8
Proposition2A.When =0,thenremovingDRMrestrictionsleadstoanincreaseinpro tsfortherecordlabeliff
1 ATeMt 1 3eT2
> = T 3eT+8t 1
22
whereA=24eTt eT 9eM 18eMt 46t2 1 212eMt 1 2.
Vernik,Purohit,andDesai:MusicDownloadsandtheFlipSideofDRM
MarketingScience,ArticlesinAdvance,pp.1–17,©2011INFORMS
ers.The lemaynotbe
ermissions@.
Proposition2Ashowsthatevenwhen =0,andtheDRMproductprovidesnodisutilitytolegalbuy-theincentivestoincreaseitcomefromthehigher
productbene tenjoyedbytheconsumers.When issuf cientlyhigh,therecordlabelearnsahigherpro twithoutDRMbecauseofeitherthehighertotalsalesorthehigherwholesalepriceforthelegaldownload,orbecauseofacombinationofthetwo.
Propositions1and2showthatrecordlabelpro tandtheoverallpiracylevelcanincreaseordecreasewhenDRMrestrictionsareremoved.Furthermore,conventionalwisdomsuggeststhatanincreaseinpiracywouldleadtolowerpro ts.However,thebpircotsers,butheitspricerestrictions.stillmightThisbeoptimalycoccursforthe rmtoremoveilooptesDRMsensitivityilbhtlabel.isremoved,ofresultingthedemandbecauseinhigherthatofthegreaterpro tscomesforwhenaligncanInterestingly,inthiscase,thedownloadretailerthevaiaddecreasesalsoearneisandithigherpro tsmainlybecausepiracyradgaeraremovalonlythetraditionalearnsretailerahigherthatmarginstandsontoalllosesales.withItmssnioitheNow,htscieitabilityimpactweofofofconsiderDRM.
theremovingtherecordlabel.
DRMgeneralrestrictionscasewhenon the>0prof-andhuwqProposition2B.Therecordlabelearnsahigherpro t,ynnoabyremovingDRMrestrictions,iff > ,where
isrdnvee
=t eTst 3eTet 1 +8Tt 1 +16t 1 et 1
ceTnsavae = 1 T3eT +8t 1
dlAPne.and
itissel =e3c’sTt 24 22
ritorAhtu· t2 16+ 1 2eT 1 2
14 23 +6eMt 1 3 3e2
M 1
saihte+8eTeMt 1 3 eM 1+ +6t
ohtttg+32e2Mt2 1 4 6e4T 1 2
hngiidryulpcofTherecordlabel’spro tisdeterminedonicthelegalse,dtimats.wholesaledownloadspricesasthatwellitchargesastraditionalbythesalesfortheCDsandloshbeaSwDRMthreshold,Propositiontotal1Bsalesshowsoflegalthataslongas twofor- isaboveMrRehtionalrestrictionsareremoved.Inmusicaddition,increasethewhenOtlegalformatlosesitscompetitiveadvantageovertradi-theFoNyTherefore,downloadsIna:thethngothisrecordwithlabelthewhenshiftsremovalDRMofrestrictionsDRM,thearesalesremoved.mixforirydthepetoswhenwholesaleeffectbecomespricestrongertowardofthetraditionalas legaldownloads,and increases.musicAlthoughCoppriceThebecauseincentivesforDRMtherestrictionslegalareremoved,thewholesaledecreasestodownloadscangoeitherway.morepricethesensitivedemanddecreasewhenforthethewholesalepriceariseDRMlegalisdownloadremoved,becomeswhereas
followingalwaysthepropositioncase.
demonstratesthatthisisnotProposition3.(1)If > S
,thenfor Spro t
goes ,piracydown.volume(2)If goes down,andtherecord∈
piracyvolumegoesup,and the< Srecord ,thenfor label’spro t ∈ label’s
S
goes up.
,theThethreshold levelthreshold Scouldbehigheror .When >max S
lowerthan
tions,goesanddowntherecordwith ,thepiracylabel’stheremovalpro tofgoesDRMup.restric-When
removal <min S
,thepiracylevelincreaseswiththepro tforgoesofdown.DRMrestrictions,Interestingly,andwhenthe record > S
label’s
,then
without S <(seeDRM <despite
thetherecordlabel’spro tislowerneedsFigureditionaltocharge2(a)).aThislowerispiracywholesalebecausevolumepricetherecordbeinglowerforthelabelremoved.formatchargeloadalowerInaddition,albumwhenDRMrestrictionstra-arewholesalethepricerecordforlabelmayalsodemand.becausetheAsFigureofthe2(b)increasedshows,pricethewhensensitivitylegaldown- ofits
S
tionsrecordup.areremovedlabel’spro t< < ,evenincreasesthoughthewhenpiracyDRMrestric-chargeThisoccursbecausetherecordlabellevelisablegoesload,andahigheritssaleswholesalemixmovespricetowardforathehigherlegalfraction
down-toFigure2
EquilibriumDemandforLegalandIllegalVersions
(a)
Piracy
Piracy
Π
S
Profit
Profit(b)
Piracy
Piracy
Π
S
Profit
Profit