Free Software Offer and Software Diffusion: The Monopolist Case

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1 Association for Information Systms AIS Elctronic Library (AISL) ICIS 3 Procdings Intrnational Confrnc on Information Systms (ICIS) Dcmbr 3 Fr Softwar Offr and Softwar Diffusion: h Monoolist Cas Zhngrui Jiang h Univrsity of xas at Dallas Sumit Sarkar h Univrsity of xas at Dallas Follow this and additional works at: htt://aisl.aisnt.org/icis3 Rcommndd Citation Jiang, Zhngrui and Sarkar, Sumit, "Fr Softwar Offr and Softwar Diffusion: h Monoolist Cas" (3). ICIS 3 Procdings. 81. htt://aisl.aisnt.org/icis3/81 his matrial is brought to you by th Intrnational Confrnc on Information Systms (ICIS) at AIS Elctronic Library (AISL). It has bn acctd for inclusion in ICIS 3 Procdings by an authorizd administrator of AIS Elctronic Library (AISL). For mor information, las contact library@aisnt.org.

2 FREE SOFWARE OFFER AND SOFWARE DIFFUSION: HE MONOPOLIS CASE Zhngrui Jiang and Sumit Sarkar School of Managmnt h Univrsity of xas at Dallas Richardson, X USA zxj11@utdallas.du sumit@utdallas.du Abstract An intrsting hnomnon oftn obsrvd is th availability of fr softwar. h bnfits rsulting from ntwork xtrnality hav bn discussd in th rlatd litratur. Howvr, th ffct of a fr softwar offr on nw softwar diffusion has not bn formally analyzd. W show in this study that vn if othr bnfits do not xist, a softwar firm can still bnfit from giving away fully functional softwar at th bginning riod of th markting rocss. his is du to th acclratd diffusion rocss and subsquntly th incrasd NPV of futur cash flows. h analysis is basd on th wll-known Bass diffusion modl. Kywords: Fr softwar, diffusion, Bass Modl Introduction An intrsting hnomnon in today s markt is th availability of a wid varity of fr softwar, ranging from businss and rofssional softwar such as Wb srvrs, orating systms, and rogramming languags, to consumr softwar such as word rocssors, sradshts, Wb browsrs, and multimdia. Basd on thir commrcial objctiv, w classify fr softwar into thr broad catgoris. h first catgory is on sourc softwar or frwar, which is dvlod and maintaind by voluntr contributors. h two most wll-known xamls in this catgory ar Linux and Aach. Fr softwar in th scond catgory is dvlod or vn maintaind by commrcial softwar comanis but is givn fr to usrs. Examls includ Ntsca, Intrnt Exlorr, and Java. hs roducts ar offrd fr bcaus roducrs ar sking othr conomic bnfits, such as boosting sals of comlmntary goods. In th third catgory, fr offr or fr trial ar mloyd as a markting tchniqu. Fr softwar is offrd only for a limitd tim or limitd contnt or both. An xaml in this catgory is th fully functional 3-day trial vrsion of Miniab. In this articl, fr softwar offr rfrs to softwar in th third catgory. Fr softwar in th first two catgoris is not th focus of this study. Softwar fr trial or fr offr as a romotion tchniqu has bn mloyd by a growing numbr of softwar roducrs. Wllarticulatd bnfits of th ractic includ ositiv ntwork xtrnality, incrasd markt shar, rducd advrtising costs, and raisd barrir to ntry. In this study, w xamin th ffct of fr softwar offr on its diffusion rocss. For simlicity, w only considr monoolist softwar roducrs. W will show that vn if th othr mntiond bnfits do not xist or ar not significant, a monoolist softwar roducr can still bnfit from fr offr bcaus of th acclratd softwar diffusion rocss. Dsit th oularity of fr softwar, w hav only sn a limitd numbr of formal conomic analyss of th ractic, most of which focus on th ositiv ntwork xtrnality ffct of fr offrs. On sourcs scnarios hav bn addrssd by a numbr of studis and a summary is rovidd in Schiff (). Gallaughr and Wang (1999) xamin th mirical vidnc of th imact of fr softwar on commrcial softwar in markts whr both frwar and aid softwar ar availabl. Haruvy and Prasad (1998) xamin how a softwar firm can xloit ntwork xtrnality by introducing limitd vrsions of commrcially availabl softwar togthr with othr aid vrsions. Anothr rlatd stram of litratur focuss on th diffusion of consumr durabls, including nw tchnologis. h basic diffusion modl was introducd by Bass (1969) and has bn th basis for numrous 3 wnty-fourth Intrnational Confrnc on Information Systms 881

3 Jiang & Sarkar/Fr Softwar Offr and Softwar Diffusion xtnsions and alications. Among thm, Mahajan and Ptrson (1978) modl th ffct of ric on th numbr of otntial adotrs; Krishnan t al. (1999) roos otimal ricing in nw roduct diffusion; Docknr and Jorgnsn (1988) roos otimal advrtising olicis for a nw roduct; and Kalish and Liln (1983) study otimal govrnmnt subsidis to acclrat nw tchnology diffusion. h rmaindr of th ar is organizd as follows. W brifly discuss th diffusion modl. W thn modl th NPV of a nw softwar roduct to a monoolist firm. W discuss th ffct of fr offrs on th softwar diffusion rocss and subsquntly th NPV of futur sals. Numrical xamls ar also rovidd in ths two sctions. Conclusions and discussions ar includd in th last sction. Diffusion Modls h most widly acctd diffusion modl for durabl consumr goods is th Bass Modl (Bass 1969). In this sction, w brifly discuss th Bass Modl and on xtnsion by Mahajan and Ptrson (1978) that has a baring on our rsarch. h Bass Modl is valid only for initial adotions of consumr durabls. h most imortant assumtion mad in th modl is that th robability a customr will mak a urchas at tim givn that no urchas has bn mad is a linar function of th numbr of rvious adotrs by tim. his is somtims rfrrd to as th word-of-mouth ffct. h mathmatical form of th assumtion is shown in quation (1). f ( ) /[1 F ( )] = + ( q / m) Y ( ), (1) whr m, and q ar constant aramtrs rrsnting th total numbr of otntial adotrs, th cofficint of innovation, and th cofficint of imitation, rsctivly. Y() is th total numbr of adotrs by tim. f() is th liklihood of urchas at and its cumulativ form is F(). Basd on this assumtion, w can obtain th sals rat at tim as shown in quation () and th total numbr of initial adotions by tim as shown in quation (3). h original drivation can b found in Bass. S( ) m( + [( q / ) = () m (1 Y ( ) = S( t) dt = m f ( t) dt = mf ( ) = ( q / ) + ) 1 (3) Figurs 1 and show th sha of th sals rat curv undr two diffrnt conditions, namly, q > and q #. If q >, sals rat rachs its ak at tim * = [1/( + ] Ln( q / ). If q #, sals rat dcrass monotonically with tim. h Bass Modl dos not tak into considration th dcision variabls such as ric, advrtismnt, and romotions. In this modl, th total numbr of otntial adotrs is assumd to b a fixd constant. As an xtnsion, a dynamic diffusion modl roosd by Mahajan and Ptrson assums that th numbr of otntial adotrs is a function of som xognous and ndognous variabls, such as ric. his allows us to st th original aramtr m in th Bass Modl to b a function of ric, dnotd by m(r). W assum that m is a non-incrasing function of ric. For xaml, m() = m(p), whr m(), m(p) dnots th numbr of otntial adotrs at ric, P, rsctivly, and P >. h Valu of a Nw Softwar Product to a Monoolist Firm Sinc th Bass Modl modls only th initial urchass of consumr durabls, for most hysical roducts, th sals rat curv stimatd using th modl will no longr b valid aftr a crtain tim riod bcaus of rurchass. Howvr, th rstriction dos not xtnd to softwar roducts. Softwar dos not war out and can gnrally b consumd ovr a long riod of tim. Nowadays, it is a common ractic for softwar roducrs to rovid fr udats to rviously urchasd softwar and thrfor th sam vrsion of a softwar is only urchasd onc by a consumr. For this rason, w assum that all softwar urchass ar initial urchass and thrfor th Bass Modl is valid for th ntir duration of th lif cycl of a givn softwar vrsion wnty-fourth Intrnational Confrnc on Information Systms

4 Jiang & Sarkar/Fr Softwar Offr and Softwar Diffusion S() S() * Figur 1. Sals Rat (q > ) Figur. Sals Rat (q < ) Softwar roducts ar costly to dvlo and cha to roduc and distribut. hrfor, a common assumtion mad about softwar roducts in th litratur is that th marginal cost of softwar roduction is zro. With this assumtion, softwar roduct dvlomnt cost can b considrd sunk cost as soon as th softwar is rady for rlas. Consquntly, maximizing th nt rofit is quivalnt to maximizing th nt rsnt valu of th total sals throughout th softwar lif cycl. For simlicity, w assum that th unit ric of th softwar is 1. Basd on sals rat in th Bass Modl, th NPV of futur sals of a softwar roduct can b rrsntd by V in quation (4). V whr r is th discount rat. = S + t rt rt ( t) dt = dt + t m( + [( q / ) (4) Although th closd form intgral of quation (4) is difficult to obtain, som of its rortis can b asily infrrd. Proosition 1. V incrass monotonically with, q, and m, and dcrass with r. All roofs of roositions ar in th Andix. In th following two sctions, w will show how a softwar firm can achiv a highr V by giving away fully functional softwar fr of charg for a riod of tim. W will considr two cass in this articl. Cas I discussd in th nxt sction assums that thr ar qual numbrs of otntial adotrs at a constant ric P and ric zro. In th subsqunt sction, w analyz cas II, in which w assum that thr ar mor otntial adotrs at ric zro than at ric P. W will show that a softwar firm is in a mor advantagous osition whn cas II is tru. Howvr, vn in cas I, th lss advantagous cas, a monoolist softwar firm can still bnfit from a fr offr. For simlicity, w assum that in both cass th fr vrsion and th latr aid vrsion ar xactly th sam. h aid softwar is sold at a fixd ric P throughout th softwar lif cycl. In both cass, w assum that fr cois ar givn to a numbr of consumrs in a vry short riod of tim (assum instantanously); howvr, only thos blonging to m() (which also includs m(p)) will install and us th fr softwar. h rst of th fr softwar rcivrs will simly discard th softwar sinc it is of no valu to thm vn if it is fr. W also assum that all adotrs will hav th sam word-of month ffct in th softwar diffusion rocss, whthr thy aid for th softwar or not. h Powr of Fr Offr: Cas I ( m() = m(p)) In this sction, w assum that th numbrs of otntial buyrs at ric P and ric zro ar qual, i.., m() = m(p) = m. his is a rasonabl assumtion if ric lasticity quals zro whn ric is btwn zro and P, or if th diffrnc in th numbrs of otntial customrs at ric P and ric zro is ngligibl. 3 wnty-fourth Intrnational Confrnc on Information Systms 883

5 Jiang & Sarkar/Fr Softwar Offr and Softwar Diffusion Fr Offr S() τ -τ Figur 3. Fr Offr at th Bginning Figur 4. Shiftd Diffusion Curv Basd on th rvious assumtions, w can imagin th rocss of fr offr undr cas I. Assum n out of m otntial consumrs rciv fr cois and adot it instantanously. hs n consumrs will nvr buy th softwar again bcaus th fr coy has th sam functionality as th latr aid vrsion dos. Aftr th fr offr nds, th softwar firm chargs a fixd ric P until th lif cycl of th softwar nds. h softwar firm achivs a highr starting sals rat bcaus of th word-of-mouth ffct of th n fr adotrs, at th ric of losing th otntial rvnu from ths consumrs rmanntly. his ractic is quivalnt to byassing th bginning ortion of th diffusion curv and starting from a tim J that is gratr than, as shown in Figur 3. It can also b intrrtd as th diffusion curv bing shiftd to th lft by J units of tim, which is shown in Figur 3. J can b stimatd from quation (5). τ = m + qn ln[ ] ( m n) + q (5) Now th nt rsnt valu of th total sals throughout th softwar lif cycl bcoms V ( τ ) m( + [( q / ) t r( t τ ) = τ t dt (6) hrfor, dciding th otimal numbr of fr offrs is an otimization roblm as shown in quation (7). Max V ( τ ) τ m( + [( q / ) t r( t τ ) = τ t dt (7) Onc again, w driv som intrsting rortis of th otimization roblm although w can not gt a closd form solution for quation (7). hy ar statd in roositions and 3. Proosition : Suos th sals rat rachs its ak at tim *. It will nvr b otimal to hav J > *. If q #, th otimal J* quals. Proosition 3: If a softwar roducr lans to giv fr offrs, th arlir thy ar offrd, th bttr, which imlis that fr offrs should b givn at th bginning riod of th markting rocss. Sinc w cannot obtain th closd form solution of V(J), w us numrical mthods to xamin th rlationshi btwn V and J. h thr aramtrs w us ar m = , =.64, and q =.5. W st th discount rat r =.1. h rdictd diffusion curv is shown in Figur 5. W calculatd th total NPV at diffrnt numbrs of fr offrs. From th numrical rsult, w find that V(J) rachs its maximum 6538 at J* = 8.9, as shown in Figur 6. h rsult clarly suorts our claim that a softwar firm can b bttr off by just giving away fr fully functioning softwar without any limitation at th bginning riod of th markting rocss wnty-fourth Intrnational Confrnc on Information Systms

6 Jiang & Sarkar/Fr Softwar Offr and Softwar Diffusion Diffusion Curv 5 V Changs with τ Sals Rat v im τ Figur 5. Estimatd Diffusion Rat Figur 6. NPV Changs with Numbr of Fr Offrs for Cas I h Powr of Fr Offr: Cas II (m() > m(p)) In th rvious sction, w assum that thr ar qual numbr of otntial buyrs at ric P and ric zro. Undr this assumtion, all fr offrs go to customrs who can also afford th softwar at a ric of P. h softwar firm loss otntial rvnu from ths customrs rmanntly. A mor gnral assumtion is that thr ar mor otntial customrs at ric zro than at ric P. In this sction, w xamin th ffct of fr offr on softwar diffusion and thus th NPV of th futur sals undr this mor gnral assumtion. Sinc thr ar mor otntial usrs at ric zro than at ric P, whn fr softwar is offrd, a ortion of th fr adotrs will b from m(p), th grou of high-valud adotrs, and th rst from m() m(p), th grou of low-valud adotrs. W assum that th total numbr of fr adotrs is (1+ 8)n, of which n ar high-valud adotrs, and 8n ar low-valud adotrs. W assum that 8 is a constant that dtrmins th ratio of low-valud and high-valud fr adotrs, and n is a dcision variabl to b otimizd. Similar to th situation in cas I, th firm will bnfit from th word-of-mouth ffct of ths (1 + 8)n adotrs; howvr, th firm only loss th otntial rvnu from thos n high-valud fr adotrs, sinc th low-valud adotrs will not buy at ric P. If w nglct thos low-valud adotrs, w find that cas II is xactly th sam as cas I. Fr offr to th high-valud adotrs is quivalnt to shifting th diffusion curv to th lft by som unit of tim J. If w tak th low-valud adotrs into account and modify th liklihood in quation shown in (1), w find that this is quivalnt to incrasing by (q/m)8n, which is shown in quation (8). W lt M = m(p) for simlicity. f ( ) /[1 F( )] = + ( q / M ) [ Y ( ) + λ n] = + ( q / M ) λ n + ( q / M ) Y ( ) = whr = + ( q / M ) λ n. + ( q / M ) Y ( ) (8) Now w can formulat th otimization roblm for cas II to dcid th otimal numbr of fr offrs. his tim w maximiz V with rsct to n. Max V ( n) n M ( + [( q / ) + t r ( t = τ ) dt τ + t whr = + ( q / M ) λ n, M + q n ln[ ] ( M n) τ = + q and (9) 3 wnty-fourth Intrnational Confrnc on Information Systms 885

7 Jiang & Sarkar/Fr Softwar Offr and Softwar Diffusion V vrsus n 3 5 V n Figur 7. NPV Changs with th Numbr of Fr Offrs for Cas II Using th sam aramtrs as in th rvious sction (M = , =.64, q =.5, and r =.1), and stting 8 =.8, w conduct th numrical analysis and find that th otimal numbr of fr offrs n* is 965 (shown in Figur 7) and J* quals V* is at this otimal amount of fr offr, which is gratr than 6538, th V* obtaind for cas I. h rsults suort our claim that cas II is mor advantagous than cas I for a softwar roducr. If w dnot th total numbr of fr adotions by N, thn N /( 1 + λ) of thm go to high-valud adotrs. Clarly, if 8 =, cas II bcoms cas I. If 8 = 4, all fr offrs go to low-valud adotrs. h latr cas turns out to b th bst ossibl scnario for a softwar firm, sinc by fr offr, it can achiv a highr diffusion rat without losing any otntial rvnu from its high-valud customrs. hrfor, a softwar firm should always try to targt fr offr to low-valud adotrs. Conclusions and Discussions In this study, w hav shown that a softwar firm can b bttr off by giving away fully functional softwar at th bginning riod of th markting rocss, vn if othr bnfits such as ntwork xtrnality do not xist. If othr bnfits xist, th acclratd diffusion rocss w hav shown in this study will b an additional advantag. As art of th ongoing rsarch, w ar conducting snsitivity analysis on four aramtrs, namly,, q, r, and 8. W ar also xtnding our modl to xamin th ffct of fr offr in comtitiv markts. In a comtitiv markt, fr offrs can b mloyd not only as a markting tchniqu to incras th nt rsnt valu of futur sals, but also as a way to gain a gratr markt shar or vn driv comtitors out of th markt. Howvr, if all firms giv fr offrs, th rofitability to all firms may dclin. Som of th assumtions w mad in th study can b rlaxd for futur xtnsions. W assum that fr softwar is offrd without any rstriction. W will xamin th ffct of fr offrs with contnt or tim rstrictions in futur studis. In th ar, w also assum that adotions of fr softwar han instantanously. his assumtion can b asily rlaxd. According to our numrical analysis, th qualitativ rsult of our study still holds as long as fr offrs last for a rlativly short riod of tim. On can argu that charging a low ric instad of making a comltly fr offr may b a bttr otion for a softwar firm. W will tak this and othr factors into considration in our futur rsarch. Rfrncs Bass, F. M. A Nw Product Growth Modl for Consumr Durabls, Managmnt Scinc (15:5), January 1969, Docknr, E., and Jorgnsn, S. Otimal Advrtising Policis for Diffusion Modls of Nw Product Innovation in Monoolistic Situations, Managmnt Scinc (34:1), January 1988, wnty-fourth Intrnational Confrnc on Information Systms

8 Jiang & Sarkar/Fr Softwar Offr and Softwar Diffusion Gallaughr, J. M., and Wang, Y. Ntwork Effcts and th Imact of Fr Goods: An Analysis of th Wb Srvr Markt, Intrnational Journal of Elctronic Commrc (3:4), Summr 1999, Haruvy, E., and Prasad, A. Otimal Product Stratgis in th Prsnc of Ntwork Extrnalitis, Information Economics and Policy (1:4), Dcmbr 1998, Kalish, S., and Lilin, L. G. Otimal Pric Subsidy Policy for Acclrating th Diffusion of Innovation, Markting Scinc (: 4), Autumn 1983, Krishnan,. V., Bass, F. M., and Jain, D. C. Otimal Pricing Stratgy for Nw Products, Managmnt Scinc (45:1), Dcmbr 1999, Mahajan, V., and Ptrson, R. A. Innovation Diffusion in a Dynamic Potntial Adotr Poulation, Managmnt Scinc (4:15), Novmbr 1978, Schiff, A. h Economics of On Sourc Softwar: A Survy of th Early Litratur, Rviw of Ntwork Economics (1:1), March, Andix Proofs of Proositions Proof of Proosition 1: Conclusion for r and m ar straightforward by xamining quation (4). o rov that V incrass with and q, w assum that w can lot th liklihood of adotion against th numbr of adotrs. Basd on quation (1), at vry oint on th X-axis, th liklihood of nxt adotion bcoms highr if or q incrass, which imlis that th xctd tim intrvals btwn all conscutiv futur adotions dcras. hrfor, th tim discount factor bcoms smallr for all adotions. Proof of Proosition : According to cas I, fr offr is quivalnt to shifting th diffusion curv to th lft by J units of tim. If w shift th curv by * units of tim, th curv bcoms a monotonically dcrasing curv. W dnot this curv by S. If w lt J > *, which imlis that w furthr shift S to th lft, th nw curv will b comltly blow S. hrfor, J > * will nvr b otimal. Proof of Proosition 3: Suos fr offrs ar givn at tim f $ and n out of m otntial adotrs rciv fr offrs and adot thm instantanously. Lt us ignor th fr adotrs and rdfin a diffusion rocss D' for th aid adotrs only. W dnot th total numbr of aid adotrs by m', th cumulativ numbr of aid adotrs by tim by Y'(), th liklihood of urchas by aid adotrs at tim by f'() and its cumulativ form by F'(). h cofficint of innovation and th cofficint of imitation for D' ar dnotd by ' and q', rsctivly. Bfor f, th liklihood quation for D' can b obtaind from quation (A1). f '( ) /[1 F '( )] = ' / m' ) Y '( ), whn < f. (A1) Aftr f, th word-of-mouth ffct of th n fr adotrs incrass th liklihood of aid-adotions. Aftr transforming th liklihood quation as shown in quation (A), w conclud that this is quivalnt to incrasing th cofficint of innovation from ' to f for D'. f '( ) /[1 F '( )] = ' / m')[ Y '( ) + n] = ' / m' ) n / m') Y '( ) = f / m') Y '( ) (whr f = ' / m') n), whn >. f (A) Similar to th roof of Proosition 1, w lot th liklihood of aid adotions against th numbr of aid adotrs. h X-axis is dividd into two arts by f. h art lft of f rrsnts th adotions bfor th fr offr, and th art right of f rrsnts th adotions aftr th fr offr. In th lft art of th diffusion rocss, th cofficint of innovation is ', and in th right art, ' is incrasd to f. Following th intr-adotion tim logic usd in th roof of Proosition 1, w conclud that th arlir fr offrs ar givn, th bttr. 3 wnty-fourth Intrnational Confrnc on Information Systms 887