6

Table1

EquilibriumOutcomeswithTwoCompetingRetailers

Vernik,Purohit,andDesai:MusicDownloadsandtheFlipSideofDRM

MarketingScience,ArticlesinAdvance,pp.1–17,©2011INFORMS

Copyright:INFORMSholdscopyrighttothisArticlesinAdvanceversion,whichismadeavailabletosubscribers.The lemaynotbepostedonanyotherwebsite,includingtheauthor’ssite.Pleasesendanyquestionsregardingthispolicytopermissions@.

Traditionalandrestricteddownloadableversionsforsale

pRT= pRD= wRT= wRD=

2

3e2TT 1 3eM +2t 5eM 1

T2

3e2TT 1 3eM +12t eM 1

TTraditionalandunrestricteddownloadableversionsforsale

pUT= pUD= wUT= wUD=

2

3 2e2TT 1 3eMMT2

3 2e2TT 1 3eMM 1

TeTM 1

eTM 1

2t eM 1 +eT 3t+ 2

T eTT 3t +4t eM 1 2

T 3eT22223

e2T 1 12eMt+13t +8t eM 1

Tt 1 3eT+8t 1

eTM 1+

eTM 1

t 2 eMT 2

Tt eTTM 1 2

T 3 eT222223

6 3e3Tt+ eT 1 12eMt+13t +8teM 1

Tt 1 3 eT+8t 1

RT= RD= RL=

UT= UD= UL=

+

DRT= DRD= SR=

2t eM 1 +eT 3t+

T2222

6e3Tt+2eTt 1 3eMMt+2tM

Tt 1 3eT+8t 1

DUT= DUD= SU=

+

2t eMT

T2

2 eTt 1 2 3e2MMt+2t Tt 1 3 eT+8t 1

eTT 3t +4t eM 1

T 3eT eTTM 1

T 3 eT2

3e2TT 3eM 1 4t eM 1

T 3eT+8t 1 2

3 2e2TT 3eMM 1

T 3 eT+8t 1

3.2.SellingTraditionalFormatand

DRM-FreeDownloads

WenowconsiderthecasewhereretailerDsellsthealbumintheDRM-freedownloadableformatandretailerTsellsitinthetraditionalformat.Followingthesamelogicasintheprevioussection,wederivetheoptimalsetofprices:

pUT

2

3 2eTT 1 3eMM2

=

T+8t 1

words,thethinkingintheindustrywasthatDRMwould ghtpiracyandprotecttheindustry.Inthissection,wespeakdirectlytotheconventionalwisdomoftheindustry:WouldtheindustrybebetteroffifDRMrestrictionswereremoved?Inwhatfollows,welookattheimpactofremovingDRMonpiracyandonrecordlabelandretailerpro ts.

4.1.EffectonPiracy

Themostcommonargumentputforwardbypropo-nentsofDRMisthateliminatingDRMrestrictionswillunconditionallyincreasethelevelofpiracy.How-ever,becausetheimpactofremovingDRMaffectspricesandquantitiesofbothtraditionalCDsandonlinedownloads,thefullimpactofeliminatingDRMrestrictionsisnotcompletelystraightforward.NotethatpiracyexistsregardlessofwhethertherecordlabelchoosesDRMornot—sotheissueiswhetheritisaffectedsigni cantlybyDRM.TofullyunderstandtheimplicationsofremovingDRM,we rstfocusonthecasewherethereisnodisutilityimposedonlegalbuyersthroughthepresenceofDRM;i.e., =0.Asnotedearlier,thisisanidealDRMscenariowherethe rmimposesahigherstealingcostwithoutanyadverseeffectsonlegalbuyers’utilities.Thisleadstothefollowingproposition.

pUD

23 2eTT 1 3eMM 1 2=

2 1 3 eT+8t 1

wUT=

eTM 1+

wUD=

eTM 1

Theequilibriumpro ts,prices,demands,andpiracylevelsaresummarizedinTable1.

4.

Recallthattheconventionalwisdomintherecordindustrywasthatlegaldownloadswouldleadtoaproliferationofcopying,thusexacerbatingtheprob-lemofpiracy.Asaresult,alllegaldownloadswere rstmadeavailablestrictlywithDRM.Inother

TheImpactofRemovingDRMRestrictions