中级微观经济学Ch27-Oligopoly

ChapterTwenty-SevenOligopoly北京大学中级微观经济学Ch27-OligopolyOligopolyAmonopolyisanindustryconsistingasinglefirm.Aduopolyisanindustryconsistingoftwofirms.Anoligopolyisanindustryconsistingofafewfirms.Particularly,eachfirm’sownpriceoroutputdecisionsaffectitscompetitors’profits.北京大学中级微观经济学Ch27-OligopolyOligopolyHowdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplyingthesameproduct.北京大学中级微观经济学Ch27-OligopolyQuantityCompetitionAssumethatfirmscompetebychoosingoutputlevels.Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1+y2.Themarketpricewillbep(y1+y2).Thefirms’totalcostfunctionsarec1(y1)andc2(y2).北京大学中级微观经济学Ch27-OligopolyQuantityCompetitionSupposefirm1takesfirm2’soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunctionas

Giveny2,whatoutputlevely1maximizesfirm1’sprofit?北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleSupposethatthemarketinversedemandfunctionis

andthatthefirms’totalcostfunctionsareand北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionis北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizing

outputlevelsolves北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizing

outputlevelsolvesI.e.firm1’sbestresponsetoy2is北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampley2y16015Firm1’s“reactioncurve”北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionis北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizing

outputlevelsolves北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizing

outputlevelsolvesI.e.firm1’sbestresponsetoy2is北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”45/445北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleAnequilibriumiswheneachfirm’soutputlevelisabestresponsetotheotherfirm’soutputlevel,forthenneitherwantstodeviatefromitsoutputlevel.Apairofoutputlevels(y1*,y2*)isaCournot-Nashequilibriumifand北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleand北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleandSubstitutefory2*toget北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleandSubstitutefory2*toget北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleandSubstitutefory2*togetHence北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampleandSubstitutefory2*togetHenceSotheCournot-Nashequilibriumis北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”6015Firm1’s“reactioncurve”45/445北京大学中级微观经济学Ch27-OligopolyQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”4860Firm1’s“reactioncurve”813Cournot-Nashequilibrium北京大学中级微观经济学Ch27-OligopolyQuantityCompetitionGenerally,givenfirm2’schosenoutput

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

Nashreactiontoy2.北京大学中级微观经济学Ch27-OligopolyQuantityCompetitionSimilarly,givenfirm1’schosenoutput

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

Nashreactiontoy1.北京大学中级微观经济学Ch27-OligopolyQuantityCompetitiony2y1Firm1’s“reactioncurve”Firm1’s“reactioncurve”Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*)北京大学中级微观经济学Ch27-OligopolyIso-ProfitCurvesForfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevelP1.Whatdoiso-profitcurveslooklike?北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm1Withy1fixed,firm1’sprofit

increasesasy2decreases.北京大学中级微观经济学Ch27-Oligopolyy2y1Increasingprofit

forfirm1.Iso-ProfitCurvesforFirm1北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?y2’北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y2’y1’北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y1’isfirm1’s

bestresponsetoy2=y2’.y2’y1’北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y1’isfirm1’s

bestresponsetoy2=y2’.y2’R1(y2’)北京大学中级微观经济学Ch27-Oligopolyy2y1y2’R1(y2’)y2”R1(y2”)Iso-ProfitCurvesforFirm1北京大学中级微观经济学Ch27-Oligopolyy2y1y2’y2”R1(y2”)R1(y2’)Firm1’sreactioncurve

passesthroughthe“tops”offirm1’siso-profit

curves.Iso-ProfitCurvesforFirm1北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm2Increasingprofit

forfirm2.北京大学中级微观经济学Ch27-Oligopolyy2y1Iso-ProfitCurvesforFirm2Firm2’sreactioncurve

passesthroughthe“tops”offirm2’siso-profit

curves.y2=R2(y1)北京大学中级微观经济学Ch27-OligopolyCollusionQ:AretheCournot-Nashequilibriumprofitsthelargestthatthefirmscanearnintotal?北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

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

equilibrium.北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

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

equilibrium.北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

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

equilibrium.北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP2HigherP1北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*HigherP2HigherP1y2’y1’北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2’y1’HigherP2HigherP1北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).北京大学中级微观经济学Ch27-OligopolyCollusionSothereareprofitincentivesforbothfirmsto“cooperate”byloweringtheiroutputlevels.Thisiscollusion.Firmsthatcolludearesaidtohaveformedacartel.Iffirmsformacartel,howshouldtheydoit?北京大学中级微观经济学Ch27-OligopolyCollusionSupposethetwofirmswanttomaximizetheirtotalprofitanddivideitbetweenthem.Theirgoalistochoosecooperativelyoutputlevelsy1andy2thatmaximize北京大学中级微观经济学Ch27-OligopolyCollusionThefirmscannotdoworsebycolludingsincetheycancooperativelychoosetheirCournot-NashequilibriumoutputlevelsandsoearntheirCournot-Nashequilibriumprofits.SocollusionmustprovideprofitsatleastaslargeastheirCournot-Nashequilibriumprofits.北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

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

higherprofitsfor

bothfirms.y2”y1”北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2~y1~(y1,y2)maximizesfirm1’sprofit

whileleavingfirm2’sprofitat

theCournot-Nashequilibrium

level.~~北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2~y1~(y1,y2)maximizesfirm1’sprofit

whileleavingfirm2’sprofitat

theCournot-Nashequilibrium

level.~~y2_y2_(y1,y2)maximizesfirm

2’sprofitwhileleaving

firm1’sprofitatthe

Cournot-Nash

equilibriumlevel.__北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2~y1~y2_y2_Thepathofoutputpairsthat

maximizeonefirm’sprofit

whilegivingtheotherfirmat

leastitsCNequilibrium

profit.北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2~y1~y2_y2_Thepathofoutputpairsthat

maximizeonefirm’sprofit

whilegivingtheotherfirmat

leastitsCNequilibrium

profit.Oneof

theseoutputpairsmustmaximizethe

cartel’sjointprofit.北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y1*y2*y2my1m(y1m,y2m)denotes

theoutputlevels

thatmaximizethe

cartel’stotalprofit.北京大学中级微观经济学Ch27-OligopolyCollusionIssuchacartelstable?Doesonefirmhaveanincentivetocheatontheother?I.e.iffirm1continuestoproducey1munits,isitprofit-maximizingforfirm2tocontinuetoproducey2munits?北京大学中级微观经济学Ch27-OligopolyCollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m).北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y2my1my2=R2(y1m)isfirm2’s

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

reactioncurve北京大学中级微观经济学Ch27-OligopolyCollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m)>y2m.Firm2’sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromy2mtoR2(y1m).北京大学中级微观经济学Ch27-OligopolyCollusionSimilarly,firm1’sprofitincreasesifitcheatsonfirm2byincreasingitsoutputlevelfromy1mtoR1(y2m).北京大学中级微观经济学Ch27-OligopolyCollusiony2y1y2my1my2=R2(y1m)isfirm2’s

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

reactioncurve北京大学中级微观经济学Ch27-OligopolyCollusionSoaprofit-seekingcartelinwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable.E.g.OPEC’sbrokenagreements.北京大学中级微观经济学Ch27-OligopolyTheOrderofPlaySofarithasbeenassumedthatfirmschoosetheiroutputlevelssimultaneously.Thecompetitionbetweenthefirmsisthenasimultaneousplaygameinwhichtheoutputlevelsarethestrategicvariables.北京大学中级微观经济学Ch27-OligopolyTheOrderofPlayWhatiffirm1choosesitsoutputlevelfirstandthenfirm2respondstothischoice?Firm1isthenaleader.Firm2isafollower.Thecompetitionisasequentialgameinwhichtheoutputlevelsarethestrategicvariables.北京大学中级微观经济学Ch27-OligopolyTheOrderofPlaySuchgamesarevonStackelberggames.Isitbettertobetheleader?Orisitbettertobethefollower?北京大学中级微观经济学Ch27-OligopolyStackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?北京大学中级微观经济学Ch27-OligopolyStackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).北京大学中级微观经济学Ch27-OligopolyStackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).Firm1knowsthisandsoperfectlyanticipatesfirm2’sreactiontoanyy1chosenbyfirm1.北京大学中级微观经济学Ch27-OligopolyStackelbergGamesThismakestheleader’sprofitfunction北京大学中级微观经济学Ch27-OligopolyStackelbergGamesThismakestheleader’sprofitfunction

Theleaderthenchoosesy1tomaximizeitsprofitlevel.北京大学中级微观经济学Ch27-OligopolyStackelbergGamesThismakestheleader’sprofitfunction

Theleaderchoosesy1tomaximizeitsprofit.Q:WilltheleadermakeaprofitatleastaslargeasitsCournot-Nashequilibriumprofit?北京大学中级微观经济学Ch27-OligopolyStackelbergGamesA:Yes.TheleadercouldchooseitsCournot-Nashoutputlevel,knowingthatthefollowerwouldthenalsochooseitsC-Noutputlevel.Theleader’sprofitwouldthenbeitsC-Nprofit.Buttheleaderdoesnothavetodothis,soitsprofitmustbeatleastaslargeasitsC-Nprofit.北京大学中级微观经济学Ch27-OligopolyStackelbergGames;AnExampleThemarketinversedemandfunctionisp=60-yT.Thefirms’costfunctionsarec1(y1)=y12andc2(y2)=15y2+y22.Firm2isthefollower.Itsreactionfunctionis北京大学中级微观经济学Ch27-OligopolyStackelbergGames;AnExampleTheleader’sprofitfunctionistherefore北京大学中级微观经济学Ch27-OligopolyStackelbergGames;AnExampleTheleader’sprofitfunctionisthereforeForaprofit-maximum,北京大学中级微观经济学Ch27-OligopolyStackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoice北京大学中级微观经济学Ch27-OligopolyStackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceA:北京大学中级微观经济学Ch27-OligopolyStackelbergGames;AnExampleQ:Whatisfirm2’sresponsetotheleader’schoiceA:TheC-Noutputlevelsare(y1*,y2*)=(13,8)sotheleaderproducesmorethanitsC-NoutputandthefollowerproduceslessthanitsC-Noutput.Thisistruegenerally.北京大学中级微观经济学Ch27-OligopolyStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP2HigherP1北京大学中级微观经济学Ch27-OligopolyStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP1Follower’sreactioncurve北京大学中级微观经济学Ch27-OligopolyStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.(y1S,y2S)istheStackelbergequilibrium.HigherP1y1SFollower’sreactioncurvey2S北京大学中级微观经济学Ch27-OligopolyStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.(y1S,y2S)istheStackelbergequilibrium.y1SFollower’sreactioncurvey2S北京大学中级微观经济学Ch27-OligopolyPriceCompetitionWhatiffirmscompeteusingonlyprice-settingstrategies,insteadofusingonlyquantity-settingstrategies?GamesinwhichfirmsuseonlypricestrategiesandplaysimultaneouslyareBertrandgames.北京大学中级微观经济学Ch27-OligopolyBertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssettheirpricessimultaneously.Q:IsthereaNashequilibrium?北京大学中级微观经济学Ch27-OligopolyBertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.北京大学中级微观经济学Ch27-OligopolyBertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.Allfirmssettheirpricesequaltothemarginalcostc.Why?北京大学中级微观经济学Ch27-OligopolyBertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.北京大学中级微观经济学Ch27-OligopolyBertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.北京大学中级微观经济学Ch27-OligopolyBertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.Hence,atanequilibrium,allfirmsmustsetthesamepr