A Note on Software Protection and Social Welfare Yi Sin Lin, P D Candidate, Deartment of Tecnology Management, Cung Hua Univerity, Hincu, Taiwan Dr Yao Hien Lee, Aociate Profeor, Deartment of Finance, Cung Hua Univerity, Hincu, Taiwan ABSTRACT Ti aer invetigate te effect of oftware rotection on te rice of te oftware and te ardware, conumer urlu and ocial welfare We find tat in te reence of oftware iracy, an increae in te baic utility of te legal oftware increae conumer urlu and ocial welfare n te cae of no oftware iracy, an increae in te unit R&D cot decreae conumer urlu and ocial oftware Te oftware firm oftware rice i iger under no oftware iracy and te ardware firm ardware rice i iger under oftware iracy Wen te oftware firm imlement oftware rotection, conumer urlu fall n addition, our reult ow tat in general te ocial welfare level i iger in te reence of oftware iracy NTRODUCTON According to te urvey conducted in 004 by te nternational Data Cororation (DC) ow tat te oftware iracy rate (43%) of Taiwan in 003 i iger tan tat of te global average rate (36%) n view of ti, Taiwan government autority and oftware firm tell conumer reeatedly not to irate oftware and wi to etabli te concet of intelligence roerty rigt and coyrigt, etc n te lat decade, in order to reduce te ramantly oftware iracy circumtance in te dometic and to rotect te oftware firm, te government autority a legilated te law uc a te coyrigt law, te intelligence roerty rigt law, and te otical media law Since oftware can almot cotle to be irated and any irated oftware i identical to te original, oftware iracy a relatively ig oibility tan oter good, eg journal, book, caette etc, to be irated (Sy, 001) Ti would ignificantly lower oftware firm rofit and woren ocial welfare n te literature on oftware rotection, autor uc a Conner and Rumelt (1991), Sy and Tie (1999), Hiao (001), and Peitz (004) find tat te unrotected oftware olicy can be te bet olicy in te reent of oitive network effect Te olicy can increae firm rofit and lower te oftware rice Moreover, te olicy i an equilibrium olicy for non-cooerative firm Givon, Maajan, and Muller (1995) ue a diffuion model aroac to etimate te irated oftware ale Cou (001) oberve tat te different brand reference of oftware uer will affect te oftware firm oftware rotection trategy Ciang (001) argue tat te network effect will influence coyrigt trategie of te oftware firm and it location Moreover, te individual etical value and eer reure all ave ignificantly imact on te eronal iracy intention and attitude (Tang, 1995; Zou, 1995; Cen, 1998; Weng, 001) We find tat te above literature doe not analyze te effect of oftware rotection on te rofit of te oftware firm woe oftware a been irated Only Gayer and y (003) develo a model in wic te government autority directly taxe eac unit of ardware urcaed by eac oftware uer and tranfer te revenue collected by te tax on te ardware to te oftware firm However, tey argue tat ardware taxation i inefficient n ti aer, we develo a model in wic a oftware firm invet R&D
exenditure on oftware rotection o a to control te oftware iracy ratio We analyze te effect of oftware rotection on te oftware firm, te ardware firm, conumer urlu and ocial welfare under te reence of oftware iracy and no oftware iracy We alo dicu and comare te different effect between oftware iracy and no oftware iracy in te aect of economic imact Te aer i organized a follow Section et u a baic model of te ardware firm and te oftware firm, were oftware uer can eiter buy te oftware or ue it illegally witout aying for it Section 3 invetigate te economic effect of oftware iracy Section 4 invetigate te economic effect of no oftware iracy Section 5 dicue and comare te difference of economic effect between oftware iracy and no oftware iracy Section 6 conclude U x Te MODEL Now, te utility of eac oftware uer indexed by x (0 x 1) can be ecified a x N if buy te ardware and te oftware x N if buy te ardware and irate te oftware (1) 0 if doe not buy te ardware and te oftware def Software uer tye are uniformly ditributed on te interval [0, 1] Te location index number x i te widely ued differentiation caracteritic arameter of a oftware uer Tu, uer indexed by x toward 1 are interreted a toe wo gain te mot out of uing ardware and oftware, werea uer indexed by x toward 0 are interreted a toe wo gain very little from uing ardware Ti i illutrated in Figure 1 Eac uer ue at mot one unit of oftware, eiter by urcaing te oftware for rice,, or irating it for free n addition, eac uer wo wie to ue te oftware mut urcae one unit of ardware (eg, comuter, CD/DVD layer, MP3 layer) for a rice of Let te arameter α>o and β>0 be a uer baic valuation for te ervice rovided by te oftware Te iger te value of α or β, te more valuable oftware ervice rovided (Sy, 001) Te arameter 0 rereent te intenity of network ize effect More reciely, γ>0 mean tat te iger oftware utilization, te iger i te uer utility Finally, wit no lo of generality, we imlify te model by etting te oftware firm marginal cot to be zero Figure 1 Pirate, nonuer, and buyer EQULBRUM N THE PRESENCE OF SOFTWARE PRACY n ti ection, we analyze te influence of oftware iracy on conumer urlu, rofit of te ardware firm and te oftware firm, and ocial welfare Uer Coice Let x denote te tye of a marginal uer wo i indifferent between uing te illegal oftware and not uing te oftware at all, o ti uer tye i olved a
x N All uer indexed on [0, x ] do not ue te ardware and te oftware Similarly, let x b () denote te tye of a marginal uer wo i indifferent between uing te illegal oftware and buying te legal oftware, o ti uer tye i olved a b x (3) b b Tu, all uer indexed on [ x, x ] ue te illegal oftware, and all uer indexed on [ x,1] buy te legal oftware Noting tat te number of oftware uer N 1 x wo legally and illegally ue te oftware N Te Software firm Te rofit function of te oftware firm i given by b x 1 So ubtituting () into N, we ave, ti i te total number of uer max 1 (5) Tu, maximizing (5), te oftware firm rofit-maximizing rice i given by (6) Ten, ubtituting (6) into (3) and (5), we ave b and x 1 4 (7) Terefore, we can tate te following rooition Prooition 1 n te reence of oftware iracy, (1) wen a legal oftware uer baic utility i larger tan tat of te illegal oftware (α>β), te oftware firm obtain exce rofit ( 0 ) () te iger baic utility of te legal (illegal) oftware, te iger (lower) i te rofit of te oftware firm, and (3) te network ize effect doe not influence te market are of te oftware firm and it rofit (4) Te Hardware firm Te rofit function of te ardware firm i given by max N Tu, maximizing (8), te ardware firm rofit-maximizing rice i given by Subtituting (9) into (4) and (8), we ave (8) (9)
N and 4 (10) Subtituting (9) and (10) into (), we can obtain te ardware firm market are a follow: x 1 (11) We now etabli Prooition n te reence of oftware iracy, (1) if te baic utility of te illegal oftware i iger tan te network ize effect, it will increae te urcae intention of ardware uer and teir willingne to ay for te ardware and ence te ardware firm will obtain exce rofit, () Te iger te network ize effect, te iger i te rofit of te ardware firm, and (3) te baic utility of te legal oftware uer doe not influence te rofit of ardware firm Social Welfare We define conumer urlu function a te um of illegal uer and legal uer net utilitie Formally, def xb 1 CS x N dx b x N dx x x (1) Subtituting te uer tye, equilibrium rice, and te number of uer into (1), we ave CS 8 8 (13) n addition, we define te ocial welfare function a te um of conumer urlu and rofit of te ardware firm and te oftware firm, we ave def 3 4 3 W CS 8 8 (14) We can ten etabli te following: Prooition 3 (1) An increae in te baic utility of te legal oftware increae conumer urlu and ocial welfare, () An increae in te network ize effect increae conume urlu, but lower ocial welfare, and (3) An increae in te baic utility of te illegal oftware decreae ocial welfare EQULBRUM N THE ABSENCE OF SOFTWARE PRACY n ti ection, we aume tat te oftware firm utilize R&D inut in term of oftware licene eriod, one-time intall olution, and oftware rotection ceme baed on mart card, etc to reduce oftware iracy (Lee, 000) Te R&D inut require te oftware firm to ue valuable reource, tat i, R&D cot follow Hence, te utility function of a oftware uer i defx N if buy te ardwareand te oftware U x 0 if doe not buy te ardwareand te oftware (15) A in te reviou ection, wen x toward 1 meaning toe wo will buy te legal oftware, and wen x toward 0 meaning toe wo will not ue oftware Ti i illutrated in Figure Tere are no illegal uer in te market becaue te oftware firm reclude oftware iracy
Figure : Nonuer and buyer Uer Coice b1 Let x denote te tye of a uer wo i indifferent between uing te legal oftware and not uing te oftware at all, o ti marginal tye i given by x b1 N b1 All uer indexed on [ x, 1] buy te legal oftware Terefore, te total uer of te oftware and te b1 ardware are equal to N 1 x N Subtituting ti reult into (16), we ave Te Software Firm n te reence of te oitive network effect, te more uer reult in te iger utilization and te iger R&D cot Let ωn denote te total R&D cot and te arameter ω denote te unit R&D cot te oftware firm ent on legal uer Hence, te more legal uer, te more R&D cot tat te oftware firm ave to end Te rofit function of te oftware firm i given by max Tu, maximizing (18), we ave te oftware firm rofit-maximizing rice a follow: (16) (17) (18) (19) Te Hardware Firm Te rofit function of te ardware firm i given by max Tu, differentiating (0) wit reect to Solving for and 3 and yield 3 Subtituting () into (16) and (17), we ave yield (0) (1) ()
b1 3 N and x 3 3 (3) Subtituting () and (3) into (18) and (0) yield te rofit of te ardware firm and te oftware firm in te abence of oftware iracy a follow: and 9 9 (4) We ten ave te following rooition Prooition 4 n te abence of oftware iracy, (1) if te baic utility of te legal oftware i iger tan te network ize effect ( ) and te unit R&D cot ( ) a well, an increae in te baic utility of te legal oftware increae te number of uer and rofit of te oftware firm and te ardware firm, () An increae in te unit R&D cot decreae rofit of te oftware firm and ardware firm, (3) An increae in te network ize effect increae rofit of te oftware firm and te ardware firm Social Welfare Following imilar te to toe in te reviou ection, we ave def 1 1 x b CS x N dx (5) Subtituting te uer tye, te equilibrium rice, and te number of uer into (5) yield CS 18 (6) Ten, we ave def 5 4 W 18 (7) Terefore, we can tate te following rooition Prooition 5 n te abence of oftware iracy, an increae in te unit R&D cot decreae conumer CS W urlu and ocial oftware, ie, 0 and 0 We ummarize te reult obtained in te above in Table 1 Table 1 te equilibrium reult R&D=0 R&D=ωN (oftware iracy-tye ) (no oftware iracy-tye ) 3 3 4 9 4 9
CS W 8 8 18 3 4 3 5 4 8 8 18 Now we are ready to comare te equilibrium outcome a own in Table 1 Before to do tat, we can ee te equilibrium rice are indeendent of te network ize effect Moreover, te rofit of te oftware firm i alo indeendent of te network ize effect in te reence of oftware iracy DSCUSSON Baed on Table 1, we ave te following dicuion Price Level We can oberve from Table 1 tat te oftware rice of oftware firm i iger under no oftware iracy and te ardware rice of te ardware firm i iger under oftware iracy We etabli te following rooition Prooition 6, if 3 Profit of te oftware firm and te ardware firm Te oftware firm rofit will be greater under te cae of no oftware iracy, ie Formally, We ave te following rooition (8) 9 4 Prooition 7 (1) if, were 1 5 ; () if 4 9 Prooition 7 indicate tat if, ten oftware rotection i te bet olicy for te oftware firm but not for te ardware firm n oter word, te oftware firm exerting R&D inut to reduce oftware iracy will increae te quantitie of legal oftware and it rofit, but decreae te quantitie of te ardware firm if 4 Hence, oftware rotection will increae te rofit of te oftware firm 9 Conumer urlu Software rotection lower conumer urlu becaue CS 0 if 3 w Terefore, we can tate te following rooition Prooition 9 f te oftware firm imlement oftware rotection, ten te conumer urlu fall, ie, CS CS Social Welfare Te oftware firm imlement trictly oftware rotection in term of iger R&D cot Ten, te oftware firm tranfer te R&D cot to conumer o tat conumer urlu and te rofit of te ardware firm fall, but it can obtain iger rofit Hence, if te abolute value of te um of te rofit difference of te ardware firm and te difference of conumer urlu are greater tan te abolute value of te difference of te oftware firm rofit, ten te ocial welfare level under no oftware iracy i larger tan tat of under oftware iracy We can conclude in te following rooition
Prooition 10 W W, if CS CONCLUSONS We ave analyzed ow te oftware firm imlementing te olicy of oftware rotection in term of R&D cot to reduce oftware iracy influence it oftware rice and rofit, te ardware rice and rofit of te ardware firm, conumer urlu, and ocial welfare Our reult ow tat in te reence of oftware iracy, an increae in te baic utility of te legal oftware increae conumer urlu and ocial welfare However, an increae in te network ize effect increae conumer urlu, but lower ocial welfare A exected, an increae in te baic utility of te illegal oftware decreae ocial welfare n te cae of no oftware iracy, we find tat an increae in te baic utility of te legal oftware increae te number of uer and rofit of te oftware firm and te ardware firm Certainly, an increae in te unit R&D cot decreae rofit of te oftware firm and ardware firm Alo, an increae in te network ize effect increae rofit of te oftware firm and te ardware firm nteretingly, an increae in te unit R&D cot decreae conumer urlu and ocial oftware Meanwile, te oftware rice of oftware firm i iger under no oftware iracy and te ardware rice of te ardware firm i iger under oftware iracy Te oftware firm imlement oftware rotection, ten conumer urlu fall n addition, our reult ow tat in general te ocial welfare level i iger in te reence of oftware iracy n te olicy imlication, we ugget tat te oftware firm ould focu on ow to increae te baic utility difference between te legal oftware and te illegal oftware For examle, after ale ervice, varietie, and ugrade, etc (Biyalogorky et al, 005) By doing ti, te otential uer are willing to buy more advanced function of te legal oftware and not to influence te uer wo refer te baic function of te oftware Ti will be rofitable all uer and te ardware firm
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