Music Downloads and the Flip Side of Digital Rights Manageme(14)

14

TheoveralldemandfortraditionalversioncomesfrombothsegmentsLandHandisgivenbyDT= 1 xH + 1 1 xL .Thetraditionalretailerchoosestheretailpricetomaximizeitspro t:

pT eTMT T= pT wT + 1

teT+2tAsafunctionofwholesaleprice,theoptimalretailpricefor

traditionalproductis

pT wT =

Vernik,Purohit,andDesai:MusicDownloadsandtheFlipSideofDRM

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

ers.The lemaynotbeermissions@.

(A1)

t eM 1 +t 1 +wT 1+ +2 +eT t 1 + wT

T

oftheconsumerwhoisindifferentbetweenbuyingthetraditionalversionandbuyingthedownloadableversion

BB

isderivedbyequatingUT x toURD x .NotethatthislocationisthesameforbothsegmentsHandLand

+

isgivenbyxH= pT pRD+t DRM / 2t forthosecon- sumerswhoprefertheDRM-restrictedversionandxH=

DRM

pT pRD+t+ / 2t forthoseconsumerswhoprefertheDRM-freeversion.

ThelocationoftheLsegmentconsumerwhoisindiffer-entbetweenbuyingthedownloadableversionandsteal-BS

ingitisderivedbyequatingURD x andURD x eL .ForthoseconsumerswhopreferDRM-freemusic,thisloca-bpircoTherecordlabelmaximizesitspro tbychoosingthetsbywholesaleucsiloop t=w pT T wT eTt+ 1 MeT wT +t

RL

TesThisyields

price:

ilbhtalignvaiw

adr=eT t 1 + T

U +t t+eM 1 +2 U

T

eadgWiththisoptimalwholesaleprice,therecordlabel’spro t

aermsisequaltosnioihts t e1 + RLc=

MU +eT t U 2

Tiehuwqstraightforwardcomparison+2t eT+t 1of+

(A2)

A(A1)withtherecord

,ynnlabel’spro tincaseswhenitsellsDRM-restrictedoroaiDRM-freedownloads(seeTable1)resultsinthefollowingsrdnobservation:

veese RL<max RRL U

RL

when <max 1 2

censawhere

vaedlAP 1ne.= t t 1+ +eT eT 6e2T 2

+13teT 1 +4t2 1 2

itiss+4 1 eMeT 3eT +5t 1

elc’srito·2e2M 3eT +4t 1 1 2

rAhtusa· eT 2 1 eT+2t 3eT +8t 1 1 1/2ihteoht

t 1 eT ettghngi6e+2t

M

T 2= 3Tt+e2

T 1 12eM+13t t 6t

idryulpc+2eTt 1 2 3e2

M+10teM+2t2

onicse, 4eM+6t 3 +8t2 1 3 eMdtilos· eT eT+2t 1 3e2

T +et 3+11 8 2

hbeSwMrRe 1++ 8et2 1 2 1 1/2

hOt×

Tt 1 eT eFoNyBecause isthebaseutilityof+listening2t

M

Ttothemusic,it

Ina:isreasonabletoassumethatitcannotbein nitelyhigh.Sothngoforreasonablevaluesofthebaseutility,itisoptimalforirtherecordlabeltostartsellinglegaldigitaldownloadsinydpetordertocapturethedemandfromtheconsumerswhohaveosCopstrongpreferencefordigitalformat.

AppendixB.EffectofDRM

Inthisappendix,weallowsomeconsumerstoseeDRMas

apositiveandotherstoseeitasanegative.Thelocation

tionisatx+L= pDR eM

L+ DRM /eT,andforthosecon-sumerswhopreferDRM-restrictedversion,itisatx pDRConsumers eML DRM /eT

.

L=

whoprefertheDRM-freeversionofthedig-italproductproducetheoveralldemandof

D+D= x+H+ 1 x+H x+L

and

D+T= 1 x+H

(B1)

fordigitalandtraditionalversionsoftheproduct,respec-tively.Similarly,consumerswhoprefertheDRM-restricted

versionoftheproducthaveanoveralldemandofD

x

D=overallH+ demand1 xHfor thexL andDlegalproductsT= 1 Dx(digital)H .Therefore,theandT(tra-ditional)isgivenby

DD= x+H+ 1 x+H x+

L

+ 1 x H+ 1 x H x

L

(B2)DT= 1 x+H + 1 1 x

H

(B3)

Substitutingtheexpressionsforlocationsofindiffer-entconsumersinto(B2)and(B3)resultsinthefollowing

demandfunctions:DD pDR pT

=

eT pTDRDRMDRM +2t 1 eL

MTDRDRMDRM

DpT pDR pT =DRT2DRMt

DRM

Afterde ningtheweightedimpactofDRMas DRM 2 1 ,thesedemandfunctionscanberewritten as=follows:DD pDR pT

=eT pTDR +2t 1 eL

MTt

DR (B4)

DpT pDR pT =DRT

(B5)

NowconsiderjustthedemandthatcomesonlyfromconsumerswhopreferDRM-freeversionoftheproduct.SubstitutingthelocationsofindifferentconsumersintoEquations(B1)resultsinthefollowingdemandfunctionsfordigitalandtraditionalproducts:D+D pDR pT

=eT pTDRDRM +2t 1 eL

M2eTt

DRDRM

(B6)D+

pTDRMT pDR pT =DR2t

(B7)