北京大学中级微观经济学课件Ch27-Oligopoly.ppt

ChapterTwenty Seven Oligopoly Oligopoly Amonopolyisanindustryconsistingasinglefirm Aduopolyisanindustryconsistingoftwofirms Anoligopolyisanindustryconsistingofafewfirms Particularly eachfirm sownpriceoroutputdecisionsaffectitscompetitors profits Oligopoly Howdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic Considertheduopolisticcaseoftwofirmssupplyingthesameproduct QuantityCompetition Assumethatfirmscompetebychoosingoutputlevels Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1 y2 Themarketpricewillbep y1 y2 Thefirms totalcostfunctionsarec1 y1 andc2 y2 QuantityCompetition Supposefirm1takesfirm2 soutputlevelchoicey2asgiven Thenfirm1seesitsprofitfunctionasGiveny2 whatoutputlevely1maximizesfirm1 sprofit QuantityCompetition AnExample Supposethatthemarketinversedemandfunctionisandthatthefirms totalcostfunctionsare and QuantityCompetition AnExample Then forgiveny2 firm1 sprofitfunctionis QuantityCompetition AnExample Then forgiveny2 firm1 sprofitfunctionis So giveny2 firm1 sprofit maximizingoutputlevelsolves QuantityCompetition AnExample Then forgiveny2 firm1 sprofitfunctionis So giveny2 firm1 sprofit maximizingoutputlevelsolves I e firm1 sbestresponsetoy2is QuantityCompetition AnExample y2 y1 60 15 Firm1 s reactioncurve QuantityCompetition AnExample Similarly giveny1 firm2 sprofitfunctionis QuantityCompetition AnExample Similarly giveny1 firm2 sprofitfunctionis So giveny1 firm2 sprofit maximizingoutputlevelsolves QuantityCompetition AnExample Similarly giveny1 firm2 sprofitfunctionis So giveny1 firm2 sprofit maximizingoutputlevelsolves I e firm1 sbestresponsetoy2is QuantityCompetition AnExample y2 y1 Firm2 s reactioncurve 45 4 45 QuantityCompetition AnExample Anequilibriumiswheneachfirm soutputlevelisabestresponsetotheotherfirm soutputlevel 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 Firm2 s reactioncurve 60 15 Firm1 s reactioncurve 45 4 45 QuantityCompetition AnExample y2 y1 Firm2 s reactioncurve 48 60 Firm1 s reactioncurve 8 13 Cournot Nashequilibrium QuantityCompetition Generally givenfirm2 schosenoutputlevely2 firm1 sprofitfunctionis andtheprofit maximizingvalueofy1solves Thesolution y1 R1 y2 isfirm1 sCournot Nashreactiontoy2 QuantityCompetition Similarly givenfirm1 schosenoutputlevely1 firm2 sprofitfunctionis andtheprofit maximizingvalueofy2solves Thesolution y2 R2 y1 isfirm2 sCournot Nashreactiontoy1 QuantityCompetition y2 y1 Firm1 s reactioncurve Firm1 s reactioncurve Cournot Nashequilibriumy1 R1 y2 andy2 R2 y1 Iso ProfitCurves Forfirm1 aniso profitcurvecontainsalltheoutputpairs y1 y2 givingfirm1thesameprofitlevelP1 Whatdoiso profitcurveslooklike y2 y1 Iso ProfitCurvesforFirm1 Withy1fixed firm1 sprofitincreasesasy2decreases y2 y1 Increasingprofitforfirm1 Iso ProfitCurvesforFirm1 y2 y1 Iso ProfitCurvesforFirm1 Q Firm2choosesy2 y2 Wherealongtheliney2 y2 istheoutputlevelthatmaximizesfirm1 sprofit y2 y2 y1 Iso ProfitCurvesforFirm1 Q Firm2choosesy2 y2 Wherealongtheliney2 y2 istheoutputlevelthatmaximizesfirm1 sprofit A Thepointattainingthehighestiso profitcurveforfirm1 y2 y1 y2 y1 Iso ProfitCurvesforFirm1 Q Firm2choosesy2 y2 Wherealongtheliney2 y2 istheoutputlevelthatmaximizesfirm1 sprofit A Thepointattainingthehighestiso profitcurveforfirm1 y1 isfirm1 sbestresponsetoy2 y2 y2 y1 y2 y1 Iso ProfitCurvesforFirm1 Q Firm2choosesy2 y2 Wherealongtheliney2 y2 istheoutputlevelthatmaximizesfirm1 sprofit A Thepointattainingthehighestiso profitcurveforfirm1 y1 isfirm1 sbestresponsetoy2 y2 y2 R1 y2 y2 y1 y2 R1 y2 y2 R1 y2 Iso ProfitCurvesforFirm1 y2 y1 y2 y2 R1 y2 R1 y2 Firm1 sreactioncurvepassesthroughthe tops offirm1 siso profitcurves Iso ProfitCurvesforFirm1 y2 y1 Iso ProfitCurvesforFirm2 Increasingprofitforfirm2 y2 y1 Iso ProfitCurvesforFirm2 Firm2 sreactioncurvepassesthroughthe tops offirm2 siso 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 maximizesfirm1 sprofitwhileleavingfirm2 sprofitattheCournot Nashequilibriumlevel Collusion y2 y1 y1 y2 y1 y2 maximizesfirm1 sprofitwhileleavingfirm2 sprofitattheCournot Nashequilibriumlevel y1 y2 maximizesfirm2 sprofitwhileleavingfirm1 sprofitattheCournot Nashequilibriumlevel Collusion y2 y1 y1 y2 Thepathofoutputpairsthatmaximizeonefirm sprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit Collusion y2 y1 y1 y2 Thepathofoutputpairsthatmaximizeonefirm sprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit Oneoftheseoutputpairsmustmaximizethecartel sjointprofit Collusion y2 y1 y1 y2 y1m y2m denotestheoutputlevelsthatmaximizethecartel stotalprofit Collusion Issuchacartelstable Doesonefirmhaveanincentivetocheatontheother I e iffirm1continuestoproducey1munits isitprofit maximizingforfirm2tocontinuetoproducey2munits Collusion Firm2 sprofit maximizingresponsetoy1 y1misy2 R2 y1m Collusion y2 y1 y2 R2 y1m isfirm2 sbestresponsetofirm1choosingy1 y1m R2 y1m y1 R1 y2 firm1 sreactioncurve y2 R2 y1 firm2 sreactioncurve Collusion Firm2 sprofit maximizingresponsetoy1 y1misy2 R2 y1m y2m Firm2 sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromy2mtoR2 y1m Collusion Similarly firm1 sprofitincreasesifitcheatsonfirm2byincreasingitsoutputlevelfromy1mtoR1 y2m Collusion y2 y1 y2 R2 y1m isfirm2 sbestresponsetofirm1choosingy1 y1m R1 y2m y1 R1 y2 firm1 sreactioncurve y2 R2 y1 firm2 sreactioncurve Collusion Soaprofit seekingcartelinwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable E g OPEC sbrokenagreements 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 Firm1knowsthisandsoperfectlyanticipatesfirm2 sreactiontoanyy1chosenbyfirm1 StackelbergGames Thismakestheleader sprofitfunction StackelbergGames Thismakestheleader sprofitfunctionTheleaderthenchoosesy1tomaximizeitsprofitlevel StackelbergGames Thismakestheleader sprofitfunctionTheleaderchoosesy1tomaximizeitsprofit Q WilltheleadermakeaprofitatleastaslargeasitsCournot Nashequilibriumprofit StackelbergGames A Yes TheleadercouldchooseitsCournot Nashoutputlevel knowingthatthefollowerwouldthenalsochooseitsC Noutputlevel Theleader sprofitwouldthenbeitsC Nprofit Buttheleaderdoesnothavetodothis soitsprofitmustbeatleastaslargeasitsC Nprofit StackelbergGames AnExample Themarketinversedemandfunctionisp 60 yT Thefirms costfunctionsarec1 y1 y12andc2 y2 15y2 y22 Firm2isthefollower Itsreactionfunctionis StackelbergGames AnExample Theleader sprofitfunctionistherefore StackelbergGames AnExample Theleader sprofitfunctionistherefore Foraprofit maximum StackelbergGames AnExample Q Whatisfirm2 sresponsetotheleader schoice StackelbergGames AnExample Q Whatisfirm2 sresponsetotheleader schoiceA StackelbergGames AnExample Q Whatisfirm2 sresponsetotheleader schoiceA 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 Follower sreactioncurve StackelbergGames y2 y1 y1 y2 y1 y2 istheCournot Nashequilibrium y1S y2S istheStackelbergequilibrium HigherP1 y1S Follower sreactioncurve y2S StackelbergGames y2 y1 y1 y2 y1 y2 istheCournot Nashequilibrium y1S y2S istheStackelbergequilibrium y1S Follower sreactioncurve y2S PriceCompetition Whatiffirmscompeteusingonlyprice settingstrategies insteadofusingonlyquantity settingstrategies GamesinwhichfirmsuseonlypricestrategiesandplaysimultaneouslyareBertrandgames BertrandGames Eachfirm smarginalproductioncostisconstantatc Allfirmssettheirpricessimultaneously Q IsthereaNashequilibrium BertrandGames Eachfirm smarginalproductioncostisconstantatc Allfirmssimultaneouslysettheirprices Q IsthereaNashequilibrium A Yes Exactlyone BertrandGames Eachfirm smarginalproductioncostisconstantatc Allfirmssimultaneouslysettheirprices Q IsthereaNashequilibrium A Yes Exactlyone Allfirmssettheirpricesequaltothemarginalcostc Why BertrandGames Supposeonefirmsetsitspricehigherthananotherfirm sprice BertrandGames Supposeonefirmsetsitspricehigherthananotherfirm sprice Thenthehigher pricedfirmwouldhavenocustomers BertrandGames Supposeonefirmsetsitspricehigherthananotherfirm sprice Thenthehigher pricedfirmwouldhavenocustomers Hence atanequilibrium allfirmsmustsetthesameprice BertrandGames Supposethecommonpricesetbyallfirmishigherthanmargina