Strategic investments with spillovers, vertical integration and foreclosure in the broadband access market

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1 Strategc nvestments wth spllovers, vertcal ntegraton and foreclosure n the broadband access market Øysten Foros Norwegan School of Economcs and Busness Admnstraton/ Telenor R&D Abstract We analyse competton between two retalers of broadband access when they dffer n ther ablty to offer value-added servces. One retaler s vertcally ntegrated and controls the nput-market for local access. Ths frm nvests to ncrease the nput qualty (upgradng to broadband) before an access prce regulaton s set. We frst show that access prce regulaton may lower consumer surplus and welfare f retalers do not dffer too much. Second, f the ntegrated frm s ablty to offer value-added servces s much hgher than that of the rval, the ntegrated frm uses overnvestment as an alternatve foreclosure tool. JEL Classfcaton: L3, L, L43, L5, L96 Keywords: Broadband, strategc nvestment, vertcal ntegraton Correspondng address: Øysten Foros, Norwegan School of Economcs and Busness Admnstraton, Department of Economcs, Helleveen 30, N-5045 Bergen, Norway. E-mal: oysten.foros@nhh.no. Fax: Phone:

2 Introducton The purpose of ths paper s to examne the nterplay between a faclty-based vertcally ntegrated frm and an ndependent compettor n the retal market for broadband Internet connectvty. The latter frm buys local access as an nput from the former frm. The vertcally ntegrated frm undertakes an nvestment (broadband upgrades) that ncreases the qualty of the nput. We assume that the regulator has only one nstrument avalable, an access prce regulaton for the nput sold to the ndependent rval. The retal market s assumed to be unregulated. Furthermore, we assume that the access prce s set after the nvestment but pror to retal market competton snce the regulator has lmted commtment ablty. Both the tmng structure and the one-sded regulaton of the nput segment correspond to the domnant regulatory paradgm n the EU and the USA (Laffont and Trole, 000, Hausman, 997, and Cave and Prosperett, 00). Installaton of fber n the local access network wll be a substantal, lumpy, and rreversble nvestment, and the economc lfe of the nvestment wll be longer than the regulaton contract used for access prces (Hausman, 997). 3 The access prce regulaton may reduce nvestment ncentves, and the man message of ths paper s that the total welfare effect of access prce regulaton crtcally depends on whch frm has the hghest ablty to transform nput to output. The qualty of the nput component sold from the ntegrated frm s the same for both retalers, but the retalers may dffer n ther ablty to offer value-added servces (broadband servces such as nteractve vdeo). 4 Except for the case where the ndependent frm has the hghest ablty to use the mproved nput qualty, the ntegrated frm wll foreclose the rval from the market through the access prce n an unregulated envronment. However, ths s not a suffcent condton to ensure that an access prce regulaton mproves consumer surplus and total welfare. If the retalers do not dffer too much wth respect to ther ablty to offer value-added servces when the nput See Laffont and Trole (000) and Armstrong (00) for comprehensve overvews of access prce theory and practce. Cave and Mason (00) gve an extensve overvew of the market structure and regulaton n the Internet. See Laffont and Trole (000) for a dscusson. 3 Prce cap regulatons n telecommuncaton do not exceed fve years, and other types of access prce regulaton are usually set for a shorter perod. In contrast to the present paper, the lterature on prce caps typcally focuses on ncentves for cost-reducng actvtes wthn the regulatory contract. 4 The ndependent frm may be anythng from the geeks n the garage to AOL Tme Warner. Compared to the faclty-based vertcally ntegrated frm, those frms ablty to offer value-added servces wll obvously vary a lot. The ntegrated frm s retaler may have an advantage n usng the mproved nput qualty due to economes of scope from ntegraton. In contrast, f the ndependent retaler s a frm lke AOL Tme Warner, t may have an advantage compared to the ntegrated frm due to ts experence from other markets.

3 qualty s mproved, we show that access prce regulaton reduces the vertcally ntegrated frm s nvestment ncentves. An access prce regulaton lowers consumer surplus and total welfare as long as the cost of nvestment s not too convex. If the vertcally ntegrated frm s ablty to offer value-added servces s much hgher than that of the ndependent rval, an ncrease n the nvestment wll reduce the quantty offered by the ndependent retaler. An access prce regulaton stll elmnates the vertcally ntegrated frm s ablty to use the access prce as a foreclosure tool, but now the ntegrated frm may use overnvestment as an alternatve tool to drve the rval out of the market. Today the majorty of resdental consumers use ther telephone lnes for the last mle of narrowband Internet connectvty, and by upgradng ther local networks the telecommuncaton provders are able to ncrease the speed of communcaton. 5 The hgh upfront nvestments of new wre lne facltes, and the possblty of ncreasng the capacty and qualty of exstng local telephony and cable-tv networks, ndcate that telephone companes and the cable-tv-companes that already have nstalled wres to homes, wll control the segment for broadband local access to resdental consumers (Macke-Mason, 999). 6 In the current regulaton only the telephone access provder s mandated to supply local access as an nput to non-faclty based rvals n the retal market. Therefore, the telephony ncumbent has been the only provder of local access as an nput to ndependent ISPs 7. Hence, gven the exstng asymmetry n regulaton of the telecommuncaton and the cable-tv technologes (see Hausman et al., 00), the present model only fts for servces offered by the telecommuncaton ncumbents. 8 5 Measured by bts per second (bps). The current narrowband access servces gve access speed between 56-8 kbps. The bandwdth requrement for broadband servces wll vary a lot, and compresson technologes may reduce the requrements consderably. The upgradng technologes gve access speed from a few hundred kbps to 0-0 mbps. 6 Wth focus on the US market several analysts have argued that the cable-tv-provders have an advantage over the local telephone provders n supplyng broadband Internet access (see e.g. Macke-Mason, 999, and Faulhaber and Hogendorn, 000). The stuaton seems to be dfferent n Europe. There may be several reasons for ths dfference. Frst, there s hgh penetraton of cable-tv n the US compared to many European countres. Second, and probably more mportant, the hstorcal separaton between local provders and long dstance provders of telephony n the US between 984 and 996 (the AT&T break-up n 984). 7 Internet Servce Provders. 8 However, snce the cable-tv provders face an analogous cost structure, the analyss wll be relevant for broadband access usng cable-tv technology f the cable-tv provders are requred to offer broadband access as a wholesale product. 3

4 We assume that the nvestment n hgher speed of communcaton may be seen as an unambguous mprovement of qualty. 9 The closer to homes the fber s nstalled, the hgher s the qualty. The trade-off between the dstance the exstng lnes are used and the network qualty (speed) mples that the upgradng costs are convex n speed of communcaton. In fgure we llustrate the Internet as a layered network wth the physcal network as the bottom layer. Local access s obvously an essental nput component for the ISPs. The functons of the retal ISPs are to combne the components local access, regonal backbone capacty and global backbone capacty, and they act as a knd of portal to the applcatons and content n the Internet. FIGURE As descrbed by Cave and Mason (00) and Faulhaber and Hogendorn (000), the retal ISPs must choose ther regonal and global backbone capacty before they serve the end users. Ths mples capacty constrants that lmt the number of consumers that can be served. 0 Wth respect to tmng n our model t s reasonable to assume that the nvestment choce of speed of communcaton n the access network s taken pror to the ISPs choce of local and global backbone capacty. The nterplay between local retal ISPs and the upstream provders of global access wll not be addressed n the present paper. Accordng to the Chcago School there s only one proft to be extracted when two goods are complementary. Therefore, when an upstream monopolst can explot ts market power n the upstream market, a vertcally ntegrated frm has no ncentves to foreclose retal rvals. However, n the present context, the vertcally ntegrated frm foreclosure ncentves are drven by the nablty to explot the monopoly power n the upstream segment. Frst, even wthout access prce regulaton, we assume that the ntegrated frm sets a lnear nput prce. Hence, there wll be a double margnalzaton problem due to mperfect competton n the 9 Frst, an ncrease n speed of communcaton gves access to new broadband servces (e.g. nteractve audo and vdeo). Second, consumers value from conventonal Internet servces lke web-browsng and e-mal ncreases when the downloadng speed ncreases. Thrd, n contrast to narrowband connectvty the broadband Internet connectvty systems are desgned to be avalable all the tme ( always on ). 0 Although the total number of retal ISPs s large, the market s qute concentrated snce the largest provders are controllng a large part of the market. The current narrowband dal-up access lmts the economes of scale n the ISP-segment. However, the stuaton wll be dfferent wth broadband access technologes, and ths wll probably also ncrease the concentraton n the ISP-segment (Cave and Mason, 00). The regonal ISPs usually have long-term contracts wth the provders of transatlantc-lnes and access to the core global backbones (Crémer, Rey and Trole, 000). To some extent, ths wll also gve capacty constrants n the end-user market. 4

5 downstream market. Second, we analyse the case where the monopoly nput s prce regulated, whle the downstream market s unregulated. A vertcally ntegrated frm whch s forced to sell the nput equal to or close to margnal costs has an ncentve to use non-prce methods to deny rvals access n the unregulated downstream market. Rey and Trole (997) analyse the ncentves for foreclosure by a vertcally ntegrated frm that controls an nput bottleneck n an unregulated market, whle Laffont and Trole (000) dscuss the ncentves for non-prce dscrmnaton under access prce regulaton. In a context where a vertcally ntegrated upstream monopolst faces an access prce regulaton, several recent papers analyse the use of non-prce foreclosure towards downstream rvals. Analogous to the present paper, Economdes (998) assumes an exogeneously gven market structure where an ntegrated frm controls the nput-segment, and where there s an unregulated Cournot duopoly n the retal segment. Economdes (998) shows that wth an exogenously gven access prce the ntegrated frm wll always use non-prce foreclosure towards the retal rval. Ths result contrasts wth Sbley and Wesman (998) and Wesman and Kang (00), who fnd that the vertcally ntegrated frm wll be less nclned to degrade the qualty of the nput f the proft margn s hgh n the nput segment. All these papers assume Cournot competton n the retal market, and that the foreclosure actvty s assumed to degrade the qualty of the nput sold to the rvals. In contrast, n our model there s no opportunty to unlaterally reduce the qualty of the nput sold to the rval. The qualty level of the nput s the same for both retalers. However, f the vertcally ntegrated frm has sgnfcantly hgher ablty to offer value-added servces than the rval, the ntegrated frm may commt tself to be more aggressve n the retal market by overnvestng n network qualty mprovement. Beard et al. (00), Wesman (995, 998) and Reffen (998) analyse the ncentves to use qualty degradaton f there are Bertand retal competton and horzontal dfferentaton. The outcome compared to Cournot competton s ambguous. Bertrand mples more ntense retal competton, and as long as the rval s not completely foreclosed from the market, ths wll reduce the ncentves to use qualty degradaton. When the degree of horzontal dfferentaton Economdes (998) does not explctly assume that the access prce s regulated, but Bergman (000) shows that ths s a crucal mplct assumpton n Economdes model (see also Economdes, 000). Mandy (000) compares the mplcatons of dfferent assumptons n the non-prce dscrmnaton lterature. 5

6 ncreases, the ntegrated frm cannot replace the rvals sale wth ts own retal sale, and both prce and non-prce methods to nduce foreclosure wll be less proftable. 3 Faulhaber and Hogendorn (000) and Foros and Knd (003) analyse the broadband access market wth focus on the choce of target market (where to upgrade to broadband), whle the coverage decson s not analysed n the present paper. Another dstncton from the present paper s that these two papers develop models of competton among several faclty-based broadband access provders, whle we analyse the nterplay between a faclty-based provder and a non-faclty-based rval. Hausman, Sdak, and Snger (00) analyse the asymmetrc regulaton of telecommuncaton provders and cable-tv provders regardng broadband access. Rubnfeld and Snger (00) analyse the merged AOL Tme Warner s ncentve to engage nto two types of non-prce foreclosure n the broadband access market. The artcle s organsed as follows. In secton we present the model. In secton 3 we gve some concludng remarks. The model In fgure we llustrate the stylsed market structure analysed n the present paper. In the retal market for Internet connectvty there s competton between a vertcally ntegrated frm s subsdary and an ndependent ISP, ISP A and ISP B, respectvely. The vertcally ntegrated frm controls the local access component. The broadband Internet connectvty s sold by the two ISPs to end-users at a fxed subscrpton fee ndependent of actual usage (the number of packets actually sent and receved) and tme connected. Hence, the ISPs face a downward slopng demand curve. When the subscrpton fee s reduced (for gven qualty), more consumers wll subscrbe. The usage by the nfra-margnal consumers s, however, not affected. 4 The access nput prce charged by the faclty-based frm wll be a fee for each broadband subscrber served by the rval ISP (ISP B) over the vertcal ntegrated frm s local network facltes. 3 There may be horzontal dfferentaton n the retal market for Internet connectvty. However, we make the assumpton of no horzontal dfferentaton n order to strengthen the foreclosure ncentves of the vertcally ntegrated frm n absence of access prce regulaton. 4 Thus, we mplctly assume that the drect network effects are nsgnfcant. In other words, for a gven speed of communcaton n the local loop, the wllngness to pay s not affected by the number of consumers subscrbng to broadband n the same area. Ths assumpton seems realstc f the user s mostly downloadng 6

7 FIGURE Hence, we assume that the vertcally ntegrated frm cannot use non-lnear access prcng even wthout regulaton. In partcular when ISP B has the hgher ablty to use the mproved nput qualty, the vertcally ntegrated frm may ncrease ts proft by usng non-lnear access prcng. However, the current regulatory methods are desgned for lnear access prcng. 5 Our purpose s to focus on the regulator s commtment problem. Therefore, we want to rule out other potental detrmental effects of the current regulaton regme, and we assume a lnear access prce both wth and wthout regulaton. When the network qualty s mproved, the demand curves for both retalers shft outwards, such that the wllngness to pay for subscrpton ncreases for all potental consumers. If the frms dffer n ther ablty to use the qualty mprovement of the nput, the market shares of the frms wll be affected. We model a three-stage game wth the followng tmng structure: Stage 0: The vertcally ntegrated frm chooses the nvestment level x. Stage : The vertcally ntegrated frm or the regulator chooses the access prce w to the rval. Stage : The two retal frms compete à la Cournot. As mentoned above, we focus on how fat ppes to homes the vertcally ntegrated frm chooses, and we do not consder the choce of target market (where to upgrade to broadband). Faulhaber and Hogendorn (000) and Foros and Knd (003) analyse the choce of target market for a gven qualty level. The choce of coverage may n fact be set street-by-street, and therefore be taken after the nvestment choce consdered here. However, as long as the ntegrated frm s oblgated to offer broadband access as a wholesale product to the nformaton from the US. However, f the user s man use of broadband Internet connectvty s to have vdeoconferences wth neghbours ths assumpton s rarely fulflled. 5 See e.g. the dscusson by Laffont and Trole (000: page 40). 7

8 ndependent ISP n the entre target market, ths wll not alter the aspects analysed n the present paper. 6 We assume Cournot competton n the retal market, and the quantty frms dump n the retal market s nterpreted as the number of subscrptons they sell. An assumpton of Cournot competton seems reasonable, snce the retalers face capacty constrants n the regonal and the global backbones (see above and the dscusson by Faulhaber and Hogendorn (000) and Crémer et al. (000)). 7 In order to offer broadband Internet connectvty the retalers need to ensure that backbones are capable of data transfer rates sgnfcantly greater than what s needed to offer narrowband connectvty. Snce backbone networks are shared facltes, a gven capacty s not dedcated to each customer. However, when more customers are connected n a gven regon, more users compete for lmted shared regonal backbone facltes (and global backbone facltes). Hence, n order to ensure a gven qualty of the end user servce, the backbone capacty must be ncreased f a larger number of customers get connected (see Faulhaber and Hogendorn, 000). Demand sde The nvestment at stage 0 s gven by x. We see ths nvestment as a qualty mprovement of the local access nput that ncreases the consumers wllngness to pay for broadband Internet connectvty. How much the nput qualty mprovement ncreases consumers wllngness to pay for Internet connectvty depends on the retal frms ablty to transform nput to output. The consumers have unt demands. We assume that the consumers are heterogeneous n ther basc wllngness to pay for Internet connectvty, but that they are homogenous n ther valuaton of the mproved network qualty. 8 Hence, consumers valuaton of ISP s servce s 6 However, an oblgaton to offer the nput n the entre target market combned wth an access prce regulaton wll probably reduce the coverage where the ntegrated frm chooses to upgrade to broadband. The reason for ths s that t reduces the revenue, but not the costs from servng a gven regon. 7 Faulhaber and Hogendorn (000) model a three-stage game where the coverage decson s taken at stage, stage s the backbone capacty choce, and at stage 3 frms choose prces. The two last stages of ther game are shown to be equvalent to a one-stage Cournot game (the Kreps-Schenkman result). The result of Kreps and Shenkman (983) rests on very strong assumptons, but snce there are rgd capacty constrants we assume that the Cournot competton assumpton seems more realstc than a Bertrand game n the retal market (see the dscusson n Trole, 988, chapter 5). A necessary condton to ensure the Kreps-Schenkman result s that the ISPs smultaneously set the backbone capacty and thereafter compete n prces. 8 More generally, the consumers may also be heterogeneous n ther valuaton of mproved network qualty. If the margnal consumer values the mproved qualty less than the average consumer, ths wll reduce the ntegrated frm s ncentves to nvest compared to the present model, ceters parbus. The reason s that for a 8

9 s + β x. We nterpret s as the consumers wllngness to pay for the basc servce wthout nvestment, and s s assumed to be unformly dstrbuted between mnus nfnte and a (where a>0). We allow for negatve values of s n order to avod corner solutons where all consumers enter the market. The consumers vew the two frms servces as perfect substtutes wthout nvestment, and the value of servce ncreases wth β for all consumers wth an nvestment x. If β > β, the x vertcally ntegrated frm has hgher ablty to offer a value-added servce from the nvestment than the non-faclty based frm. In contrast, f β > β, the non-faclty based frm has the hghest ablty to ncrease consumers wllngness to pay. We assume that β β, 0,. The parameters β and β are the demand sde spllover from the faclty-based frm to ts own subsdary and the ndependent ISP, respectvely. The demand structure s analogous to Katz and Shapro (985) where the network qualty depends on the number of expected consumers connected to frm. 9 When s + p s the prce charged by ISP, a consumer of type s buys from ISP f s + β x p > β j x p j (where j ). If s + β x p <0 for both retalers, the consumer of type s wll not buy from any of them. If both frms are actve n the market, the qualty-adjusted prces need to be the same: p β x = p x = P β Subscrpts and ndcate the faclty-based and the non-faclty-based frm, respectvely. For a gven value of P, consumers whom have s P enter the market, and snce we assume unform dstrbuton there are a-p actve consumers. The two frms offer the total quantty Q= q + q, and prces must ensure that Q = a - P as long as both frms are actve. From above, we have a demand sde spllover from the local access provder to the retalers: a = a+β x and a = a+β x Thus, the nverse demand functons faced by the frms are (as long as both frms are actve): gven output level the frms wll be able to ncrease the prce by less than the ncrease n the average consumer s wllngness to pay. 9

10 p = a q q p = a q q Note that the parameters β and β x do not affect the slope of the nverse demand x functons, so that an ncrease n x mples parallel shfts n the demand functons. If β there wll be dfferent magntudes n the demand shfts. Net consumer surplus s: β, CS = a p q a + p q In absence of the nvestment we assume that the servces offered by the frms are dentcal. For the exstng network qualty (absence of the nvestment), the ISPs offer access to conventonal PC-centrc servces lke www and e-mal. For these servces there exst known and accepted standards, but the stuaton may change when new technology s mplemented. When the access network qualty s upgraded, the ISPs may offer new TV-centrc nteractve broadband servces that are very dfferent from conventonal PC-centrc servces. Then, there may be dfferences n ther ablty to offer such servces due to economes of scope from ntegraton and/or dfferent experence. As long as β = β the end user servces from the two ISPs wll be dentcal also when the nvestment s postve (x>0). Then the nvestment ncreases the qualty level of the retalers end-user servces by the same level. In contrast, f β > β j, then there wll be a qualty dfferental between the two retalers servces, and ISP wll offer a hgher qualty than ISP j (where, j=,). We assume lnear demand. However, the qualtatve results hold wth a more general demand functon. Suppose that frm faces the followng nverse demand functon: P Q, θ ), where ( θ = β x. The assumptons P ( Q, θ ) / θ > 0 and P ( Q, θ ) / θ 0 mply that the wllngness to pay s ncreasng both n β and x, smlar to the present model wth lnear demand. Furthermore, an assumpton of P ( Q, θ ) / Q θ = 0 mples that a change n β and x, only affects the retal demand through a parallel shft (and not n the slope) of the nverse demand functon (analogous to what s assumed n the present model). 9 In the Katz and Shapro-model consumers value servce at v q ) expectatons of the sze of frm s network. s + ( e, where e q s the consumers 0

11 Supply sde Regardng the vertcal ntegrated frm s cost structure n the upstream segment for local access we assume that cost per user s a constant margnal cost c. Ths cost s the same rrespectve of whether ts own downstream subsdary or the rval s servng the end-user. We assume that the nfrastructure qualty,.e. the nvestment level, does not have any effect on the margnal cost c. The faclty-based frm faces a quadratc network nvestment cost wth respect to nvestment n hgher speed (bandwdth) n the local loop, gven by C ( x) = ϕ x /. The nvestment cost x s not related to each user; the nvestment s for every potental user. For smplcty, the margnal costs of buyng all other nputs than local access (regonal and global backbone capacty) are assumed to be the same for the two retalers, and normalsed to zero. The proft functons for the frms are gven by: π = ( p c) q + ( w c) q ϕx / π = ( p w) q The vertcally ntegrated frm s actve n both the upstream and the retal segment, whle the non-faclty based frm earns proft only n the retal segment. The parameter w s the access prce charged by the faclty-based frm n the upstream segment. Throughout we make the followng assumpton: Assumpton : π 0, π 0, w c, x 0 The frst two constrants state that each frm should have a non-negatve proft. The thrd term says that the vertcally ntegrated frm must have a non-negatve prce cost margn on ts sale to the ndependent frm n the retal segment. The last term states that the nvestment must be non-negatve. Welfare The welfare functon: W = CS+ π + π

12 A benchmark Let us consder a market context n absence of the nvestment n qualty mprovement (x=0). In an unregulated market the faclty-based frm chooses the access prce n the upstream market at stage. In a regulated market the regulator chooses the access prce at stage. At stage the frms compete à la Cournot. In ths context the results can be summarsed n the followng lemma: Lemma : If the vertcally ntegrated frm does not nvest n qualty mprovement (x=0), the regulator sets the access prce equal to margnal cost. If the access prce s unregulated, the vertcally ntegrated frm sets an access prce that forecloses the rval from the market. The consumer surplus and total welfare level are hgher under the access regulaton regme compared to the unregulated regme.. Retal market competton We solve the model by backward nducton and assume Cournot competton between the two frms (the ISPs) n the retal market for broadband Internet connectvty. Equlbrum quanttes n the compettve segment are: q = [( a c) + ( w c) + x( β β )] / 3 q = [( a c) ( w c) + x( β β )] / 3 Untl otherwse stated, we make the followng assumpton: Assumpton : β β j 0where, j =,, j Assumpton ensures that the dfference n ablty to offer value-added servces between the retal frms s not too hgh. When β β 0, the rval s quantty s non-decreasng by the nvestment n x for gven access prce w. Hence, the vertcally ntegrated frm cannot use the nvestment as an alternatve foreclosure tool under access prce regulaton. In secton.5 we modfy ths assumpton and assume β β < 0. Then the vertcally ntegrated frm may use overnvestment as an alternatve foreclosure tool under access prce regulaton.

13 . Unregulated access prce The vertcally ntegrated frm sets the access prce at stage, and stage s as above... Stage : The objectve functon for the faclty-based frm at stage s: π = q + ( w c) q ϕx / The frst order condton wth respect to w gves the equlbrum access prce at stage : w = ( a+ c)/ + x( 4β + β )/ 0 If we nsert for w nto the equlbrum quanttes, we have the followng: q = [( 5 a c) + x( 7β β )]/ 0 q = x( β β )]/ 5 Q = [( 5 a c) + x( 3β + β )]/ 0 Proposton : Let us assume no regulaton of the access prce. The condton β > β s necessary and suffcent to ensure that the downstream rval s actve n the market. From Lemma we know that n absence of the nvestment (x=0) the ndependent frm s foreclosed from the market. In contrast, we see that under nvestment n qualty mprovement (x>0) the ndependent retal frm wll be actve n the market f t has hgher ablty to use the mproved nput qualty such that β > β... Stage 0: Foreclosure: From Proposton t follows that as long as β β, the vertcally ntegrated frm wll use the access prce n the next stage to practce foreclosure towards the rval (frm ). Hence, n the case where t s optmal to practce foreclosure t chooses the nvestment level as a 3

14 downstream monopoly. Downstream monopoly quantty s qm = 05.[ a c+ β x], and the objectve functon for the faclty-based frm when t sets x as a downstream monopolst s π m = ( q ) 05. ϕx. Superscrpt m ndcates downstream monopoly. m The frst order condton wth respect to x gves the followng nvestment level: π x = 0 x = ( a c) β / A where A = ϕ β m m m The second order condton s fulflled as long as A m >0. 0 Insertng for x m gves the followng equlbrum quantty: ( a c) ϕ qm = ϕ β Market sharng: From Proposton we know that both retal frms are actve as long as β > β. The objectve functon for the faclty-based frm when t sets x s: max π = ( q ) + ( w c) q 05. ϕx x We nsert for w, q and q. Then the frst order condton wth respect to x gves the followng nvestment level: π x = 0 x = 5β ( a c)/ A where A = 0ϕ 9β + 8β β 4β The second order condton s fulflled as long as A > 0. Comparng the nvestment level under foreclosure (.e. β β ) wth the market sharng equlbrum ( β > β ), we fnd the followng (see appendx): Lemma : Let us assume no regulaton of the access prce. For a gven level of β the nvestment wll be hgher under market sharng (.e. β > β ) than under foreclosure, (.e. 0 At the nvestment stage (stage 0) the second order condton ( A m > 0 ) ensures that the cost parameter ϕ s suffcently hgh, such that the nvestng frm wll not make an nfnte nvestment n qualty mprovement. Analogously, we have A > 0 n the case of market sharng wthout regulaton and r A > 0 n the case wth regulaton (see below). 4

15 β β ) as long as the second order condtons are fulflled. Moreover, the nvestment and the rval s quantty ncrease wth the rval s ablty to use the qualty mprovement when β > β,.e. that dx / dβ > 0 and dq / dβ >. 0 Wthout access prce regulaton, the vertcally ntegrated frm may mtate the strategy of the foreclosure case n the market sharng case as well. Hence, when the vertcally ntegrated frm chooses to serve the rval, ths means that the proft by dong so s hgher than the monopoly outcome. When the rval s more effcent n usng the mproved qualty of local access, β > β, the consumers have hgher wllngness to pay for the servce from ISP than for that from ISP. Hence, t wll be optmal to let the rval be actve n the market n order to capture some of the rent from ISP. The access prce wll, however, be set such that the quantty offered by ISP wll be low n order to dampen the competton. Insertng for x gves the followng total quantty: Q a c = A [ 5ϕ 3β + 5β β β ] The reason why the vertcally ntegrated frm does not outsource the retal market to the more effcent rval s the assumpton of a lnear access prce. In contrast, f the vertcally ntegrated frm can use a two-part tarff for access, t wll set a unt access prce equal to the margnal cost c, and then capture the monopoly proft of the more effcent rval (ISP ) through the fxed fee. In other words, f the network owner offers the two-part tarff T ( q ) = π m + cq, the retal rval (ISP ) makes no proft, and the upstream monopolst wll acheve the same outcome as f ISP were ts own subsdary (see e.g. Rey and Trole, 997). As mentoned n the ntroducton, we do not consder non-lnear access prcng. However, f the vertcally ntegrated frm can charge ISP B a fxed fee combned wth a unt prce equal to the margnal cost, then the outcome wthout regulaton does not depend on whether ISP A or ISP B has the hgher ablty to use the qualty mprovement of the nput..3 Access prce regulaton The government may regulate w to maxmse welfare. In prncple, the regulator can act as a frst-mover and set w before the faclty-based frm sets x. Such a commtment to ex ante regulaton may, however, not be credble. We assume that the regulator has no ablty to regulate the access prce ex ante of the nvestment, and, hence, the only dfference n the game 5

16 from the complete unregulated regme s that the regulator rather than the ntegrated frm decdes the access prce at stage..3. Stage : The welfare functon may be wrtten as W ( q = + q ) ϕ x + q + q + ( w c) q The frst term s the consumer surplus. The second term s the proft by the ndependent frm. The last three terms are the vertcally ntegrated frm s proft. The regulator sets the access prce w after the nvestment n x has taken place. The frst order condton wth respect to w gves the regulated access prce margn: w c= ( a c) + x( 4β 5β ) When (w c) <0, t s a volaton of the constrant that w c. We then have the followng result (gven the assumpton that w c): Proposton : Let us assume regulaton of the access prce. A necessary and suffcent condton to ensure that t s optmal for the regulator to set access prce equal to margnal cost, ( w r = c), s ( a c) + x( 4β 5β ) < 0. In ths secton we assume that the necessary and suffcent condton n Proposton s fulflled, such that optmal regulated access prce wll be set to margnal cost ( w r = c) at stage. Superscrpt r ndcates regulated access prce. Insertng for w=c nto the equlbrum quanttes from stage gves: r q = [( a c) + x( β β )] / 3 The second order condton s fulflled. Note that f the regulator were allowed to set the access prce below the margnal cost (w<c), t would have done that n order to correct for the mperfect competton n the retal market. If the regulator may use a two-part tarff, t could set w<c, and stll ensure through the fxed fee that the upstream unt of the ntegrated frm has non-negatve proft. In ths case, the regulator could use a unt-prce w below margnal cost c n order to correct for the mperfect competton n the retal market. 6

17 r q = [( a c) + x( β β )] / 3 r Q = [ ( a c) + x( β + β )]/ 3.3. Stage 0: Now the faclty-based frm has no revenue from the upstream market, and the objectve functon for the faclty-based frm s: max π = ( a c) + x( β β )] / ϕx x The frst order condton wth respect to x gves the followng nvestment level: π x = 0 x r = ( a c)( β β )/ A r wherea r = 9ϕ ( β β ) Insertng for x r nto Q r gves: Q r ( a c) = + r ( 6 ϕ ( β β )( β β ) ) A From Lemma we know that under market sharng n the unregulated case the nvestment level ncreases when β ncreases. In contrast to the unregulated case, we now see that the nvestment level decreases n the rval s ablty to offer value-added servces as the nput qualty s mproved, snce dx r / dβ < 0 (see proof of Proposton 3 n appendx). Snce the faclty-based frm has no revenue from ts upstream sale, t sees the advantage of the nonfaclty-based frm from the nvestment as a pure spllover. The hgher the non-faclty based frm s ablty to use the nvestment, the hgher the spllover from the nvestment to the rval. Not surprsngly, the hgher the spllover, the lower the ncentves to make an nvestment. Moreover, from Lemma we know that wthout regulaton the rval s quantty ncreases wth β under market sharng. Under access prce regulaton we fnd that: dq r r ( x + ( dx / β )(β ))/ 3 / dβ = d β The frst term s postve and ndcates that for a gven nvestment level, the rval s quantty ncreases when β ncreases. The second term ndcates that an ncrease n β wll have an 7

18 effect on the nvestment level and that ths n turn wll affect the quantty offered by the rval. We know that dx r / dβ < 0 and n ths secton we assume that ( β β ) > 0. Hence, the second term s negatve. Ths s due to the fact that for the vertcally ntegrated frm the parameter β s now seen as a pure spllover, whch reduces the nvestment ncentves. And therefore, when the spllover ncreases, the ncentves to nvest wll be reduced. The total effect on the rval s quantty s then ambguous. Related to the quantty offered by the vertcally ntegrated frm s retaler, we have that the hgher the spllover, the lower the retal quantty sold from the faclty-based frm (such that dq / dβ < ). There are two effects leadng to ths result. Frst, the hgher the spllover s, r 0 the lower s the nvestment. When the nvestment s reduced, the faclty-based frm lowers ts retal quantty. Second, snce the quanttes offered by the two rvals are strategc substtutes, the faclty-based frm reacts to an ncrease n the quantty from the rval by reducng ts own quantty (Bulow, Geanakoplos, and Klemperer, 985). The second effect may be postve or negatve (see above), but the total effect on the vertcally ntegrated frm s quantty from an ncrease n β s negatve..4 Comparson of results wth and wthout access prce regulaton The motvaton behnd an access prce regulaton s to prevent foreclosure and ncrease competton such that welfare ncreases. Industry proft wll be hgher wthout regulaton than wth regulaton. Hence, a necessary, but not suffcent, condton to ntervene wth an access prce regulaton s that the consumer surplus ncreases compared to the case wthout regulaton. In order to compare the levels of consumer surplus wth and wthout regulaton we must make a dstncton between the case of foreclosure and the case of market sharng n the unregulated market. Foreclosure wthout regulaton: For smplcty we now make the followng assumpton: β β In the access prce regulaton equlbrum, the vertcally ntegrated frm has no proft from the nput segment. From assumpton we have that β 05.. Moreover, we assume that the cost 8

19 parameter ϕ s so hgh that the second order condtons are fulflled,.e. ϕ >ϕ crt =0.5 n ths case. We have the followng results for nvestment and consumer surplus wth and wthout regulaton (see appendx): Proposton 3: In the case where β β we have the followng results regardng nvestment and consumer surplus:. the nvestment level s lower wth than wthout access prce regulaton,.e. x r x < 0. m. the consumer surplus s lower wth than wthout regulaton as long as the nvestment r r cost s not too convex,.e. q + q < q crt crt ff ϕ < ϕ < ˆ ϕ =. m Hence, the parameter ϕ must be above a crtcal value ϕˆ crt to ensure that regulaton mproves consumer surplus. To see ths, let us consder the case where ϕ s hgh. Even f x r x < m 0, the absolute value of x m s low. Hence, the ncrease n total quantty due to hgher nvestment wthout regulaton s low compared to the ncrease n total quantty that may be acheved by forcng the vertcally ntegrated frm to set the access prce equal to the margnal cost. In contrast, when ϕ s low, the total quantty under monopoly and than the total quantty of duopoly and r x. x m s hgher Smlarly, snce ndustry proft s lower wth than wthout regulaton, we fnd that the total welfare s lower wth than wthout regulaton when the nvestment cost s not too convex. The crtcal value of ϕ that ensures that access prce regulaton mproves welfare s hgher than the crtcal value of ϕ that ensures that regulaton ncreases consumer surplus. In ths case the vertcally ntegrated frm has hgher ablty to transform nput nto output than the rval. Then, f t s allowed to do so, t wll prevent the rval from enterng the market through the access prce. In order to ensure entry the regulator may then mpose an access prce regulaton that prevents the vertcally ntegrated frm from practsng foreclosure. The regulator faces a classc trade-off between trggerng competton and dampenng nvestment ncentves. Moreover, ths trade-off mples that t may be better f the rval has sgnfcantly lower ablty to offer value-added servces than the vertcally ntegrated frm snce ths wll reduce the spllover from the nvestment. Put dfferently, the closer β s to β, the hgher ϕ 9

20 has to be to ensure that the consumer surplus s hgher wth than wthout regulaton. Thus we have: Corollary : In the case where 0.5< β β, a lower β makes t more lkely that consumer surplus s hgher wth than wthout access prce regulaton. Ths gves rse to a paradox. It s more lkely that t s optmal for the regulator to ensure entry by access prce regulaton f frm has low ablty to offer value-added servces compared to the vertcally ntegrated frm. Usually, we see that the potental entrants are argung n the opposte drecton. They argue that the regulator should encourage entry snce they have at least the same ablty to offer value-added servces as the ncumbent. Put dfferently, n the present model t may be better for the regulator to allow for an neffcent entrant than havng an effcent retal monopoly. Market sharng wthout regulaton: Both frms are actve n the market also n the market equlbrum, and we make the followng assumpton: β < β We compare the results wth and wthout regulaton when the rval has the hghest ablty to transform the nput to output, and we stll assume that ϕ >ϕ crt =0.5. Then we have the followng results (see appendx): Proposton 4: In the case where β < β we have the followng results regardng nvestment and consumer surplus:. the nvestment level s lower wth than wthout access prce regulaton,.e. x r x < 0.. the consumer surplus s lower wth than wthout regulaton as long as the nvestment r r cost s not too convex,.e. q + q < q + q ff crt ~ crt ϕ < ϕ < ϕ = ( β (3β ) + ). 3 As n the prevous case total welfare s also lower wth than wthout regulaton when the nvestment cost s not too convex. 0

21 For β close to 0.5 the welfare loss from dampened competton n the case wthout access prce regulaton wll be hgh. The loss from dampened competton, for a gven nvestment level, n the unregulated regme may be separated nto two effects. Frst, there wll be a loss due to the fact that total quantty s reduced when the rval pays an access prce hgher than the margnal cost. Ths loss s hgher the lower β s compared to β (whch s equal to one). Second, there wll be a loss due to the fact that the less effectve frm wll serve most of the market. For a gven nvestment level, these two competton effects wll mply that the consumer surplus and total welfare may be enhanced by access prce regulaton. However, access prce regulaton wll reduce the nvestment ncentves of the vertcally ntegrated frm. For β =0.5 the nvestment s zero. However, for β close to 0.5 the pro-compettve effects of regulaton domnate the negatve nvestment ncentves effect even f the cost parameter ϕ s low. As n the prevous case (Corollary ) t s more lkely that the consumer surplus s hgher under access prce regulaton compared to the case wthout regulaton f the dfference between the frms ablty to offer value-added servces s large. We have assumed Cournot competton and no horzontal dfferentaton. The potental detrmental effect of the regulator s lmted ablty to commt to a gven access prce may be even hgher wth Bertrand competton. To see ths, consder a smple model where the retalers compete á la Hotellng, and the retalers are located at the extremes of the Hotellng lne. If the degree of horzontal dfferentaton s hgh compared to the degree of vertcal dfferentaton, x β β, the vertcally ntegrated frm may want to serve ISP B even f β > β. Hence, Proposton wll not hold wth horzontal dfferentaton. As mentoned n the ntroducton, the reason s that the ntegrated frm cannot fully replace the rval s sale. Wth the tmng structure assumed above, and the assumpton that the consumers are homogenous n ther valuaton of the mproved network qualty, t wll be optmal for the regulator to set the access prce equal to the margnal cost (w=c) n order to reduce retal prces. Gven Bertrand competton between the retalers, there are no benefts to any of the frms from an equal ncrease n the qualty of ther retal servces. Snce nvestment s costly, there wll be no nvestment (x=0) f β = β. Ths wll be the outcome both wth and wthout regulaton. Wth regulaton, w=c, the vertcally ntegrated frm wll obvously not nvest n qualty mprovement when β < β (snce, ths gves an advantage to ISP B). Hence, wth competton á la Hotellng, a necessary condton for havng a postve nvestment wth regulaton, x>0, s that β > β.

22 .5 Access prce regulaton and non-prce foreclosure In ths secton we analyse whether the vertcally ntegrated frm may have ncentves to overnvest as an alternatve foreclosure tool when assumpton s altered. Untl now we have assumed that the rval frm s quantty ncreases when the nvestment ncreases for a gven access prce (assumpton ). In contrast, we now assume that β β < 0, such that the rval wll reduce ts quantty when the nvestment ncreases for a gven access prce (snce dq / dx < n stage ). For smplcty, we make the followng assumpton: 0 Assumpton 3: β > β > 0 At stage 0 the vertcally ntegrated frm sets x, and at stage the vertcally ntegrated frm or the regulator sets the access prce. We know that for low values of β, t may be optmal for the regulator to set the access prce above margnal cost (see above). For the sake of smplcty, we assume that the optmal regulated access prce at stage s w c. At stage the frms compete à la Cournot when both frms are actve n the market. The strategc nvestment game has the tmng structure analysed by Dxt (980). The stage quanttes gven that w c are q = ( a c+ w + x( β ))/ 3 and q = ( a+ c w + x( β ))/ 3. We analyse whether the vertcally ntegrated frm (the frstmover) chooses to nvest to foreclose the rval (deterrence of entry) or to share the market wth the rval (accommodaton of entry). Blockaded entry The monopoly nvestment gven assumpton 3 s x = ( a c)/( ϕ ). If we nsert x m nto m q β c we fnd that entry s blockaded wth the monopoly nvestment when β ( a c)( ϕ) + ( w c)(ϕ ) /( a c ). The queston s whether the vertcally ntegrated frm wll overnvest n x when β c < β 05.. Entry deterrence through non-prce foreclosure: The effect of the nvestment x on the rval s proft s dπ dx = β q + q )(( β ) / 3) = q (β ) / 3 (

23 The frst term s the drect effect of x on the rval s proft, and t s postve. The second term s the strategc effect, whch wll be negatve. An ncrease n x ncreases the second stage choce of q. Snce the quanttes offered by the two frms are strategc substtutes, an ncrease n q wll lower the proft margn for ISP. When assumpton 3 s met ( β <0), the strategc effect domnates the drect effect. To foreclose the rval the vertcally ntegrated frm should overnvest such that q f = 0 (superscrpt f ndcates foreclosure by overnvestment): q f f a w c = 0 x = + β For x=0 we assume that both frms are actve n the market, such that a w + c> 0. Then t follows that for β < 0.5: f dx dw = β < 0 and f dx dβ a w c = ( + ) > 0 ( β ) For a lower local access prce, the vertcally ntegrated frm s response s to ncrease the nvestment f t wants to deter entry. The hgher β (but lower than 0.5), the hgher the nvestment must be to enhance a gven reducton n the rval s quantty. When the rval s foreclosed, the vertcally ntegrated frm sets the monopoly quantty n stage. Insertng for x f f we fnd that q = [( a c)( β ) + ( w c)] / ( β ). For β < 0.5 we see that: f dq dw = β < 0 Hence, a restrctve access prce regulaton may be effectve even f no nputs are sold to the rval. When the access prce ncreases, the vertcally ntegrated frm must overnvest less compared to the monopoly nvestment level. If we nsert for nvestment level and quantty 3

24 offered by the vertcally ntegrated frm, we fnd the proft and the welfare functons under foreclosure: π = ( q ) 05. ϕ( x ) f f f W = π + 05.( q ) f f f Now t can be shown that: f dw dw ( a c)( 3β 3+ ϕ) + ( w c)( 3 4ϕ) = ( β ) When ths s negatve, we see that an access prce regulaton may be effectve even f the rval s stll foreclosed from the market. The reason s that an access prce regulaton forces the vertcally ntegrated frm to ncrease the nvestment f t wants to foreclose the rval. The nvestment s an nvestment n qualty, and we know that a monopolst may have too hgh or too low ncentves to offer qualty seen from the socal planner s pont of vew (Spence, 975). We now check that n ths partcular settng the monopolst offers too low qualty (nvestment) seen from the regulator s pont of vew. Gven entry deterrence, we have non- f prce foreclosure such that q = q = 0. The vertcally ntegrated frm chooses the monopoly m quantty n stage,.e. q = ( a c+ x) /. As long as q = 0, the welfare level wll be gven by W = ( 3q ϕ x )/. Thus we have dw / dx = ( 3q ( dq / dx) ϕ x). We know that wthout access prce regulaton x = ( a c)/( ϕ ). The socal optmal nvestment level s gven by m x s arg maxw. Insertng for x m we fnd that dw / dx ( a c ) /( ( )) = ϕ ϕ > 0. Hence, x= x m we have that s x > xm. f Even f q = q = 0, the welfare wll ncrease f the regulator through a bndng access prce regulaton gves the vertcally ntegrated frm an ncentve to ncrease the nvestment compared to x m. 4

25 If the vertcally ntegrated frm chooses not to foreclose the rval (accommodaton of entry) t wll set x to maxmse ts own proft. We nterpret β c as the crtcal value for whether foreclosure s optmal or not. Hence we have three ntervals analogous to Dxt (980):. Blockaded entry when β β c : The rval s blocked from entry by the monopoly nvestment level x m. c c. Deterrence of entry when β < β < β < 05. : The vertcally ntegrated frm overnvests to foreclose the rval.. Accommodaton of entry when 05. > β β c : Then t s more proftable for the vertcally ntegrated frm to set x that maxmses ts own proft, even f the rval s actve n the market. We see that the outcome may be foreclosure even f the access prce s regulated. Ths s n contrast to the prevous sectons where both frms were actve n the market under access prce regulaton. Note that the man dfference from the prevous case s that β > β. The lterature on non-prce foreclosure typcally focuses on the detrmental mpact on welfare when an access prce regulaton gves ncentves to extend the untapped market power by non-prce methods. In contrast, n our context, t may ncrease welfare. We then have the followng results: Proposton 5: Let us assume that β > β > 0and that there s a bndng access prce regulaton. Then we have the followng results:. The vertcally ntegrated frm overnvests compared to the monopoly equlbrum f wthout access prce regulaton,.e. x xm > 0.. The unconstraned monopoly undernvests seen from the regulator s pont of vew, s x > xm, and access prce regulaton ncreases welfare snce t forces the vertcally ntegrated frm to nvest more.. If the rval has a low ablty to offer value-added servces compared to the vertcally ntegrated frm, the rval wll be foreclosed from the market both wth and wthout f c access prce regulaton,.e. q = q = 0 f β < β < Some concludng remarks In ths paper we have analysed a market structure where a vertcally ntegrated frm controls an essental nput for retal provders of Internet connectvty. The vertcally ntegrated frm 5