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The effects of (private, small-scale) copying on the pricing behavior of producers of information goods are studied within a unified model à la Mussa-Rosen (1978). When the copying technology involves a marginal cost and no fixed cost, producers act independently. In this simple framework, we highlight the trade-off between ex ante and ex post efficiency considerations (how to provide the right incentives to create whilst limiting monopoly distortions?). When the copying technology involves a fixed cost and no marginal cost, pricing decisions are interdependent. We investigate the strategic pricing game by focussing on some significant symmetric Nash equilibria.
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Pricinginformationgoodsinthepresence ofcopying
Paul Belleamme¤
April 4,2002
Abstract
The e¤ectsof piracyonthepricingbehaviorof producersofinformation
goodsis studiedwithinauniedmodelàlaMussa-Rosen(1978). Whenthe
copyingtechnology involvesamarginalcostand noxedcost,producers
actindependently. Inthis simpleframework, wehighlight thetrade-o¤
betweenexanteand exposte¢ciencyconsiderations(howtoprovidethe
rightincentivestocreatewhilstlimitingmonopoly distortions?). When
the copyingtechnology involvesaxedcostand nomarginalcost,pricing
decisionsareinterdependent. Weinvestigatethestrategicpricing gameby
focussing onsomesignicantsymmetricNashequilibria.
JELClassicationNumbers:L13,L82,L86, K11, O34.
Keywords:Informationgoods,piracy, copyright,pricing.
¤DepartmentofEconomics,QueenMary,Universityof London,MileEnd Road,LondonE1
4NS(phone:+44 20 7882 5587,fax:+44 20 8983 3580,e-mail: p.belleflamme@qmul.ac.uk,
homepage:http://www.qmul.ac.uk/~ugte186/).
1
1Introduction
Informationcan bede…nedverybroadly asanythingthatcan bedigitized(i.e.,
encodedasastreamof bits),suchastext, images, voice,data,audio and video
(see Varian,1998).Informationisexchanged underawiderangeof formats
orpackages(whicharenotnecessarily digital).Theseformatsaregenerically
calledinformationgoods.Books,movies,music,magazines,databases,tele-
phone conversations,stock quotes,web pages,news,etcall fall intothiscate-
gory.
Mostinformationgoodsare expensivetoproduce butcheaptoreproduce.
Thiscombinationof high …xedcostsand low(often negligible)marginalcosts
impliesthatinformationgoodsareinherently nonrival.1Moreover,because
reproductioncostsarealsopotentially very lowforanybodyelsethanthe creator
ofthegood, informationgoodsmightbenonexcludable, inthesensethatone
personcannotexcludeanotherperson fromconsumingthegoodinquestion.
Thedegree ofexcludabilityofaninformationgood(and hence the creators
abilityto appropriatetherevenuesfromtheproductionofthegood)can be
enhanced by legalauthority(typically bytheadoptionoflawsprotectingin-
tellectualproperty)orbytechnicalmeans(e.g., cablebroadcastare encrypted,
so-calledunrippableCDshaverecently appeared).However,complete ex-
cludabilityseemshardto achieve:simply specifyingintellectualproperty laws
doesnotensurethat theywill be enforced;similarly, technicalprotectivemea-
suresareoftenimperfectand can becracked.Asaresult,piracy(orillicit
copying)cannotbe completely evacuated.
Overthelastdecade,thefastpenetrationoftheInternetand theincreased
digitizationofinformation haveturned piracyofinformationgoods(in partic-
ularmusic,moviesand software)into a topicofintensedebate.Aselection
of newsheadlinesgatheredoverthelast twomonths(February-March2002)
illustratesthe currentextentofthedebate.Theseheadlinesareabout (i)a
proposedanti-piracybill intheUSthatwould ultimately require computerand
consumerelectronicscompaniestobuild piracy-preventionsoftwareintotheir
products,(ii)aman facingjail inCaliforniaforWebsalesofCDs,(iii) there-
leaseof newpeer-to-peerle-sharingsoftwaresaimingtoreplace Napster,(iv)
musicdistributorsestimatingthatretail salesmaybedownasmuchas10 per-
centduringthepastyearasconsumers shift tonewtechnologieslike copying
CDsand downloadingsongs,(v)music companies settling a lawsuitwithaCD
consumerwho allegedthat theCDshepurchased did notmeetconsumerex-
pectationsbecauseitcould notbeplayedonacomputer,or(vi)aTaiwanese
Websitethato¤ersaccess to a hugelibraryof …lmsforjust$1 each(and which,
1Nonrivalness inconsumptionisusuallyde…ned bysayingthat the consumption possibilities
ofoneindividualdonotdepend onthequantitiesconsumed byothers.Thisisequivalent to
saythat,foranygivenlevelofproduction,themarginalcostofprovidingthegoodto an
additonalconsumeriszero.
2
understandably, hasdrawnHollywoodsire).2
Notsurprisingly, economistshaverecently shownarenewedinterestininfor-
mationgoodspiracy. Herefollowsaselectionofrecentworkingpaperswhich
investigateanumberoftopical issues.Gayerand Shy(2001a)showthein-
e¢ciencyof usinghardwaretaxationtocompensate copyrightownersforin-
fringementsoftheirintellectualproperty(IP).Inanotherarticle(Gayerand
Shy, 2001b),thesameauthorsinvestigatehowproducersof digital information
goodscan utilize theInternetsdistributionchannels,suchaspeer-to-peersys-
tems,toenhance salesoftheirgoods soldinstore.Thewelfareimplications
of peer-to-peerdistributiontechnologiesarealsothe concernofDuchêneand
Waelbroeck(2001);theyshowthat thelossesgenerated by illegalcopiescan
beo¤setbytheintroductionof newproducts,whichcreatesapositivesurplus
fortheircreators,aswell asconsumers.Theideathatcopyrightinfringement
could bestrategically promoted bycreatorsisalsoexplored byBen-Shaharand
Jacob(2001);theyshow, inadynamicmodel, thatcreatorsmightfavorse-
lective copyrightenforcementasaformof predatorypricinginordertoraise
barrierstoentry. Turningtopolicymatters,Harbaughand Khemka(2001)ar-
guethatcopyrightenforcement targetedathigh-valuebuyersraisescopyright
holderprotsbut,at thesametime, increasespiracyrelativetonoenforce-
ment;therefore,theycontend thateithernoenforcementor relatively extensive
enforcementisthebestpolicyagainstInternetpiracy. Inthesamevein,Chen
and Png(2001)examinehowthegovernmentshouldset the…neforcopying,
taxoncopyingmedium,and subsidyonlegitimatepurchases,whileamonopoly
publishersetsprice and spending on detection;theyconcludethatgovernment
policiesfocussing on penaltiesalonewouldmiss thesocialwelfareoptimum.
Finally, Hui, Png and Cui(2001)provideoneoftherareattemptstoestimate
empirically theactual impactof piracyonthelegitimatedemand forinforma-
tiongoods.UsinginternationalpaneldataformusicCDsand cassettes,they
…nd that thedemand forbothgoodsdecreasedwith piracy.
Theserecentcontributionsrevivetheliteratureonthe economicsofcopying
and copyright,whichwasinitiatedsometwenty yearsago.Theseminalpa-
persdiscussedthe e¤ectsof photocopying and examined,among otherthings,
howpublisherscanappropriateindirectly somerevenuesfromillegitimateusers
(Novosand Waldman,1984,Liebowitz,1985,Johnson,1985,and Besenand
Kirby, 1989).The economicsofIPprotectionwasthenaddressedmoregener-
2Sources:(i)Proposed anti-piracybill drawsre,byStefanieOlsen(CNETNews.com,
March25,2002),(ii)ManfacesjailforWeb salesofCDs,byLisaM.Bowman(CNET
News.com,March22,2002),(iii)GoodbyeNapster,HelloMorpheus (andAudiogalaxyand
Kazaa andGrokster...),byErickSchonfeld(Business2.com,March15,2002),(iv)Digital
MusicFightTraps Retailers,byBennyEvangelista(Newsfactor.com,March12,2002),(v)
ConsumerclaimsvictoryinCD lawsuit,byLisaM.Bowman(CNETNews.com,February22,
2002),(vi)Plugpulled onsiteselling$1 movies,byJohn Borland (CNETNews.com,February
19,2002).
3
ally byLandesand Posner(1989)and Besenand Raskind (1991).Both papers
discuss thefollowingtrade-o¤betweenexanteand exposte¢ciencyconsider-
ations.Fromanexantepointofview,IPprotection preservestheincentiveto
createinformationgoods,which(asarguedabove)areinherently public(absent
appropriateprotection,creatorsmightnotbeabletorecoup theirpotentially
highinitialcreationcosts). Ontheotherhand,IPrightsencompass various
potential ine¢cienciesfromanexpostpointofview(protectiongrantsdefacto
monopoly rights,whichgeneratesthestandard deadweightlosses;also,by in-
hibitingimitation,IPrightsmightlimit the creatorsabilitytoborrowfrom,
orbuild upon,earlierworks,and thereby increasethe costof producingnew
ideas).Athirdwaveof paperspaidcloserattentiontosoftwaremarketsand in-
troduced networke¤ectsintheanalysis.Connerand Rumelt (1991),Takeyama
(1994),and Shyand Thisse(1999)sharethefollowing argument:becausepiracy
enlargestheinstalled baseof users, itgeneratesnetworke¤ectsthatincrease
thelegitimateuserswillingness topayforthesoftwareand,thereby, poten-
tially raisestheproducersprots.Finally, and closerfromus, Watt (2000)
has surveyed–and extensively supplementedtheliteratureonthe economicsof
copyright.
Theaimofthepresentpaperisto address severalofthethemes studied
sofarintheliteraturewithinasimpleand uniedmodel. Asanumberof
recentpapers,weusetheframeworkproposed byMussa and Rosen(1978)
formodellingvertical(quality)di¤erentiation:copiesareseenaslower-quality
alternativesto originals(i.e., ifcopiesand originalswerepricedthesame,all
consumerswould preferoriginals).Inabenchmarkmodel, we considerthe
marketforasingleinformationgood.Amonopolistmustset theprice forthe
originalgood,takinginto account thatconsumerscanalternatively acquirea
lower-qualitycopyataconstantcost.Theoptimalstrategyforthemonopolist
can usefully bedescribed byusingBain(1956)staxonomyofanincumbents
behaviourintheface ofanentrythreat.Unless thequality/price ratio of
copiesisvery low(meaningthatpiracyexertsnothreatand will thereforebe
blockaded),theproducerwill havetomodifyhisbehaviorand decidewhether
tosetaprice lowenoughtodeterpiracy, ortoaccommodatepiracyand
makeup foritbyextracting a highermargin fromfewerconsumersoforiginals.
Whatevertheproducersoptimaldecision,weshowthatpiracyreducesthe
producersprotsbutincreasesconsumers surplusmorethan proportionally:
asaresult,piracy(whichamountsheretotheprovisionofacheaperand lower-
qualityalternativeto a monopolizedgood)enhances socialwelfare.
Thepreviousconclusionsimply restatestheexposte¢ciencyconsideration
ofthetraditionaleconomicanalysisofcopying: iftheinformationgoodwas
(legally ortechnically)betterprotected,theproducerwould fully enjoyhis
monopoly positionand socialwelfarewould bereduced.Asarguedabove,such
expostine¢ciencyhastobebalancedagainstexanteconsiderationsrelating
4
tocreationcosts.Toincorporatethisdimension,we extend thebenchmark
modelbyconsidering anarbitrarynumberofinformationgoods.TheMussa-
Rosen frameworkcontinuesto apply foreachinformationgood.Moreover,to
focusonthe e¤ectsof piracy, weassumethatcopyingistheonly source of
interdependence betweenthedemandsforthevariousinformationgoods.In
particular,thegoodsare completely di¤erentiatedand consumersareassumed
tohaveasu¢cient (exogenous)budget tobuythemall iftheywishso.
Whetherdemandsareinterdependentornotdependsonthenatureofcopy-
ingtechnology. InthespiritofJohnson(1985),we examinetwoextremesce-
narios:the copyingtechnology involveseitheraconstantunitcostand noxed
cost,orapositivexedcostand nomarginalcost.Intheformercase,de-
mandsfororiginalsare completely independentofoneanother:all producers
act thuslikethesingle-goodmonopolistofthebenchmarkmodel. Assuming
axedcreationcost thatvariesthrough producers,we can derivethenumber
ofinformationgoodsthatare createdat thelong-run,free-entry, equilibrium.
Obviously, piracyreducesthisnumber. We canthen balance exanteand ex
poste¢ciencyconsiderationsand showthatpiracy islikely todamagewelfare
inthelongrun (unless copiesareapooralternativeto originalsand/orare
expensiveto acquire).
Thetractabilityofthemodelwithvariable-copyingcostsallowsustoenrich
thewelfareanalysisby introducingnetworkexternalitiesand apeer-to-peer
technology(therstextensionappliesmoretosoftwareand thesecond,to
music).Inconstrastwiththeafore-mentioned paperswhicharguethatpiracy
could benetproducersoforiginalsinthepresence of networkexternalities,we
showthatnosuchoptimistic conclusion holdshere.Networkexternalitiesdo
notresolvethetrade-o¤betweenexanteand exposte¢ciencyconsiderations;
theyseem,however,to attenuateslightly thenegativelong-run welfareimpactof
piracy. Asforthepeer-to-peertechnology, ouranalysis suggeststhatitse¤ects
onconsumersareambiguous. Wemodelthepeer-to-peertechnologybypositing
anegativerelationship betweenthemarginalcostofcopying and thenumber
ofillegitimateusers(orpirates).Surprisingly, asthisrelationshipintensies
(i.e., asthepeer-to-peertechnologybecomesmoreperformant),thenumber
ofillegitimateusersmightdecrease: lowercopyingcostsinduce producersto
reduce theprice oforiginalsand thisreductionmaywell overcomethedecrease
inthe copyingcost,meaningthatless usersdecidetomake copies.
Thepicture changesdramatically whenthe copyingtechnology involvesonly
apositivexedcost.Thedemandsfororiginalsnowbecomeinterdependent
because consumersbasetheirdecisiontoinvestinthe copyingtechnologyon
the costofthistechnologyand onthepricesofall originals.Therefore,piracy
introduces strategicinteraction betweentheproducersoforiginalswhomevery-
thingelseotherwiseseparates.This strategicinteractionmakestheproducers
pricingbehavior(whichtakestheformofasimultaneousBertrand game)more
5
interesting–butalsomuchmoreintricateto analyze.Duetothe complexityof
thesystemof demands,weareunabletoprovideacomplete characterization
ofthesetofBertrand-Nashequilibria. Weshed,nevertheless,somelighton
symmetric equilibriainwhich piracy iseitherblockaded,deterredoraccommo-
dated. Weshow, in particular,that thelattertwoequilibriarely onasetof
rather restrictive conditions,astheincentivesforunilateraldeviationarehigh:
producerstend tofree-ride(bysettinghigherprices)whenitcomestodeter
piracy, ortheytend toundercutwhenitcomesto accommodatepiracy.
Therestofthepaperisorganizedasfollows.In Section2,welayouta
benchmarkmodelwithasingleinformationgoodand weanalyze theshort-run
welfare e¤ectsof piracy. Then,we extend thebenchmarkmodeltowardsa
multi-goodsettingintwodi¤erentways.In Section3,weassumethatcopying
involvesaconstantmarginalcostand noxedcost.Underthisassumption,we
examinethelong-run welfare e¤ectsof piracy; wealsoenrichtheanalysisby
introducingnetworkexternalitiesand peer-to-peersystems.In Section4,we
assumeinsteadthatcopyinginvolvesapositivexedcostand nomarginalcost.
Duetotheintricaciesofthemodelunderthisalternativeassumption,weleave
welfare considerationsasideand try insteadtounravelthe complexsituation
ofstrategicinteractionthatpiracy inducesbetween producersoforiginals. We
concludeand proposeanagendaforfutureresearchin Section5.Finally, we
providetheproofsofthemain propositionsin Section6.
2Asimplesinglegoodmodel
Westartbyconsidering a verysimplemarketforaninformationgoodsupplied
byasingleproducer. Weusetheframeworkproposed byMussa and Rosen
(1978)formodellingvertical(quality)di¤erentiation.Thereisacontinuumof
potentialuserswho are characterized bytheirvaluation,µ,fortheinformation
good. Weassumethatµisuniformly distributedontheinterval[0;1].Each
usercanobtaintheinformationgoodintwodi¤erentways. Onepossibility is
tobuythelegitimateproduct (an“original)atprice p. Originalsareproduced
byasingleproduceratzeromarginalcost.Thealternativeistocopythe
productatacostc¸0:(In bothcases,each userconsumesatmostoneunitof
theinformationgood.)Thetwovariantsoftheinformationgoodareindexed
bytheirquality: letso>0denotethequalityofanoriginaland sc(with
0<sc<so),thequalityofacopy.
The costccan bethoughtofasthe costofthe copyingmedium.3The
assumptionthat thequalityofacopy islowerthanthequalityofanoriginal
(sc<so)iscommon(see,e.g., Gayerand Shy, 2001a)and maybejustiedin
severalways.Inthe caseofanalog reproduction,copiesrepresentpoorsubsti-
tutesto originals.Forinstance,eventhebestphotocopyinglosesinformation
3See the end ofthepresentsectionforadiscussionontheprecisenatureofthiscost.
6
suchas…nelines,…neprintand true colorimages.Furthermore,copiesofanalog
media arerathercostly todistribute.Althoughthisisnolongertruefordigital
reproduction,originalsmightstill provideuserswithahigherlevelofservices,
insofarasthat theyarebundledwithvaluable complementaryproductswhich
can hardly beobtainedotherwise.4Finally, theuserwhoillegally copiesthe
productmightbedetectedand thenwill bedeprivedofthe copy. Ifwelet
½´(so¡sc)=sodenotetheprobabilityof beingdetected,thenconsumerµs
utilityfromacopy, µsc;can beunderstoodasthe expected utilityofenjoying
thequalityofanoriginalwithoutbeingdetected,(1¡½)µso.
Accordingly, auserindexed byµhasautilityfunction de…ned by
Uµ=8
>
<
>
:
µso¡pif buying anoriginal,
µsc¡cifmaking a copy,
0if notusingtheinformationgood.
(1)
Weassumethatc<sc,sothat theuserwiththehighestvaluation forthe
productisbettero¤ makingacopythan notusingtheproduct (otherwise,
piracywouldtrivially notbeanissue).
2.1 Userbehaviour
Auserindexed byµwill buythelegitimateproductunderthefollowingtwo
conditions.First,buyingmustprovideahigherutilitythan notusing:µso¸p:
Second,buyingmustprovideahigherutilitythancopying:µso¡p¸µsc¡c,
whichisequivalent to
µ¸µ1´p¡c
so¡sc
:
Ontheotherhand,thesameuserwill copytheproductifthepreviouscondition
isreversed(µ<µ1)and ifcopyingprovidesahigherutilitythan notusing:
µsc¡c¸0,or
µ¸µ2´c
sc
:
Accordingtothevalueofp,three demand patternsmightemerge.First, if
theprice ofthelegitimateproductistoo high(moreprecisely, ifp¸so¡sc+c),
then nouserwill buythelegitimateproduct:usersindexedon[µ2;1]copythe
productwhilstothersdonotuse.Since theproducerwouldmakenoprotin
suchacase,we cansafely ignoreit.Letusexaminethedemand patternin
theothertwocases,withorwithoutpiracy. Weusethefollowingnotation.
LetL(p),I(p)and N(p)denote,respectively, thedemand forthelegitimate
product,thedemand forcopies,and totaldemand.
4Forinstance,manypiecesofsoftware comewithfree manualsand supportingservices,
orwith discounton upgrades,all advantagesthatuserswhopiratethesoftwarewill haveto
acquireatapositiveprice.
7
Piracyexists.Forintermediateprices(i.e., forcso=sc·p·so¡sc+c),
usersindexedon[µ1;1]buythelegitimateproduct,usersindexedon[µ2;µ1]
copytheproduct,othersdonotuse.Accordingly,
L(p)=1¡p¡c
so¡sc
;(2)
I(p)=p¡c
so¡sc¡c
sc
;(3)
N(p)=1¡c
sc
:(4)
Looking at thedemand forthelegitimateproduct,wenotice thatL(p)shifts
outwardascincreases(i.e., astheprice” ofsubstitutable copiesincreases).
Also,asscdecreases(i.e., asthequalityofcopiesisdegraded,e.g.through
strongercopyrightenforcement),L(p)becomesless elastic:theproducerof
thelegitimateproductenjoysmoremarketpowerascopiesbecomeapoorer
substituteto originals. Obviously, thereverseresultsapply forthedemand for
copies.Finally, noteworthy isthefact that totaldemand dependsonly onthe
attributesofcopies(i.e., cand sc):theprice ofthelegitimateproductonly
determinethesplitbetweenlegaland illegalusers(thisisbecausethemarginal
userisjustindi¤erentbetween pirating and notusing).
De…ningconsumersurplusforacategoryof usersasthesumoftheirutilities,
we easily get thefollowing:
CL(p)=Z1
µ1
(µso¡p)dµ=L(p)³so¡p¡so
2L(p)´forlegitimateusers,
CI(p)=Zµ1
µ2
(µsc¡c)dµ=sc
2(I(p))2forillegalusers.
Piracydoesnotexist.Forlowprices(i.e., for0·p·cso=sc),users
indexedon[p=so;1]buythelegitimateproduct,whilstothersdonotuse.The
followingisthenreadily checked(withtheindex0indicatingtheabsence of
piracy):
I0(p)=0;L0(p)=N0(p)=1¡p
so
;
CI0(p)=0;CL0(p)=C0(p)=Z1
p=so
(µso¡p)dµ=1
2so
(so¡p)2:
Notethatinthepresentcase,totaldemand dependsontheprice ofthelegit-
imateproductsince themarginaluserisjustindi¤erentbetween buying and
notusing.
Thepreviousdemand patternwouldalsobeobservedinahypothetical
economywherepiracywould notbeanoptionand whereuserswouldsim-
ply decidetobuytheinformationgoodornot. Keepingthisreference in
8
mind, itisworthcomparingthetwodemand patternsand drawsomepri-
maryconclusionsabout the e¤ectof piracy. Easycomputationsestablishthat
L(p)+(sc=so)I(p)=1¡(p=so);whichimplies
L0(p)¡L(p)
I(p)=sc
so
<1:
Inwords,fora given price oftheinformationgood,theratiobetweenthe
numberoflostbuyersduetopiracyand thenumberofillegalusersisless than
unity. Therefore, itwouldwewronginthese circumstancestobaseanestimate
ofthelossesresultingfrompiracyontheassumptionthatall illegaluserswould
necessarily becomebuyersif piracywereinfeasible.
We canalsohavearstidea about the e¤ectof piracyonconsumersurplus.
Fromthefact thatsoL(p)=so¡p¡scI(p), itfollowsthat
CL0(p)¡CL(p)=(sc=so)CI(p);
C(p)=C0(p)+so¡sc
so
CI(p):
Therstresultsaysthat,fora given price oftheinformationgood,piracyre-
ducesthesurplusoflegitimate consumersbyanamountequaltoaproportion
(sc=so)ofthesurplusofillegalusers.Accordingtothesecond result,piracyin-
creasestotalconsumersurplusbyanamountequalto a proportion(so¡sc)=so
ofthesurplusofillegalusers.Thismeansthat thedecreaseinthelegitimate
userssurplusismorethancompensated bythe creationoftheillegalusers
surplus.
Itmustbekeptinmind that thepreviouscomparisonsareonly indicative.
Theytell ushowpiracya¤ectsthedemand forthelegitimateproductand the
consumersurplus,undertheassumptionthat theprice remainsthesamewith
orwithoutpiracy.However,thisassumptiongenerally doesnothold.Aswewill
nowshow,theproducerofthelegitimateproductmodieshispricingbehaviour
when hefacescopying.
2.2Producersbehaviour
Theproducersproblemistochoosetheprice pofthelegitimateproductso as
tomaximize prots,pL(p),with demand given by
D(p)=8
>
<
>
:
0forp¸so¡sc+c;
1¡p¡c
so¡scforcso
sc·p·so¡sc+c;
1¡p
sofor0·p·cso
sc:
(5)
Theproducersproblemiscomplicated bythefact thatsomeusersarebetter
o¤copyingtheproductonce theprice exceeds somethreshold.Thereisthus
akink inthedemand curveand theproducerhastochooseinwhichsegment
ofthedemand curveto operate.ByanalogywithBain(1956)staxonomyof
9
anincumbentsbehaviourintheface ofanentrythreat,wewill saythat the
produceriseitherabletoblockadepiracy, orthathemustdecidewhetherto
deterpiracyoraccommodate’ it.Letusnowde…neand comparethesethree
options.
Theproducerblockadesordeterspiracy.Bysettingaprice su¢ciently
low,theproducercaneliminatepiracy. Theproducersmaximization program
isthen
max
p¼(p)=pL0(p)=pµ1¡p
sos.t.p·cso
sc
:
Theunconstrained prot-maximizingprice and protsare easily computedas
pb=so
2;¼b=so
4:
This solutionmeetsthe constraintsifand only ifc¸sc=2.Inthiscase,we
cansaythatpiracy isactually blockaded:theproducersafely setshisprice as
ifcopyingwasnotathreat. Otherwise,piracycannotbeblockaded but the
producermodieshisbehaviourtosuccessfully deterpiracy: hewill chosethe
highestprice compatiblewiththe constraints, i.e.
pd=cso
sc
;whichimplies¼d=cso(sc¡c)
s2
c
:
Theproduceraccommodatespiracy.Theotheroptionistosetahigher
price and toleratepiracy. Theproducersprogrambecomes
max
p¼(p)=pL(p)=pµ1¡p¡c
so¡scs.t.cso
sc·p·so¡sc+c:
Here,theunconstrained prot-maximizingprice isequalto
pa=so¡sc+c
2;whichimplie¼a=(so¡sc+c)2
4(so¡sc):
This solutionsatisesthe constraintsifand only if
so¡sc+c
2¸cso
sc() c·sc(so¡sc)
2so¡sc
:
Ifthelatterconditionisnotmet, itiseasily checkedthat the cornersolutionis
equivalent topiracydeterrence.
Blockade,deteroraccommodate?Collectingthepreviousresults,weob-
servethat theproducersoptimalstrategydependsontherelativeattractiveness
ofcopies(i.e., onthevaluesofcand sc),as summarizedinProposition1 and
illustratedinFigure1(whichisdrawn forso=1).
10
0
0.2
0.4
0.6
0.8
1
c
0.2 0.4 0.6 0.8 1
sc
blockade
deter
accommodate
Figure1:Producersattitudetowardspiracy
Proposition1Theproducersprot-maximizationprice is
¯¯¯¯¯¯¯¯¯¯¯
pb=so
2;forsc
2·c·sc(piracy isblockaded),
pd=cso
sc;forsc(so¡sc)
2so¡sc·c·sc
2(piracy isdeterred),
pa=so¡sc+c
2;for0·c·sc(so¡sc)
2so¡sc(piracy isaccommodated).
2.3Welfare e¤ectsofpiracyin theshortrun
Nowthatwehave characterizedtheproducerspricingbehaviour,weareina
positiontore…neourpreviousanalysisofthe e¤ectsof piracy. Theprevious
analysiswascarriedoutbyreferringto a hypotheticaleconomywherepiracy
would beinfeasible,and undertheassumptionthatpiracydid nota¤ect the
price ofthelegitimateproduct.Now,weknowthatpiracydoesa¤ect the
producerspricingdecision. We canalsode…neprecisely thenotionof‘infeasible
piracy’: itcorrespondstothe caseof blockaded piracy, de…ned bythe condition
c¸sc=2.
Copiesarerelativelyunattractive.Ifsc(so¡sc)=(2so¡sc)·c·sc=2;
weknowthat theproducerpreferstodeterpiracy. Inthiscase,theonly
e¤ectof piracy istoforce theproducertosetalowerprice thantheonehe
wouldsetif piracywerenotathreat (pd<pb).Althoughmoreusersbuy
thelegitimateproduct (Ld>Lb),theproducersprotfalls,meaningthat
piracyhurtshim(¼d<¼b).However,the consumersurplusclearly increases
and thisincreaseo¤setsthereductionin prot,whichresultsinanincreasein
11
socialwelfare(computedasthesumofconsumersurplusand producersprot:
Wd=so¡s2
c¡c2¢=2s2
c>Wb=3so=8).Thepossibilityofmakingcopiescan be
seenasapotentialcompetitionthatdisciplinestheproducerofthelegitimate
productinawelfare-enhancingway.
Copiesarerelativelyattractive.Forlowervaluesofc(i.e., c·sc(so¡sc)=
(2so¡sc)),piracy isaccommodated.Thewelfareanalysisbecomesabitmore
complicatedand alsomoreinstructive.Therearenowuserswho getapositive
surplusbycopyingthelegitimateproductand theyhavetobetakeninto ac-
countinthewelfareanalysis.Considerrst theproducer.Beingjustathreat
(asinthepreviouscase)oranactualfact (ashere),piracyhasthesame e¤ect
ontheproducerspricingbehaviour:price hastogodown(thoughless than
underthedeterrence option,pd<pa<pb)and theincreased demand thisgen-
erates(La>Lb)isnotenoughtopreventprotfromfalling(¼a<¼b).So,as
inthepreviouscase,the