Note: Ti aer i a reque to te new tudy to be reented on May, 00. Handout of te ide wi be rovided at te tak. Market Segentation for Inforation Good wit Network Externaity Bing Jing Abtract Poitive externaitie caracterize te conution of a ajority of inforation good uc a oftware and onine content ervice incuding virtua counitie. We ow tat network externaity i critica for te arket egentation and roduct ine tructure of uc inforation good. A onooy of utie exiting roduct offer exacty two ditinct quaitie. Eentia for uc a iited egentation reut i te coeentary effect between te two roduct due to externaity. In articuar, te ow quaity oud be offered for free under very genera condition. Wen deveoent cot are taken into account, te ow quaity i deveoed ony if te gain in revenue due to an enarged network exceed te extra deveoent cot. Facing ig-end coetition, a ow-end eer never egent i arket. Te ig-end eer ay cooe to offer two roduct if e oee a cear-cut quaity advantage. (Inforation Good; Network Externaity; Market Segentation; Product Line Pricing Acknowedgeent: Ti aer a ignificanty benefited fro te coent and uggetion by te Aociate Editor and tree anonyou referee. He fro Mara Freier, Roy Jone, Jon Long, and Abraa Seidann i ao vauabe. A reaining error are te oe reonibiity of te autor. 1
1 Introduction Inforation a been art of uan civiization, even toug te ter inforation good ony gained ouarity recenty. TV rogra, book, digita iage, oftware, and onine trading ervice are a exae of inforation good. A defining roerty of inforation good i tat te firt coy i coty to ake but te cot of reroducing te ubequent coie are negigibe (Sairo and Varian [1999]. By ti criterion, inforation good ay be ore revaent tan we tink: te roduct deign buit into te nuerou yica good uc a car and aircraft are ao inforation good. Te roinence of inforation good a been rooted by wave of new tecnoogie. Te boo of erona couter ade ackaged oftware tandard cooditie in te 1980. In te at decade, te roiferation of te Internet a brougt about even ore varietie of inforation good and coey tied te to our everyday ive. Interetingy, a vat aount of inforation good on te Internet are freey avaiabe, wic ave recirocated te raid adotion of tee new tecnoogie. Many inforation good uc a oftware and onine content incuding onine counitie deontrate aient conution externaitie: te arger te uer bae, te greater te uer erceived vaue. Te network externaity in oftware i due to te cae econoie in uage, uc a excange of data and earning ti. Meber in a virtua counity contribute and are a ignificant ortion of te content (Hage and Artrong [1997]. In ti aer, we focu on te roe of externaity in te arket egentation of uc inforation good and rovide a new teoretica underinning for free inforation good fro te erective of roduct ine eection. Te current aer draw uon tree ine of exiting reearc: network externaitie, vertica roduct differentiation, and inforation good. Econoit firt reaized tat conuer
of any roduct benefit fro te roduct intaed bae a we a teir intrinic utiitie. Te teecounication indutry i a caica exae (Rof [1974] and Oren and Sit [1981]. Suc arket wit network externaitie (or network arket ave roertie not deontrated in conventiona arket: bot arket itory and conuer exectation about te utiate network ize are crucia to network foration. Due to tee idioyncraie of network arket, an inferior roduct ay beat a uerior one (Artur [1989], Farre and Saoner [1986]. Tee unique feature coicate te coeting trategie of fir oerating in a network environent, uc a roduct coatibiity, tecnoogy onori, enetration ricing, and roduct reannounceent (Katz and Sairo [1985,1986], Farre and Saoner [1986]. Aong tee trategie, enetration ricing i of articuar reevance to u. A cear reaon for offering ow rice (even beow argina cot i to obtain an intaed bae advantage at te exene of ort-run rofit acrifice. In te cae of inforation good wit negigibe argina cot, ti invove giving away roduct for free (Been and Farre [1994], Sairo and Varian [1999]. In te context of yte coetition (uc a Acrobat Reader and Ditier, te vendor of te yte ay ower te rice of one roduct (to even zero to gain better contro over te arket of te coeentary roduct (Katz and Sairo [1994], Parker and van Atyne [1999]. In contrat to te redatory ricing and cro-ubidization exanation for te arket roviion of free inforation good, our reearc draw uon te teory of roduct ine ricing to ow tat a onooy ay ao offer a free ow quaity roduct to exand te network for it ig quaity roduct. Foowing te ead of Hoteing [199], ater econoit introduce ode of vertica differentiation in wic a conuer refer te iget avaiabe quaity but differ in teir argina wiingne to ay (Gabzewicz and Tie [1979], Mua and Roen [1978]. Mua 3
and Roen [1978] etabi te otiaity of inducing conuer ef-eection via rice dicriination. In a ie and eegant ode, Saked and Sutton [198] ow tat fir can reduce rice coetition by differentiating teir roduct. A univera aution in ti iterature i tat eac conuer a a contant argina wiingne to ay for quaity (Moorty [1988], Saant [1989], Tiroe [1988], wic wi be inerited in ti aer. To our bet knowedge, tere are tree tudie exaining te network externaity aect of oftware, but none of te addree te iue of arket egentation. Conner and Ruet [1991] ow tat no rotection can be te bet oicy againt iracy in certain circutance. Two ore recent tudie (Brynjofon and Keerer [1996], Gaauger and Wang [1999] eiricay invetigate te iact of network effect on oftware rice, wit te atter treing te roe of free good. By reducing te cot for ditributing inforation, te Internet a otigted te iortance of inforation good and inired ronounced reearc interet in teir econoic iue. Bunding unreated inforation good i own to be uc ore rofitabe tan eing te earatey and arger bunde can better coete againt aer one (Bako and Brynjofon [1999,000]. Dewan et a [000] tudy ow a rorietary content rovider can bet organize i ditribution canne in te Internet etting. Extending te ode of Moorty [1988], Jone and Mendeon [1998] exaine te roduct and rice coetition for generic inforation good witout network externaitie. Auing a quadratic cot of roduct deveoent, tey coute te otia roduct oitioning and ricing under aternative arket tructure (wefare axiization, onooy, duooy, and oigooy. One tarting reut tey obtain i tat a uti-roduct onooy wi not egent i arket by eing ony te iget quaity 1. Reaizing tat any iortant 1 Ignoring externaity and adoting a rare aution tat eac conuer a a decreaing argina wiingne to ay for quaity, Varian [1997] ow tat quaity differentiation can be otia. However, Varian reut i not 4
inforation good do deontrate aient externaitie, we incororate network externaity and tigty focu on it ignificant iact on te arket egentation for uc inforation good. We ow tat, wit externaity, te eer i incined to exand te engt of i roduct ine to arvet te axiu network benefit. Our finding can better exain te ouar ractice of offering quaity-differentiated roduct and giving away te ow-end roduct for free aong near-onooy vendor uc a rorietary content rovider (e.g., WSJ Interactive, AOL, etc.. Our ajor contribution i two-fod. Firt, te critica roe of externaity in te arket egentation for inforation good i ceary own in bot onooy and duooy etting. Wit externaity, a onooy of utie exiting roduct wi adot iited egentation by roviding no ore tan two roduct. Coetition i own to retrain a fir abiity to rice dicriinate. Market egentation wit exiting roduct a ignificant bearing for deterining te roduct ine tructure of inforation good wen deveoent cot are taken into account. Second, we rove tat wen te ow quaity i deveoed, it oud be offered for free under very genera condition. Te free ow-quaity roduct i eentia for exanding arket coverage and enancing conuer vauation of te ig quaity. Te ret of te aer i organized a foow. A ode i reented in Section. Section 3 exaine a onooy otia deign and ricing of a roduct ine. Fir arket egentation reent coetition i anayzed in Section 4. Section 5 dicue our iitation and oint out otentia extenion. Te Aendix contain a notation tabe and te roof of Prooition, wic i engty but not eentia for te ogica fow of te aer. Mode rereentative a i baic aution deviate fro tat of te broad iterature of vertica differentiation. See Section 6 for an exanded dicuion. 5
Our baic fraework i iiar to tat of Katz and Sairo [1985] and te way we incororate network externaity i due to Conner [1995], wic exaine te otia coning trategy of an innovator..1 Conuer Preference Eac conuer a a deand for at ot one unit of te inforation good. Conuer wiingne to ay i unifory ditributed on [ A,1 ] wit denity 1, were A i a finite oitive nuber. Abent externaity, a conuer ay erceive a diutiity if te cot of adoting te inforation good exceed it intrinic vaue for i. Ti i refected by te negative egent in conuer ditribution. A conuer of tye θ vaue quaity contant argina wiingne-to-ay or tate. at θ. Here θ i te conuer In our one-eriod ode, rationa conuer for identica exectation about te utiate network ize and ake correonding coice. Te equiibriu concet we deoy i te o-caed Fufied Exectation Equiibriu, i.e., te ex ot equiibriu network ize i exacty a exected by conuer rior to teir urcae (cf. Katz and Sairo [1985]. A fir foow a Stackeberg trategy vi-à-vi conuer and fir in a duooy foow Na riceetting trategie vi-à-vi eac oter.. Te Network Benefit Network externaity increae eac conuer tate by Q, were Q i te intaed bae or network ize of te inforation good and i te externaity intenity wic refect te increae in wiingne to ay wen an additiona conuer join te network. Externaity intenity i a concetua etric for te interdeendence aong conuer, and different Bot Katz and Sairo [1985] and Conner [1995] aue A to be infinity to focu on te arket-not-covered cae. Our aution for A to be finite i ore reaitic and doe not caue tecnica difficutie, a we a ee ater. 6
inforation good ay ave different agnitude of externaity intenity. For exae, onine counitie and roductivity oftware tyicay deontrate tronger externaity intenitie tan reguar onine content and ot couter gae, reectivey. Wen urcaing roduct in a network of ize Q at rice, conuer θ obtain net utiity ( θ + Q. In te jargon of Farre and Saoner [1986], θ i te roduct networkindeendent or tandaone vaue, wic deend on bot conuer tate and roduct quaity. Te network-generated vaue i Q and exibit coeentarity between network ize and quaity. Terefore, in te ae network, a ig quaity a bot iger tandaone and network vaue tan a ower quaity (ee Figure 1. For exae, eai uer do benefit fro uc advanced feature a auto rey and inine eing cecker, wic e te uer convey an iage of being oite and carefu. To be reaitic, we ioe a ower bound * on quaity for a * roduct to create network benefit, i.e., te feaibe region for roduct quaity i [,. In Katz and Sairo [1985] and ot oter reearc on network externaity, roduct are oogeneou and conuer differ in teir tota wiingne to ay 3 ; te network-generated benefit ony deend on te network ize. Vaue ($ θ θ Q Q 0 Q Network Size Figure 1. Te tandaone and network-generated vaue of roduct and ( > for conuer θ. 7
Te araeter in our ode aow ric intuitive interretation, but not a of te can be oerationaized. Since we focu on te arket for conuer inforation good, network ize can be eaured by te tota ae of a roduct (or coatibe roduct. However, bot externaity intenity and quaity are concetua in nature and ard to eaure..3 Hig-to-Low Verioning In eecting it roduct ine, te fir deveo te ig-end verion firt and ten degrade to obtain ower quaity verion. Inforation good vendor uuay adot uc a igto-ow or vaue-ubtraction verioning trategy to exoit te cot aving in content, deign, and code reue (Deneckere and McAfee [1996], Sairo and Varian [1999]. A our eai i on te tructure of te roduct ine, not te exact oitioning of te ig quaity, we do not ecify a cot function for deveoing te ig quaity. We ony odety aue te cot for deveoing te ow quaity after te ig quaity i buit, f, i non-decreaing. Inforation good ave zero argina cot trougout ti tudy. ( 3 Market Segentation in a Monooy To deterine a onooy otia roduct ine tructure, we firt ave to identify i arket egentation oicy wit a et of exiting coatibe roduct 4. Terefore roduct deveoent cot i not conidered unti ubection 3.. 3.1 Market Segentation Conider a onooy offering a ow quaity roduct at rice and a ig quaity * roduct at rice ( <. To avoid triviaity, aue <. Denote θ to be te 3 An excetion i Farre and Saoner [1986], wo conider eterogeneou tecnoogie but aue conuer are oogeneou. 4 Obviouy, a onooy wi ake coatibe roduct to take fu advantage of te network effect. 8
conuer indifferent between urcaing and doing noting and θ te conuer indifferent between urcaing and. We tu ave ( θ Q = 0 (1 + and ( θ + Q = (θ + Q, ( were Q i te tota exected (and ao reaized ae of te two roduct. It i eay to verify tat ( θ + Q > ( θ + Q θ < θ 1 and tat ( θ + Q > ( θ + Q θ θ < θ. Terefore conuer in [ θ, θ wi urcae and conuer in [ θ,1] wi urcae, a own in Figure beow. A θ Purcae Purcae 0 θ 1 Figure. Market egentation of a two-roduct onooy. Te equiibriu tota ae of te two-roduct onooy atify Q = 1 θ. (3 Fro (1 and (3, we ave ( Q =, (4 (1 and θ ( =. (5 (1 9
For te ake of anaytica tractabiity, we aue A < to focu on te arket-not-covered A +1 cae even wen te ow quaity i free ( = 0. Pugging (4 into (, we obtain θ =. (6 ( (1 Notice tat θ and θ can take negative vaue. Te ae of and are Q = 1 θ, (7 and Q = θ θ (8 reectivey. Te onooy cooe rice to axiize i revenue: ( Max, 1+ + (1 (9.t. 0. Te oter contraint > i guaranteed wenever > 5 and tu not exicity incuded. An obervant reader igt ave noticed tat te network effect ony directy exand te deand for te ig quaity. Ti i due to our aution tat te network-generated vaue of a roduct i roortiona to it quaity 6. We ave te foowing Lea regarding te rice of te ow quaity. Lea 1. Wen [( ] >, = > 0. Wen (, = 0. 5 See (10 and (11 beow. 6 In a arket of verticay differentiated good, our current aution i ore aroriate tan te aternative aution tat te network-generated vaue ony deend on te network ize but not on quaity. We can verify 10
Proof: Denote λ to be te Lagrangian utiier for te contraint. Te Kun-Tucker anayi give te otia oution: (1 [ λ ( + ( λ ] * * * =, (10 ( * [ + ( + (1 λ ] =, (11 * ( and λ * * = 0. (1 Lea 1 ten foow fro (11 and (1. Q.E.D. roduct. Ceary, te onooy otia oution deend uon te reative quaitie of te two Cae 1: Wen. Fro Lea 1, te onooy otia rice are (1 = and ( [( ] =. ( Te two-roduct onooy revenue i w =. ( Te ae of and are ( = (13 Q ( tat, under ti aternative aution, te network effect directy exand te deand for te ow quaity but a no direct iact on te deand for te ig quaity. See Section 6 for a ore detaied dicuion. 11
and =, (14 Q ( reectivey. Cae : Wen <. In ti cae, te otia rice are = and = 0. Te ae of and are (1 1 Q = Q =. (15 (1 Te onooy revenue i = w. (16 4(1 Te ae of te ow quaity are not zero in eiter cae. Ti give te foowing reut. Prooition 1. Wit oitive externaity, te two-roduct onooy wi rovide bot roduct and benefit fro arket egentation. Coroary 1. Witout network externaity ( = 0, te two-roduct onooy wi ony rovide te iget quaity roduct. Coroary 1 foow fro (14 a Cae dro out of conideration wen = 0. Coroary 1 tu confir te no-egentation concuion of Jone and Mendeon [1998] wen externaity i abent. Unike indutria good (ee Moorty [1988], a ig quaity inforation good doe not ave a argina cot diadvantage coared wit a ow quaity; any inforation good a negigibe duication cot. But a iger quaity create iger vaue for 1
conuer, aowing te onooy to carge a iger rice. If te onooy enforce egentation by adding a ow quaity roduct, tota ae ay increae, but cannibaization ao coe into ay: ef-eection wi aure oe otentia buyer of te ig quaity away to te ow-quaity ow-rice roduct. Ti iit te rice tat can be carged for te ig quaity. Witout network externaity, te ae increae due to egentation i doinated by te cannibaization between te two roduct. Wit externaity, adding a ow-end coatibe roduct exand te network and eevate te network-generated vaue of bot roduct. However, te increenta vauation for te ig quaity i iger tan tat for te ow quaity (ee Figure 1. Te network effect directy increae te deand for te ig quaity roduct (ee (9 but ony indirecty raie te deand for te ow quaity roduct troug affecting te rice (ee (14 and (15. Network externaity create an ayetric coeentary effect between te two roduct, wic doinate te cannibaization effect. Wi te onooy benefit fro furter egenting i arket? It turn out tat two roduct are enoug. Prooition. Wit network externaity, a uti-roduct onooy wi not rovide a tird, interediate roduct ( < <. Te roof i deegated to te Aendix. Prooition ow tat a uti-roduct onooy adot iited arket egentation. Ti i becaue inerting an interediate quaity a ixed effect. Firt, it increae te onooy tota ae. Second, a arger network ao drive u conuer wiingne to ay. Laty, adding te idde quaity ao ae in ore 13
cannibaization aong tee roduct. It ee tat te reuting iger ae and network benefit do not jutify te exacerbated cannibaization. Two roduct can acieve te bet baance between fuy exoiting te network effect and iniizing cannibaization. Wen, fro (13 and (14 we can find te onooy tota ae and te arket are of and. Taking te derivative of rice, ae, and arket are wit reect to, we obtain te foowing reut. Prooition 3. Wen, tronger externaity intenity induce iger rice for te ig quaity roduct, ower rice for te ow quaity roduct, arger ae for bot roduct, but a aer arket are for te ig quaity roduct. Price.5 1.5 1 0.5 0. 0.4 0.6 0.8 Figure 3. Monooy rice adjutent to tronger externaity intenity. Paraeter vaue: = ; = 3; [0,0.8] Surriingy, wen externaity intenity increae, te onooy adjut te rice of te two roduct in ooite direction (ee Figure 3. Facing tronger externaity intenity, te onooy a a greater incentive to enarge i network, wic neceitate a ower rice for te 14
ow quaity (ee (4. An exanded network iie iger conuer wiingne to ay. Te onooy ten raie te rice for te ig quaity, aking iger rofit. Intuitivey, te two roduct erve ditinct uroe: te ow quaity e infate te network and te ig quaity extract te network benefit and i te riary ource of revenue. 3. Product Line Seection We ave own tat a onooy of utie exiting roduct ony activey e two of te. We next deterine te otia oitioning of te ow-end roduct if it deveoent cot jutify te increae in revenue due to an exanded network. We can eaiy verify te foowing: wen w, = < 0, (( and wen w 1 <, = 0 4(1 <. For any given ig quaity, onooy revenue i decreaing in te ow quaity (ee Figure 4. However, te cot of deveoing, f, i ( non-decreaing by aution. Togeter wit Lea 1, ti ead to Prooition 4. Revenue (1 ( 4(1 0 * * Figure 4. Monooy revenue a a function of ow quaity ( <. 15
* * Prooition 4. Wen, te onooy deveo a ow quaity of = if f * * ( ( * ; wen 4(1 <, te onooy deveo a ow quaity of * * * * = if f ( 4(1. In articuar, te otia rice for te ow quaity i = 0 wen *. Wen deveoing bot roduct, te onooy away et te ow quaity at te treod feaibe quaity and ay offer te ow-end roduct for free if it i beow a certain fraction of te ig quaity. Offering te ow-end roduct for free i an extree verion of uing te ow quaity to exand network coverage and uing te ig quaity to extract conuer uru, a ointed out earier. Buit uon te teory of roduct ine ricing, Prooition 4 ed igt on te roviion of free inforation good by onooy vendor. Wen taking deveoent cot into account, te onooy rovide at ot two ditinct quaity eve. Rooted in a tyized, abtract odeing etu, uc a rediction can find it uort in nuerou rea-word obervation. Onine eriodica often offer oe baic artice for free browing but require ubcrition or a fee for acceing te fu-featured artice. Siiary, it i not atyica for onine broker (uc a E*Trade to offer one et of free ervice and one et of reiu ervice to teir account oder. Gae ayer can downoad free, unregitered verion of couter gae wit iited ayabe eve, but ave to ay to obtain te fu verion (www.cnet.co. 16
We ao oberve tat any vendor of roductivity oftware, uc a office uite and Enterrie Reource Panning (ERP yte, do not iutaneouy carry utie verion wit ditinct quaitie. Ti i becaue, for ti kind of oftware, carving a coerent ow-quaity verion out of a ig-quaity one take treendou effort. In te ean tie, teir coartentaized roduct tructure ideay uit te for anoter ouar differentiation knack bunding. 4 Market Segentation in a Duooy In ti Section, we exaine ow coetition affect te arket egentation for inforation good. To eae exoition, we aue one eer roduct are a tricty uerior to toe of te oter, excuding two intereaving roduct ine. 4.1 Market Segentation wit Hig-end Coetition We firt ook at a ow-end eer arket egentation deciion. Te ig-end eer offer at rice, and te ow-end eer offer at rice and ( < < at rice 0. Teir revenue-axiizing robe are foruated a 0 0 Max ( 0 0 1+ (1 0 (17 and Max 0 0 0 + 0, (18 0, 0 0 0 reectivey. Soving (17 and (18 iutaneouy give te equiibriu rice. We can verify tat te owet quaity roduct 0 a zero ae. 17
Prooition 6. In te reence of a uerior coeting inforation good, te ow-end eer wi not egent i arket by offering ony one roduct. Te ow-end eer wi never egent i arket, regarde of externaity intenity. Becaue network externaity a no direct iact on te deand of te ow-end eer, te exanion in ae due to carrying ditinct roduct doe not offet te reuting cannibaization. 4. Market Segentation wit Low-end Coetition We now turn to te ig-end eer egentation coice. Suoe e offer at rice and at rice, and te ow-end eer offer at rice ( < <. Ti iutaneou ricing gae can be foruated and oved iiary to te one in (17 and (18. Soe ie agebraic anayi on te ig-end eer equiibriu revenue ead to te foowing Prooition. Prooition 7. Wen coeting wit an inferior inforation good, te ig-end eer doe not egent i arket by eing ony if e a an inufficient quaity advantage: 0 + 3 + 400 + 9 (4 + <. 48 Te ig-end eer refer arket egentation by adding a ower-quaity roduct ( < < wen i quaity advantage i arge enoug: 1 7 > ( 1 6. 18
For a given externaity intenity, te arket egentation deciion of te ig-end vendor criticay deend on i reative quaity advantage. Adding ( < < force te ow-end eer to ower i rice due to weaker roduct differentiation, reuting in a arger tota deand and iger conuer wiingne to ay. It ao increae te ig-end eer ae. However, coetition fro te ow-end eer iit te rice of te interediate roduct, wic furter retrain te rice of te iget quaity. Weter te gain in ae and network effect can exceed cannibaization deend uon te quaity diarity in ti duooy. Reca fro Section 3 tat a uti-roduct onooy away rovide two roduct if tere exit oitive externaity. In a duooy, te ow-end eer never egent i arket and te ig-end eer adot egentation ony wen i quaity advantage i ufficienty arge. Ti ugget tat te reence of coetition crie a eer abiity to internaize cannibaization witin i own roduct ine. Prooition 6 and 7 ave te foowing coroary a teir extree cae wen = 0. Coroary. Witout externaity, bot eer ony rovide one roduct. Abent externaity, eac coeting eer rovide a inge roduct becaue adding a econd roduct wi reut in exceive cannibaization, a in te onooy cae. 5 Concuding Reark In a etting of vertica differentiation, we ave own tat deand externaity of inforation good i crucia for teir arket egentation and roduct ine eection. Since conuer differ not ony in enitivity to quaity, in reaity arket egentation i ao 19
conducted troug uc oter tecnique a godiock ricing, cutoization, bunding, and icening. Our anayi doe not confict, and oud not be confued wit tee ractice. Sairo and Varian [1999] ention a rue-of-tub rice dicriination etod of offering tree ditinct roduct wen te caification of eterogeneou conuer i not directy addreabe (te o-caed godiock ricing. Godiock ricing i baed on a conuer ycoogy yotei of extreene averion (Sionon and Tverky [199] intead of conuer rationaity. Licening i eentiay a ecia for of non-inear ricing. Cutoization i an intance of orizonta, rater tan vertica differentiation. For exae, oftware vendor often taior deign teir roduct for different uer egent. Te ditinction between bunding and quaity differentiation i ubte and yet iortant. One bunde i aid to ave a iger quaity tan anoter if te forer acieve iger erforance on te ae et of coonent feature or if it a additiona feature tat are vaued by a uer. An entrereneur wo ony need a ubet of te odue in an ERP ackage ay not ace extra vaue on te woe yte. A i true wit a teoretica tudie, our anayi ao buid on certain aution. Te two ot crucia one are contant argina wiingne to ay (MWP for ort and te coeentarity between network ize and quaity, wic togeter render te reut of iited egentation and free ow quaity. Saant [1989] ow tat te otiaity of inducing conuer ef-eection for yica good by rice dicriination criticay inge on te curvature of cot and conuer utiity. It i ten no urrie tat Jone and Mendeon [1998] and Varian [1997] draw divergent concuion on te arket egentation of inforation good witout externaity. Even toug decreaing MWP for quantity i a we-acceted reie, contant MWP a been te nor for tudying vertica differentiation ince te ate 1970, due to it virtue of being ie and yet reaonabe. Te botto ine of ti aer, owever, i indeendent 0
of te contant MWP aution: a onooy of inforation good a an incentive to extend te an of i roduct ine to take fu advantage of te network effect. In tudying te network externaity of oogeneou good, it i natura to aue tat te network-generated vaue ony deend on te network ize. However, te ae aution ay not be a aroriate wen aied to differentiated good. For exae, te (networkgenerated vaue of a teeone wit ore advanced feature ike ca waiting or caer ID i ceary iger tan a one witout tee feature. Farre and Saoner [1986] firt erit different network-generated benefit for eterogeneou tecnoogie and Conner [1995] exicity ake te network-generated benefit roortiona to quaity. In our aer, due to te coeentarity between network ize and quaity, te network effect doe not directy enarge te deand for te ow quaity inforation good. Our inge-eriod ode entai a ig-to-ow verioning trategy, wic i te foundation for Prooition 4. A inge-eriod ode inevitaby ignore te inter-teora aect of network foration and roduct innovation. Even toug tere exit a ric iterature on roduct innovation for yica good [Levinta and Puroit 1989, Reiganu 1981], reearc on te quaity iroveent and ugrading oicy of inforation good uc a oftware i ti rare. Terefore one iortant extenion woud be to devie a uti-eriod ode to exaine externaity roe in roviding ucceive verion of inforation good wit iroving quaitie. In addition, conuer uru i not addreed in ti tudy. Anoter direction wortwie uruing i to ook at te wefare iact of arket egentation. 1
Aendix Tabe 1. Suary of Notation f ( Cot of deveoing a ower quaity roduct after a iger quaity i in ace. Price. ( Price of te ig (ow quaity roduct. Q Network ize or tota ae of a roduct or coatibe roduct. Q (Q Sae of te ig (ow quaity roduct. Product quaity. ( Quaity of te ig- (ow- end roduct. * w θ θ θ π Te iniu quaity eve for te inforation good to generate network benefit. A contant. Seer revenue. Conuer tye or argina wiingne to ay for quaity. Te conuer indifferent between urcaing te ig- and ow-quaity roduct. Te conuer indifferent between urcaing te ow-quaity roduct and not urcaing. Externaity intenity, or te degree of conuer interdeendence. Seer rofit. Proof of Prooition : We coete te roof for tree earate cae, ince te objective function a different foruation deending on te reative araeter vaue. Cae 1: Wen. Te onooy robe of roviding tree roduct,, and ( < < can be foruated a Max W ( ( 1+ (1 + + (A1, were tand for te vector (,., Te Heian atrix of ti robe i
= ( (1 (1 H Denote by te eading rincia ubatrix of i H H deterined by te firt ( row and coun. We rove te concavity of (A1 by owing tat i. = 1,,3 i H i Heritian (ee Definition 4.1.1 of Horn and Jonon 1985 and tat 0 det 1 < H,, and det (ee Teore 7..5 of Horn and Jonon 1985. Te Heian atrix > 0 det H 0 < H 3 H i Heritian ince it i yetric. It i traigtforward to verify tat det 0 1 < H and for a quaitie uc tat 0 det H > < <. After oe agebra, we can ee tat (1 ( (1 (1 ( (1 ( ( 8 1 ( det 3 = H Te firt ter i ceary negative. Te econd and tird ter are ao negative wen. We tu ave verified te objective in (A1 i concave wen. Soving te firt-order condition give te otia rice ( (1 =, ( ] ( [ + =, and ( ] ( [ + =. 3
It i eay to ee tat te interediate roduct,, a zero ae a = 0 = θ θ > 0, wie te oter two roduct ave tricty oitive ae wen. Cae : Wen < <. In ti cae, roduct i away offered for free. Te onooy robe can be tated a Max, + 1 1 We can eaiy verify tat te ae of te interediate roduct are again zero. Cae 3: Wen < <. In ti cae, bot and are offered for free. Since a a iger quaity tan, roduct a zero uer bae, i.e., ony roduct and are activey urcaed or ued. We ave coeted te roof. Q.E.D. 4
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