theutil- x andthensrdnwithinveesisecensp thesameeachformat,Becausetheretailofthepriceperfectforcompetition
each
format
avaetionRD=.Weasthenthesolvewholesaletherecordprice:pRT=wRTanddlAPsaleprices:
problemwRD
toobtainthefollowinglabel’soptimaloptimiza-whole-ne.itissew RT
lc’s=eTM 1
r2 1
and
itorAhtusaw RDi=
eTMh 1
teohtttghnisThegiroptimalsolvedcaseretail/wholesaleinwhenthesamedigitalfashion,musicissoldwithoutDRMidyuprices:
yieldingthefollowinglpconicse,p eTUTdti=w UT=
M 1+
2 1
and
loshbeSwp UDMr=w eTUD=
M 1
RehOtFoTheNyIna:withFromfullsolutiontheaboveisexpressions,providedinTableitis2.
thngoinirydpeforthethetraditionaleliminationformatofDRM,thepriceeasyfortotheseealbumthattosdecrease.themusicCopmainHereinagain,thedigitaldecreases,butthepricethetrade-offformatmayincreaseortalwhichmusicmodelbecomesapplies.moreOnattractivetheoneobservedinthetohand,beltoOnincreaseconsumers,theother
theincreasetiontion,6advantageretailersshowsordecreasethatarenotwithwithDRMremoval.Proposi-ableperfecttoincreaseintraformatpricecompeti-totakeremovalvolumeofofDRMtheincrementalrestrictions.utilityAsprovidedbythethatalwaysgoesdown.Thisaresultresult,alsotheimpliespiracycientlywhenfortotherecordstrong,thelabelsomeintraformatareofreducedthebene tscompetitionisnotsuf -bytheofremovingretailers’abilityDRMwhenWhenchargecomparinghigherpricesrecordforthelabels’DRM-freepro tsmusic.
DRM,stillholds,wetheseedigitalmusicissoldwithandinwithoutcasesjustthatwiththeadifferentresultstatedcutoffinpoint:
Proposition2B eT =
tM 1
eT t+ 22te 3
1
T 1 t 4 3 1
+2eTeM eM 1 +2t 1 2
4e2Mt 1 3 1 1/2
· eT+2t 1 1 1
meansTheabovetheleadeliminationthatthecutoffrecordpointcouldbenegative,whichofDRMlabel’sevenpro twhenmaydoingincreasewithtotoahigherutilityforconsumers.ThissoisdoessimilarnotbyInthesummary,resultinPropositionwe2Ainthebasicmodel.duceourmainmodel ndarethatpreservedtheinsightswhenweprovidedever,intraformatforwhenremovingcompetitionDRMleadsamongtoretailers.How-intro-capitalizeconsumers,thedigitalretailersareahighernotableutilitytoThisbiggermeansonthattheremovinghigherutilityDRMbyalwaysincreasingprices.toincreaseinthesalesoflegalmusic.leadsIttoapro tsseethattheretailersdonotearnanyeconomiciseasyanyrecordpositiveevenwhenlabel.impactDRMofremovingrestrictionsDRMareaccruesremoved,tobutthe5.3.
CompetitionBetweenPiratedDigitalandLegalTraditionalFormats
Inourthisloadablemainsection,ditionalformatformatmodel.weconsiderthe nalextensionofcompetedInthemainortheillegalagainstmodel,downloadableeitherthethelegallegaldown-format
tra-
Vernik,Purohit,andDesai:MusicDownloadsandtheFlipSideofDRM
MarketingScience,ArticlesinAdvance,pp.1–17,©2011INFORMS
11
Table2EquilibriumOutcomesUnderPerfectCompetition
Traditionalandunrestricteddownloadableversionsforsale eTM 1+
eM 1
pUD=wUD=T
pUT=wUT=
2
4eTeM 1 +2e2M 1 T t+2e t =
T 1
1
DUT=
2eT 2eM
DUD=M
T e eM 1
SU=T
T UL
Copyright:INFORMSholdscopyrighttothisArticlesinAdvanceversion,whichismadeavailabletosubscribers.The lemaynotbepostedonanyotherwebsite,includingtheauthor’ssite.Pleasesendanyquestionsregardingthispolicytopermissions@.
TraditionalandrestricteddownloadableversionsforsaleeTM 1
eM 1
pRD=wRD=T
pRT=wRT=
222
2e2Tt+eT 4eMt+ t 1 +2t eM 1 =
Tt 1
t+
DRT=
e t +2t eM 1
DRD=T
Tt
eM 1
SR=T
T RL
(seeFigure1).However,therewasnodirectcompe-titionbetweenthelegaltraditionalandthepirateddownloadableformats.Onemightarguethatsomeconsumerschoosebetweenbuyingthelegaltradi-tionalversionandpiratingthedigitalcopyfromtheInternet.Inthissectionweaugmentthemainmodelbyallowingdirectcompetitionbetweenallthreeversions.
Asbefore,thelocationofthedownloadablemusicformatisattheleftextremeandthetraditionalmusicformatisattherightextremeoftheHotelling(1929)linesegment.Weassumethat proportionofcon-sumershasatotalcostofpiracyasinthemainmodel:
i
ei=eTx+eMwithDRMrestrictionsandeiU= eTx+ieM(where0< ≤1,i∈ H L )withoutDRMrestric-tions.Theremainingproportionof 1 consumers
i
hasatotalcostofpiracythatisei=eT+eMwithDRM
Ui
restrictionsandei= eT+eMwithoutDRMrestric-tions.Inotherwords,thepiracycostfor consumersisrelatedtotheirlocation,andfortheremaining 1 consumers,itisindependentoftheirlocation.Thus,forthe proportionofconsumers,theequi-libriumdemandwillbeasinFigure1,andfortheremaining 1 consumers,theequilibriumdemandwillbeasdepictedinFigure3.Therestofthemodelandouranalysisapproachremainunchanged,andthefullsolutionispresentedinTable3.
Inthisextendedmodel,whenwecomparethepiracyvolumewithandwithoutDRMrestrictions,we ndthattheresultstatedinProposition1Bstillholds,albeitwithadifferentcutoffpoint: