nicholson微观经济理论（答案+ppt+习题库）-190-03-033593-0

TRADITIONALMODELSOFIMPERFECTCOMPETITIONINTHISCHAPTERWEEXAMINEMODELSOFPRICEDETERMINATIONINMARKETSTHATFALLBETWEENTHEPOLAREXTREMESOFPERFECTCOMPETITIONANDMONOPOLYALTHOUGHNOSINGLEMODELCANBEUSEDTOEXPLAINALLPOSSIBLEFORMSOFSUCHIMPERFECTCOMPETITION,WEWILLEXAMINEAFEWOFTHEBASICELEMENTSCOMMONTOMANYOFTHEMODELSINCURRENTUSETOTHATENDWEWILLFOCUSONTHREESPECICTOPICS1PRICINGOFHOMOGENEOUSGOODSINMARKETSINWHICHTHEREARERELATIVELYFEWRMS2PRODUCTDIFFERENTIATIONANDADVERTISINGINSUCHMARKETSAND3THEEFFECTTHATENTRYANDEXITPOSSIBILITIESHAVEONLONGRUNOUTCOMESINIMPERFECTLYCOMPETITIVEMARKETSINASENSE,THEN,THISCHAPTERCONCERNSHOWTHESTRINGENTASSUMPTIONSOFTHEPERFECTLYCOMPETITIVEMODELCANBERELAXEDANDWHATTHERESULTSOFCHANGINGTHOSEASSUMPTIONSAREFORTHISSTUDY,THEPERFECTLYCOMPETITIVEMODELPROVIDESAUSEFULBENCHMARKBECAUSEDEPARTURESFROMTHECOMPETITIVENORMMAYINVOLVEEFCIENCYLOSSESTWOSPECICCRITERIAWEWILLUSEINTHISCOMPARISONARE1WHETHERPRICESUNDERIMPERFECTCOMPETITIONEQUALMARGINALCOSTS,AND2WHETHER,INTHELONGRUN,PRODUCTIONOCCURSATMINIMUMAVERAGECOSTWEWILLSEETHATIMPERFECTLYCOMPETITIVEMARKETSOFTENLACKONEORBOTHOFTHESEDESIRABLEFEATURESOFPERFECTCOMPETITIONMANYOFTHESESAMETOPICSAREREEXAMINEDFROMTHEPERSPECTIVEOFGAMETHEORYINCHAPTER2019CHAPTERPRICINGUNDERHOMOGENEOUSOLIGOPOLYINTHISSECTIONWEWILLEXAMINETHEGENERALTHEORYOFPRICEDETERMINATIONINMARKETSINWHICHRELATIVELYFEWRMSPRODUCEASINGLEHOMOGENEOUSPRODUCTASBEFORE,WEWILLASSUMETHATTHEMARKETISPERFECTLYCOMPETITIVEONTHEDEMANDSIDETHATIS,THEREAREASSUMEDTOBEMANYDEMANDERS,EACHOFWHOMISAPRICETAKERWEWILLALSOASSUMETHATTHEREARENOTRANSACTIONORINFORMATIONCOSTS,SOTHEGOODINQUESTIONOBEYSTHELAWOFONEPRICEANDWEMAYSPEAKUNAMBIGUOUSLYOFTHEGOODSPRICELATERINTHISCHAPTERWEWILLRELAXTHISASSUMPTIONWHENWECONSIDERPRODUCTDIFFERENTIATIONINTHISSECTIONWEWILLALSOASSUMETHATTHEREAREAXEDNUMBEROFNIDENTICALRMSWHERENISTAKENTOBEARELATIVELYSMALLNUMBERLATER,WEWILLCONSIDERASPECICNUMERICALEXAMPLEOFDUOPOLYINWHICHNH110052,BUTFORTHEMOMENTTHEREISNOREASONTORESTRICTOURANALYSISTOANYSPECICNUMBERTHROUGHOUTTHISSECTIONWEWILLASSUMETHATNISXED,BUTLATERINTHECHAPTERWEWILLALLOWNTOVARYTHROUGHENTRYANDEXITINRESPONSETORMSPROTABILITYBASICSTRUCTUREOFTHEMODELTHEOUTPUTOFEACHRMINOURMODELWILLBEDENOTEDBYQIIH110051NBECAUSERMSAREASSUMEDTOBEIDENTICAL,SYMMETRYINCOSTSWILLUSUALLYREQUIRETHATTHESEOUTPUTSAREEQUAL,ALTHOUGHITWOULDBEASIMPLEMATTERTOALLOWFORSOMEDIFFERENCESAMONGRMSTHEINVERSEDEMANDFUNCTIONFORTHEGOODBEINGEXAMINEDWILLBEDENOTEDBYFQ,ANDTHISSHOWSTHEPRICE,P,THATDEMANDERSASAGROUPAREWILLINGTOPAYFORANYPARTICULARLEVELOFINDUSTRYOUTPUTTHATIS,PH11005FQH11005FQ1H11001Q2H11001H11001QN191EACHRMSDECISIONPROBLEMISTOMAXIMIZEITSOWNPROTSH9266I,GIVENTHISMARKETPRICEOFTHEGOODANDTHERMSTOTALCOSTS,WHICHAREDENOTEDBYTCIQIHENCE,THERMSGOALISTOMAXIMIZEH9266IH11005PQIH11002TCIQI192H11005FQQIH11002TCIQIH11005FQ1H11001Q2H11001H11001QNQIH11002TCIQIMOSTOFTHEISSUESDISCUSSEDINTHISSECTIONULTIMATELYCENTERAROUNDHOWRMSAREASSUMEDTOMAKETHISPROTMAXIMIZINGOUTPUTCHOICEINPERHAPSOVERLYSIMPLEMATHEMATICALTERMS,THERESULTSWILLDEPENDONPRECISELYWHATISASSUMEDABOUTHOWEQUATION192ISTOBEDIFFERENTIATEDTOSOLVEFORAPROTMAXIMUMINECONOMICTERMS,THECENTRALQUESTIONCONCERNSHOWONERMASSUMESOTHERRMSREACTTOITSDECISIONSFOURPOSSIBLEMODELSWILLBEEXAMINEDHERETHESEARESUMMARIZEDINTHEFOLLOWINGDENITIONSWEWILLSEETHATTHESEDIFFERENTMODELSYIELDRATHERDIFFERENTRESULTSANDTHATEQUILIBRIAARISINGFROMTHECONJECTURALVARIATIONSMODELAREGENERALLYINDETERMINATEEXCEPTINAFEWSPECIALCASESOLIGOPOLYPRICINGMODELSQUASICOMPETITIVEMODELASSUMESPRICETAKINGBEHAVIORBYALLRMSPISTREATEDASXEDDEFINITION528PARTVIMODELSOFIMPERFECTCOMPETITIONCARTELMODELASSUMESRMSCANCOLLUDEPERFECTLYINCHOOSINGINDUSTRYOUTPUTAND,THEREFOREPCOURNOTMODELASSUMESTHATRMITREATSRMJSOUTPUTASXEDINITSDECISIONSH11128QJ/H11128QIH110050CONJECTURALVARIATIONSMODELASSUMESTHATRMJSOUTPUTWILLRESPONDTOVARIATIONSINRMISOUTPUTH11128QJ/H11128QIH110140QUASICOMPETITIVEMODELASWASTHECASEUNDERPERFECTCOMPETITION,EACHRMINTHEQUASICOMPETITIVEMODELISAPRICETAKERTHATIS,EACHRMASSUMESPROBABLYINCORRECTLYTHATITSDECISIONSWILLNOTAFFECTMARKETPRICEINTHISCASETHERSTORDERCONDITIONFORPROTMAXIMIZATIONISTHATH11005PH11002H110050193ORPH11005MCIQIIH110051,N194THESENSUPPLYEQUATIONS,TOGETHERWITHTHEMARKETCLEARINGDEMANDEQUATION,PH11005FQH11005FQ1H11001Q2H11001H11001QN,195WILLENSURETHATTHISMARKETARRIVESATTHESHORTRUNCOMPETITIVESOLUTIONTHATSOLUTIONISILLUSTRATEDFORTHECASEOFCONSTANTMARGINALCOSTSASPOINTCINFIGURE191ALTHOUGHNMAYBEASMALLNUMBER,THEASSUMPTIONOFPRICETAKINGBEHAVIORINTHISCASERESULTSINACOMPETITIVEOUTCOMECARTELMODELOFCOURSE,THEASSUMPTIONOFPRICETAKINGBEHAVIORMAYBEPARTICULARLYINAPPROPRIATEINOLIGOPOLISTICINDUSTRIESINWHICHEACHRMRECOGNIZESTHATITSDECISIONSHAVEANOBVIOUSEFFECTONPRICEANALTERNATIVEASSUMPTIONWOULDBETHATRMSASAGROUPRECOGNIZETHEYCANAFFECTPRICEANDMANAGETOCOORDINATETHEIRDECISIONSSOASTOACHIEVEMONOPOLYPROTSINTHISCASETHECARTELACTSASAMULTIPLANTMONOPOLYANDCHOOSESQ1,Q2,QNSOASTOMAXIMIZETOTALINDUSTRYPROTSH9266H11005PQH11002TC1Q1H11001TC2Q2H11001H11001TCNQN196H11005FQ1H11001Q2H11001H11001QNQ1H11001Q2H11001H11001QNH11002H20913NI1TCIQI197THERSTORDERCONDITIONSFORAMAXIMUMARETHATH11005PH11001Q1H11001Q2H11001H11001QNH11002MCIQIH110050198H11005MRQH11002MCIQIH110050199NOTICETHATMRCANBEWRITTENASAFUNCTIONOFTHECOMBINEDOUTPUTOFALLRMSBECAUSEITSVALUEISTHESAMENOMATTERWHICHRMSOUTPUTLEVELISCHANGEDATTHEPROTMAXIMIZINGPOINTTHISCOMMONMARGINALREVENUEWILLBEEQUATEDFOREACHH11128PH5007H11128QIH11128H9266H5007H11128QIH11128TCIQIH5007H11128QIH11128H9266IH5007H11128QICHAPTER19TRADITIONALMODELSOFIMPERFECTCOMPETITION529RMSMARGINALPRODUCTIONCOSTASSUMINGTHESEMARGINALCOSTSAREEQUALANDCONSTANTFORALLRMS,THEOUTPUTCHOICEISINDICATEDBYPOINTMINFIGURE191BECAUSETHISCOORDINATEDPLANREQUIRESASPECICOUTPUTLEVELFOREACHRM,THEPLANWILLALSODICTATEHOWMONOPOLYPROTSEARNEDBYTHECARTELARETOBESHAREDINTHEAGGREGATETHESEPROTSWILLBEASLARGEASPOSSIBLE,GIVENTHEMARKETDEMANDCURVEANDTHEINDUSTRYSCOSTSTRUCTUREVIABILITYOFTHECARTELSOLUTIONTHEREARETHREEPROBLEMSWITHTHISCARTELSOLUTIONFIRST,ANDMOSTOBVIOUSLY,SUCHMONOPOLISTICDECISIONSMAYBEILLEGALINTHEUNITEDSTATES,FOREXAMPLE,SECTIONIOFTHESHERMANACT1890OUTLAWS“CONSPIRACIESINRESTRAINTOFTRADE,”SOWOULDBECARTELMEMBERSMAYEXPECTAVISITFROMTHEFBISIMILARLAWSEXISTINMANYOTHERCOUNTRIESASECONDPROBLEMWITHTHECARTELSOLUTIONISTHATITREQUIRESTHATACONSIDERABLEAMOUNTOFINFORMATIONBEAVAILABLETOTHEDIRECTORSOFTHECARTELSPECIFICALLY,THEYMUSTKNOWTHEMARKETDEMANDFUNCTIONANDEACHINDIVIDUALRMSMARGINALCOSTFUNCTIONTHISINFORMATIONMAYBECOSTLYTOOBTAIN,ANDSOMECARTELMEMBERSMAYBERELUCTANTTOPROVIDEITFINALLY,ANDMOSTIMPORTANT,THECARTELSOLUTIONMAYBEFUNDAMENTALLYUNSTABLEBECAUSEEACHCARTELMEMBERWILLPRODUCEANOUTPUTLEVELFORWHICHPH11022MCI,EACHWILLHAVEANINCENTIVETOEXPANDOUTPUTIFTHEDIRECTORSOFTHEOLIGOPOLYARENOTABLETOPOLICESUCH“CHISELING,”THEMONOPOLISTICSOLUTIONMAYCOLLAPSETHEDIFCULTIESOFTHEOPECCARTELINDICTATINGPRECISETARGETOUTPUTLEVELSTOITSMEMBERSATTESTTOTHESEPROBLEMSINCHAPTER20WEWILLEXAMINETHESTABILITYOFCARTELPRICINGSTRATEGIESINMOREDETAIL530PARTVIMODELSOFIMPERFECTCOMPETITIONALTERNATIVESOLUTIONSTOTHEOLIGOPOLISTICPRICINGPROBLEMMARKETEQUILIBRIUMUNDERANOLIGOPOLYCANOCCURATMANYPOINTSONTHEDEMANDCURVEINTHISGUREWHICHASSUMESTHATMARGINALCOSTSARECONSTANTOVERALLOUTPUTRANGES,THEQUASICOMPETITIVEEQUILIBRIUMOCCURSATPOINTC,THECARTELEQUILIBRIUMATPOINTM,ANDTHECOURNOTSOLUTIONATPOINTAMANYOTHERSOLUTIONSMAYOCCURBETWEENPOINTSMANDC,DEPENDINGONTHESPECICASSUMPTIONMADEABOUTRMSSTRATEGICINTERRELATIONSHIPSPRICEQUANTITYPERPERIODQAQMQCPAPMPCDMACMRMCDFIGURE191COURNOTSOLUTIONONEOFTHERSTRESEARCHERSTODEVELOPAMODELOFMARKETSCONTAININGFEWRMSWASTHEFRENCHECONOMISTAUGUSTINCOURNOT,WHOPRESENTEDAFORMALANALYSISOFDUOPOLYBEHAVIORIN18381INOURNOTATIONCOURNOTASSUMEDTHATEACHRMRECOGNIZESTHATITSOWNDECISIONSABOUTQIAFFECTPRICEBUTTHATITSOWNOUTPUTDECISIONSDONOTAFFECTTHOSEOFANYOTHERRMTHATIS,EACHRMRECOGNIZESTHATH11128P/H11128QIH110140BUTASSUMESTHATH11128QJ/H11128QIH110050FORALLJH11014IUSINGTHESEASSUMPTIONS,THERSTORDERCONDITIONSFORAPROTMAXIMUMINOURMODELAREH11005PH11001QIH11002MCIQIH1100501910FORALLIH110051,NNOTICEFROMTHISEQUATIONTHATTHERMASSUMESTHATCHANGESINQIAFFECTITSTOTALREVENUEONLYTHROUGHTHEIRDIRECTEFFECTONTHEMARKETPRICEOFITSOWNSALESHENCETHEEQUATIONDIFFERSBOTHFROMTHECARTELSOLUTIONWHERETHEEFFECTOFACHANGEINPRICEONTOTALINDUSTRYREVENUESISTAKENINTOACCOUNTSEEEQUATION198ANDFROMTHECONJECTURALVARIATIONSCASE,DISCUSSEDNEXT,INWHICHINDIRECTEFFECTSOFRMISOUTPUTONRMJSOUTPUTARETAKENINTOACCOUNTINGENERAL,THENEQUATIONSIN1910,TOGETHERWITHTHEMARKETCLEARINGDEMANDEQUATION195,WILLPERMITANEQUILIBRIUMSOLUTIONFORTHEVARIABLESQ1,Q2,QNANDPANEXAMINATIONOFTHEPROTMAXIMIZINGEQUATION1910SHOWSTHATASLONGASMARGINALCOSTSAREINCREASINGASTHEYGENERALLYMUSTBEFORATRUEPROTMAXIMUM,EACHRMSOUTPUTINTHECOURNOTSOLUTIONWILLEXCEEDTHECARTELOUTPUTBECAUSETHE“RMSPECIC”MARGINALREVENUEINTHATEQUATIONISLARGERTHANTHEMARKETMARGINALREVENUENOTIONINEQUATION198ONTHEOTHERHAND,THERMSOUTPUTWILLFALLSHORTOFTHECOMPETITIVEOUTPUTBECAUSETHETERMQIH11080H11128P/H11128QIINEQUATION1910ISNEGATIVEMARKETEQUILIBRIUMWILLTHEREFOREOCCURATAPOINTSUCHASAINFIGURE191ATTHISPOINTPRICEEXCEEDSMARGINALCOST,BUTOUTPUTISHIGHERANDINDUSTRYPROTSLOWERTHANINTHEMONOPOLYCASEINGENERAL,ITMIGHTALSOBESUPPOSEDTHATTHEGREATERTHENUMBEROFRMSINTHEINDUSTRY,THECLOSERTHEEQUILIBRIUMPOINTWILLBETOTHECOMPETITIVEPOINTCWITHALARGERNUMBEROFRMSTHETERMQIH11080H11128P/H11128QIINEQUATION1910TENDSTOAPPROACHZERO,ANDTHEEQUATIONTHEREFORECOMESTORESEMBLETHEQUASICOMPETITIVESOLUTIONREPRESENTEDBYEQUATION193FORANILLUSTRATION2OFTHISLIMITPROPERTYOFTHECOURNOTMODEL,SEEEXAMPLE191LATERINTHECHAPTERITSHOULDBENOTEDTHATTHECOURNOTEQUILIBRIUMDESCRIBEDHEREISALSOANASHEQUILIBRIUMINOUTPUTSTRATEGIESFORMOREONGAMETHEORETICFORMULATIONSOFTHEPRICINGPROBLEM,SEECHAPTER20CONJECTURALVARIATIONSMODELSOFAROURMODELSOFOLIGOPOLISTICPRICEDETERMINATIONHAVENOTALLOWEDFORSTRATEGICINTERACTIONSAMONGRMSINMARKETSWITHFEWRMS,THATISAPARTICULARLYUNTENABLEASSUMPTIONFORDMUSTOBVIOUSLYTAKESOMEACCOUNTOFHOWGENERALMOTORSWILLRESPONDTOITSPRICINGANDOUTPUTDECISIONSALLOTHERSOFTWARECOMPANIESMUSTWORRYABOUTWHATMICROSOFTWILLDOANDMEMBERSOFTHEOPECCARTELMUSTBEH11128PH5007H11128QIH11128H9266IH5007H11128QICHAPTER19TRADITIONALMODELSOFIMPERFECTCOMPETITION5311ACOURNOT,RESEARCHESINTOTHEMATHEMATICALPRINCIPLESOFTHETHEORYOFWEALTH,TRANSNTBACONNEWYORKMACMILLAN,18972FORAFORMALDISCUSSIONOFTHESEISSUES,SEEJFRIEDMAN,“OLIGOPOLYTHEORY,”INKJARROWANDMDINTRILIGATOR,EDS,HANDBOOKOFMATHEMATICALECONOMICS,VOL2AMSTERDAMNORTHHOLLAND,1982CONCERNEDWITHNEWOILEXPLORATIONTHROUGHOUTTHEWORLDTHEPROBLEMFACEDBYECONOMICTHEORISTSISHOWTOCAPTURETHESESTRATEGICCONSIDERATIONSINSOMESORTOFTRACTABLEANALYTICALMODELONEAPPROACHRELIESONGAMETHEORYTOEXAMINESTRATEGICCHOICESINASIMPLIEDSETTINGINCHAPTER20WEWILLILLUSTRATEHOWSUCHTOOLSCANBEAPPLIEDTOTHEANALYSISOFDUOPOLISTICMARKETSHEREWEEXPLORESOMEOFTHEWAYSINWHICHSTRATEGICCONCERNSCANBEINTEGRATEDINTOTHEMODELSWEHAVEALREADYDEVELOPEDTHEPRIMARYWAYOFBUILDINGSTRATEGICCONCERNSINTOOURMODELISBYCONSIDERINGTHEASSUMPTIONSTHATMIGHTBEMADEBYONERMABOUTOTHERRMSBEHAVIORINMATHEMATICALTERMS,WEWISHTOEXAMINETHEPOSSIBLEASSUMPTIONSTHATRMIMIGHTMAKEABOUTHOWITSDECISIONSMIGHTAFFECTTHOSEOFRMJSPECICALLY,FOREACHRMIWEARECONCERNEDWITHTHEASSUMEDVALUEOFTHEDERIVATIVEH11128QJ/H11128QIFORALLRMSJOTHERTHANRMIITSELFBECAUSETHEVALUEOFTHISDERIVATIVEWILLBESPECULATIVE,MODELSBASEDONVARIOUSASSUMPTIONSABOUTITSVALUEARETERMEDCONJECTURALVARIATIONSMODELSTHATIS,THEYARECONCERNEDWITHRMIS“CONJECTURES”ABOUTRMJSOUTPUTVARIATIONSTHUSFARINOURMODELSWEHAVEASSUMEDTHATH11128QJ/H11128QIH110050FORALLJH11014IWETHEREFOREHAVEASSUMEDNOSTRATEGICINTERACTIONAMONGRMSONCETHISASSUMPTIONISRELAXED,EACHRMSPROTMAXIMIZINGDECISIONBECOMESVERYCOMPLEXNOWTHERSTORDERCONDITIONFORMAXIMIZINGEQUATION192BECOMESH11005PH11001QIH20900H11001H20913JH11014IH11080H20901H11002MCIQIH1100501911THATIS,THERMMUSTNOWNOTONLYBECONCERNEDWITHHOWITSOWNOUTPUTAFFECTSMARKETPRICEDIRECTLY,BUTALSOMUSTCONSIDERHOWVARIATIONSINITSOWNOUTPUTWILLAFFECTMARKETPRICETHROUGHEFFECTSONOTHERRMSOUTPUTDECISIONSBECAUSEANYNUMBEROFPLAUSIBLEASSUMPTIONSMIGHTBEMADEABOUTSUCHRESPONSES,THEREISNOGENERALLYACCEPTEDTHEORYOFTHETYPEOFEQUILIBRIUMLIKELYTOEMERGEFROMTHERESPONSESGIVENBYEQUATION1911AFEWINTERESTINGMODELSHAVEBEENDEVELOPEDFORTHEDUOPOLYCASE,ANDWEWILLDEMONSTRATEASIMPLENUMERICALEXAMPLEOFTHESELATERINTHISCHAPTERNEXTWEWILLEXAMINEAPARTICULARFORMULATIONOFEQUATION1911THATYIELDSASIMPLE“PRICELEADERSHIP”MODELBUTTHESETWOEXAMPLESAREQUITESPECICCASESTHATFAILTOCAPTUREALLOFTHEINTRICACIESTHATMAYOCCURINTHECONJECTURALVARIATIONSMODELINITSFULLGENERALITYPRICELEADERSHIPMODELONETRACTABLEFORMOFTHECONJECTURALVARIATIONSMODELISBASEDONTHEASSUMPTIONTHATTHEMARKETINQUESTIONISCOMPOSEDOFASINGLEPRICELEADERANDAFRINGEOFQUASICOMPETITIVECOMPETITORSASSUMINGTHELEADERISRM1,AMATHEMATICALREPRESENTATIONOFTHISMARKETWOULDINCLUDEAPRICETAKINGREACTIONSUCHASTHATGIVENBYEQUATION194FORRMS2N,WITHONLYRM1REQUIRINGACOMPLEXREACTIONFUNCTIONOFTHETYPEGIVENBYEQUATION1911AGRAPHICALANALYSISOFSUCHAMARKETISPROVIDEDBYFIGURE192THEDEMANDCURVEINTHEGUREREPRESENTSTHETOTALDEMANDCURVEFORTHEINDUSTRYSPRODUCT,ANDTHESUPPLYCURVESCREPRESENTSTHESUPPLYDECISIONSOFALLTHENH110021RMSINTHECOMPETITIVEFRINGEITISSIMPLYTHEHORIZONTALSUMOFTHEIRSHORTRUNMARGINALCOSTCURVESUSINGTHESETWOCURVES,THEDEMANDCURVEDH11032DH11032FACINGTHEINDUSTRYLEADERISDERIVEDASFOLLOWSFORAPRICEOFH11128QJH5007H11128QIH11128PH5007H11128QJH11128PH5007H11128QIH11128H9266IH5007H11128QI532PARTVIMODELSOFIMPERFECTCOMPETITIONP1ORABOVE,THELEADERWILLSELLNOTHING,BECAUSETHECOMPETITIVEFRINGEWOULDBEWILLINGTOSUPPLYALLTHATISDEMANDEDFORPRICESBELOWP2THELEADERHASTHEMARKETTOITSELF,BECAUSETHEFRINGEISNOTWILLINGTOSUPPLYANYTHINGBETWEENP2ANDP1THECURVEDH11032DH11032ISCONSTRUCTEDBYSUBTRACTINGWHATTHEFRINGEWILLSUPPLYFROMTOTALMARKETDEMANDTHATIS,THELEADERGETSTHATPORTIONOFDEMANDNOTTAKENBYTHEFRINGERMSGIVENTHEDEMANDCURVEDH11032DH11032,THELEADERCANCONSTRUCTITSMARGINALREVENUECURVEMRH11032ANDTHENREFERTOITSOWNMARGINALCOSTCURVEMCTODETERMINETHEPROTMAXIMIZINGOUTPUTLEVEL,QLMARKETPRICETHENWILLBEPLGIVENTHATPRICE,THECOMPETITIVEFRINGEWILLPRODUCEQC,ANDTOTALINDUSTRYOUTPUTWILLBEQTH11005QCH11001QLOFCOURSE,THISMODELDOESNOTANSWERSUCHIMPORTANTQUESTIONSASHOWTHEPRICELEADERINANINDUSTRYISCHOSENORWHATHAPPENSWHENAMEMBEROFTHEFRINGEDECIDESTOCHALLENGETHELEADERFORITSPOSITIONANDPROTSBUTTHEMODELDOESILLUSTRATEONETRACTABLEEXAMPLEOFTHECONJECTURALVARIATIONSMODELTHATMAYEXPLAINPRICINGBEHAVIORINSOMEINSTANCESFOREXAMPLE,ITHASBEENARGUEDTHATTHEMODELMAYATTIMESHAVEOFFEREDANAPPROPRIATEEXPLANATIONFORPRICINGINMARKETSSUCHASTHOSEFORPRIMECOMMERCIALLOANSHERETHEMAJORMONEYCENTERBANKSARETHE“LEADERS”,STANDARDIZEDSTEELPRODUCTSUSSTEELISTHELEADER,AND,PERHAPS,THEOPECCARTELWHERESAUDIARABIA,BYVIRTUEOFPOLITICSANDGEOLOGY,CANPLAYTHEROLEOFLEADEROFCOURSE,ALLSUCHPURPORTEDEXAMPLESREQUIRECHAPTER19TRADITIONALMODELSOFIMPERFECTCOMPETITION533FORMALMODELOFPRICELEADERSHIPBEHAVIORTHECURVEDH11032DH11032SHOWSTHEDEMANDCURVEFACINGTHEPRICELEADERITISDERIVEDBYSUBTRACTINGWHATISPRODUCEDBYTHECOMPETITIVEFRINGEOFRMSSCFROMMARKETDEMANDDDGIVENDH11032DH11032,THERMSPROTMAXIMIZINGOUTPUTLEVELISQL,ANDAPRICEOFPLWILLPREVAILINTHEMARKETPRICEQUANTITYPERPERIODQCQLQTPLP1P2SCDDMCMCDH11032DH11032MRH11032FIGURE192SUBSTANTIALEMPIRICALINVESTIGATIONTODETERMINETHEVALIDITYANDSCOPEOFTHEPRICELEADERSHIPMODELEXAMPLE191COURNOTSNATURALSPRINGDUOPOLYASANUMERICALEXAMPLEOFSOMEOFTHESEIDEAS,WEWILLCONSIDERAVERYSIMPLECASEINWHICHTHEREARENOPRODUCTIONCOSTSANDONLYTWORMSFOLLOWINGCOURNOTSNINETEENTHCENTURYEXAMPLEOFTWONATURALSPRINGS,WEASSUMEEACHSPRINGOWNERHASALARGESUPPLYOFPOSSIBLYHEALTHFULWATERANDFACESTHEPROBLEMOFHOWMUCHTOPROVIDETOTHEMARKETTHEDEMANDFORSPRINGWATERISGIVENBYTHELINEARDEMANDCURVEQH11005Q1H11001Q2H11005120H11002P1912ANDISILLUSTRATEDINFIGURE193WEWILLNOWEXAMINEVARIOUSMARKETEQUILIBRIAALONGTHISDEMANDCURVE534PARTVIMODELSOFIMPERFECTCOMPETITIONSOLUTIONSTOTHEDUOPOLYPROBLEMGIVENTHEDEMANDCURVEQH11005120H11002P,THEPOINTSM,A,S,ANDCREPRESENT,RESPECTIVELY,THECARTEL,COURNOT,STACKELBERG,ANDQUASICOMPETITIVESOLUTIONSTOTHEDUOPOLYPROBLEM12010080604020120100806040200QH11005120H11002PDMASCPRICEQUANTITYPERPERIODFIGURE193QUASICOMPETITIVESOLUTIONBECAUSEEACHRMHASZEROMARGINALCOSTS,THEQUASICOMPETITIVESOLUTIONWILLRESULTINAMARKETPRICEOFZEROTOTALDEMANDWILLBE120INTHISPARTICULAREXAMPLETHEDIVISIONOFOUTPUTBETWEENTHETWOSPRINGSISINDETERMINATEBECAUSEEACHHASZEROMARGINALCOSTOVERALLOUTPUTRANGESTHEQUASICOMPETITIVEOUTPUTLEVELISINDICATEDBYPOINTCINFIGURE193CARTELSOLUTIONTHECARTELSOLUTIONTOTHISEXAMPLECANBEFOUNDBYMAXIMIZINGTOTALINDUSTRYREVENUEANDPROTSH9266H11005PQH11005120QH11002Q21913THERSTORDERCONDITIONFORAMAXIMUMISH11005120H110022QH110050ORQH11005601914PH1100560H9266H110053,600AGAIN,THEPRECISEDIVISIONOFTHESEOUTPUTLEVELSANDPROTSBETWEENTHETWOSPRINGSISINDETERMINATETHECARTELSOLUTIONISINDICATEDBYPOINTMINFIGURE193COURNOTSOLUTIONFROMEQUATION1912ITISEASYTOSEETHATTHETWORMSREVENUESANDPROTSAREGIVENBYH92661H11005PQ1H11005120H11002Q1H11002Q2Q1H11005120Q1H11002Q21H11002Q1Q21915H92662H11005PQ2H11005120H11002Q1H11002Q2Q2H11005120Q2H11002Q22H11002Q1Q2IFEACHSPRINGOWNERASSUMESTHEOTHERWILLNOTREACTTOHISORHEROWNOUTPUTDECISIONS,H11128Q1/H11128Q2H11005H11128Q2/H11128Q1H110050,ANDTHERSTORDERCONDITIONSFORAMAXIMUMAREH11005120H110022Q1H11002Q2H1100501916H11005120H110022Q2H11002Q1H110050EQUATIONS1916ARECALLEDREACTIONFUNCTIONSBECAUSETHEYSHOWHOWEACHRMREACTSTOTHEOTHERSOUTPUTLEVELINEQUILIBRIUMTHESEEQUATIONSMUSTBEMUTUALLYCONSISTENTTHATIS,EACHRMMUSTPRODUCEWHATTHEOTHERTHINKSITWILLGIVENTHISASSUMPTION,EQUATIONS1916CANBESOLVEDSIMULTANEOUSLYFORTHEEQUILIBRIUMVALUESOFQ1ANDQ2TOYIELDQ1H11005Q2H11005401917PH11005120H11002Q1H11001Q2H1100540H92661H11005H92662H11005PQ1H11005PQ2H110051,600MOREWILLBESUPPLIEDUNDERTHECOURNOTASSUMPTIONSTHANUNDERTHECARTELCASE,ANDINDUSTRYPROTS3,200WILLBESOMEWHATLOWERTHANWHENOUTPUTDECISIONSAREFULLYCOORDINATEDTHISCOURNOTSOLUTIONISDENOTEDBYPOINTAINFIGURE193INTHISPARTICULARCASEITISEASYTOSHOWTHATASMORERMSAREINTRODUCEDINTOTHEH11128H92662H5007H11128Q2H11128H9266IH5007H11128Q1H11128H9266H5007H11128QCHAPTER19TRADITIONALMODELSOFIMPERFECTCOMPETITION535ANALYSIS,THEEQUILIBRIUMMOVESTOWARDTHECOMPETITIVEPOINT3FORASOMEWHATMOREREALISTICCASETHATALSOYIELDSTHISSOLUTION,SEEPROBLEM192QUERYGIVENTHATONESPRINGOWNERSOUTPUTIS40INTHECOURNOTMODEL,WHYCANTTHEOTHEROWNERGAINBYPRODUCINGMORETHAN40UNITSOFOUTPUTDOESTHISCONCLUSIONCONICTWITHOURDISCUSSIONOFCARTELSWHEREWEEXPECTEDCHISELINGWHENEVER