微观经济学Microeconomics英文课件 27 Oligopoly

ChapterTwenty-SevenOligopoly寡头垄断OligopolyAmonopolyisanindustryconsistingasinglefirm.Aduopolyisanindustryconsistingoftwofirms.Anoligopolyisanindustryconsistingofafewfirms.Particularly,eachfirm’sownpriceoroutputdecisionsaffectitscompetitors’profits.TheFourTypesofMarketStructureCopyright©2004South-Western•

Tapwater•

CableTVMonopoly•

Novels•

MoviesMonopolisticCompetition•

Tennisballs•

CrudeoilOligopolyNumberofFirms?Perfect•

Wheat•

MilkCompetitionTypeofProducts?IdenticalproductsDifferentiatedproductsOnefirmFewfirmsManyfirmsOligopolyHowdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplyingthesameproduct.QuantityCompetition〔数量竞争〕Assumethatfirmscompetebychoosingoutputlevels.Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1+y2.Themarketpricewillbep(y1+y2).Thefirms’totalcostfunctionsarec1(y1)andc2(y2).

AugustinCournot

(1838)createdamodelthatisbasedonrelativelysimpleassumption:ignoretheinterdependencywithrivals.

QuantityCompetitionSupposefirm1takesfirm2’soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunctionas

Giveny2,whatoutputlevely1maximizesfirm1’sprofit?QuantityCompetition;AnExampleSupposethatthemarketinversedemandfunctionis

andthatthefirms’totalcostfunctionsareandQuantityCompetition;AnExampleThen,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizing

outputlevelsolvesI.e.firm1’sbestresponsetoy2isQuantityCompetition;AnExampley2y16015Firm1’s“reactioncurve〞QuantityCompetition;AnExampleSimilarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizing

outputlevelsolvesI.e.firm2’sbestresponsetoy1isQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve〞45/445QuantityCompetition;AnExampleAnequilibriumiswheneachfirm’soutputlevelisabestresponsetotheotherfirm’soutputlevel,forthenneitherwantstodeviatefromitsoutputlevel.Apairofoutputlevels(y1*,y2*)isaCournot-Nashequilibrium〔古诺均衡〕ifandQuantityCompetition;AnExampleandSubstitutefory2*togetHenceSotheCournot-NashequilibriumisQuantityCompetition;AnExampley2y1Firm2’s“reactioncurve〞6015Firm1’s“reactioncurve〞45/445QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve〞4860Firm1’s“reactioncurve〞813Cournot-NashequilibriumQuantityCompetitionGenerally,givenfirm2’schosenoutput

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

Nashreactiontoy2.QuantityCompetitionSimilarly,givenfirm1’schosenoutput

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

Nashreactiontoy1.QuantityCompetitiony2y1Firm1’s“reactioncurve〞Firm1’s“reactioncurve〞Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*)Case:CournotSolution:假设两家欧洲电子公司西门子(厂商S)和汤姆森-CSF(厂商T)共同持有一项用于机场雷达系统的零件的专利权.(13-1)(13-3)(13-2)Iso-ProfitCurvesForfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevelP1.Whatdoiso-profitcurveslooklike?y2y1Iso-ProfitCurvesforFirm1Withy1fixed,firm1’sprofit

increasesasy2decreases.y2y1Increasingprofit

forfirm1.Iso-ProfitCurvesforFirm1y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?y2’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y1’isfirm1’s

bestresponsetoy2=y2’.y2’y1’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.

Wherealongtheliney2=y2’istheoutputlevelthat

maximizesfirm1’sprofit?

A:Thepointattainingthe

highestiso-profitcurvefor

firm1.y1’isfirm1’s

bestresponsetoy2=y2’.y2’R1(y2’)y2y1y2’R1(y2’)y2〞R1(y2〞)Iso-ProfitCurvesforFirm1y2y1y2’y2〞R1(y2〞)R1(y2’)Firm1’sreactioncurve〔反响曲线〕passesthroughthe“tops〞offirm1’siso-profit

curves.Iso-ProfitCurvesforFirm1y2y1Iso-ProfitCurvesforFirm2Increasingprofit

forfirm2.y2y1Iso-ProfitCurvesforFirm2Firm2’sreactioncurve

passesthroughthe“tops〞offirm2’siso-profit

curves.y2=R2(y1)IfthereareN-firmsinthemarketQuestion:HowtofindCournotNashEquilibriumsolution?WhatifNisanumberbigenough?Collusion〔串谋〕Q:AretheCournot-Nashequilibriumprofitsthelargestthatthefirmscanearnintotal?Collusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

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

equilibrium.Collusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

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

equilibrium.Collusiony2y1y1*y2*Arethereotheroutputlevel

pairs(y1,y2)thatgive

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

equilibrium.Collusiony2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP2HigherP1Collusiony2y1y1*y2*HigherP2HigherP1y2’y1’Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).CollusionSothereareprofitincentivesforbothfirmsto“cooperate〞byloweringtheiroutputlevels.Thisiscollusion.Firmsthatcolludearesaidtohaveformedacartel〔卡特尔〕.Iffirmsformacartel,howshouldtheydoit?CollusionSupposethetwofirmswanttomaximizetheirtotalprofitanddivideitbetweenthem.Theirgoalistochoosecooperativelyoutputlevelsy1andy2thatmaximizeCollusionThefirmscannotdoworsebycolludingsincetheycancooperativelychoosetheirCournot-NashequilibriumoutputlevelsandsoearntheirCournot-Nashequilibriumprofits.SocollusionmustprovideprofitsatleastaslargeastheirCournot-Nashequilibriumprofits.Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

bothfirmsthandoes(y1*,y2*).Collusiony2y1y1*y2*y2’y1’HigherP2HigherP1(y1’,y2’)earns

higherprofitsfor

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

higherprofitsfor

bothfirms.y2〞y1〞Collusiony2y1y1*y2*y2~y1~(y1,y2)maximizesfirm1’sprofit

whileleavingfirm2’sprofitat

theCournot-Nashequilibrium

level.~~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.__Collusiony2y1y1*y2*y2~y1~y2_y2_Thepathofoutputpairsthat

maximizeonefirm’sprofit

whilegivingtheotherfirmat

leastitsCNequilibrium

profit.Collusiony2y1y1*y2*y2~y1~y2_y2_Thepathofoutputpairsthat

maximizeonefirm’sprofit

whilegivingtheotherfirmat

leastitsCNequilibrium

profit.Oneof

theseoutputpairsmustmaximizethe

cartel’sjointprofit.Collusiony2y1y1*y2*y2my1m(y1m,y2m)denotes

theoutputlevels

thatmaximizethe

cartel’stotalprofit.CollusionIssuchacartelstable?Doesonefirmhaveanincentivetocheatontheother?I.e.iffirm1continuestoproducey1munits,isitprofit-maximizingforfirm2tocontinuetoproducey2munits?CollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m).Collusiony2y1y2my1my2=R2(y1m)isfirm2’s

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

reactioncurveCollusionFirm2’sprofit-maximizingresponsetoy1=y1misy2=R2(y1m)>y2m.Firm2’sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromy2mtoR2(y1m).Similarly,firm1’sprofitincreasesifitcheatsonfirm2byincreasingitsoutputlevelfromy1mtoR1(y2m).Collusiony2y1y2my1my2=R2(y1m)isfirm2’s

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

reactioncurveCollusionSoaprofit-seekingcartelinwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable.E.g.OPEC’sbrokenagreements.CollusionversusCompetition?SometimescollusionsucceedsSometimesforcesofcompetitionwinoutovercollectiveactionWhenwillcollusiontendtosucceed?Therearesixfactorsthatinfluencesuccessfulcollusionasfollows:

FactorsAffectingLikelihoodofSuccessfulCollusion1. NumberandSizeDistributionofSellers.Collusionismoresuccessfulwithfewfirmsorifthereexistsadominantfirm.2. ProductHeterogeneity.Collusionismoresuccessfulwithproductsthatarestandardizedorhomogeneous3. CostStructures.Collusionismoresuccessfulwhenthecostsaresimilarforallofthefirmsintheoligopoly.4. SizeandFrequencyofOrders.Collusionismoresuccessfulwithsmall,frequentorders.5.SecrecyandRetaliation.Collusionismoresuccessfulwhenitisdifficulttogivesecretpriceconcessions.6. PercentageofExternalOrders.Collusionismoresuccessfulwhenpercentageofordersoutsideofthecartelissmall.

TheOrderofPlaySofarithasbeenassumedthatfirmschoosetheiroutputlevelssimultaneously.Thecompetitionbetweenthefirmsisthenasimultaneousplaygameinwhichtheoutputlevelsarethestrategicvariables.TheOrderofPlay〔决策顺序〕Whatiffirm1choosesitsoutputlevelfirstandthenfirm2respondstothischoice?Firm1isthenaleader〔领导者〕.Firm2isafollower〔追随者〕.Thecompetitionisasequentialgameinwhichtheoutputlevelsarethestrategicvariables.TheOrderofPlaySuchgamesareStackelberg〔斯塔克尔伯格〕games.Isitbettertobetheleader?Orisitbettertobethefollower?StackelbergGamesQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=R2(y1).Firm1knowsthisandsoperfectlyanticipatesfirm2’sreactiontoanyy1chosenbyfirm1.StackelbergGamesThismakestheleader’sprofitfunction

Theleaderthenchoosesy1tomaximizeitsprofitlevel.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-Nash

equilibrium.HigherP2HigherP1StackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.HigherP1Follower’sreactioncurveStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.(y1S,y2S)istheStackelbergequilibrium.HigherP1y1SFollower’sreactioncurvey2SStackelbergGamesy2y1y1*y2*(y1*,y2*)istheCournot-Nash

equilibrium.(y1S,y2S)istheStackelbergequilibrium.y1SFollower’sreactioncurvey2SPriceCompetition〔价格竞争〕Whatiffirmscompeteusingonlyprice-settingstrategies,insteadofusingonlyquantity-settingstrategies?GamesinwhichfirmsuseonlypricestrategiesandplaysimultaneouslyareBertrandgames.BertrandGamesEachfirm’smarginalproductioncostisconstantatc.Allfirmssimultaneouslysettheirprices.Q:IsthereaNashequilibrium?A:Yes.Exactlyone.Allfirmssettheirpricesequaltothemarginalcostc.Why?BertrandGamesSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenocustomers.Hence,atanequilibrium,allfirmsmustsetthesameprice.BertrandGamesSupposethecommonpricesetbyallfirmishigherthanmarginalcostc.Thenonefirmcanjustslightlyloweritspriceandselltoallthebuyers,therebyincreasingitsprofit.Theonlycommonpricewhi