On the Regulation of A Vertically Differentiated Market Through Taxation/Subsidization of Product Quality

Lambertini, Luca; Mosca, Manuela Working Paper On the Regulation of A Vertically Differentiated Market Through Taxation/Subsidization of Product Quality Quaderni - Working Paper DSE, No. 247 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Mosca, Manuela (1996) : On the Regulation of A Vertically Differentiated Market Through Taxation/Subsidization of Product Quality, Quaderni - Working Paper DSE, No. 247, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/5063 This Version is available at: https://hdl.handle.net/10419/159090 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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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/ OntheRegulationofaVertically Di¤erentiatedMarket1 LucaLambertini-Manuela Mosca DipartimentodiScienze Economiche Universitàdegli StudidiBologna StradaMaggiore45,40125 Bologna,Italy tel. 0039-51-6402600,fax0039-51-6402664 e-mail [email protected] e-mail [email protected] November10,1998 1Thispaperwaswrittenwhilethe…rstauthorwasat theInstituteofEconomics,UniversityofCopenhagen.Apreviousversionwaspartofthe…rstauthor’sDPhil thesisatLinacreCollege, Oxford.WethankSvend Albæk,Norman Ireland,Paul Klempererand Martin Slaterforhelpfuldiscussionand suggestions ontopicstreatedinthispaper.Theresponsibilityobviouslyrestswith usonly. Abstract Theaimofthispaperistoinvestigateaverticallydi¤erentiatedmarket servedeitherbyamultiproductmonopolistorbyduopolists, inwhicha publicauthorityaiming atincreasingthewelfarelevelcanchooseamongtwo instruments,namely,qualitytaxation/subsidization,and minimumquality standard.Inthemonopolycasetheyare equivalentastothesocialwelfare level, inthatbothallowtheregulatorto achievethesecondbestlevelofsocial welfarehewouldattainifheweretosetqualitiesunderthemonopolypricing rule,whiletheyarenotequivalentintermsofthedistributionofsurplus. Intheduopolyregime,weshowthat there existsataxation/subsidization schemeinducing…rmstoproduce thesociallyoptimalqualites. JEL classi…cation: H21,L12,L13 Keywords:verticalproductdi¤erentiation,taxation/subsidization,minimumqualitystandard 1Introduction Thewelfareanalysisoftaxationorsubsidizationinimperfectlycompetitive markets stemsfromthe convergence oftwo originallydi¤erentstreams.The …rstdealswiththede…nitionofsocialwelfare.Thesecond derivesfromthe notionofmarketfailureand the consequentenvisaging ofapublicinterventiontocorrectit.The earliestanalyticaltreatmentoftheseissuesdates backtoDupuit (1844,1849),whoclaimsthatamonopolist, independently ofherpropertystructure,should price-discriminateamongconsumers(see also Ekelund,1970),althoughtheprivate entrepreneurwouldentirelyextract consumersurplus,whilethesocialplannerwould price proportionallytoindividualreservation prices,so astobreakeven(Dupuit,1854).Theissueof optimalpricing appearsintheEnglishliteraturewithRamsey(1927)who analysesatari¤scheduleminimizingthedistortiona¤ectingdemand,under theconstraintthat…rms’pro…tsbenon-negative.1InHotelling’s(1938)view, apublic…rmshould price atmarginalcostand …nance anyloss throughtaxation. Questioningtheapplicabilityofmarginalcostpricing,Allais(1947,p. 220)proposestheadoptionoftari¤sdepartingproportionallyfrom marginal costs.Then,Boiteaux(1956)adoptsanapproachto optimalpricingthat completelydispenseswiththe conceptofconsumersurplus. Theliteratureinthis…eld haslargelydisregardedtheinteraction between …rms’pricingbehaviourand theirabilitytodi¤erentiateproducts,although Dupuit (1849)stressesthatamonopolistsupplyingseveralvarietiesofthe samegoodorservice mayo¤ersuboptimalqualitiestolow-income consumers inordertoforce richeronestopayhigherpricesforsuperiorqualities.This issuehasreceiveda…rstcharacterization bySpence (1975),whohighlights thatapro…t-maximizingmonopolistwilldistorttheoutputforagivenquality level, and vice versa.Inthesamevein,Mussa and Rosen(1978)showthat, underfull marketcoverage,the extent towhichamultiproductmonopolist undersuppliesqualitiesincreasesastheincomeofconsumerswhopurchase suchqualitiesdecreases,sothat,asthenumberofvarietiestendstoin…nity, onlytop-incomeconsumersarebeingprovidedwiththesamequalityasunder socialplanning.AninductiveproofofthisisinLambertini(1997a),where itisalsoshownthat thequalitydistortionvanishesunderpartialmarket coverage.Severalmeasureshavebeenenvisagedtoregulatethebehaviour 1Forarecentexpositionofthistopic,see Baumoland Bradford(1970).Laterdevelopmentsarediscussed byYang and Stitt (1995),interalia. 1 ofaverticallydi¤erentiatedmultiproductmonopolist.Spence (1975)shows thatrateofreturnregulation(RORR)can beattractiveifqualityiscapitalintensive.Besankoetal.(1987,1988)comparesuchapolicywithminimum qualitystandard(MQS)and maximumprice regulation(MPR).They…nd that,underprice ceiling,themonopolistincreasesthedistortionat thehigh end ofthemarket,and converselyat thelowend,and welfareincreasesif price regulationis slightenough.AstotheMQS policy,theyclaimthat itswelfare e¤ectsareambiguousbecauseitmightexcludesome consumers fromthemarket;moreover,those consumersforwhomthestandardisnot bindingreceivethesamequalitytheywould purchaseintheabsence ofMQS. Agrowing amountofe¤ortisbeingdevotedtoinvestigatingthedesignof MQSs(Ronnen,1991;Motta and Thisse,1993;Crampesand Hollander, 1995;Ecchia and Lambertini, 1997;Scarpa,1998).Somegeneralresultsare that (i)all qualitiesincreaseasareactiontotheMQS;(ii) theMQSmay increasethepro…tofthelow-quality…rm;(iii)welfareishigherafterthe introductionoftheMQS,providedthelatterdoesnotinduce any…rmto exit.MQS’smainshortcomingistheasymmetryintroducedinthequality stage,sothat theresultingmisallocationofdemand preventstheregulator fromattainingthe…rstbest.Tothebestofourknowledge,theonlyexisting studyoftaxationinaverticallydi¤erentiated duopolyisduetoCremerand Thisse(1994),whoconsidertheimpactofanadvaloremtax,showingthata uniformadvaloremtax,withthesamerateapplyingtobothproducts, lowers bothequilibriumqualitiesand distortstheallocationofconsumersbetween …rms.Ifthetaxrateis su¢cientlylowand itsproceedsareredistributedas alump-sumtransfer, it turnsout tobealwayswelfare-improving,although unableto attainthe…rstbest.Theadoptionofanon-uniformtaxscheme mayormaynotappearsociallydesirable. Intherealworld,aregulatormay…nd itpro…tabletouseamixofseveral instruments,butouraimistoinvestigatetheimpactofregulativemeasures directlya¤ectingqualitylevelsinamultiproductmonopoly, inisolationfrom anyotherpolicyinstruments,suchasRORR,MPRoradvaloremand excise taxation.Thepolicywe considerarerelatedtothehedonic characteristicsofthegoodsunderconsideration,and cantaketheformofeithera taxation/subsidizationscheme,oranMQS.Examplesofboth policiescan befound intheautomobileindustry,with(i) taxschedulesrelatedto…scal horsepowerratherthantheactualenginehorsepower;and(ii) thewidespread compulsoryadoptionofairbagsand safetybelts,while examplesoftheformerarepenaltiesintroducedtolimit theproductionofpollutingcomponents 2 inthe chemical industry,wherequalitystandardshavealsobeenadoptedin ordertopreservethe environment.Weshowthat the e¤ectiveness ofthese instrumentsdrasticallydependsuponmarketstructure.Inaduopolyregime withsingle-product…rms,qualitytaxation/subsidizationachievethesocial optimum,whileanMQS policyisunabletodoso,duetoitsinherentasymmetryina¤ectingproductqualities.Inamultiproductmonopolyregime,we provethat,whenthequalityrangeisdiscretewhile consumerdistributionis continuous,theadoptionofanMQSa¤ectsthe entirerange.Thiscontrasts with previouscontributionsinthis…eld(Besankoetal., 1987,1988).Moreover,weshowthat,unlikewhathappensinoligopolisticsettings,thetwo policiesare equivalentinamonopolisticmarket,beingbothableto achieve thesecond bestlevelofsocialwelfarethatapublicauthoritywouldattain bychoosingqualitiesunderthemonopolypricingrule,thesocialoptimum remaining outofreach. Theremainderofthepaperis structuredasfollows.Thebasicmodel isdescribedinsection2.Section3dealswithsocialplanning and theunregulatedmonopolyand duopolyregimes.Theoptimaldesignofregulation policiesisinvestigatedinsection4,and …nallysection5provides some concludingcomments. 2TheSetting Weadopt themodelofverticaldi¤erentiation duetoCremerand Thisse (1994),whichisatwo-productspeci…cationofMussa and Rosen’s(1978). Themodel isworkedoutunderthehypothesisofcompleteinformation.In particular,weassumethatqualitylevelsarecommonknowledge, i.e., theyare immediatelyobservablebytheregulator.2Twoverticallydi¤erentiatedgoods aresupplied,whoserespectivequalitylevelsaredenoted byqH>qL>0: Bothvarietiesarebeingproducedthroughthesametechnology,represented bythefollowingcostfunction: Ci=tq2 ixi;t>0;i=H;L;(1) 2Thisamountsto assumingthat technologyiscommonknowledge.Awideliterature dealswiththe casewherethere existsaninformationasymmetrybetween producersand thepublicauthorityconcerningthe coststructure(and thusproductquality).See La¤ont and Tirole(1989a,b;1993). 3 wherexidenotes…rmi’soutputlevel. Consumersareuniformlydistributed overtheinterval[µ;µ];withµ=µ¡1:Theirtotaldensitycan benormalised to onewithoutloss ofgenerality.Parameterµrepresentseachconsumer’s marginalwillingness topayforquality.Themarketisfullycovered,and eachconsumerbuysoneunitofthevarietyiwhichmaximizesthefollowing indirectutilityfunction:U=µqi¡pi¸0:(2) Given productioncosts(1),themaximizationofconsumersurplus(2)would implythat thequalitypreferred bya generic consumerindexed byamarginal willingness topayµwould beµ=(2t),sothat therangeofpreferredqualities isde…ned by[(µ¡1)=(2t);µ=(2t)](see Cremerand Thisse,1994,p.617). Consumerscan bedividedintotwo groups:thosebuyingthehigh-quality good,and thosebuyingthelow-qualitygood,theindi¤erentconsumerbeing ate µ=(pH¡pL)=(qH¡qL):Hence thedemandsforthetwocommoditiesare, respectively: xH=µ¡e µ=µ¡(pH¡pL) qH¡qLiff 0<µ¡e µ<1;(3) xH=1iff µ¡e µ¸1;xH=0iff µ¡e µ·0; xL=e µ¡(µ¡1)iff 0<e µ¡(µ¡1)<1;(4) xL=1iff e µ¡(µ¡1)¸1;xL=0iff e µ¡(µ¡1)·0: 3Socialoptimumand theunregulatedequilibria Underfull marketcoverage,pricing abovemarginalcostonlyactivatesa mechanismtoredistributesurplusfromconsumerstoproducers,withoutaffectingtheoverall levelofwelfare.Hence,providedthatproducersareamong consumers,asocialframercan neglectanyredistributionissue.Then,the problemofwelfaremaximizationconsistsin…ndingthequalitypairthatmaximizesthefollowingsocialwelfarefunction,de…nedasthesumofconsumer and producersurplus: SW=Ze µ µ(µqL¡tq2 L)dµ+Zµ e µ(µqH¡tq2 H)dµ:(5) 4 By solvingthesystemof…rstderivativesof(5)w.r.t.qHand qL, itcan beveri…edthat thesocialplanner”locates”qualitiesinthe…rstand third quartilesoftheintervalofconsumers’preferredvarieties,settingqsp H=(4µ¡ 1)=(8t)and qsp L=(4µ¡3)=(8t):Thelevelofwelfareat thesocialoptimumis SWsp=(16µ2¡16µ+5)=(64t):Equilibriumdemandsarexsp H=xsp L=1=2: Forfuturereference,webrie‡yillustratetheunregulated duopolyand monopolyequilibria.WeborrowtheformerfromCremerand Thisse(1994) and Lambertini(1996).Firms’objectivefunctionsare¼H=(pH¡tq2 H)xH and ¼L=(pL¡tq2 L)xL,respectively.Theyplayanon-cooperativetwo- stagegameinqualitiesand prices,whosesolutionyieldsqd H=(4µ+1)=(8t); qd L=(4µ¡5)=(8t);and pd H=49=(64t);pd L=25=(64t):Notice thatequilibriumqualitiesarepositionedwell outsidethesociallypreferredinterval, i.e., duopolyischaracterized byexcess di¤erentiationatequilibrium.Demand isequallysplitatequilibrium,withxH=xL=1=2:Socialwelfareunder duopolyisSWd=(16µ2¡16µ+1)=(64t):Thewelfareloss,ascompared tothesocialoptimum, isduetothestrategic e¤ectleading…rmstoseek reciprocaldi¤erentiationinordertosoften price competition(Shakedand Sutton,1982;1983).3The constraintµ>9=4mustbesatis…edinorderfor thepoorestconsumerlocatedatµtobeabletobuyinequilibrium. Considernowan unregulated pro…t-seekingmonopolisto¤eringbothvarieties(see Lambertini, 1997a).Shemaximizes¼m=(pH¡tq2 H)xH+(pL¡ tq2 L)xLw.r.t.pricesand qualities.Providedthat thepoorestconsumermust beabletobuythelow-qualitygood,theoptimalmonopolyprice forthat varietyispm L=(µ¡1)qL,atwhichthe consumerwhosemarginalwillingness topayisµ=µ¡1isexactlyindi¤erentbetween purchasingthelow-quality goodand notpurchasing atall. Theoptimalprice forthehigh-qualitygood obtainsfromthe…rstordercondition(FOC): @¼m @pH=µqH+µqL¡2pH¡2qL+tq2 H¡tq2 L qH¡qL=0;(6) yieldingpm H=(µqH+µqL¡2qL+tq2 H¡tq2 L)=2:Then,di¤erentiating¼mw.r.t. 3Thisisanalogoustoawell knownresultcharacterizingtheHotellingduopolymodel withquadratictransportationcosts.Cremerand Thisse(1991,p.386)establishitsformal equivalence totheverticallydi¤erentiated duopolywithquadraticvariable costsofquality improvementsemployed here. 5 qualities,weobtainthefollowingFOCs: @¼m @qH=(µ¡tqH¡tqL)(µ¡3tqH+tqL) 4=0;(7) @¼m @qL=(2¡µ¡tqH+3tqL)(µ¡2¡tqH¡tqL) 4=0;(8) whosesolutionyieldsthemonopolist’soptimalqualities, i.e., qm H=(2µ¡ 1)=(4t)andqm L=(2µ¡3)=(4t):Equilibriumpricesarepm H=(2µ2¡3µ+2)=(4t) and pm L=(µ¡1)(2µ¡3)=(4t);equilibriumdemandsarexm H=xm L=1=2; pro…tsamount to¼m=(4µ2¡8µ+5)=(16t):The correspondingwelfareis SWm=µ(µ¡1)=(4t):Theconstraintensuringthepositivityofallequilibrium magnitudesisµ>3=2: Thepro…t-maximizingmonopolistundersuppliesbothqualitiesascom- paredtosocialplanning,thedistortion beinglargerinthelow-qualityseg- mentofthemarket.Furthermore,thedegree ofdi¤erentiationchosen bythe monopolististwice aswideasundersocialplanning,duetothemonopolist’s attemptatextracting asmuchconsumersurplusaspossiblebyenhancing di¤erentiation beyond thesociallypreferablelevel. Asaconsequence,the monopolist’sprice-and-qualityschemedeterminesdi¤erentdemandsaswell asdi¤erentpro…tsforthetwovarietiesatequilibrium.Thiswill haverelevant bearingsonthe choice oftheoptimalpolicybytheregulator. 4Alternativeregulation policies Thepolicymenu weanalyseincludestwokindsofinterventionthatshare thefeaturesofbeing aimedata¤ectingproductchoice, i.e., qualitytaxation/subsidizationand minimumqualitystandard.Intheprevious section, wehave calculatedthelevelofsocialwelfareinthe…rstbestcon…guration.It will become clearintheremainderofthis sectionthatasecond bestanalysis isunnecessaryinthe caseofduopoly, inthatwewill showthat there existsa policymeasure capableto attainthesocialoptimum. Onthe contrary,asa benchmarkfortheregulationofatwo-productmonopolist,weneedtowork out themaximumlevelofsocialwelfareattainablegiventhemonopolist’s pricingrule.Underthelatter,maximizingsocialwelfareasde…nedin(5) yields qsb H=6µ¡3+p3 12t;qsb L=2µ¡3+p3 4t;(9) 6 Thenewlevelofthehighqualityisthebestreplyofthehigh-quality…rmto theMQS: qd H(MQS)=20¹ µ+2+3p6 40 :(27) Thenewequilibriumpro…tsare¼d L(MQS)=0:22153 and ¼d H(MQS)= 0:06714:AsaresultoftheadoptionoftheMQS,thedegree ofdi¤erentiation decreases,and thedemand forthehighqualitydecreaseswhilethedemand forthelowqualityincreases.Moreover,notice thedrasticreductioninthe high-quality…rm’spro…ts.Since theincreaseobservedinthepro…taccruing tothelow-quality…rmislower,total industrypro…tsdecrease considerably ascomparedtotheunregulatedequilibrium. SocialwelfareamountstoSWd(MQS)=[200¹ µ(¹ µ¡1)+18p6¡13]=800; whichisobviouslyhigherthanthatobservedintheunregulatedsetting,but lowerthanSWsp.Theincreaseinwelfareisduetotwoe¤ects:(i) the increasein bothqualitylevels;(ii) theincreasein price competition,dueto a reduced degree ofproductdi¤erentiation.However,the e¤ectoftheMQSon consumersurplusisnotidenticalacross consumers.TheMQSincreasesthe surplusofconsumerspurchasingthelowqualityforall acceptablevaluesof¹ µ, whileitdecreasesthesurplusofconsumerspatronizingthehighqualityif¹ µis su¢cientlyhigh.Summingup, inthiscaseitappearsthat theMQS policy, provideditisdesignedtomaximize welfareregardless ofitsredistributive e¤ects,tradeso¤thelosses su¤ered bytheagents(…rmand consumers) dealingwiththehighqualitywiththegainsenjoyed bytheotheragents,but remainsfarfromtheidealtargetrepresented by…rstbest. 4.3Discussion Theine¢ciencyarisinginmarketswherea…rmcontrolsproductquality aswell asprice isassociatedwiththedi¤erence betweentheaverageand themarginalconsumer’sevaluationofquality,represented byparameterµ: Spence (1976,pp.426-7)showsthat,whenqualityisacapital-intensive ratherthanlabour-intensivefeature,rate-of-returnregulationisanappeal- ingmeasure.Thisisthe case,e.g., when productqualityistheresultof R&D e¤ort,sothat the costfunctionexhibitsnointeraction betweenqualityand quantity.(Ronnen,1991;Motta and Thisse,1993).Inourmodel, the costfunction(1)mightsuggest thatqualityrequiresacombined useof capitaland labourinvariableproportions.Thispromptsforthedesignof 13 alternativeinterventions,asthosedepictedabove.Inthemonopolysetting, although bothmeasuresyieldthesamelevelofwelfare,theadoptionofa taxation/subsidizationscheme entailsasurplustransferfromthemonopolist toconsumers,which doesnot takeplace undertheMQSregime.Since the regulatorisassumed not tobeinterestedinsurplusdistributionandtheMQS policyise¤ort-saving ascomparedtothedesignofataxation/subsidization policy,onemight thinkthat theformerpolicyismorelikelytobeadopted. Theperspective changesconsiderablywhenthemarketisaduopolywith singleproduct…rms, inwhichcasethetwopoliciesarenotequivalent,with theMQS beingunabletoyieldthe…rstbestwhiletaxation/subsidization allowstheregulatorto attainsucha goal. Acrucialquestion naturallyspringstomind,thatis,whethertheintroductionoftheMQSinducesthemonopolist todroponeofthetwoproducts, and reoptimize withrespect to a singlevariety.Thiswould haveundesirable welfare consequences(foranexamplepertainingto oligopolysettings,see Scarpa,1998).To address thisquestion,we canworkout thesingle-product pro…t themonopolistwouldgain byproviding a qualitycorrespondingto theoptimalMQSwithasinglegood,qm=(2µ¡1)=(4t),theprice being pm=(µ¡1)qm.Suchapro…tamountsto¼m 1(MQS)=(4µ2¡8µ+3)=(16t): Hence,wehave ¼m 2(MQS)¡¼m 1(MQS)=11¡5p3 48(3¡p3)t>0;(28) sothat theadoptionofanMQS doesnotinduce the…rmtorestrict the productrange. Ananalogousquestioncan beaskedconcerningtheduopolysetting.In the casewhereanMQSisadopted,wealready knowthatpro…tsarestrictly positive.Inthe caseoftaxation/subsidization,…rms’pro…tsarepositiveif c < bc=¡(4µ¡1¡8tjH)(4µ¡7¡8tjH)=(64t2);withbc¡ec>0everywhere and bc > 0forall jH2£(2µ¡1)=(4t);(4µ¡1)=(8t)¤;whereinsecond order conditionsaresatis…ed.Hence,theadoptionofsuchapolicydoesnotdrive …rmsoutofbusiness,aslong ascis su¢cientlylow. 5Concludingremarks Wehaveinvestigatedtheissueofregulatingeitheramultiproductmonopolist orsingle-productduopolistsoperatingunderverticaldi¤erentiation,through 14 policiesa¤ectingherqualitychoice.Therelative e¤ectiveness ofthepolicy instrumentsincludedinthemenu wehave consideredturnsout tobevery sensitivetomarketstructure.Inthemonopolycase,neitherofthetwo alternativepolicymeasuresisableto attain …rstbest.Wehaveshownthat there existsasecond bestqualityrange characterized by qualitylevelshigher thantheircounterpartsundersocialplanning,and wehavedescribed how suchsecond bestcon…gurationcan beattainedthroughthealternativeadoptionofeitherhedonictaxation/subsidizationoraminimumqualitystandard (MQS).Astotheir…nalresults,thesemeasuresare completelyequivalent, whiletheyarenotintermsofthedistributionofsurplus.Wehavealso shownthat theintroductionofastandard doesnotleadtoareductionin thenumberofavailablevarieties.Intheduopolycasethesetwoinstruments o¤eraverydi¤erentperformance.Theasymmetric e¤ectsexerted bythe MQSonthetwoproductspreventsthepublicauthoritytoinduce …rmsto supplythe…rstbestqualitylevels,whichonthe contrarycan beobtained underthetaxation/subsidization policywehave envisaged.Thisleadsto preferthelatterinterventiontotheformer. 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