Vertical Differentiaiton, Trade and Endogenous Common Standards

Lambertini, Luca; Rossini, Gianpaolo Working Paper Vertical Differentiaiton, Trade and Endogenous Common Standards Quaderni - Working Paper DSE, No. 263 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Rossini, Gianpaolo (1996) : Vertical Differentiaiton, Trade and Endogenous Common Standards, Quaderni - Working Paper DSE, No. 263, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/5048 This Version is available at: https://hdl.handle.net/10419/159106 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ VerticalDi®erentiation,Tradeand EndogenousCommon Standards1 LucaLambertini-GianpaoloRossini DipartimentodiScienze Economiche Universitµa degli StudidiBologna StradaMaggiore45 I-40125 Bologna fax:39.51.6402664 e-mail: [email protected] e-mail: [email protected] June19,1998 1Acknowledgements.Wewouldliketothanktheaudience at the24thEARIE Conference (Leuven,September1997)forcommentsand discussion.Theusualdisclaimerapplies. Abstract Di®erentmarketsettingsare consideredinafree trade environment,where¯rms canchoosetechnology,quality,and price orquantity.Theshapeofcompetition in pricesrequirestheinterventionofgovernments,viaacommonantidumping policy,tomake¯rmsconvergeonthesimultaneousequilibriumwhichis socially optimal. IntheCournotframework,the equilibriaweobtainimpingeuponthe kind ofprecommitmentsundertaken by¯rms.The coincidence between ¯rms' behaviourand socialpreference obtainseitherwhencompetitionistough,since incomeislow,orwhen ¯rmsmustcompeteinquantitiesinthemarketstage, since theycannotmodify qualities.Thespontaneouscoordinationovercommon standardshastobe contrastedwith boththe caseofa²uentconsumersand Bertrand competition. JELclassi¯cation:F12, F13, L13 Keywords:quality,technology,standardcoordination 1Introduction Whentradetakesplaceamongcountriesproducingverticallydi®erentiatedgoods, competitionmayassumevariousforms,namely,¯rmsmayalternativelysetprices, quantitiesand qualities,accordingtothe commitmentsinheritedfromeither autarchyoraprevious stageofinfantdevelopmentwhentherelevantmarketis limitedand fairlysheltered,e.g.bythepresence ofsomepatented process or productwhoseprotectionisgeographicallycon¯nedtothehome country.1The kind ofcompetition underfree trademaybe conditionaluponthetechnological menu totheavail ofproducers.We¯gureout twomain possibilitiesaccordingto previousliteratureinthe¯eld(Mussa and Rosen,1978;Shakedand Sutton,1982; 1983).The¯rstisrepresented byatechnologywherequalityimprovementsrely onavariable cost.For thesecond technologytheprovisionofqualityimpinges upona¯xedcost thatcan beinterpretedasanR&De®ort.Thenwe enrichthe menu byconsidering alsodi®erentlevelsofe±ciencyassociatedwiththesame technologies. Theavailable contributionsinthe¯eldare con¯nedtotheanalysisofprice competition(Shakedand Sutton,1984;Lambertini, 1997;Motta,Thisseand Cabrales,1997)and quantitycompetition(Motta,1992),underbothashortrun and along-run perspective,accordingtowhetherqualitiesarethesame asinautarchy,orareadjustedafter tradeliberalization.These contributions aremainlyaimedatoutliningtheimplicationsofliberalizationonwelfareand marketstructurewhen ¯rmsface similarproductionopportunitiesbutcountries di®erintermsofincomedistributionorconsumerdensity.Noneofthetwotakes into account thepossible consequencesofeither¯rms'technologicalchoicesor e±ciency,or thearising ofqualitycompetitionwhen ¯rmsaresupposedtobe quantity-constrained. The choice ofatechnologyoutofamenu or theavailabilityofacertain technologyinheritedfromthepastshapesthenatureofcompetition, insuchaway thateitheraproblemofcoordinationover tradepoliciesarisesforgovernments, oraproblemofcoordinationoverqualitystandardsand theproduction process arisesfor¯rms. The¯rstcaseariseswhen ¯rmscompeteµa laBertrand and operatewithtechnologiescharacterized bydi®erentdegreesofe±ciency:marketincentivesnever let¯rmscoordinatespontaneouslyoversimultaneousplay,sothatgovernments' interventionisneededinorder toensuretheattainmentoftheuniquewelfaremaximizingequilibrium.Tothispurposeweimagineasort ofantidumpingpolicy thatfollowsaphilosophy quitenear totheonethatinspires someoftheinterventionoftheEUCommission,accordingtowhichtheremaybeacasein pointfor 1Therearemanyinstancesofcommercialdisputesamong¯rmsastothegeographic e®ectiveness ofapatent.Insome casestheresultisapartial insulationofthehomemarketfora ¯rmthathasintroducedeitheranewproductoranewprocess inthe countryinwhichithas itsmainestablishment.Insuchcasesaconditionakinto autarchyarises. 1 anantidumpingintervention,whentheprice oftheimportedgoodismuchlower thantheprice ofthe correspondingdomesticallyproducedgood.2Surprisingly enough,theantidumpinghas, inthiscase,aprocompetitive e®ectand therefore doesnotbring about thedeadweightloss usuallyassociatedwithsuch policy. Thismeansthat thesort ofantidumpingpolicyweshall describebelowcan be undertaken byanantitrustagencytopursueawelfaremaximizationobjective. Thesecond situationmayemergewhen ¯rmsbehaveµa laCournotafter trade liberalization.Here,¯rmsface atwinchoice between usingeitherquantityor qualityasacontrol inthemarketstage.Asaconsequence di®erentequilibriaemerge,accordingtothea²uence ofthemarket.Whenthemarkethasa su±cientlylowreservation price,aspontaneouscoordinationobtainsasfaras qualitystandardsand technologyare concerned,while,asthemarketshowsa higherwillingness topay,multiple equilibria areassociatedwithmultiplestandards.The correspondingevaluationofwelfareshowsthatitwould besocially desirabletohave¯rmsconvergingtothesamequalitystandardand themost e±cient technology. Thishaspolicyimplicationswhicharedi®erentaccordingtothe consumers' evaluationofqualityinthe countriesengagingintrade.Ifsuchevaluationis relativelylowthereseemstobenopointinsupportingneithernationalnor commoninternationalstandards, inthatane±cientcommonstandardarisesout ofthe endogenousmarketinteraction.Theoppositehappenswhenconsumers exhibiting a highmarginalevaluationofquality,since inthatcasethevariance ofstandardsbecomesrelevantand noendogenouscoordinationemerges.Again theremaybeacasein pointfora governmentinterventionthatmaytaketheform ofaqualitystandardthatcorrespondstoaPareto-superiorequilibrium.Thetime consistencyoftheseinterventionsisanalyzedin Jensenand Thursby(1996)who describean uncertainR&Drace between ¯rmsofdi®erentcountriesand show thatadomestic(autarchic)simplestandardisbound tobetimeinconsistent.3 Our resultshowsthat thistimeinconsistencyneverarises,becauseitisoptimal forgovernmentsto¯xthesamestandardregardless ofthemarket regime. Theremainderofthepaperisorganizedasfollows.Insection2weprovide theautarchy model, whileinsection3wedealwithBertrand competitionin free trade.Section4isdedicatedtoCournotcompetition.Section5provides concludingcomments. 2Thebasicsetting We¯rstconsideracountrywithonlyone¯rmproducingadi®erentiatedgoodof qualityqsoldtoapopulationofconsumerswhoseincomedistributionisassumed 2Onthistopicsee forinstance Vandenbussche(1996),Bronkers(1996). 3There existsawideliterature(see Katzand Shapiro,1985 and 1986;Farrell and Saloner, 1985;1987;Matutesand Regibeau,1988,interalia),wheretheissueofstandardization depends oncompatibilityamongproducts,withorwithoutnetworkexternalities. 2 uniformand themarginalwillingness topayfor thedi®erentiatedgoodisgiven byµ2[µ;µ]withµ=µ¡1 and µ>0.4Moreoverwenormalize thepopulation densityto 1,for thesakeofsimplicity.Hence thetotalmass ofconsumersinthe marketisalso 1. Eachconsumerhasunitdemand and buysifand onlyifhisnetsurplusis non-negative U=µq¡p¸0;(1) wherepistheprice charged bythemonopolist. Wearethenableto obtainthemarketdemand function: x=µ¡p q:(2) We canconsider two alternativetypesoftechnology.The¯rstisgiven bythe followingcostfunction: Cv=tq2x;(3) wherebytotalcostsare convexinqualityand linearinquantity,and no¯xed costisassociatedeither toqualityor toquantity.Theparametert2]0;1] isan e±ciencyindicatorofthe¯rm'smarginalcost. Thesecond technologylooksasfollows: Cf=tq2;(4) implyingthatproductioninvolvesexclusivelya¯xedcostand marginalcostis zero. We can now writethepro¯tfunction ¼i=px¡Cifori=f;v:(5) Westart consideringthe casefori=v;de¯nedasvariable cost technology. The¯rstorderconditions(FOCs)forpro¯tmaximizationare: @¼v @p=µ¡2p q+qt=0;(6) @¼v @q=tp+p2 q2¡2µtq=0;(7) 4Thisformalizationofconsumers'preferenceshasbeenintroduced byMussa and Rosen (1978).Since µcan beseenasthereciprocalofthemarginalutilityofnominal income,we can interpret thereservation price asthe closestproxy toconsumers'a²uency(see Tirole,1988,p. 96). 3 whichyieldthefollowingsolutions:5 qv=µ 3t;pv=2µ2 9t:(8) Using(2)and (5),we canestablishthatequilibrium quantityand pro¯tare: xv=µ 3;¼v=µ3 27t:(9) The correspondingsocialwelfarelevel isWv=3µ3=(54t):Wheni=f,de¯ned as¯xedcost technology,theFOCsforpro¯tmaximization become @¼f @p=µ¡p q(1¡p)=0;(10) @¼f @q=p2 q2¡2tq=0;(11) Solving(10)and (11)yields qf=µ2 8t;pf=µ3 16t;(12) whilepro¯tsand quantitysoldare xf=µ 2;¼f=µ4 64t:(13) SocialwelfareisWf=µ4=(32t):Quickcomparison between pro¯tsand socialwelfarewiththetwotechnologies suggeststhat,while¯rmsalwaysprefer technology vtof;socialpreferences switchfromvtofwhenµ>48=27:Consumersare partiallyservedwith bothtechnologiesifthehighestmarginalwillingness topay µisless than2:Weshall takeinto account thisconstraintonµintheremainder ofthepaper. Inthefollowingsectionswedealwith di®erentkindsofcompetitioninthe internationalmarket.Acommonfeatureofall settingswill betheinheritance fromautarchy,orfromaperiodofmarketinsulation duetotradebarriers,of anin°exible choice relating alternativelyeither tocapacityor toquality.Any departurefromthatcan bethoughtofasentailingsuchahugeadjustmentcost thatnoviable¯rmwould undertakeit.Quality maybestucktotheautarchy levelduetopatentsprotectingtheacquiredR&Dknowledge.Quantity may belimited bycapacityconstraintsdrivingmarginalcost toin¯nity(Krepsand Scheinkman,1983;Davidsonand Deneckere,1986). 5Observethat, independentlyofthetechnologyadopted,themonopolistsuppliesthesame qualityasthesocialplanner,since thedemand functionislinear(Spence,1975,pp.419-21). 4 3Bertrand competitionand free trade Wenowfocusonfree tradesettings.First,we consider the casewhere¯rms competein prices,adoptingdi®erent technologiesand playingdi®erent rolesin themarketgame.Weassumethatnobarriersofany kind existbetweencountries. Theresultsweshall obtainmaypromptforantidumpingmeasures,triggered byprice di®erentialsbetweencountriesengagingintrade.Thedesirabilityof antidumpingpoliciesistheninvestigatedaccordingtothe endogenous shapeof competitionontheinternationalmarket. 3.1 Variable costsand free trade Wenowconsiderfree tradebetweentwocountriescompetinginanindustrywhere eachonehasasingle¯rmadoptingthevariable cost technology. Thetwocountriesare equal inall respectsbutfor the e±ciencyoftheir respective¯rms.Inotherwordsweassumethatone¯rmhasacostfunction whichisthesameas(3),whiletheother¯rmhasthesame costfunctionwith t=1:Asaconsequence thequalityofthegoodsold bytheless e±cient¯rmis lower thantheonesupplied bythemore e±cient¯rm.Theformer¯rmislabeled LwhilethelatteriscalledH:Thesameidenti¯cationcodeisusedfor thetwo countries. Assumingthat thequalitystandardsaresetinautarchyasanirreversible commitmentdueto anarbitrarilylargeadjustmentcost,possiblyduetothe existence ofapatent,we can determinethedemand functionsoftheintegrated market,whosedensityistwice aslargeasthatoftheautarchicmarketfaced byeach ¯rm.Tothispurposewehavetode¯nethepositionsofthe consumers indi®erentbetween buyingeitherofthetwo goods,and between buyingthelow qualitygoodornothing: k=pL qL;h=pH¡pL qH¡qL:(14) Thenwe can determinethemarketdemand: xH=2[µ¡3t(pH¡pL) µ(1¡t)]; (15) xL=6(tpH¡pL) µ(1¡t):(16) Therefore,thepro¯tfunctionslookasfollows: ¼H=2(pH¡µ2 9t)(µ¡3t(pH¡pL) µ(1¡t));(17) 5 ¼L=2(µ2¡9pL)(tpH¡pL) 3µ(t¡1):(18) Firmsnoncooperativelyand simultaneouslyoptimize w.r.t.prices.TheFOCs are: @¼H @pH=6µ2t¡8µ2+36tpH¡18tpL 3µ(t¡1)=0;(19) @¼L @pL=¡2(µ2¡18pL+9tpH) 3µ(t¡1)=0;(20) whosesolutionis pH=µ2(8¡5t) 9t(4¡t);pL=µ2(2¡t) 3(4¡t);(21) sothat therelativeprice pH=pL>1forall t2]0;1]:Substituting(21)into(17-18) and rearranging,yieldstheNashequilibriumpro¯ts ¼n H=32µ3(1¡t) 27t(t¡4)2;¼n L=8µ3(1¡t) 27(t¡4)2:(22) Itisquicklyestablishedthat¼n H>¼n L: Welfare evaluationsarestraightforwardsince consumersin bothcountries enjoythesamelevelofsurplusand theonlydi®erence betweenthetwocountries isduetotherespectivelevelsofproducer's surplus,whichishigherincountryH. 3.2 Endogenouschoiceofroles Intheprevious sectionwefocussedontheBertrand-Nashequilibriumemerging fromsimultaneousplay,whichappearsasthenaturalwayofplayingwhen ¯rms cannotchoosethetiming oftheir respectivemoves,beforeactualcompetition takesplace.Now wemayaddress thequestionwhether¯rmsmaychoosetoplay sequentially,whenweintroduce apreplaystagewheretheynoncooperativelyset thetiming.FollowingHamiltonand Slutsky (1990),weanalyze anextended gamewithobservabledelay,consisting oftwostages.Inthe¯rst,¯rmscan choosebetween playing at the¯rstavailableoccasion(F)ordelayaslong as possible(S).Ifbothselect thesamestrategy,asimultaneousequilibriumobtains. Otherwise,asequentialequilibriumisobservedoutofthetwopossible.Then ¯rmsproceedto optimallysetpricesaccordingtothetiming ofmovespreviously decided.Themarketequilibrium,emergingfromsuchaprocess, ispart ofthe two-stagesubgameperfectequilibriumofthe extendedgamewithobservable delay. 6 WehavetocomparethesesolutionswiththesimultaneousNashequilibrium pro¯ts(33)and (34).Foreach ¯rmwe canwritethesequence ofpro¯ts: ¼f L>¼l L>¼n L;¼l H>¼f H>¼n H:(53) Providedthetwo¯rmscanchoosethetiminginanextendedgamewith observabledelay,twosubgameperfectequilibria arise,where¯rmsmovesequentially.The equilibriumwherethemore e±cient¯rmprovidingthehighquality goodmoves¯rst,Pareto-dominatestheotherwheretheleadershipistaken by thelow-quality¯rm, i.e.¼l H+¼f L>¼f H+¼l L:The equilibriuminwhichthemore e±cient¯rmisleadercan be consideredasafocalpoint. Wemaynowconsider thesocialdesirabilityofanon-cooperativetradepolicy aimedat themaximizationofsocialwelfare.Theoutcomescan beorderedin thefollowingway:Wn L>Wl L>Wf L;and Wn H>Wf H>Wl H:Hence,toreachthe socialoptimum,governmentsmovesimultaneouslyand spontaneouslycoordinate overacommonantidumpingpolicyagainst therespectiveforeign ¯rm.Asinthe previous section,these coordinatedantidumpingpolicieshaveaprocompetitive e®ect. 3.4.2Highqualitywithvariable costs Wenowturntothesettingwherethehighqualitygoodisproduced bythe¯rm operatingwiththevariable coststechnology.Whensheactsastheleaderin prices,herobjectiveis: max pH¼H=2õ¡24t(pH¡pL) µ(3¡8µt) !(pH¡µ2 9t) (54) s.t.: @¼L @pL=0:(55) The equilibriumoutcomeisgiven bythefollowingpro¯ts: ¼l H=µ3(15µt¡32)2 108t(3µt¡16)(3µt¡8);(56) ¼f L=µ4(14336¡7680µt+288µ2t2+243µ3t3) 576(3µt¡16)2(8¡3µt):(57) Intheopposite case,theless e±cient¯rmplaystheleader'sroleand solves theprogram: max pL¼L=2pL Ã24t(pH¡pL) µ(3¡8µt)¡8pL µ2 !¡µ4 64 (58) s.t.: @¼L @pL=0:(59) 13 The equilibriumpro¯tsare: ¼l L=µ4(896¡504µt+81µ2t2) 73728¡41472µt+5184µ2t2;(60) ¼f H=µ3(512 ¡288µt+27µ2t2)2 1728t(3µt¡16)2(8¡3µt):(61) Ifwe evaluatethepro¯tsassociatedwitheithersimultaneousorsequentialmoves, we¯nd that thefollowingsequence ofinequalitiesholdsforboth ¯rms: ¼f i>¼l i>¼n i;i=H;L:(62) Thisentailsthat the extendedgamewithobservabledelayhastwosubgameperfectequilibria,where¯rmsplaysequentially.Moreover,since both ¯rms strictly prefer thefollower'srole,suchequilibriacannotbePareto-ordered.Acaselargely similar totheonepreviouslyseen,whenthehighqualitywasprovidedthrough technologyf,arisesfor tradepolicy.Again,acoordinatedantidumpingpolicy bybothgovernmentspushes¯rmstoplayasimultaneousBertrand equilibrium. Thekind ofinterventionwe¯gureoutisquitesimilarinspirit tosomeofthose undertaken bytheEUCommission,mainlyagainstEasterncountries.These antidumpingmeasuresaretriggeredsimplybyrelevantdi®erencesin pricesof goodsbelongingtothesameindustry,butusuallyleadto greaterdistortionsand additionalwelfarelosses.Inourcaseanantidumpingmeasuremaybetriggered bythesamefactsbuthasade¯niteprocompetitive e®ect,provideditisbilateral. Tosumup theresultsobtainedinthesection,wemayformulatethefollowing: Proposition1When ¯rmsoperate witheitherhomogeneousorheterogeneous technologiesandcompeteµa laBertrand, theyprefersequentialplay.Ifgovernmentsmaximize welfare,theymightindependentlyimplementanantidumping policythatendsup havingareciprocalpro-competitive e®ect. 4 Cournotcompetitionand free trade Now we conductouranalysiswithinaframeworkwheretherelevantmarket variableisnolongerprice.Once Cournotcompetitionisconsidered,several possiblescenariosmayarise.Firmscan ¯xtheiroutputsunderautarchyand thenadjustqualitiesunderfree trade,orvice versa,accordingtothedi®erent degree of°exibilitycharacterizingtheir technologyand theircapacity.If¯rms operatewithatechnologythatinvolves¯xedcostsofqualityproduction,they canonlyadjustoutput.Ifinsteadtheyadoptavariable cost technology,they havetheoptionto¯xeither theoutputor thequalityat theautarchylevel. The e±ciencylevel isthesameforbothtechnologies, i.e., t=1. 14 4.1 Symmetric choices (a)Qualitycompetitionundercapacityconstraints.Asituationcan be envisaged, wherethe existence ofcapacityconstraintsobliges¯rmstomaintaintheoutput leveladoptedinautarchy,whilebeing°exibleintermsofqualitysuppliedin duopolybecauseofthe°exibilityassociatedwithavariable cost technology.This assumptionmaybe consistentwiththosemodelsofintraindustrytradewherethe opening oftradehasonlyavarietye®ect, leavingthetotalnumberof¯rmsas well astheiractivityleveluna®ected(Krugman,1979). Westill consider twocountrieswhichare equivalentinall respects.Both ¯rms operatewithavariable cost technology,asin(3).Theinversedemand functions are: pH=2µqH¡qHxH¡qLxL 2;(63) pL=qL(2µ¡xH¡xL) 2:(64) Thepro¯tfunctionsare: ¼H=xH 2(2µqH¡qHxH¡qLxL¡2tq2 H);(65) ¼L=qLxL 2(2µ¡xH¡xL¡2tqL):(66) Provided bothquantitiesare¯xedat theautarchylevel, i.e., xi=µ=3,we can derivetheoptimalqualitiesbydi®erentiatingthepro¯tfunctionsw.r.t.their controls: qH=5µ 12;qL=µ 3:(67) Itisworth notingthatqListhesameasinautarchy,duetotheabsence of strategicinteractionemerginginthiscase.Asaconsequence,thelow-quality goodis soldat theautarchicprice (8),whilepH=7µ2=24.Equilibriumpro¯ts are: ¼vv H(xA)=17µ3 432 ;¼vv L(xA)=µ3 27;(68) wheresuperscriptvv indicatesthatboth ¯rmsoperatewithavariable cost technology,whilexAmeansthatquantityis¯xed underautarchy. The consumersurplusisthesameforeachcountry,CSi=17µ3=864.This obviouslyentailsthatsocialwelfareishigherinthecountrywherethehigh-quality ¯rmislocated. 15 (b)Quantitycompetitionunderqualityconstraints.Herewe consider the oppositecasewherequalitiesare¯xedinautarchyand¯rmscompeteinquantities afterliberalization.A¯rstintuitiveresultisthatbothgoodsaresoldat the sameprice,since theirqualitiescoincide:pH=pL=µ(2µ¡xH¡xL)=6:Optimal quantitiesarexH=xL=4µ=9;whilepro¯tsare: ¼vv H(qA)=¼vv L(qA)=8µ3 243;(69) whereqAmeansthatqualitycorrespondstotheautarchylevel. Again,consumer surplusisthesamein bothcountries,CSi=8µ3=243.Thesameobviouslyholds forsocialwelfare. (c) Cournotcompetitionwith¯xedcosts.When both ¯rmsoperatewitha ¯xedcost technology, itappearsreasonableto assumethat theycanonlyadjust quantitiesunderfree trade,since qualitiesaretheresultofR&Dinvestments undertakeninautarchy, interpretedasaperiodofpatentshelter.Qualitiesare asin(12),sothatgoodsareperfectsubstitutes.Thepro¯tfunctionsare: ¼H=µ2 64(8µxH¡µ2¡4xHxL¡4x2 H);(70) ¼L=µ2 64(8µxL¡µ2¡4xHxL¡4x2 L):(71) TheoptimalquantitiesarexH=xL=2µ=3:Equilibriumpro¯tsare: ¼ff H(qA)=¼ff L(qA)=7µ4 576:(72) Ofcourse,pH=pL=µ3=24;and CSi=µ4=36: Wemaysumup theaboveresultsinto Proposition2Inall casesinwhichtechnologicalchoicesarethesameforthe twocontenders,thesequence of payo®sdoesnotdepend ontheupperbound of the marginalwillingness to pay(µ), i.e.: ¼vv H(xA;xA)>¼vv L(xA;xA)>¼vv H(qA;qA)= ¼vv L(qA;qA)>¼ff H(qA;qA)=¼ff L(qA;qA):Thisentailsthat°exibilityinquality settingstrictlydominates°exibilityinquantity. 4.2 Asymmetric choiceswithvariable costs (a)Highqualityvariable,low quality¯xed. Here,we comebacktothesetting whereboth ¯rmshaveavariable cost technology,and consider the casewhere thelowqualityis setunderautarchy,whilethehigh-quality¯rmisconstrained toproduce thesamequantityasinautarchy.Hence,qL=µ=3=xH:Thepro¯t functionslookasfollows: 16 ¼H=µ 18(5µqH¡6q2 H¡µxL);(73) ¼L=µxL 6(µ¡xL):(74) Atequilibrium,qH=5µ=12,xL=µ=2,and pro¯tsare: ¼vv H(xA)=13µ3 432 ;¼vv L(qA)=µ3 24;(75) with¼vv H(xA)<¼vv L(qA).Thelow-quality¯rmisableto obtain higherpro¯ts thanthehigh-quality¯rmbyfree-riding over therival'soutputconstraint; in otherwords shetakesadvantageofthehigh-quality¯rm'sinabilitytoexpand productionwhenmarketsize increasesasaconsequence oftradeliberalization. Thisimpliesthat¯rmL'smarketshareincreases.Astoconsumersurplus,we obtainCSi=13µ3=432: (b)Highquality¯xed, low qualityvariable.Wenowdescribetheopposite case, wherethehigh-quality¯rmsetsherqualityinautarchy,and thelow-quality¯rm isconstrainedtoproduce theautarchiclevelofoutput,qH=µ=3=xL:The pro¯tfunctionsare: ¼H=µxH 18 (4µ¡3qL¡3xH);(76) ¼L=µqL 18 (5µ¡6qL¡3xH):(77) Wethenget theoptimalcontrols,xH=11µ=21 and qL=2µ=7:Equilibrium pro¯tsamount to: ¼vv H(qA)=121µ3 2646 ;¼vv L(xA)=4µ3 147:(78) Again,consumersin bothcountriesenjoythesamesurplus,CSi=295µ3=10584: Since ¼vv H(qA)>¼vv L(xA);itisimmediately veri¯edthatsocialwelfareishigher inthe countrywhere¯rmHoperates. (c)Highqualitywithvariable costs,low qualitywith¯xedcosts, andCournot competition.Inthismixedcase,thehigh-qualitygoodisproducedwithavariable cost technology.Notice that theotherwayround isnotpossiblebecausethe¯xed technologyisless e±cientand thereforeiscon¯nedtotheproductionofthelow quality.Bothqualitiesaresetinautarchy,and ¯rmsoptimize overquantities. Theirpro¯tfunctionsare: ¼H=µxH 144 (32µ¡24xH¡9µxL);(79) 17 ¼L=µ2 64(8µxL¡µ2¡4xHxL¡4x2 L):(80) Equilibrium quantitiesand pro¯tsare: xH=2µ(9µ¡32) 9µ¡96 ;xL=64µ 96 ¡9µ; ¼vf H(qA)=2µ3(9µ¡32)2 27(3µ¡32)2;¼vf L(qA)=µ4(224 ¡9µ)(32 +9µ) 576(3µ¡32)2:(81) Consumersurplusisthesamein bothcountries,and amountsto CSvf i(qA)=µ3(1024+576µ¡135µ2) 54(3µ¡32)2: From(81), itemergesthat¼vf L(qA)>¼vf H(qA)ifµ>1:509:Since theonly di®erence betweenthetwocountriesisduetopro¯ts,thesame condition holds forsocialwelfare comparisonaswell. Astoquantities,xL>xHforall acceptable valuesofµ: (d)Highqualitywithvariable costsandquantityconstraint,low qualitywith ¯xedcostsandqualityconstraint.Thelastcasethat remainstobeinvestigated isthatwherethehighquality¯rmoperateswithvariable costsand suppliesthe samequantityasinautarchy,whilethelowqualitybeingproducedthrough ¯xed costs, isobviouslysetinautarchy.Pro¯tfunctionsare: ¼H=µ(40µqH¡48q2 H¡3µ2xL) 144 ;¼L=µ2(6xL¡µ)(3¡2xL) 192 :(82) Atequilibrium,wegetqH=5µ=12,and xL=5µ=6,sothatpro¯tsare: ¼vf H(xA)=5µ3(10 ¡3µ) 864 ;¼vf L(qA)=µ4 36:(83) If1<µ<1:282,then¼vf H(xA)>¼vf L(qA):Consumersurplusis: CSvf i(xA;qA)=5µ3(8+27µ) 6912 : We canthensumup theasymmetric caseswith Proposition3Intheasymmetricsetting,thepayo® rankingisnotinvariant withrespect toµ;i.e.thereisno dominance inthe choice of controls. 18 4.3 Athree-stagegame Wemaynow¯gureout theinteractionsbetweenthetwo¯rmsastakingplace throughthree di®erentstages.Inthe¯rst,the choice oftechnologybetween ¯xedand variable costshastobeundertaken.Thedecisionto adopt thevariable cost technologyleavesopenthepossibilityto¯xeitherqualityorquantityinthe second stage,whiletheadoptionofthe¯xedcost technologyimpliesthat the ¯rm mustcompeteinquantitiesgiventheautarchicqualitychosen beforehand. Thethirdstagedescribesmarketcompetition. Matrix3describesthethree-stagegamein normalform,wherethepayo®s arethosefound intheprevious section.Firmsarelabelledas1 and 2,since theirlocationalongthequalityspectrumdependsuponthespeci¯csubgame considered.Ineachcell, the¯rstpayo®refersto¯rm1,thesecond to¯rm2. 2 fv qAqAxA fqA¼ff L(qA;qA);¼ff H(qA;qA)¼vf L(qA;qA);¼vf H(qA;qA)¼vf L(qA;xA);¼vf H(qA;xA) 1vqA¼vf H(qA;qA);¼vf L(qA;qA)¼vv H(qA;qA);¼vv L(qA;qA)¼vv H(qA;xA);¼vv L(qA;xA) xA¼vf H(xA;qA);¼vf L(xA;qA)¼vv H(xA;qA);¼vv L(xA;qA)¼vv H(xA;xA);¼vv L(xA;xA) Matrix 3 Wenowconsiderdi®erent three-stagegamesaccordingtothelevelofthekey parameterµ;whoseadmissiblerangeis]1;2]. i)Homogeneous productsandvariablecost technology Proposition4Inthemostpartof theadmissiblerange of µ;thesubgameperfect equilibriumofthethree-stage gameinvolvesboth¯rmschoosingthe variable cost technologyandtheautarchic quality.Then,theycompeteinquantitiesinthe marketstage with homogeneousproducts. Proof.When1<µ<1:498,we canorder thepayo®sinmatrix3 accordingto thefollowinginequalities: ¼vf H(qA;qA)>¼vv H(qA;xA)>¼vv L(xA;qA)>¼vf H(qA;xA)= =¼vf H(xA;qA)>¼vv H(xA;xA)=¼vv L(xA;xA)>¼vv H(qA;qA)= 19 =¼vv L(qA;qA)>¼vv H(xA;qA)>¼vf L(xA;qA)=¼vf L(qA;xA)> >¼vv L(qA;xA)>¼vf L(qA;qA)>¼ff H(qA;qA)=¼ff L(qA;qA):(84) Giventhis sequence ofinequalities,thethree-stagegamehasauniquesubgame perfectequilibriumrepresentedbythetriplepairsofsequentiallychosenstrategies f(v,v),(qA;qA),(x,x)g.The corresponding outcomeis¼vv H(qA;qA)=¼vv L(qA;qA): Thisisaperfectlysymmetric equilibriumwhere¯rmsbecomeindistinguishable inall respects. Notice that thesubgameperfectequilibriumofthethree-stagegameis simultaneouslythe equilibriumofthesubgamewherestrategyxAisabsent,sothat thelatterappearstoberedundant. ii)Heterogeneityof productsandtechnologies:multiple equilibriawithpredeterminedquality Proposition5For reasonablyhighvaluesof µ,thethree stage gamehastwo subgameperfectequilibria. Firmsoperate with heterogeneoustechnologies,¯x qualitiesinautarchyandthencompeteµa laCournotwith di®erentiated products. Proof.Whenµ2[1:498;1:919], wehavethefollowinginequalities: ¼vf L(xA;qA)=¼vf L(qA;xA)>¼vv H(qA;xA)>¼vv L(xA;qA)> >¼vv H(xA;xA)>¼vf L(qA;qA)>¼vv L(xA;xA)>¼vv H(qA;qA)= =¼vv L(qA;qA)>¼vv H(xA;qA)>¼vf H(qA;qA)>¼vf H(xA;qA)= =¼vf H(qA;xA)>¼vv L(qA;xA)>¼ff H(qA;qA)=¼ff L(qA;qA):(85) Onthebasisof(85),wehavetwosubgameperfectequilibria ofthethreestagegame,whicharerepresented bythetriplepairsf(v;f);(qA;qA);(x;x)g; f(f;v);(qA;qA);(x;x)g: Again,strategyxAcan bedisregarded,and the equilibriumbelongstothe subgamewhere¯rms setqualitiesinautarchy.Firmsturnthusout tobeunable tocoordinateover thetechnologicalchoice and thenalso onqualitystandards. 20 iii)Heterogeneityof productsandtechnologies:multiple equilibriawithmixedpredeterminedvariables Proposition6Forvaluesof µneartotheupperbound of theadmissiblerange, thethree stage gamehastwosubgameperfectequilibria. Firmsoperate with heterogeneoustechnologies,setdi®erentvariablesinautarchyandusedi®erentcontrolsinthemarketgame. Proof.Whenµ2]1:919;2], wehavethefollowingsequence ofinequalities: ¼vf L(xA;qA)=¼vf L(qA;xA)>¼vf L(qA;qA)>¼vv H(qA;xA)> >¼vv L(xA;qA)>¼vv H(xA;xA)>¼vv L(xA;xA)>¼vv H(qA;qA)= =¼vv L(qA;qA)>¼vv H(xA;qA)>¼vv L(qA;xA)>¼vf H(qA;xA)= =¼vf H(xA;qA)>¼ff H(qA;qA)=¼ff L(qA;qA)>¼vf H(qA;qA):(86) Given(86),thethree-stagegame exhibitstwosubgameperfectequilibriawhere ¯rmschooseheterogeneoustechnologiesandsetdi®erentcontrolsasaresultofthe commitmentstakeninautarchy.Wethenobtainthetriplepairsf(f;v);(qA;xA); (x;q)g;f(v;f);(xA;qA);(q;x)g: Notice that the equilibriumofthethree-stagegamedoesnotcoincidewith the equilibriumofthesubgamewhere¯rmsare constrainedto adoptquantity asthe controlvariableinthemarketstage.This subgamehasactuallyaunique symmetric equilibriumrepresented byf(f;f);(qA;qA);(x;x)g,whichistheresult oftheadoptionofdominantstrategiesinasituationreproducingtheprisoner's dilemma. 4.4 Discussion Wewishtoinvestigatethe coordinationaspectsofequilibriaintermsoftechnologiesand qualitystandards.Moreoverweare concernedwiththetime consistency ofthe choice oftechnologybyeach ¯rm,since anyasymmetric equilibriumentailstimeinconsistency,and,fromtheautarchicperspective,thevariable cost technologyischosenwhen1<µ<48=27 » =1:777 and vice versa. Wehaveseenthatinmostofthe cases(i.e.when1<µ<1:498),automatic coordinationoverbothtechnologyand qualitystandardobtains.Thisappears toimplythatifthemarketisnotextremelya²uent,¯rmstend to adopta highlycompetitivebehavior,supplyinghomogeneousgoodsproducedthrough 21 themoste±cient technology.Thisisacasewhere complete coordinationand time consistencyemerge. Asconsumersget richer (µ2[1:498;1:919]),wedonotobserveany morea uniquesubgameperfectequilibrium.Weloosethe commonstandardsince the increaseinmarketa²uence leads¯rmstodivergeinqualitiesand technologies, adoptingthusaless competitivebehavior.This,however, isjustapart ofthe story.Since weassumethatcountriesaresimilarinall respects,weshould plausiblyanticipatethatboth ¯rmsadopt themoste±cient technology, i.e., technology v,aslong as1<µ<48=27 » =1:777:Ifthatisthe case,weshouldcon¯neto atwo-stagegamewhichcorrespondstothesouth-eastquadrantofMatrix3, wherethesubgameperfectequilibriumin dominantstrategiesisrepresented by f(qA;qA);(x;x)g;where¯rmsproduce thesamequalityand thesamequantity. Thisistheonly meansto get time consistencyinthisrangeofµ:Thepairof strategies(f;f)isneversubgameperfect,nomatterhowthematrixisreduced. Foreven higherlevelsofthemarginalwillingness topay(µ2]1:919;2]),we still get twosubgameperfectequilibria ofthethree-stagegame,where¯rmsfail tocoordinateinall stagesand thusbehaveinconsistently.However,di®erent resultsobtainifwego throughtwosubgames.Consider the¯rst,represented bythenorth-westquadrantofMatrix3,whichobtainsbydroppingstrategy xA.The equilibriumin dominantstrategiesisgiven byf(f;f);(x;x)gwhichis time consistentsince itcan be envisagedastheresultofautarchic choice.The second subgameisrepresented bythesouth-eastquadrantofMatrix3.Again, wehaveanequilibriumin dominantstrategies,given byf(qA;qA);(x;x)g:>From the¯rms'standpoint,thelatterequilibriumispreferredtothatassociatedwith theformersubgame,yetitsu®ersfromtimeinconsistency. 4.5 Welfareassessment Wenowconsidersocialwelfareineachcountry,con¯ning ourattentiontothose marketcon¯gurationsthatare candidatesas subgameperfectequilibria ofthe gamebetween ¯rms.Tothispurpose,wemayconsideranalternativethree-stage gameplayed bythegovernmentsofthetwocountries,aiming atmaximizing socialwelfare. 2 fv qAqAxA fqAWff 1(q;q);Wff 2(q;q)Wvf 1(q;q);Wvf 2(q;q)Wvf 1(q;x);Wvf 2(q;x) 1vqAWvf 1(q;q);Wvf 2(q;q)Wvv 1(q;q);Wvv 2(q;q)Wvv 1(q;x);Wvv 2(q;x) xAWvf 1(x;q);Wvf 2(x;q)Wvv 1(x;q);Wvv 2(x;q)Wvv 1(x;x);Wvv 2(x;x) Matrix 4 22