Piracy and Quality Choice in Monopolistic Markets

Alvisi, Matteo; Argentesi, Elena; Carbonara, Emanuela Working Paper Piracy and Quality Choice in Monopolistic Markets Quaderni - Working Paper DSE, No. 436 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Alvisi, Matteo; Argentesi, Elena; Carbonara, Emanuela (2002) : Piracy and Quality Choice in Monopolistic Markets, Quaderni - Working Paper DSE, No. 436, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4862 This Version is available at: https://hdl.handle.net/10419/159277 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/ Piracyand QualityChoice inMonopolistic Markets¤ MatteoAlvisi DepartmentofEconomics,UniversityofBologna ElenaArgentesi EuropeanUniversityInstitute,Florence EmanuelaCarbonara DepartmentofEconomics,UniversityofBologna April 2002 Abstract Westudytheimpactofpiracyonthequalitychoicesofamonopolist.Intheabsence ofpiracy,themonopolisthasnoincentive todi¤erentiateitsproducts.With piracythemonopolistmightinstead produce morethanonequality,sothatdi¤erentiationarisesas theoptimalstrategy.Thisisbecausetheproducerwantstodivert consumersfromthepiratedgoodtotheoriginalone.Di¤erentiation involveseitherproducing a new, low-qualitygoodsuchthatpiracyis eithereliminatedorstill observedinequilibrium. JELClassi…cationNumbers:L12,L15,L82,L86. Keywords:Productdi¤erentiation,Multiproductmonopolist,Quality,Piracy. ¤WearegratefultoMassimoMottaforcomments,discussionsand advice,aswell asto GiacomoCalzolari, VincenzoDenicolò,PaoloGarella and LucaLambertiniforcomments and suggestions. 1 1Introduction Thehugeincreaseof piracyand private copyingisaphenomenonthatinrecentyearshasgreatly a¤ectedthemarketforinformationgoods,and speci…- callydigitalgoods suchassoftwareand musiccompactdisks.Thewidespread practice of …le-sharingthroughtheInternet,togetherwiththeimprovements and thegreateravailabilityofcopyingtechnologies(likepeer-to-peerconnections), leadtoaboomof unauthorizedcopies. Thereproductionof digital information di¤ersfromthereproductionof non-digitalmediasuchasjournals,books,audio and videocassettes.Digital media are characterized bya “vertical”patternofreproduction,1since it isenoughtohaveanoriginaland thencopiescan bemadeoutofcopies withoutaprogressivedeclineintheirquality. Thereforeinmarketsfordigital goodsthetraditionalresultof“indirectappropriability”cannotapply.2With indirectappropriabilitythesellercanextract therentsfromall usersby charging a higherprice fortheoriginalsince theirtotalwillingness topayas awholeishigherthanthesinglebuyer’s. Whenqualitydoesnotdeclinewith thenumberofcopiestheprice thatextractsall surplusfromall userswould betoo hightobea¤ordablebythesinglebuyer.Thesefeaturesenhance the harmful impactof piracyon pro…ts.3 Fromalegalperspective,oneway inwhich …rmscancounteract thisphenomenonisbyundertakinglegalactionsagainst theinfringementsofcopyrightlaws(themostrecentcaseisthesuitbroughtbythe…vemajor record companiesagainstNapster)and by lobbyingforstrictercopyrightlaws.4 Thegoalofourpaperisinsteadtoexaminefromaneconomicperspective theimpactof piracyonthebusiness strategiesofa…rm.5 Westudyhowpiracya¤ectsthe…rm’sincentivestovertically di¤erentiate thequalityofitsproducts.Ingeneralthepresence of piracyreducesthe demand fortheoriginalgoodand thereforepro…ts.Themonopolistcould thenintroduce alow-qualitygoodinordertocaptureatleastpartofthe demand forpiracy, shiftingitfromtheillegalmarket,where copiesofthe 1Foraclassi…cationanddescriptionofinformationreproduction,see Shy(2001). 2Thisconceptwas…rstintroduced byLiebowitz(1985). 3AspointedoutbyShyand Thisse(1999),thenegativeimpactofcopyingon producers’ pro…tscan bemitigated bythepresence ofnetworkexternalities,i:e:whenconsumers’ utilityincreasesinthenumberofotherconsumersusingthegood(eitherboughtor copied).Thisassumptionisquiteplausiblewithrespect tosoftwarebutitishardly applicableto otherinformationgoods suchasmusicand printeditems. 4Forinstance,theEuropeanUnion hasrecentlyissuedadirectiveoncopyrightprotectionofonlinedigitalgoods(Directive2001/29/CE). 5We considerasituationwherepiracycannotbe completelyeliminated bycopyright protectionlaws. 2 high-qualitygoodare exchanged. In practice,producinganew, low-qualitygoodmeansthat the…rmintroducesareducedversionofwhatwaspreviously producedwithoutsomeof itsfeatures.Examplesofverticaldi¤erentiationinthesoftwaremarketare thereducedversionsreleasedas sharewareorfreewareontheInternet.In classicalmusic, lower-quality(and lower-cost) CDsaresoldwithoutabookletand performed by less famousorchestras.Similarly, music companiesare developingtechnologiestosell musicon-line6(withoutpackageand without abookletwith photos, lyricsand informationontheartists)asawaytocapture consumerswithlow willingness topaywhocouldotherwisebepotential pirates. Inourmodel, thegoodsproduced bythemonopolistcan beobtained intwodi¤erentways:consumerscaneitherpurchasethemintheoriginal versionorpayforunauthorizedcopies. Ourde…nitionofacopy includes bothacopymadebysomebodyelseand boughtillegally (i:e:aCDfroman unauthorizedvendor)and acopymadebythe consumerherself(i:e:aCD copiedwithaCDburner).Giventhatwerefermainly todigitalgoods,we assumethat theoriginalgoodand itscopiesareidentical intermsofquality. Wealso assumethatconsumersareheterogeneousintworespects. First, thereisacontinuumofconsumersidentical intastesbutwith di¤erentpreferencesforquality. Second,consumersare characterized bytwodi¤erent costsof pirating(orgoingtotheillegalmarket),undertheassumptionthat ahighercostofcopyingisassociatedwithahigherwillingness topayfor quality. Ourmainresultsareasfollows.Intheabsence of piracy, themonopolist hasnoincentivetodi¤erentiateitsproducts. With piracythemonopolist mightinstead produce morethanonequality, sothatdi¤erentiationarises astheoptimalstrategy. Theanalysisinvolvestwodistinctcases.Iftheproportionofconsumers with highcostof piratingislowand themonopolistdi¤erentiatesitsproducts,pricesaresetsuchthat thehigh-costconsumersbuythehigh-quality good,whereaslow-costconsumerswill eitherbuythelow-qualitygoodor pirate.Inthiscase, verticaldi¤erentiationwill bemorepro…tablethan no di¤erentiationwhentheheterogeneityofconsumerswithrespect totheir costof piratingis su¢ciently high.Here,themonopolistindeed …ghtspiratesthroughverticaldi¤erentiation,producinganewandlowerqualitythat eliminatesdemand forcopiesand hence piracy. Wheninsteadconsumersare moresimilarintheircostsof pirating,themonopolistwill …ghtpiracybyset6The…veMajorshaverecentlymadetwojointventurestosell musiconline,namely MusicNetand Pressplay. 3 tingaprice lowenoughsuchthateverybodybuysthegood,and novertical di¤erentiationtakesplace. Iftheproportionof high-costconsumersishighand themonopolistproducestwogoods,pricesaresetsuchthathigh-costconsumersbuybothgoods. Inthis situation,aninterestingtrade-o¤inthe choice ofquality levelsarises. Themonopoliststill hasanincentiveto o¤eralowquality levelthatishigh enoughto attractconsumerswithlow willingness topay. However, ifthis level ishighenough,somehigh-costconsumersmayswitch fromthehigh-to thelow-qualitygood.This second e¤ectmaycounterbalance theincentive toeliminatepiracyby increasingthelowquality leveland, inequilibrium, themonopolistmightadmitsomepiracywhilestill di¤erentiating. Ourworkbuildsontheliteratureoncopying and piracy. In particular, itisrelatedtoarecentpaperbyGayerand Shy(2001) thatanalyzesthe incentivesof publisherstodistributeviatheInternetversionsof digitalgoods thatcompetewith products soldinstores.Undertheassumptionof network externalitiesbetween buyersoftheoriginalgoodand “downloaders”fromthe Internet,theyshowthat theintroductionofaproductof(exogenously-given) lowerqualityovertheInternetispro…t-enhancingforthemonopolist.The issueofcopyrightprotectioninthepresence of networkexternalitiesisalso addressedbyConnerandRumelt(1991)and, inan horizontally di¤erentiated duopoly, byShyand Thisse(1999). Onemajordi¤erence ofourapproachrelativetothepreviousliteratureis thatwe endogenize the choice of productqualitybymakinguseofamodel ofverticaldi¤erentiation.Moreover,wedonotassumenetworkexternalities between buyersoftheoriginalgoodand “downloaders”fromtheInternet, whichinstead driveGayerand Shy’sresults.7Thepreviousmodels showed that thedistributionofalower-qualitygoodovertheInternetmaybeprofitablefortheproducerbecauseitmayraisethedemand fortheoriginalgood through demand-side externalities. Onthe contrary, inourframeworkthe introductionofalowerqualityallowstheproducertodivertsome consumers fromcopyingthegoodtobuying anoriginal(lower-quality)versionand is thereforeawaytoreduce (oreliminate)piracy. Ourmodel ismoregenerally relatedtotheliteratureoncopying(e.g., Johnson,1985;Liebowitz,1985;Besenand Kirby, 1989;Varian,2000).These papersgenerally assumethatcopiescan bemadeonly fromoriginals8and thereforeproducerscanappropriatesomeofthe consumersurplusfromillegal 7Indeed,Huietal. (2001) testedempiricallytheimpactofpiracyonthelegitimate demand for recordedmusicand found that thepotentialpositive e¤ectsofpiracy(network externalities,sampling,sharing,and others),iftheyexist,donotcompensateforthedirect loss ofcustomers. 8Alternatively,copiesofcopieshavealowerqualitythancopiesmadefromoriginals. 4 copies.9Therefore,evenintheabsence of networkexternalities,copyingmay bepro…tablebecauseofindirectappropriability. Ourpaperinsteadrulesout anypotentialbene…ciale¤ectof piracyforproducers(eitherthroughsome kind ofappropriabilityorthrough networke¤ects)and studiesthepricing policiesofamonopolistfacedwiththisproblem. Ourpaperisalso anapplicationofthetheoretical literatureonvertical di¤erentiation byamonopolist.Themainidea ofthisliteratureisthata monopolistmaywant tosegment themarketbyo¤eringdi¤erentqualities ofthesamegoodinordertoextractmore consumersurplus.Twoclassesof modelsinvestigatedi¤erentassumptionsonqualitycosts.10 Gabszewicz etal. (1986),building onthemodelbyShakedand Sutton(1982),assume…xed costsofquality improvementand showthat thenumberof products sold dependsonthedispersionofconsumers’ incomes.Mussa and Rosen(1982), Itoh(1983),Maskinand Riley(1984),and Lambertini(1987)study instead the casewhereunitproductioncostsareincreasinginquality, and …nd that themonopolisthasanincentivetoproduce abroadrangeofqualitiesinorder tosegment themarket. Ourcontributiontothisliteratureisthatweproposeanalternative explanation forverticaldi¤erentiation,namely piracy. Wedothisbyfocusing onacasewherenoverticaldi¤erentiationwouldariseinanequilibriumwithoutpiracy. Inthis setting,weshowthatwhen piracy isinstead possible, it maybemorepro…tabletointroduce alowerqualityratherthantoproduce onequalityonly. Thepaperisorganizedasfollows.Section2presentsthebasemodel. In sections3 and 4weanalyze theprice and qualitystrategiesofamonopolist producing asingleproductandtwoproductsrespectively. Section5compares thepro…tsofverticaldi¤erentiationwiththoseresultingfromthestrategy ofasinglequality leveland derivesconditionsfortheintroductionofalower quality. Section6concludes. 2Themodel Weassumethatconsumerscanobtainthegoodintwodi¤erentways:they can purchaseitsoriginal versioninthelegalmarketor,alternatively, obtain acopy inanillegalmarket,whereonly unauthorizedcopiesareavailable.11 9Thereforethesemodelsareapplicablemainlytonon-digitalgoods. 10Foramodelthatconsidersbothtypesofassumptionsoncostsinanoligopolistic setting,see Motta(1993). 11Thisiswhatwelabelpiracyintherestofthepaper,althoughwedisregardcopyright issuesand relatedlegalpunishments. 5 ExamplesofgoodswhereillegalcopiesexistincludemusicCDs,software, videosand alsodesignclothesand accessories. 2.1Production We consideramonopolistoperatinginamarketwhere consumershavethe possibilityof piratingthegood(orobtaining a copyontheillegalmarket).12 Piracyreducesdemand inthelegalmarketand potentially …rms’pro…ts. Whenchoosingitsbusiness strategies,themonopolist triestocounterthis problem.Throughout thepaper,weassumethatprice discrimination for productsofthesamequality isnotanavailableoption forthemonopolist (forinstance,becausearbitrageispossible).However,themonopolistcan choosetovertically di¤erentiateitsgoods.Themonopolisthastwomain strategies: itcan produce onegoodonly, whosequalityand price areqand p;ortwo goods,whosequalitiesareq1and q2,withq1<q2;and qi2[0;+1), i=1;2.Letp1denotetheprice ofthegoodofqualityq1and p2theprice ofqualityq2. Weassumethat the…rmhasneithervariableproductioncosts norquality-dependent (…xed)costs.13 Wearelooking atathree-stagedecisionalprocess wherethemonopolist …rstchooseswhethertoproduce oneortwoqualities, inthesecond stage quality levelsaresetand inthethirditchoosesmarketprice(s).14 2.2Consumers Consumersareheterogeneousintworespects. First,weassumeacontinuum ofconsumersidentical intastesbutwith di¤erentpreferencesforqualityµ (likeinMussa and Rosen(1978)).Consumersareuniformly distributedover theinterval[µ;µ],withµ>0.Second,consumersdi¤erintheircostof piratingthegood.Thisassumptionisintroducedtoensuretheproductionof 12We considerasituationwherepiracycannotbe completelyeliminated bycopyright protectionlaws. 13Astothevariable costs, itwould be equivalent to assumeaconstantmarginalcost ofproduction.Theabsence ofquality-dependent…xedcosts,besidesmakingtheanalysis moretractable,helpsustoisolatetheimpactofpiracyontheincentivestodi¤erentiate fromthatgenerated byacostlyproductionofquality.Itisinfactawellestablishedresult thatamonopolistdi¤erentiatesitsqualityinthepresence ofqualitycosts(see Spence, 1975 and Mussa and Rosen,1978). 14Thisassumptiononthestructureofthedecisionalprocess isintendedtocapture theideathat theprice canin practice bevariedatwill, whileachangeinthequality speci…cationofthegoodinvolvesamodi…cationoftheappropriate“productionfacilities” (Shakedand Sutton,1982). 6 an high-qualitygoodinequilibrium.15 A…rstgroup ofconsumers sustainsa highcostcHwhen buyinganon-originalcopyofthegood.Consumerswith costcHhavealsohigh preference forqualityµ2[^ µ;µ].Asecond group of consumershasalowcostofcopying,cL,withcH>cL.Consumerswith costcLhavepreference forqualityµ2[µ;^ µ].Assumingthatahighercost ofcopyingisassociatedwith highertasteforquality isratherplausibleand empirically relevant.16 Thisisevenclearerifwereinterpretconsumers’heterogeneitynotintermsoftasteforquality, butratherintermsofincome.In fact,cicanalsobe consideredastheopportunitycostofgoingtotheillegal marketorspendingtimeand resourcestomakeacopy. Underthisinterpretation,richerpeople(with highwillingness topayforquality)usually prefer tobuytheoriginalratherthanapiratedgood. Weare examiningacasewhereall individualsconsumethegood,either purchasedorcopied(we call this“coveredmarket”,eventhough notall consumersnecessarily buythegood butsomepirateit).17 Eachconsumer consumesoneunitofthegood.Theutilityofaconsumeroftypei=H;L with preference forqualityµ2[µ;¹ µ]whenshelegally buysqualitykis U(µ;qk;pk)=µqk¡pk(1) whereas,whensheobtainsacopy is U(µ;qk;ci)=µqk¡ci(2) 15Ifconsumerswereidentical intheircostsofcopying,c;and themonopolistproduces twoqualitiesatpricesp1and p2,p1<p2thefollowingcasesarepossible. i)Ifc<p1<p2, consumerswouldratherpiratebothgoodsthan purchasethem.Thedemand forboth goodsiszero; ii)ifp1·c<p2,noconsumeriswillingtobuyq2,sothat thelatteris notproduced; iii)ifp1<p2·c,pricesaresolowthatnoconsumerwill pirate.The monopolistwill then produce asinglequalitylevel. Itisthenclearthatanyprice strategyeliminatesboth piracyand theincentivefor verticaldi¤erentiation.Therefore,onlywhenconsumersareheterogeneousintheircostc; productdi¤erentiationcan bepro…table. 16Wealsoexaminedacaseinwhichtherelationship betweenthe costofpiratingciand thepreference forqualityµisnegative, i.e.consumerswithµ2[µ;^ µ]haveahighcostof pirating(cL)whilethosewithµ2[^ µ;µ]sustainacostcH.Resultsarequalitativelysimilar tothosepresentedinthisarticleand verticaldi¤erentiationmightstill beanequilibrium strategyofthe…rm. 17Theassumptionofacoveredmarketcon…gurationwhenthemonopolistisproducing asinglequalityisactuallynotrestrictiveinthepresence ofpiracy.Infact, it turns out that theuncoveredmarketcon…gurationisless pro…tablethanletting all individuals consumethegood.Morespeci…cally,whenthemarketisnotfullycovered,pro…tsare ¦=p µ¡µ(µ¡p q).Nomattertheprice strategyadopted, itcan beshownthat thesepro…ts arealwayslowerthantheonesobtainedwithacoveredmarketcon…guration. 7 Giventhatwemainly refertodigitalgoods,weassumethat theoriginal goodand itscopiesareidentical intermsofquality. Weusethe expressions “piratedgood” and “copy”indi¤erently: ourde…nitionofacopy includes bothacopymadebysomebodyelseand boughtillegally18 (i:e:aCDfrom an unauthorizedvendor)and acopymadebythe consumerherself(i:e:a CDcopiedwithaCDburner).(Net) utilityoftheoriginalgood di¤ersfrom thatofthe copybecausethe consumerbearsdi¤erentcostswhen purchasing theoriginalgoodand whenobtainingacopy. Inthe caseof purchase(onthe legalmarket),the costisclearly themarketprice ofthegood.Inthe caseof acopy, the costcicanrepresentbothacostof purchasingthegoodonthe illegalmarket,whichalsoembodiesapsychologicalcostof nothavingthe originalgood,and/orthematerialcostofmakingthe copy(i:e:theprice of theCDburner).Thisjusti…esdi¤erentcostsfordi¤erentconsumers. Qualitykispurchasedratherthan downloadedifand only if µqk¡pk¸µqk¡ci(3) whichyieldspk·ci(4) Weassumethatwhenindi¤erentbetween piratingandpurchasinga good, consumersalwayspurchaseit. 2.3Thebenchmarkcase:nopiracy Thegoalofourpaperistoshowthat thepossibilityofcopyingmay induce themonopolist todi¤erentiateitsproduct.Theissueisrelevantsince,as thefollowingPropositionshows, ifcopyingisnotanavailableoption for consumers,noverticaldi¤erentiationwouldariseinequilibrium. Proposition1Whenconsumerscannotpiratethe good,thepricingstrategy ofthemonopolistentailsno di¤erentiation. Proof.See Appendix. Giventhisbenchmarkcase, inthenextsectionswestudytheimpact of piracyonthepro…t-maximizingstrategiesofthemonopolist. We…rst analyze price and qualitydecisionswhenthemonopolistproducesoneand twoqualitiesrespectively. Wethencomparethepro…tsobtained underboth cases, inorderto…nd the equilibriumstrategy intermsofthenumberand levelofthequalitiesproduced. 18Inorderforthisinterpretationtowork,weshouldassumethatontheillegalmarket thereisalargenumberofidentical…rmscompetingàlaBertrand and wheretherefore marketprice isequaltomarginalcost. 8 Which,giventhat2cH(¹ µ¡^ µ+µ) 3¹ µ¡2^ µ<2cH(¹ µ+^ µ¡µ) 3¹ µ¡2µalwayswhen¹ µ>2^ µ;can be rewrittenasaunique condition 2cH ³¹ µ¡^ µ+µ´ 3¹ µ¡2^ µ<cL·2cH ³¹ µ+^ µ¡µ´ 3¹ µ¡2µ(23) Aswewill needtorefertocondition(23)severaltimesinwhatfollows, wede…ne cL=2cH ³¹ µ¡^ µ+µ´ 3¹ µ¡2^ µ(24) ¹cL=2cH ³¹ µ+^ µ¡µ´ 3¹ µ¡2µ(25) Thefollowingpropositionestablishesthe conditions suchthatmaximum di¤erentiationyieldshigherpro…tsthanminimumdi¤erentiation: Proposition8When^ µ<¹ µ 2andthemonopolistdi¤erentiatesitsproduct, there existsavaluefor^ µ; ^ µ1=¹ µ2 4¡¹ µ¡µ¢(26) suchthat: 1.If^ µ<^ µ1maximumdi¤erentiationyieldsoverall higherpro…tsthan minimumdi¤erentiation. 2.If^ µ>^ µ1there existsavalueforcL;~cL1;suchthatminimumdi¤erentiationyieldshigherpro…tsforall ~cL1<cL<¹cLandmaximum di¤erentiationyieldshigherpro…tsforcL<cL<~cL1: Proof.See Appendix. Theintuition forthisresultcan begivenasfollows. When^ µislow (thesituation depictedinFigure1) thehigh-costsegmentofthemarket, consisting ofcustomerswithµ2h^ µ;¹ µi;islarge.Therefore,themonopolist wouldratherproduce highly di¤erentiatedquality levelstobesoldathigh prices(noticethat@pi @f>0;thatispricesdependpositively onthedi¤erencein quality levels) thanselling atlowerpricesqualitiesthatare closesubstitutes. 15 Inotherwords,pro…tsfromselling athigh prices20 onthehighsegmentof themarketmorethancompensatetheloss ofcustomersduetopiracy inthe segmenth~ µ;^ µi: L c L c cL Π Πmax Πmin Figure1 Conversely, when^ µishigh(thesituation depictedinFigure2),thehighqualitysegmentofthemarketis small and thepro…taccruingfromitlittle. Themonopolistprefersmaximumdi¤erentiationonly whencLisvery low. Thishappensbecause,whencLisclosetozero,¦minisclosetozerotoo (both pricesand thedi¤erence betweenqualities,fmintend tozero)whereas withmaximumdi¤erentiation pricesareboth highand pro…tsfromthehigh segmentofthemarkethightoo notwithstandingthehigh numberoflow-cost consumerspiratingthegood.21 20Theprice forthehighqualitywhenthemonopolistappliesmaximumdi¤erentiation, p2=cH;ishigherthantheprice forthehighqualitywithminimumdi¤erentiation. Therefore,pro…tsfromsellingtothehigh-costsegmentofthemarket (consumerswith µ2h¹ µ 2;¹ µi)arehigherwithmaximumdi¤erentiation.Thesameappliestop1: 21Itispossibletoshowthatdemand forthelow-qualitygoodfromthelow-costconsumers(demand de…nedasxL 1=~ µ¡µ ¹ µ¡µ)isincreasingincL: 16 L c 1 ~L c L c cL Π Πmin Πmax Figure2 Nextsectioncomparesall strategiesavailabletothemonopolist,withthe aimtoestablishwhen productdi¤erentiationisanequilibriumstrategyand the conditionsunderwhich piracyoccursinthemarket. 5Oneortwoqualities? Inthe…rststage,themonopolistchooseswhethertoproduce oneortwoqualities.Inordertomakethisdecision, itcomparespro…tsfromeachavailable alternative.Themain …ndingisthatpiracymay induce themonopolist to produce di¤erentqualitiesevenwhentherearenoproductioncosts.In fact, the existence of piracy itselfmayjustifytheintroductionoflowerqualities, intheattempt tomoveawayconsumerswithlowerwillingness topayfrom theillegalmarket,where copiesofthehighqualitygoodare exchanged,and let thembuythelowquality instead. Whentheproportionof high-costconsumersislow, inequilibriumthemonopolistmayproduce alowqualitythat ishighenoughtobeappealingto all consumers:thiswill eliminatedemand forcopiesand hence piracy. Piracy ishoweverobservedinmanymarkets.In ourmodel, thepresence of piracymayariseinadi¤erentiatingequilibrium whentheproportionof high-costconsumersishigh. 5.1High-costconsumersbuy qualityq2only When^ µ>¹ µ 2, inequilibriumthemonopolistproducestwoquality levelsonly ifthisyieldshigherpro…tsthan producing onequalityonly (bysettingprices suchthatpiracy iseithereliminatedortolerated). 17 Thefollowingpropositionindicatesthe conditionsunderwhich producing twoqualitiesisthe equilibriumstrategy. Proposition9Inequilibrium,themonopolistchoosesto produce twoquality levelsif cL<cH(¹ µ¡^ µ)(2^ µ¡µ) ¹ µ(2^ µ¡µ)¡^ µ2.Otherwise, itismorepro…tableto produce one quality.Inbothcases,pricesandqualitylevelsaresetsuchthatno piracy arises. Proof.See Appendix. Theintuition forthisresultcan begiven by Figure3below.Thepro…t whenthemonopolistdi¤erentiates,¦diff;isalwaysabove¦¤¤ (thepro…t withonequalityonly and piracy)butforthe casewherecL=0.Thiscan beseenimmediately byrewriting¦diff inexpression(18)asfollows ¦diff =cH¹ µ¡^ µ ¹ µ¡µ+cL^ µ¡µ 2^ µ¡µ=¦¤¤ +cL^ µ¡µ 2^ µ¡µ(27) Producing onequalitywhileallowingsomepiracy isneveranequilibrium strategybecausethemonopolistcouldalwayspro…tably introduce another (lower)qualitywhichwouldattractatleastsomeofthelow-costconsumers thatwould haveotherwisepiratedthegood. ForveryhighlevelsofcL(close tocH) themonopolistpreferstoproduce onequalitybecauseahigh price p·cLcan besetand itisthen pro…tabletosell thesame(high)qualityto thewholemarket.IfcLislowand cHismuch higherthancL,astrategy suchthatp1<cL<p2·cHismorepro…table,wherethemonopolistsells tothehigh-costsegmentofthemarketataveryhigh price and capturesthe low-costsegmentbysellingalow-price, low-qualitygood.22 22Itisimmediatetocheckthat¦diff crosses¦¤=cLforcL>cH¹ µ¡^ µ ¹ µ¡µ: 18 θθ θθ − −ˆ H c ( )( ) ( ) 2 ˆˆ 2 ˆ 2 ˆ θθθθ θθθθ −− −− H c cL Π Π ** θθ θθ − −ˆ H c ( )( ) ( ) 2 ˆˆ 2 ˆ 2 ˆ θθθθ θθθθ −− −− H c cL Π Π diff Π * Figure3 5.2High-costconsumersbuybothqualities Wenowproceed byshowingthe existence ofanequilibriumwithmaximum di¤erentiation(aswell asequilibriawithonequalityonly). Weobtainthefollowingresults. Proposition10 There existone valueforcL;cpir L;suchthat 1.If^ µ<^ µ1thefollowing casesarise: (a)if ¹ µ>¡3+p5¢µthen: if ^ µ2<^ µ<^ µ1themonopolistchooses maximumdi¤erentiationforall cpir L<cL<¹cLand producesone qualityallowingpiracyif cL<cpir L;if ^ µ<^ µ2<^ µ1thenthemonopolistalwaysproducesone qualityallowingpiracy; (b)if ¹ µ<¡3+p5¢µthemonopolistalwaysproducesone qualityallowingpiracy. 2.If^ µ>^ µ1themonopolistproducesone quality,eitherbylettinglow-cost consumerspiratethe good (if cL<cH¹ µ¡^ µ ¹ µ¡µ)orbysettinga price that inducesbothtypesofconsumerstobuy(if cL>cH¹ µ¡^ µ ¹ µ¡µ). Proof.See Appendix. Theintuition fortheresultsin Proposition10 can begivenasfollows. FromProposition8weknowthatpro…tsarehigherwithmaximumrather 19 thanminimumdi¤erentiationwhen^ µ<^ µ1:However, itcanalsobeshown thatinthiscaseminimumdi¤erentiationisbetterthanselling onequality tothewholemarket:Thereforeitfollowsthatmaximumdi¤erentiationis preferredtoselling a singlequalitytothewholemarket.Thislatter result followsfromthemuch higherpro…tsthemonopolistcanextractfromthe high-cost,high-qualitysegmentofthemarketh¹ µ 2;¹ µi(which nowislarge), whereq2can besoldatp2=cHinsteadofp=cL: Therelevantcomparisonwhen^ µ<^ µ1isthereforebetween¦maxand ¦¤¤; the curveand thestraightlineparalleltothex¡axisinFigure4below.It isthenimmediatetocheckthat¦¤¤ >¦maxforall cL<cL<cpir L:Then,for lowcL;selling onequalitytothehigh-costsegmentofthemarketisabetter strategythansellingtwoqualitiestothatsegmentofthemarket,whileselling thelowerqualityto a share~ µ¡µ ¹ µ¡µofthelow-costsegmentand letting all other consumerspirateq2:WhencLislow,the extrapro…t themonopolistmakes bysellingq1tothe consumerswithµ2hµ;~ µiisvery low(recall thatp1is positively relatedtocL).Theloss of pro…tsfromsellingq2only toa share¹ µ¡¹ µ 2 ¹ µ¡µ ofthemarketand q1atp1totheremainingshareisinsteadquitesubstantial. Thatexplainswhy¦¤¤ >¦maxforlowcLwhereastheorderisreversed for su¢ciently highvaluesofcL: L cpir L c L c cL Π Πmax Πmin Π** Π* Figure4 Aless interestingcaseariseswhenconsumersare enough homogeneous intheirtasteforquality(¹ µ<¡3+p5¢µ).Inthiscasethemonopolist always…ndsmorepro…tabletosell asinglequalitytohigh-costconsumers only (whoseproportionisrelatively highgiventhat^ µ<^ µ1)ratherthan 20 di¤erentiatingitsproduct. When^ µ>^ µ1and thehigh-costsegmentofthemarketsmallerthaninthe …rstpartof Proposition10,selling onequalitytothewholemarketisoverall betterthanminimumdi¤erentiation.Therelevantcomparisonthereforeis between¦max;¦¤¤ and ¦¤:However, it turnsout thatintherelevantrangeof theparameters,maximumdi¤erentiationisalwaysdominated bythestrategy ofsellingasinglequalitytothewholemarket.Maximumdi¤erentiation yieldslowerpro…tsthatselling onequalitytothewholemarketbecause theloss frompiracyfromconsumerswithµ2h~ µ;^ µiisnotcompensated by thehigherpro…tsfromselling a higherqualityatp2=cHinthesegment h¹ µ 2;¹ µiofthemarket,as suchsegmentistoo small. Therelevantcomparison isthereforebetweenthestrategyofselling a singlequalitytothewhole marketand thestrategyoflettinglow-costconsumerspiratethegood,asin Proposition4.ThiscaseisdepictedinFigure5below. Π Π * Π ** 3 ~L cL c θθ θθ − −ˆ H c L c 4 ~L c cL Πmin Πmax Figure5 6Conclusions Wehaveanalyzedthe choice ofquality levelsbyamonopolistinamarket wherepiracyexists.Themainideaisthat theintroductionofalowerqualitymaybeadevice throughwhichthemonopolistmanagestocapturesome consumersthatwouldotherwiseprefertopiratethegood. Wehaveshown that therearerangesoftheparametersforwhichthemonopolistprefersto 21 produce twoqualitiesratherthanonequalityonly. Therelativepro…tabilityofthesetwostrategiesessentially dependsonthedegree ofconsumers’ heterogeneity inthe costof pirating and ontherelativeproportionofthe twotypesofconsumers(thosewithlowcostof pirating and thosewith high costof pirating).In particular,wehaveshowedthat,whentheproportion of high-costconsumersislowand di¤erentiationistheoptimalstrategy, the quality levelchosen forthelow-qualitygoodis suchthatpiracy iscompletely eliminatedinequilibrium. Wheninsteadtheproportionof high-costconsumersishigh,thereis anequilibriumwithmaximumdi¤erentiationwherethemonopolistadmits somepiracy. Thishappensbecause,since inthiscasethemonopolist…nds pro…tabletosell bothqualitiestothehigh-costsegmentofthemarket,the demand ofthehigh-qualitygood dependspositively onp1.In particular, themorethetwoquality levelsare closetoeachothers,thelowertheprices thatcan besetforthetwo goods,and thereforethelowerthepro…tsthat can be extracted fromthehigh-costsegmentofthemarket.Therefore,the low-quality isnotnecessarily setsohighthat thedemand forthepirated goodiszero and inthe equilibriumwemightexperience both di¤erentiation and piracy. Aninterestingextensionwould betoevaluatetheimpactofmorerestrictive copyrightlawsonequilibriumpricesand qualitiesinamarketwhere consumerscan piratethegood. We can dosoby incorporatinginthe cost ofcopyingthe expected …nethat the consumerhastopay ifcaughtin possessionoftheillegalgoodand studyhowthemonopolist’s strategieswould respond to anincreaseinthe expected …ne. We expect thatanincreased copyrightprotection,bymakingpiratingmore costly and thereforeless viableforconsumers,wouldreduce themonopolist’sincentivetoproduce a second (lower)quality inordertoreduce piracy. Thedegree ofcopyright enforcementcouldalsobeseenasanendogenouschoice ofthemonopolist byappropriately specifyingitsobjectivefunction. A Appendix:Proofs ProofofProposition1Whentwoquality levelsareproducedina “coveredmarket”con…guration,thedemandsforquality1 and quality2 are x1=µ±¡µ µ¡µ;x2=¹ µ¡µ± µ¡µrespectively, whereµ±=p2¡p1 q2¡q1isthepreference for qualityofthemarginalconsumerwhoisindi¤erentbetween buyingquality 1 and quality2.Pro…tsare ¦(p1;p2)=1 µ¡µ ·p1 µp2¡p1 q2¡q1¡µ¶+p2 µµ¡p2¡p1 q2¡q1 ¶¸(28) 22 Followingthethree-stagedecisionalprocess describedabove,themonopolist will …rstde…neitsoptimalprice strategy. Notehoweverthatx1¸0implies @¦ @p1>0,8p2>0.Themonopolistwouldthen …nd optimaltosetp1as highaspossible, i.e.suchthatx1=0.Thisimpliesp1=p2¡µ(q2¡q1) and x2=1.Therefore, inthequalitystagethemonopolistwouldchooseto produce asinglequality. ProofofLemma2Whenp·cL<cH;pro…tsare¦(p)=psince at thisprice all consumersbuythegood.Themonopolistwill set thehighest possibleprice subject tothe constraint that the consumerwiththelowest willingness topay(µ)hasnon-negativeutility, thatis p=µq Totalpro…tsarethereforeincreasinginq:Thehighestqthemonopolistcan produce istheonesuchthatp¤=cL: q¤=p µ=cL µ(29) Equilibriumpro…tsare¦¤=cL(30) ProofofLemma3WhencL<p·cH;high-costconsumersbuythe goodand low-costonespirateit.Demand isthereforegiven bythehigh-cost fractionofconsumersx=1 ¹ µ¡µ[µ¡^ µ](31) and pro…tsare¦(p)=p ¹ µ¡µ[µ¡^ µ](32) Since pro…tsareincreasinginp,themonopolistwill choosethehighestprice suchthat themarginalbuyer(theonewithµ=^ µ)haszerosurplus, i.e. p=^ µq.Pluggingthisinto(32),weget ¦(q)=^ µqµ¡^ µ µ¡µ(33) Pro…tsareincreasinginthequalityofthegoodand themonopolistwill set qashighaspossiblegiventhe constraint thatp·cH, i.e.q·cH ^ µ.Hence, 23 the equilibriumprice and qualityare p¤¤ =cH(34) q¤¤ =cH ^ µ(35) The equilibriumpro…tsare ¦¤¤ =cHµ¡^ µ µ¡µ(36) ProofofProposition4Theoptimalstrategyforthemonopolistisdetermined bycomparingthe equilibriumpro…tsunderthethree strategies.Since the…rststrategy, i.e.settingsuchahigh price thatnobodypurchasesthe good, leadstozeropro…tsand isneveroptimal, therelevantstrategiesare only thesecond and thethirdones.It turnsout that¦¤>¦¤¤ (i:e:itis bettertosetaprice thatinducesbothtypesofconsumerstobuy(p=cL)if and only if cL>cHµ¡^ µ µ¡µ(37) ProofofLemma5High-costconsumerscaneitherbuy1 orbuy2,and theybuy1i¤µ<µ±´p2¡p1 q2¡q1 Hence,demand forthegoodofquality1is x1=1 µ¡µ ³~ µ¡µ+µ±¡^ µ´(38) Similarly, demand forthegoodofquality2is x2=1 ¹ µ¡µ¡µ¡µ±¢(39) Themonopolist’spro…tsthusare ¦(p1;p2)=1 µ¡µ ·p1 µcL+p2¡2p1 q2¡q1¡µ¡^ µ¶+p2 µµ¡p2¡p1 q2¡q1 ¶¸(40) Thepro…tfunctionisglobally concavein(p1;p2)and the…rst-ordercondition@¦(:) @p2=0givesp2=p1+µ 2(q2¡q1),whichimpliesµ±=µ 2.Hence,high costconsumersbuythelowqualitygoodi¤^ µ<µ 2: 24 ItispossibletoprovethatR1<0:Tocheckthis see thatR1<0for ¹ µ>^ µ+1 2 q2^ µ2+2µ2and ¹ µ<^ µ¡1 2 q2^ µ2+2µ2but,as¹ µ>2^ µ;itmustbe ¹ µ>^ µ+1 2 q2^ µ2+2µ2always.De…necpir L=R2: Thenweshowthat¦maxcrosses¦¤¤ once forcL>cLand,forcL<cpir L; ¦¤¤ >¦max;whereas¦¤¤ <¦maxforcL>cpir L:Tosee thisjustcheckthat, forcL=cL;¦max<¦¤¤:In fact, ¦¤¤ ¡¦maxjcL=cL=cH¹ µ³¹ µ¡2^ µ´ 2¡¹ µ¡µ¢³3¹ µ¡2^ µ´>0 (recall that¹ µ>2^ µand ¦¤¤ isinvariantwithrespect tocL). Wehaveshown intheprooftoproposition8that¦maxisincreasing and convex, so¦maxcuts ¦¤¤ frombelowand is smallerthan¦¤¤ forcL<cpir Land largerforcL>cpir L: However,whilecpir L>cLalways,cpir L<¹cLi¤^ µ>^ µ2;where^ µ2=¹ µ2¡4¹ µµ¡4µ2 2(3¹ µ¡2µ): Whencpir L>¹cL,¦¤¤ >¦maxalwaysintherelevantrangeofcL: Recall thatin part1.oftheproposition^ µ<^ µ1:Thereforecpir L<¹cLi¤ ^ µ2<^ µ<^ µ1:Tohave^ µ2<^ µ1itmustbethat¹ µ>¡3+p5¢µ:Whenthis happens,we can havetwocases.1)^ µ2<^ µ<^ µ1,thatiscpir L<¹cL:Inthis case,wehaveshownthat¦max>¦minwhen^ µ<^ µ1:We canthenconclude that,forall cL<cpir L;¦¤¤ >¦maxand forall cL>cpir L;¦max>¦¤¤:Figure 4illustratesthis situation.2)^ µ<^ µ2<^ µ1and cpir L>¹cL:Inthiscase,the largestpro…tis¦¤¤ inthewholerelevantrange. Conversely, when¹ µ<¡3+p5¢µ;cpir L>¹cLand ¦max<¦¤¤ inthewhole relevantrange. Toprovepart2., recall thatwhen^ µ>^ µ1;¦¤>¦minand ~cL1<¹cL:Hence, ¹cListhelargestsolutionto¦max=¦min. ¦maxcrosses¦¤=cLtwice.Solve¦max=cLand obtaintwosolutions ~cL3=cH[(4¹ µ2¡¹ µ^ µ¡5¹ µµ+2µ(µ+^ µ))¡q(2¹ µ¡^ µ¡µ)2(4^ µ(¹ µ¡µ)¡¹ µ2)] (5¹ µ2¡2¹ µ(^ µ+3µ)+2µ(^ µ+µ)) ~cL4=cH[(4¹ µ2¡¹ µ^ µ¡5¹ µµ+2µ(µ+^ µ))+q(2¹ µ¡^ µ¡µ)2(4^ µ(¹ µ¡µ)¡¹ µ2)] (5¹ µ2¡2¹ µ(^ µ+3µ)+2µ(^ µ+µ)) Itcan bereadily checkedthat~cL3<¹cL<~cL4;Moreover,~cL3<cL: Toprovethis,considerthat, ifcL<~cL3;then,atcL=cL;itmustbe ¦max>¦¤:Thisisveri…ed forall ^ µ<^ µ0=1 2 h¡¹ µ+µ¢¡pµp2¹ µ¡3µi and ^ µ>^ µ00 =1 2 h¡¹ µ+µ¢+pµp2¹ µ¡3µi:Consideringthatweareinthe casewhere^ µ<¹ µ 2(see Lemma 5)and that^ µ0<¹ µ 2<^ µ00 therelevantvalue 31 is^ µ0:Checkthat^ µ1>^ µ0always,sotheonly feasible caseis^ µ0<^ µ<¹ µ 2 (theotherpossible case,^ µ<^ µ0isruledoutbythefact that^ µ1>^ µ0and weare considering^ µ>^ µ1).Then,atcL=cL;¦max<¦¤alwaysand ~cL3<cL;ThereforeintherelevantrangeforcL(cL<cL<¹cL)¦¤>¦min and ¦¤>¦max: Since di¤erentiationisneveranoptimalstrategy inthiscase,themonopolistwill produce onequalityeitherbysettingsuchalowprice thatpiracy is eliminatedorbysettingahigherprice and allowingsomepiracy. Thelatter strategy, whichyieldspro…ts¦¤¤;ismorepro…tablethantheformer(whose correspondingpro…tsare¦¤)ifand only ifcL<cH¹ µ¡^ µ ¹ µ¡µ(see Proposition4). ThiscaseisdepictedinFigure5. Notice thatcH¹ µ¡^ µ ¹ µ¡µ>cL;thereforeitisneverthe casethat¦¤>¦¤¤ on thewholerange(cL;¹cL),whereas¦¤¤ isoverall greaterthan¦¤intherange (cL;¹cL)ifcH¹ µ¡^ µ ¹ µ¡µ>¹cL;thatisif^ µ>¹ µ2+2¹ µµ¡2µ2 5¹ µ¡4µ: References [1]Besen,S., and S. Kirby(1989),PrivateCopying,Appropriability, and OptimalCopyingRoyalties,JournalofLawandEconomics,32,255-280. [2]Conner, K., and R.Rumelt (1991),SoftwarePiracy: AnAnalysisof Protection Strategies,ManagementScience,37,125-139. [3]Crampes,C., and A.Hollander(1995),Duopoly and QualityStandards, EuropeanEconomicReview,39,71-82. [4]Gabszewicz,J.J., A.Shaked,J.Sutton,and J.-F. Thisse(1986),SegmentingtheMarket:TheMonopolistOptimalProductMix, Journalof EconomicTheory,39(2),273-289. [5]Gayer,A., and O. Shy(2001),Internet,Peer-to-Peer,and Intellectual Property inMarketsforDigitalProducts,mimeo,UniversityofHaifa. [6]Hui, K.L., Png,I.P.L., and Y.Cui(2001),Piracyand theDemand for LegitimateRecordedMusic,mimeo,NationalUniversityof Singapore, downoadablefromhttp://www.ssrn.com/. [7]Itoh,M.(1983),Monopoly, Product Di¤erentiationand EconomicWelfare,JournalofEconomicTheory,31,88-104. [8]Johnson, W. (1985),TheEconomicsofCopying,JournalofPolitical Economy,93,158-174. 32 [9] Kahin,B., and H.Varian(eds.) (2000),InternetPublishingandBeyond:TheEconomicsofDigitalInformationandIntellectualProperty. Cambridge,MA:TheMITPress. [10]Lambertini, L.(1997),TheMultiproductMonopolistunderVerticalDifferentiation:AnInductiveApproach,RecherchesEconomiquesdeLouvain,63(2),109-22. [11]Liebowitz,S.(1985),Copying and IndirectAppropriability: Photocopying ofJournals,JournalofPoliticalEconomy,93,945-957. [12]Maskin E., and J.Riley(1984),Monopoly withIncompleteInformation, RandJournalofEconomics,15(2),171-196. [13]Motta,M.(1993),EndogenousQualityChoice:Price vs. QuantityCompetition,JournalofIndustrialEconomics,41(2),113-31. [14]Mussa,E., and S.Rosen(1978),Monopoly andProductQuality, Journal ofEconomicTheory,18,171-196. [15]Spence,M.(1975),Monopoly, Qualityand Regulation,Bell Journalof Economics,6,417-429. [16]Shaked,A., and J.Sutton(1982),RelaxingPrice Competitionthrough Product Di¤erentiation,ReviewofEconomicStudies,49,3-13. [17]Shy, O. (2001),TheEconomicsofNetworkIndustries,CambridgeUniversityPress. [18]Shy, O., and J.-F. Thisse(1999),AStrategicApproachtoSoftware Protection,JournalofEconomicsandManagementStrategy,8,163-190. [19]Tirole,J.(1988),TheTheoryofIndustrialOrganization,Cambridge, MA:MITUniversityPress. [20]Varian,HalR.(2000),Buying,Sharing and RentingInformationGoods, JournalofIndustrialEconomics,48(4),473-88. 33