北京大学中级微观经济学Ch27-OligopolyPPT优秀课件

ChapterTwenty-SevenOligopolyOligopolyAmonopolyisanindustryconsistingasinglefirm.Aduopolyisanindustryconsistingoftwofirms.Anoligopolyisanindustryconsistingofafewfirms.Particularly,eachfirm’sownpriceoroutputdecisionsaffectitscompetitors’profits.OligopolyHowdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplyingthesameproduct.QuantityCompetitionAssumethatfirmscompetebychoosingoutputlevels.Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1+y2.Themarketpricewillbep(y1+y2).Thefirms’totalcostfunctionsarec1(y1)andc2(y2).QuantityCompetitionSupposefirm1takesfirm2’soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunctionasGiveny2,whatoutputlevely1maximizesfirm1’sprofit?QuantityCompetition;AnExampleSupposethatthemarketinversedemandfunctionisandthatthefirms’totalcostfunctionsareandQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizingoutputlevelsolvesQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizingoutputlevelsolvesI.e.firm1’sbestresponsetoy2isQuantityCompetition;AnExampley2y16015Firm1’s“reactioncurve”QuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisQuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizingoutputlevelsolvesQuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizingoutputlevelsolvesI.e.firm1’sbestresponsetoy2isQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”45/445QuantityCompetition;AnExampleAnequilibriumiswheneachfirm’soutputlevelisabestresponsetotheotherfirm’soutputlevel,forthenneitherwantstodeviatefromitsoutputlevel.Apairofoutputlevels(y1*,y2*)isaCournot-NashequilibriumifandQuantityCompetition;AnExampleandQuantityCompetition;AnExampleandSubstitutefory2*togetQuantityCompetition;AnExampleandSubstitutefory2*togetQuantityCompetition;AnExampleandSubstitutefory2*togetHenceQuantityCompetition;AnExampleandSubstitutefory2*togetHenceSotheCournot-NashequilibriumisQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”6015Firm1’s“reactioncurve”45/445QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”4860Firm1’s“reactioncurve”813Cournot-NashequilibriumQuantityCompetitionGenerally,givenfirm2’schosenoutputlevely2,firm1’sprofitfunctionisandtheprofit-maximizingvalueofy1solvesThesolution,y1=R1(y2),isfirm1’sCournot-Nashreactiontoy2.QuantityCompetitionSimilarly,givenfirm1’schosenoutputlevely1,firm2’sprofitfunctionisandtheprofit-maximizingvalueofy2solvesThesolution,y2=R2(y1),isfirm2’sCournot-Nashreactiontoy1.QuantityCompetitiony2y1Firm1’s“reactioncurve”Firm1’s“reactioncurve”Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*)Iso-ProfitCurvesForfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevelP1.Whatdoiso-profitcurveslooklike?y2y1Iso-ProfitCurvesforFirm1Withy1fixed,firm1’sprofitincreasesasy2decreases.y2y1Increasingprofitforfirm1.Iso-ProfitCurvesforFirm1y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?y2’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y2’y1’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1’isfirm1’sbestresponsetoy2=y2’.y2’y1’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1’isfirm1’sbestresponsetoy2=y2’.y2’R1(y2’)y2y1y2’R1(y2’)y2”R1(y2”)Iso-ProfitCurvesforFirm1y2y1y2’y2”R1(y2”)R1(y2’)Firm1’sreactioncurvepassesthroughthe“tops”offirm1’siso-profitcurves.Iso-ProfitCurvesforFirm1y2y1Iso-ProfitCurvesforFirm2Increasingprofitforfirm2.y2y1Iso-ProfitCurvesforFirm2Firm2’sreactioncurvepassesthroughthe“tops”offirm2’siso-profitcurves.y2=R2(y1)CollusionQ:AretheCournot-Nashequilibriumprofitsthelargestthatthefirmscanearnintotal?Collusiony2y1y1*y2*Arethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?(y1*,y2*)istheCournot-Nashequilibrium.Collusiony2y1y1*y2*Arethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?(y1*,y2*)istheCournot-Nashequilibrium.Collusiony2y1y1*y2*Arethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?(y1*,y2*)istheCournot-Nashequilibrium.Collusiony2y1y1*y2*(y1*,y2*)istheCournot-Nashequilibrium.HigherP2HigherP1Collusiony2y1y1*y2*HigherP2HigherP1y2’y1’Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).CollusionSothereareprofitincentivesforbothfirmsto“cooperate”byloweringtheiroutputlevels.Thisiscollusion.Firmsthatcolludearesaidtohaveformedacartel.Iffirmsformacartel,howshouldtheydoit?CollusionSupposethetwofirmswanttomaximizetheirtotalprofitanddivideitbetweenthem.Theirgoalistochoosecooperativelyoutputlevelsy1andy2thatmaximizeCollusionThefirmscannotdoworsebycolludingsincetheycancooperativelychoosetheirCournot-NashequilibriumoutputlevelsandsoearntheirCournot-Nashequilibriumprofits.SocollusionmustprovideprofitsatleastaslargeastheirCournot-Nashequilibriumprofits.Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).(y1”,y2”)earnsstillhigherprofitsforbothfirms.y2”y1”Collusiony2y1y1*y2*(y1,y2)maximizesfirm1’sprofitwhileleavingfirm2’sprofitattheCournot-Nashequilibriumlevel.~~Collusiony2y1y1*y2*(y1,y2)maximizesfirm1’sprofitwhileleavingfirm2’sprofitattheCournot-Nashequilibriumlevel.~~(y1,y2)maximizesfirm2’sprofitwhileleavingfirm1’sprofitattheCournot-Nashequilibriumlevel.__Collusiony2y1y1*y2*Thepathofoutputpairsthatmaximizeonefirm’sprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit.Collusiony2y1y1*y2*Thepathofoutputpairsthatmaximizeonefirm’sprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit.Oneoftheseoutputpairsmustmaximizethecartel’sjointprofit.Collusiony2y1y1*y2*(y1m,y2m)denotestheoutputlevelsthatmaximizethecartel’stotalprofit.CollusionIssuchacartelstable?Doesonefirmhaveanincentivetocheatontheother?I.e.iffirm1continuestoproducey1munits,isitprofit-maximizingforfirm2tocontinuetoproducey2munits?CollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m).Collusiony2y1y2=R2(y1m)isfirm2’sbestresponsetofirm1choosingy1=y1m.R2(y1m)y1=R1(y2),firm1’sreactioncurvey2=R2(y1),firm2’sreactioncurveCollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m)>y2m.Firm2’sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromy2mtoR2(y1m).CollusionSimilarly,firm1’sprofitincreasesifitcheatsonfirm2byincreasingitsoutputlevelfromy1mtoR1(y2m).Collusiony2y1y2=R2(y1m)isfirm2’sbestresponsetofirm1choosingy1=y1m.R1(y2m)y1=R1(y2),firm1’sreactioncurvey2=R2(y1),firm2’sreactioncurveCollusionSoaprofit-seekingcartelinwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable.E.g.OPEC’sbrokenagreements.TheOrderofPlaySofarithasbeenassumedthatfirmschoosetheiroutputlevelssimultaneously.Thecompetitionbetweenthefirmsisthenasimultaneousplaygameinwhichtheoutputlevelsarethestrategicvariables.TheOrderofPlayWhatiffirm1choosesitsoutputlevelfirstandthenfirm2respondstothischoice?Firm1isthenaleader.Firm2isafollower.Thecompetitionisasequentialgameinwhichtheoutputlevelsarethestrategicvariables.TheOrderofPlaySuchgamesarevonStackelberggames.Isitbettertobetheleader?Orisitbettertobethefollower?StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).Firm1knowsthisandsoperfectlyanticipatesfirm2’sreactiontoanyy1chosenbyfirm1.StackelbergGamesThismakestheleader’sprofitfunctionStackelbergGamesThismakestheleader’sprofitfunctionTheleaderthenchoosesy1tomaximizeitsprofitlevel.StackelbergGamesThismakestheleader’sprofitfunctionTheleaderchoosesy1tomaximizeitsprofit.Q:WilltheleadermakeaprofitatleastaslargeasitsCournot-Nashequilibriumprofit?StackelbergGamesA:Yes.TheleadercouldchooseitsCournot-Nashoutputlevel,knowingthatthefollowerwouldthenalsochooseitsC-Noutputlevel.Theleader’sprofitwouldthenbeitsC-Nprofit.Buttheleaderdoesnothavetodothis,soitsprofitmustbeatleastaslargeasitsC-Nprofit.StackelbergGames;AnExampleThemarketinversedemandfunctionisp=60-yT.Thefirms’costfunctionsarec1(y1)=y12andc2(y2)=15y2+y22.Firm2isthefollower.ItsreactionfunctionisStackelbergGames;AnExampleTheleader’sprofitfunctionisthereforeStackelbergGames;AnExampleTheleader’sprofitfunctionisthereforeForaprofit-maximum,StackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceStackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceA:StackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceA:TheC-Noutputlevelsare(y1*,y2*)=(13,8)sotheleaderproducesmorethanitsC-NoutputandthefollowerproduceslessthanitsC-Noutput.Thisistruegenerally.StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nashequilibrium.HigherP2HigherP1StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nashequilibrium.HigherP1Follower’sreactioncurveStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nashequilibrium.(y1S,y2S)istheStackelbergequilibrium.HigherP1y1SFollower’sreactioncurvey2SStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nashequilibrium.(y1S,y2S)istheStackelbergequilibrium.y1SFollower’sreactioncurvey2SPriceCompetitionWhatiffirmscompeteusingonlyprice-settingstrategies,insteadofusingonlyquantity-settingstrategies?GamesinwhichfirmsuseonlypricestrategiesandplaysimultaneouslyareBertrandgames.BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssettheirpricessimultaneously.Q:IsthereaNashequilibrium?BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.Allfirmssettheirpricesequaltothemarginalcostc.Why?BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.Hence,atanequilibrium,allfirmsmustsetthesameprice.BertrandGamesSupposethecommonpricesetbyallfirmishigherthanmarginalcostc.BertrandGamesSupposethecommonpricesetbyallfirmishigherthanmarginalcostc.Thenonefirmcanjustslightlyloweritspriceandselltoallthebuyers,therebyincreasingitsprofit.BertrandGamesSupposethecommonpricesetbyallfirmishigherthanmarginalcostc.Thenonefirmcanjustslightlyloweritspriceandselltoallthebuyers,therebyincreasingitsprofit.Theonlycommonpricewhichpreventsundercuttingisc.HencethisistheonlyNashequilibrium.SequentialPriceGamesWhatif,insteadofsimultaneousplayinpricingstrategies,onefirmdecidesitspriceaheadoftheothers.Thisisasequentialgameinpricingstrategiescalledaprice-leadershipgame.Thefirmwhichsetsitspriceaheadoftheotherfirmsistheprice-leader.SequentialPriceGamesThinkofonelargefirm(theleader)andmanycompetitivesmallfirms(thefollowers).Thesmallfirmsareprice-takersandsotheircollectivesupplyreactiontoamarketpricepistheiraggregatesupplyfunctionYf(p).SequentialPriceGamesThemarketdemandfunctionisD(p).SotheleaderknowsthatifitsetsapricepthequantitydemandedfromitwillbetheresidualdemandHencetheleader’sprofitfunctionisSequentialPriceGamesTheleader’sprofitfunctionissotheleaderchoosesthepricelevelp*forwhichprofitismaximized.ThefollowerscollectivelysupplyYf(p*)unitsandtheleadersuppliestheresidualquantityD(p*)-Yf(p*).