbergGames;AnExample,Theleadersprofitfunctionistherefore,Foraprofit-maximum,.,StackelbergGames;AnExample,Q:Whatisfirm2sresponsetotheleaderschoice,.,StackelbergGames;AnExample,Q:Whatisfirm2sresponsetotheleaderschoiceA:,.,StackelbergGames;AnExample,Q:Whatisfirm2sresponsetotheleaderschoiceA:,TheC-Noutputlevelsare(y1*,y2*)=(13,8)sotheleaderproducesmorethanitsC-NoutputandthefollowerproduceslessthanitsC-Noutput.Thisistruegenerally.,.,StackelbergGames,y2,y1,y1*,y2*,(y1*,y2*)istheCournot-Nashequilibrium.,HigherP2,HigherP1,.,StackelbergGames,y2,y1,y1*,y2*,(y1*,y2*)istheCournot-Nashequilibrium.,HigherP1,Followersreactioncurve,.,StackelbergGames,y2,y1,y1*,y2*,(y1*,y2*)istheCournot-Nashequilibrium.(y1S,y2S)istheStackelbergequilibrium.,HigherP1,y1S,Followersreactioncurve,y2S,.,StackelbergGames,y2,y1,y1*,y2*,(y1*,y2*)istheCournot-Nashequilibrium.(y1S,y2S)istheStackelbergequilibrium.,y1S,Followersreactioncurve,y2S,.,PriceCompetition,Whatiffirmscompeteusingonlyprice-settingstrategies,insteadofusingonlyquantity-settingstrategies?GamesinwhichfirmsuseonlypricestrategiesandplaysimultaneouslyareBertrandgames.,.,BertrandGames,Eachfirmsmarginalproductioncostisconstantatc.Allfirmssettheirpricessimultaneously.Q:IsthereaNashequilibrium?,.,BertrandGames,Eachfirmsmarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.,.,BertrandGames,Eachfirmsmarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.Allfirmssettheirpricesequaltothemarginalcostc.Why?,.,BertrandGames,Supposeonefirmsetsitspricehigherthananotherfirmsprice.,.,BertrandGames,Supposeonefirmsetsitspricehigherthananotherfirmsprice.Thenthehigher-pricedfirmwouldhavenocustomers.,.,BertrandGames,Supposeonefirmsetsitspricehigherthananotherfirmsprice.Thenthehigher-pricedfirmwouldhavenocustomers.Hence,atanequilibrium,allfirmsmustsetthesameprice.,.,BertrandGames,Supposethecommonpricesetbyallfirmishigherthanm