Bundling in Vertically Differentiated Communication Markets

Transcription

1 unding in Verticy Differentited Communiction Mrkets Tierno Dio strct We ook t te cometition nd te wefre effects of unding in te context of verticy differentited communiction services Teevision, Teeone nd Internet. We consider twostge gme wit two symmetric firms. In te first stge firms simutneousy commit to dot unding or comonent ricing. Tese decisions give four ossie configurtions: i configurtion were ot firms use comonent ricing; ii configurtion were ot firms use unding; nd finy iii te two configurtions were one firm use unding nd te oter firm does not. In te second stge firms set simutneousy rices. We sow tt unding is dominnt strtegy equiirium for ot firms. Te reson is tt unding increses te differentition of services nd reduces te intensity of rice cometition. We so find tt toug te unding-unding equiirium reduces consumers surus, tot economic wefre is iger tn wen ot firms use comonent ricing. For comments nd discussions I tnk rm Honder, Lrs Eers nd seminr rticints t te Cometition ureu, Industry Cnd. Corresondnce: Tierno Dio, ssistnt Professor, Dértement des sciences économiques et dministrtives, Université du Quéec à Cicoutimi, 555, ouevrd de Université, Cicoutimi Quéec G7H, emi : tierno_dio@uqc.c

2 . Introduction Tody consumers re offered teeone, ig seed Internet nd teevision services y ce oertors nd teecom comnies. Ce oertors suy rodnd Internet ccess nd voice teeony in ddition to teir trdition video services. imiry, teecom comnies suy teeone, video imges nd ig seed Internet. Tyicy ce oertors nd teecoms require suscriers to tke teir trdition service nd tey offer dd-on services for n extr yment tt is ower tn te stnd one rice of tese services. Te urcse of services from singe suier is sid to e convenient for uyers. It is so sid to e deterrent to curn ecuse disointment wit one service cn e comensted y stisfction wit noter service 3. It is eieved tt te trdition teeone oertor rovides etter teeone service tn te ce oertor, weres te tter rovides etter teevision. ot offer simir quity of ig seed Internet 4. Consumers terefore ve to coose, etween ower quity teeone comined In Queec te dominnt ce oertor, Videotron rovides digit teevision, teeone nd ig-seed Internet services wit te coxi ce tecnoogy wie te dominnt teecommuniction comny, e Cnd rovides te sme services wit steite trnsmission nd twisted ir. Coxi ce is te kind of ce used y ce TV comnies etween te community ntenn nd te user omes nd usinesses. It crries rodnd services for gret distnce. To offer ig seed Internet services, ce oertor cretes dt network tt oertes over its yrid fier/ cox HFC nt. twisted ir is n ordinry coer wire tt connects ome nd usiness comuters to te teeone comny. DL Digit uscrier ine Internet ccess rovided y te oc teeone comny convert existing twisted-ir teeone ines into ccess ts for mutimedi nd ig-seed dt communictions. o wit steite nd twisted ir tecnoogies, oc teecommuniction comny cn so suy sme kind of services s oc ce oertor. Te rte t wic customer discontinues service in order to sift to cometitor - mong ig usge customers, t te exense of rofit mrgins: Keit Dmse Teecom unding seem uring customers. Grouing services togeter for ower rices uids oyty, turn curn ow. tudy sys Te Goe nd Mi, 9 etemer 003, t.38, citing Convergence Consuting Grou td study: Te tte for te Nort mericn Couc Pottoes, nd referring to Cox Communictions, extremey ow curn rte wit te trie y services of digit teevision, ig seed internet ccess, nd oc teeone services. 3 On te oter nd consumers cn dro services wen tey re disointed wit one of tem. 4 Indeed ce teeony s some imittions: e.g. it doesn t work wen tere is ower fiure nd dro out wen rodnd3.5 demnd te iity of te user to view content cross te internet tt incudes rge fies, suc s video, udio nd 3D is ig. so not res re served y te POC since yrid fier/ cox HFC nts re exensive to inst. Consequenty ddition costs of roviding services to ddition customers re iger for co-x HFC tecnoogy tn twisted ir tecnoogy. On te oter nd te teevision service of teecoms s so severe

3 wit ig quity teevision offered y te ce oertor, nd iger quity teeone wit ower quity teevision offered y te teeone comny. Tis er ddresses te foowing questions: i under wt conditions do suiers unde? tt is under wt conditions does it se two or more services s ckge ony? ; ii ow does unding comre to comonent seing in terms of wefre? ; nd iii wt ttitude soud cometition utorities dot towrd suc unding? Tere re no cer-cut resuts ertining to te rofitiity nd wefre effect of unding s oosed to serte seing of comonents. dms nd Yeen 976, cmensee 98, 984, Mc fee et 989, nd Winston 990 sow tt under monooy unding rises rofits wen vrie costs re zero. However, te vst mjority of consumer services re suied in non-monooistic environments. Ony few ers [Mtutes nd egieu, 989; Economides, 993; nderson nd Lerut, 993; Koe nd, 999] exmine te nonmonooistic cse were firms ve te otion of unding. Teses ers ssume orizont differentition of services nd teir concusions re numeric. Economides 993 considers two-stge gme nd sows tt te Ns equiirium is mixed unding 5 rter tn comonent seing. ecuse cometition is more intense under mixed unding, risoner s diemm rises, tt is firms woud e etter off if tey coud commit not to unde. nderson nd Lerut 993 sow in two-stge mode tt te Ns equiirium is ot firms offer comonents seing. Te reson is tt firms fer te extr degree of cometition intrinsic to mixed unding. Koe nd 999 reconcie te resut of Economides 993 nd nderson nd Lerut 993 y incororting te roe of mrket exnsion on equiirium unding strtegies. Tey sow tt for comementry comonents mixed unding domintes comonent seing ony wen it cretes new mrket for te unde. imittions in cometing wit ce TV. It encounters some constrints due to rodnd trnsmission, to cities rcitectures, to weter conditions nd it needs n insttion of non estetic device, te dis. 5 Mixed unding mens tt te ckges s we s te individu comonents of te ckge re vie. 3

4 Mtutes nd egieu 99 consider gme were in te first stge tere is coice etween comtiiity versus incomtiiity 6. In te second nd te tird stge of te gme firms coose te seing strtegy nd rices resectivey. Mtutes nd egieu sk weter firms woud coose to mke teir roducts comtie nd weter tey woud se teir roducts s unde. For comtie comonents, tey find tt, deending on consumer s reservtion rice tere cn e two kinds of equiiri. In te first, one firm undes nd one firm does not. In te second, ot firms unde 7. None of te forementioned ers i is concerned wit verticy differentited services; ii Tey do not give cer resuts out te wefre effect of unding. Te underying motivtion of tis er is to nyze te cometition nd te wefre effect of unding in te communiction mrket witin te context of verticy differentited services. We consider two-stge gme wit two symmetric firms. In te first stge firms simutneousy commit to use unding or comonent ricing. Tese decisions give four ossie configurtions: i configurtion were ot firms use comonent ricing; ii configurtion were ot firms use unding; nd finy iii te two configurtions were one firm use unding nd te oter firm does not. In te second stge firms set rices simutneousy. We sow tt unding is dominnt strtegy equiirium for ot firms. Te reson is tt unding increses te differentition of services nd reduces te intensity of rice cometition 8. We so find tt toug te unding-unding equiirium reduces consumers surus, te tot economic wefre is iger tn wen ot firms use comonent ricing. 6 comonent is incomtie wit comonents sod y oter firms, if it cnnot e ssemed wit tem to form use system. Te economic consequence of comtiiity versus incomtiiity ve een exmined y Mtutes nd egieu 988, Economides 989, 99, nd Einorn 99. Tey ve ooked t te cse were ec firm suied te necessry goods. 7 Te first equiirium occurs wen consumer s reservtion rice is ow, wie te second one occurs wen it is ig. 8 Cen 997 so nyzes unding s differentition too. He studies te cse were two seers comete in first mrket, nd ot so se noter roduct in second cometitive mrket. sent unding, ertrnd cometition drives ot seers rofits in te first mrket to zero. If one seer uses unding nd te oter does not, owever, ot cn ern ositive rofits since te unde nd te individu first-mrket roduct re effectivey differentited roducts. 4

5 Te er is structured s foows. In section, we resent duooy mode, were ec firm s te coice to se its services eiter sertey or s unde. In section 3, we nyze te gme. In section nd 4, we derive te equiirium seing strtegy of ec firm. In section 5, we nyze te wefre consequences of unding. In section 6, we rovide n iction of te mode to te communiction mrket nd we concude.. Te Mode Tere re two firms, denoted nd. E.g. firm is teecom comny nd firm is ce oertor. Ec firm ses two services, denoted nd. E.g. service is teeone service nd service is n Internet service. Te service comes in two quities, nd suied resectivey y firm nd firm, > 0. Te quity of service is te sme for ot > firms. ot te vrie cost nd te fixed cost re zero for ec service. Every consumer demnds one or zero unit of service of nd/or. consumer wit rmeter derives utiity i from quity i of service, i =,. imiry, consumer wit rmeter derives utiity from quity of service. If te consumer cooses not to uy service, se receives er reference utiity wic is normized to zero. consumer wit reference indices, wo uys one unit of of quity i t rice nd one unit of t rice receives net surus: U =, i =, i i Ec consumer mkes er urcse decision to mximize er consumer surus. Consumer reference indices nd re indeendenty nd uniformy distriuted on [ 0,] [0,]. i We mode te cometition s two-stge gme. In te first stge, firms decide weter to unde, or not to unde; in te second stge 9 tey set rices. Tere re four ossie sugmes t stge : i C, C denotes te gme were ot firms se comonents sertey; ii, denotes 9 Firms oserve te coices mde in te first stge. 5

6 te gme were ot firms unde; iii, C denotes te gme were firm undes, nd firm ses its comonents sertey; nd iv C, denotes te gme were firm ses its comonents sertey, nd firm undes. We wi exmine under wt conditions ec of te sugme is n equiirium. 3. Price determintion 3. Cse i: C, C, Pure Comonents y ot Firms ince ot firms roduce te sme quity of service, ertrnd cometition insures tt its rice is driven down to mrgin cost, wic is zero. Wit regrd to service, we know 0 tt n equiirium wit two ctive firms requires :. We designte y te consumer indifferent etween not urcsing nd urcsing one unit of is indifferent etween urcsing nd ~ nd for firm wen firms comete in rices., nd y ~ te consumer wo ~ for firm. Figure disys mrket sres s 0 ~ uy: Noting Figure. Mrket res under te regime C, C 0 ee Tiroe 988 Te condition sttes tt te rice er unit of quity is iger for tn for. Tis mens tt ow quity is not dominted y ig quity. If ow quity is dominted y ig quity ten te firm wit te ow quity exits te mrket. 6

7 Te firms rofits re: C, ~ C for firm, = C, ~ C for firm, = were = nd ~ =. Prices re cosen otimy wen tey stisfy te conditions eow = 4, nd = 4. Ten: 4. C C =, nd = Cse ii:,, unding y ot Firms: Denote y G nd G te rices of undes nd resectivey. Te individurtionity constrints re for consumers of for consumers of : 0, G : 0. G ef-seection constrints re for consumers of for consumers of : G G, : G G. Te condition Mx 0, must e stisfied y uyers of. Te G G condition Mx 0, must e stisfied y uyers of. G G 7

8 We find gin tt mrket res deend on te rnking of rice er unit of quity of service. To see ow, we define te reference rmeter of te consumer indifferent etween te undes nd y G G. We distinguis tree cses. Cse : Cse : Cse 3: G G G G. G nd <. G nd > In cse te rice er unit of quity of is ower tn rice er unit of quity of. In cse nd cse 3 te rice er unit of quity of is iger tn te rice er unit of quity of. Te difference etween cse nd cse 3 is tt in te tter tere is no consumer indifferent etween nd. 8

9 Cse : G G. Te rice of unde er unit of quity of service is ower tn te rice of unde er unit of quity of service. Te ines eed in Figure re te individurtionity constrints of ig nd ow quity uyers. nd G G = I 0 G Figure : Mrket res under te regime, wen G G G Te ines nd reresent te sef-seection constrint fced y consumers. Consumers wit reference rmeters ove rmeters ove derive ositive utiity from. Consumers wit reference derive ositive utiity from. We note tt,, nd intersect t I G G G G ;. Te constrints nd yied te sme ine. 9

10 Te ig quity firm serves consumers wit reference rmeters [,] nd ove ; te ow quity firm serves consumers wit reference rmeters [0, ] nd ove. Te size of mrket served y te firm is D G = nd te size of mrket served y te firm G is DG =. Firm nd firm rofits re resectivey: = =. P P GDG nd G DG In contrst to te stndrd mode of singe differentited good, we find tt tere cn e two ctive firms even wen G G 3. Te Difference is s foows: in stndrd modes of singe differentited good, consumers mke te comrison on service y service sis. If is dominted y urcses, consumers otin more surus from tn from. Noody. We so know tt for service, ertrnd cometition nd zero mrgin cost imy tt consumers otin for free from ot firms. Tus firm is excuded from mrket, ut remins in mrket. In te regime of, tere is cometition for verticy differentited system goods. Terefore, te est vie terntive for consumers wo wis to urcse ony service is to urcse te ow quity unde dominted y. In tt cse, if is te ow quity firm cn survive in ot mrkets ecuse it serves te unde to consumers wo cre very itte out service, wie te ig quity firm serves te unde to consumers wo cre for service nd for service. 3 Tt is te ow quity system is dominted y te ig quity system. 0

11 Cse : G G nd <. Te rice of unde er unit of quity of service is iger tn te rice of unde er unit of quity of service nd tere exist consumer wo is indifferent etween te undes. Mrket res re sown in Figure 3. = G G 0 Figure 3: Mrket res under te regime, wen G G I G G nd <. Te ig quity firm serves consumers wit reference rmeters [,] nd ove. Te ow quity firm serves consumers wit reference rmeters [0, ] nd ove. Consumers wit reference rmeters eow do not urcse t. Te mrket res for nd re resectivey: D G = nd = G DG.

12 Cse 3: G G nd. Te rice of unde er unit of quity of service is iger tn te rice of unde er unit of quity of service nd noody is indifferent etween te undes. Mrket res re disyed in Figure 4. = G G 0 G G I Figure 4: Mrket res under te regime, wen G G nd. ecuse, te demnd for te unde is zero. Te ow quity firm serves consumers wit reference rmeters [0, ] nd ove 4. Consumers wit reference rmeters eow do not urcse t. Te mrket res for nd re resectivey: D = 0 G nd D G G = 4 In tt cse, firm mkes zero rofit nd it esy to see tt tis is not n equiirium ecuse firm is wys etter off mkes ositive rofits y coosing its rice suc tt.

13 3.. Determintion of te equiirium rices in, In cse te first order conditions re: G G = 3 G G G G = 0 G = G G 3 3 G G G G = 0 We cn see tt te first order conditions re quite comex. We otin simir comicted first order conditions for oters cses. For tis reson, we serc te rice equiiri numericy for rnge of vues of nd. In cse, te equiirium rices tt we otin wys stisfy G G. Figure 5 sows te equiirium vues of G nd G for different vues of. G =0., = G G Figure 5: Comrison of rices er unit of quity under regime, In cse nd 3, te equiirium rices tt we otin do not stisfy wi ony ook t cse. G G >. Terefore, we 3

14 It is interesting to comre rofits in, to rofits in C, C. Te rofits under te regime C, C nd te regime, for different vues of re sown in Figure 6., is C wys iger tn, C. imiry,, C is wys iger tn, C. We otin simir resuts for vrious vues of. =0., = , C, C, C, C Figure 6: Comrison of firms rofits under te regimes C, C nd,. We see tt ot firms re etter wen tey unde. Te reson is tt unding ffects te intensity of cometition vi two cnnes: i it reduces te intensity of te cometition for service y incresing differentition; nd ii it increses te intensity of te cometition for service y reducing differentition. Te net effect of unding is decrese of cometition etween te two firms ecuse te cometition for under comonent ricing is extreme ertrnd cometition. Terefore ec mkes more rofit in te sugme, tn in te sugme C, C. 3.3 Cse iii:, C, unding y firm, Pure Comonent eing y firm Te individu-rtionity constrints re now for consumers of for consumers of : 0, G : 0, for consumers of : 0, 4

15 for consumers of 5 : 0. m Te sef-seection constrints re for consumers of for consumers of : Mx,,, G : Mx ; ;, G for consumers of : Mx ; ;, G for consumers of : Mx ; ;. G m Te condition Mx 0,,, must e stisfied y uyers of. G Te condition Mx 0, ; ; must e stisfied y uyers of one. G Te condition Mx 0, ; ; must e stisfied y uyers of one. G nd finy te condition Mx 0, must e stisfied y uyers of ot nd. G From, we derive tt te reference index of te consumer indifferent etween urcsing nd urcsing nd sertey is G ˆ. Note tt,, nd intersect t ˆ I ; ˆ G.ˆ cn e understood s te imicit rice er unit of quity of, wen te quity of is vued t te rice set y firm. Note so tt,, nd 5 Consumers of mens consumers of ot nd ut ec comonent is urcsed sertey. 5

16 intersect t G ; 6. Te mrket res deend on weterˆ, te imicit rice er unit of quity of is greter, ower or equ to, te exicit rice er unit of quity of set y firm. We now distinguis tree cses. Cse : G > nd ˆ >. Cse : Cse 3: G > nd ˆ.. G In cse nd cse te rice of te unde is iger tn te rice of ot nd. Te difference etween te two cses is tt in cse te imicit rice er unit of quity of is greter tn te exicit rice er unit of quity of set y firm. Wie in cse te imicit rice er unit of quity of is ower tn te exicit rice er unit of quity of set y firm. In cse 3 te rice of te unde is ower tn te rice of ot nd. 6 ervice is sod s rt of te unde G of te unde >. Te rtio G. emrk tt < G ˆ reresents te imicit rice er unit of quity of 6 cn e written s: wen it is sod s rt. Tus mrket res deends on weter tis imicit rice er unit of quity is greter, ower or equ to te exicit rice er unit of quity of.

17 Cse : > nd G ˆ > It is te cse were te imicit rice er unit of quity of is rger tn te exicit rice er unit of quity of. Figure 7 sows tt rmeter sce divides into five segments 7 ˆ G G Î G Figure 7: Mrket res under te regime, C wen G > nd Consumers wit reference rmeters to te rigt of G ˆ G ˆ > nd ove urcse te unde. Te mrket re of tose consumers is D G ˆ =. Consumers wit reference rmeters etween nd nd eow urcse one. Te mrket re of tose consumers is = ˆ G D. Consumers wit reference rmeters to te eft of, to te rigt of, nd ove urcse nd. Te mrket re of tose 7 We rec tt ˆ. G ˆ nd G 7

18 consumers is D te eft of = ˆ G nd ove G is = D. Oters don t urcse.. Finy consumers wit reference rmeter to urcse one. Te mrket re of tose consumers Cse : > nd G ˆ It is te cse were te imicit rice er unit of quity of is ower tn te exicit rice er unit of quity of. Figure 8 sows tt rmeter sce divides into four segments. ˆ G G 0 ˆ G P Î Figure 8: Mrket res under te regime, C wen G > nd P G G ˆ Te oction of consumers is s foows: consumers wit reference rmeters to te rigt of, ove nd ove urcse. Tose wit reference rmeters to te eft of 8

19 nd ove nd eow urcse one. Finy consumers wit reference rmeter to te rigt of urcse one. Oters don t urcse. G We see in Figure 8 tt ˆ < nd is to te rigt of. Terefore noody uys tt is no consumer urcses sertey wen se so urcses exicit rice of is iger tn te imicit rice of unde., 8. Te reson is tt te wen urcsed s rt in te For te rticur cse were ˆ, we ve in te rmeter sce is te sme s ove. nd te oction of consumers 8 ec tt uy mens uy ot nd. 9

20 Cse 3: G It is te cse were consumers wo urcse sertey, so urcse services rice iger tn te rice of te unde nd is zero since consumers cn urcse rice. ut consumers urcse G nd y for ot. In tis cse te demnd for ot, tt is tey cn get etter unde t ower one nd one. Mrket res re sown in Figure 9. ˆ G ˆ G P Î P G G Figure 9: Mrket res under te regime, C wen G Figure 9 deicts simir ttern s for Figure 3.8. Terefore cse nd cse 3 give te sme oction of consumers in te rmeter sce. 0

21 3.3. Determintion of te equiirium rices in, C Here so te first order conditions re quite comex. We serc te rice equiiri numericy for rnge of vues of nd. Figure 0 sows te equiirium vues of ˆ nd for rnge of vues of 9 in cse. Te equiirium rices tt we otin wys stisfy ˆ >. In cse nd 3, te equiirium rices tt we otin do not stisfy ˆ. Terefore, we wi ony ook t cse. 0.5 =0., = ˆ G Figure 0: Comrison of rices er unit of quity under te regime of, C Note tt g etween te exicit rice of service nd te imicit rice of service ecomes rger wen ecomes rger. 9 Te equiirium condition ˆ is not stisfied for te rmeter vues tt we ve cooses for simution.

22 3.4 Pure Comonents y Firm, unding y Firm : C, Te rticition constrints re for consumers of for consumers of : 0, G : 0, for consumers of : 0, for consumers of Te sef-seection constrints re 0 : 0. m for consumers of for consumers of : Mx 0,,,, G : Mx ; ;, G for consumers of : Mx ; ;, G for consumers of : Mx ; ;. G m Te condition Mx 0; ; ; must e stisfied y uyers of. G Te condition Mx 0; ; ; must e stisfied y uyers of one. G Te condition Mx 0; ; ; must e stisfied y uyers of one. G nd finy Mx 0; ; ; must e stisfied y uyers of ot nd. G 0 Consumers of mens consumers of ot nd ut ec comonent is urcsed sertey.

23 From nd, we derive tt te reference index of te consumer indifferent etween urcsing G nd urcsing nd sertey is. Now,, nd intersect t t I = ; G. cn e understood s te imicit rice er unit of quity of, wen te quity of is vued t te rice set y firm. Note so tt nd intersect t G,, ;. Te mrket res deend on weter tis imicit rice is greter, ower or equ to te exicit rice er unit of quity of set y firm. Tere re now four cses to consider tt corresond to numer of ces in Te. Te : Different cses under te regime of C, < < Cse Cse G G < Cse 3 Cse 4 < In ces excet ce 3 we ve, i.e. te reference rmeter of te consumer indifferent etween < nd ot nd is ower tn one. For ce 3, we consider sertey te cse were nd te cse were. so remrk tt < G te imicit rice er unit of quity of cn e written s: 3 G > wen it is sod s rt of te unde. Te rtio G reresents. Tus mrket res deends on weter tis imicit rice er unit of quity is greter, ower or equ to te exicit rice er unit of quity of Tere is no equiirium wit G > ecuse noody uys..

24 Cse : < nd G < Figure sows segmenttion of te sce of reference rmeters into five segments. G = is derived from G. G G I t G Figure : Mrket res under te regime C, wen G < nd < Consumers wit reference rmeters to te eft of, to te rigt urcse. Te mrket re of tose consumers is: nd ove nd D G = G G G, D = G. Consumers wit reference rmeters to te rigt of nd ove urcse ot nd.consumers wit reference rmeters to te eft of nd ove, urcse one. 4

25 Finy consumers wit reference rmeters to te rigt of nd eow urcse ony. Demnds D for nd D for re resectivey: G D =, nd D =. Te oters consumers do not urcse. Cse : < nd G < < Wen Figure disys so segmenttion of te sce of reference rmeters into five segments. We otin te sme segmenttion of reference rmeters sce tn in cse. Terefore < demnds in cse wen re simir to demnds in cse. G I G G P Figure : Mrket res under te regime C, wen G <, nd. G < < 5

26 Wen Figure 3 sows segmenttion of te sce of reference rmeters into tree segments. G G G G I P = = G Figure 3: Mrket res under te regime C, wen G <, nd < Consumers wit reference rmeters to te rigt of, ove nd ove urcse. Tose wit reference rmeters to te eft of nd ove, urcse one. Consumers wit reference rmeters eow urcse ony, to te rigt nd ove nd urcse. Oters don t urcse. No one urcses ot nd. 6

27 Cse 3: < nd G Figure 4 sows segmenttion of te sce of reference rmeters into four segments. I G I G P G G Figure 4: Mrket res under te regime C, wen G <, nd G > Consumers wit reference rmeters to te rigt Tose wit reference rmeters to te eft of nd ove nd ove urcse ot nd., urcse one. Consumers wit reference rmeters to te rigt urcse. Demnd for is zero. nd eow urcse ony. Oters don t 7

28 Cse 4: < nd G Figure 5 deicts te sme segmenttion of reference rmeters sce tn in cse 3. Terefore demnds in cses 4 re simir to demnds in cse 3. G I G P G G Figure 5: Mrket res under te regime C, wen G < nd 8

29 3.4. Determintion of te equiirium rices in C, We note tt tere is no duooy equiirium wit ecuse tis condition entis zero ses y te ow quity firm. Terefore, te remining cse to nyze is te cse were < nd or. o te question is wt sucse constitutes Ns equiirium in rices? < s in te revious sections, nytic difficuties ed us to serc te rice equiiri numericy for rnge of vues of nd. Figure 6 disys te vue of nd rnge of vues of 3. We find tt te ony equiirium rices tt we ever get wys re < < consistent wit. so t equiirium. Terefore we ook ony t cse wen. < for =0., = Figure 6: Equiirium crcteristic of te sugme C, Here so te g etween te exicit rice of service nd te imicit rice of service ecomes rger wen ecomes rger. 3 Te equiirium condition is not stisfied for te rmeter vues tt we ve cooses for simution. 9

30 4. Equiirium trtegy of te Gme We now comre rofit under ec of te four ossiiities. We et nd interv [ 0., [. Figure 7 sows firms rofit in ec ossiiity. We wys find tt: vry in te, C,, C C, C,, C C, C, C We concude tt, is n equiirium in dominnt strtegy. 0,4 0,3 0, 0, 0 0,4 0,5 0,6 0,7 0,8 0,9, C, C, C, C, C, C C, C, Tus we stte te foowing resut: Figure 7: Equiirium trtegy of te Gme i Pure unding is dominnt strtegy equiirium for ot firms. unding is dominnt strtegy for ot firms ecuse it reduces te intensity of te cometition etween te two firms y incresing te differentition of services. Terefore firms rofits re iger under, tn under te oter sugmes were one of two firms t est ses its services sertey. 30

31 3 5. Wefre Imictions Now et us see ow consumers surus nd soci wefre re ffected wen te regime sifts from, C C to,. For, C C, consumers surus denoted y C is: = 0 ~ ~ 0 d d P d P C C. Te first, second nd tird exression of C re resectivey te surus of urcsers of, nd. We otin: ~ ~ ~ ~ = C C Te soci wefre denoted y C W gives: C C C C C C C W,, =. For,, te surus of consumers of denoted y C is: = 0 G G G G G d d d d C G G G C 6 3 = Wie te surus of consumers of is: = 0 G G G G G d d d d C [ ] G G C 6 3 = Tus, consumers surus under, is: C C C =

32 Te soci wefre under, denoted y W is: W = C,, We now comre soci wefre under C, C nd, for nd vrying in te interv [ 0., [. Figure 8 disys te tot economic wefre under C, C nd, sows tt: C W > W.. It, W 0,8 0,6 0,4 W C W 0, 0 0,5 0,6 0,7 0,8 0,9, Figure 8: Tot wefre under te regimes of C, C nd, Tus we stte te foowing resut: ii sift from C, C to, resuts in decrese in soci wefre wen tere is sm differentition etween services. It is ovious tt unding in tis context reduces consumers surus. Indeed unding increses rices nd tere re more constrints under te regime of, ecuse to otin consumers must urcse even toug tey don t wnt. o for wefre to increse, ggregte rofits must rise enoug to offset te reduction of ggregte consumer surus nd ten resut in 3

33 otenti efficiency gin. For te rmeters we ve cooses we find tt tot wefre increse. 6. Concuding emrks In te trdition iterture on unding y duooists, te concusion is unding is dominnt strtegy equiirium for ot firms ut it is not rofite strtegy for ot firms. We find so tt unding is dominnt strtegy equiirium. ut contrry to oter studies, we find tt unding is rofite strtegy for ot firms. Te reson is tt in te context of verticy differentited services, unding cn e used s differentition too. It ten reduces te intensity of cometition etween te firms nd ten tey mke more rofits under unding tn tey woud under comonent seing. We so find tt unding increses tot wefre. Ce oertors nd teecommuniction comnies offer te comintion of teeone, teevision, nd Internet s unded service. Our resuts suggest tt tey woud comete more vigorousy nd woud reize ess rofit if tere were restriction on unding. If uyers cre for te quity of services teir surus is reduced under unding. However, te fct tt singe suier offers services mkes unding convenient for uyers. o te enefit of te convenience must e nced wit te reduction of consumers surus to otin te effects of unding on uyers wefre. so utorities must decide wt weigt tey give to te uyers surus nd to te suiers rofits to otin te net wefre effects of unding. Our resut soud e interreted under te ssumtions tt ot te vrie cost nd te fixed cost re zero for ec service nd services re verticy differentited. It woud e interesting to nyze te cse were te fixed costs re ositive. so since we know tt firms in communiction mrkets re ot orizonty nd verticy differentited, we cn study ot differentitions to see ow te resuts of tis er re roust to tese ssumtions. 33

34 eferences dms, W., J., nd Yeen, J., L., 976, Commodity unding nd te urden of Monooy, Qurtery Journ of Economics, 90, ges nderson, nd Lerut, L., 993, "Wy firms my refer not to rice discriminte vimixed unding," Interntion Journ of Industri Orgniztion, Esevier, vo., ges Economides, N., 993, Mixed unding in Duooy. tern coo of usiness, working er, tern coo of usiness, N.Y.U. Koe, P., Krisn,., nd ssunco, J., 999, Te oe of Mrket Exnsion on Equiirium unding trtegies, Mngeri nd Decision Economics, 0, Mtutes, Crmen nd egieu, Pierre, 99, Comtiiity nd unding of Comementry Goods in Duooy, Journ of Industri Economics, 40, Mcfee.. Preston, McMin, Jon, nd Winston, Mice D, 989, Mutiroduct Monooy, Commodity unding, nd Corretion of Vues, Qurtery Journ of Economics, 84, Muss, Mice nd erwin osen, 978, Monooy nd Product Quity, Journ of Economic Teory, 8, cmensee, icrd, 98, Commodity unding y inge-product Monooies, Journ of Lw nd Economics, 5, cmensee, icrd, 984, Gussin Demnd nd Commodity unding, Journ of usiness, 57, Tiroe, Jen, 988, Te Teory of Industri Orgniztion, Te MIT Press. Winston, Mice.D., 990, Tying Forecosure, nd Excusion, mericn Economic eview 80,