Strategic Investment and Market Structure under Access Price Regulation

Transcription

1 Strategi Investent and Market Strtre nder Aess Prie Reglation Keizo Mizno Shool of Bsiness Adinistration Kwansei Gakin University Ihiro Yoshino Shool of Bsiness Adinistration Nagoya University of Coere and Bsiness Adinistration Otober 008 Abstrat This paper exaines a relationship between infrastrtre investent and arket strtre in an open aess environent. In or odel, an entrant is allowed to vertially erge with an pstrea fir that has a bypass tehnology (i.e., an alternative tehnology to an inbent s infrastrtre), and the (horizontal and vertial) arket strtres are endogenosly deterined by the inbent s investent in infrastrtre. Then, we show that in eilibri, the inbent strategially gives birth to exessive vertial erger and insffiient aess to its infrastrtre fro a welfare viewpoint. In addition, two types of exess entry (i.e., "exess entry with aess" and "exess entry with vertial erger") an or in eilibri. We also show the prevalene of nderinvestent in infrastrtre with the eilibri arket strtres, irrespetive of the inbent s tehnology for infrastrtre investent. Keywords: aess priing, infrastrtre investent, bypass, vertial erger. JEL lassifiation: L3, L5, L96. We are gratefl to Noriaki Matsshia and Kazhiko Mikai for the valable oents that iprove the paper. We thank seinar partiipants at Contrat Theory Workshop, Niigata University, Seinan Gakin University, and University of Hyogo for helpfl disssion. Finanial spport fro MEXT (Grant No.95306) and Teleoniations Advaneent Fondation (TAF) is grateflly aknowledged. Corresponding to: Keizo Mizno, Shool of Bsiness Adinistration, Kwansei Gakin University, --55 Uegahara, Nishinoiya, Hyogo, , Japan; tel: ; fax: ; e-ail: kizno@kwansei.a.jp

2 Introdtion Introding opetition has been an effetive ethod to enlarge an alloative effiieny in network indstries. We are, however, still wondering if a new type of infrastrtre sh as broadband networks an be bilt soothly in a opetitive environent. The prpose of this paper is to investigate a fir s inentive for infrastrtre investent in a syboli opetitive environent of network indstries, alled an "open aess" environent. alletti (003) and Gthrie (006) dealt with a fir s inentive for infrastrtre investent in an open aess environent. 3 However, ost related researhes to this paper are Foros (00) and Kotakorpi (006). Foros (00) exained the effet of aess prie reglation when a network owner has a strategi opportnity to invest in infrastrtre. Coparing the environents with and withot aess prie reglation, he fond the possibility of welfare-reding reglation in the sense that it ay lower onser welfare if an inbent and an entrant provides the sae ality servie. Kotakorpi (006) also insisted that an inentive for infrastrtre investent is reded ore with aess prie reglation than withot it. This paper is siilar to theirs in the sense that it featres a strategi aspet of a network owner s inentive in infrastrtre investent. However, or approah differs fro these two papers in the following way. We sppose that aess prie reglation is a neessary tool to enhane an alloative effiieny in a retail arket. Given aess prie reglation, however, we allow an entrant to vertially erge with an pstrea fir that has a bypass tehnology (i.e., an alternative tehnology to an inbent s infrastrtre). See Arstrong and Sappington (006) for the sary on the theoretial jstifiation of several poliy tools adopted in network indstries, inlding the introdtion of opetition. In its broad eaning, an open aess environent an be fond even in other kind of indstries, as long as soe fis se the other fir s faility pstrea (or downstrea) in an idential indstry. 3 Needless to say, aess priing literatre is related to or paper. See Arstrong (00) and ogelsang (003) for its srvey. Laffont and Tirole (990) also dealt with the ase where a bypass tehnology is available. However, they fosed on the isse of rea-skiing by assing ltiple types of onsers. Arstrong (00) exained the appropriability of niversal fnd poliy when there exists a bypass tehnology. These two papers did not deal with the isse on infrastrtre investent.

3 Then, an inbent akes a strategi investent in infrastrtre, whih affets the entrant s hoie of strategy to enter the arket; aess strategy or vertial-erger strategy. This iplies that horizontal and vertial arket strtres are endogenosly deterined by the inbent s strategi investent, the entrant s strategy, and aess prie reglation. In other words, or fos is the relationship between infrastrtre investent and a arket strtre in an open aess environent. In or odel, infrastrtre investent has deand-enhaning effet, and there exists spillover of this effet when an entrant aesses an inbent s infrastrtre. Then, two ain findings are obtained fro the analysis in this paper. First, we show that in eilibri, the inbent strategially gives birth to exessive vertial erger and insffiient aess to its infrastrtre, when the spillover is large and the inbent s investent tehnology is ineffiient. This finding is onerning the vertial side of eilibri arket strtre. Seond, two types of exess entry ors in eilibri. 5 In partilar, when the inbent s aess ost is lower than the prodtion ost of bypass tehnology, the "exess entry with aess" ors in the eilibri arket strtre. Otherwise, the "exess entry with vertial erger" ors in eilibri. This is onerning the horizontal side of eilibri arket strtre. The driving fore that generates these two findings is an inbent s weaker inentive in infrastrtre investent than the one desired fro a welfare viewpoint. In fat, we also show the prevalene of nderinvestent in infrastrtre with the eilibri arket strtres, irrespetive of the inbent s tehnology for infrastrtre investent. Hene, we assert that a poliy sggestion be ade onerning how to give an appropriate inentive for infrastrtre investent to a network owner. The next setion explains the fraework of the odel. Then, the analysis in Setion 3 provides a preliinary analysis that deals with the ase where an entrant has only the 5 In this respet, or paper is also related to the "exess entry" literatre sh as Mankiw and Whinston (986) and Szra and Kiyono (987). However, the driving fore that generates the exess entry phenoenon is totally different fro theirs. See the disssion in Setion III.

4 strategy of the aess to an inbent s infrastrtre, Setion gives the analysis of the odel. Soe poliy ipliations of the analytial reslts are disssed in Setion 5. Setion 6 onldes the paper. The Model Let s onsider a vertially related setors, alled an pstrea setor and a downstrea setor, and the two setors are reired to spply goods to onsers in a arket. There are three firs; fir, fir e, andfir. Fir has an infrastrtre pstrea and a prodtion faility downstrea (i.e., a vertially integrated fir). Fir e has only a prodtion faility downstrea, while fir has a bypass pstrea. The bypass an be sed to provide an inpt for the prodtion downstrea, as is the sae as fir s infrastrtre. However, its harateristi is inferior to that of infrastrtre in the sense that it is too ostly to expand its apaity size, so that only one fir an se it. 6 On the other hand, the expansion of fir s infrastrtre an be ahieved with soe investent ost, and its expansion has a deand-enhaning effet throgh the iproveent of the ality of goods. To serve its onsers, fir e needs an pstrea tehnology. In this paper, fir e is allowed to vertially erge fir thathasabypass. Thiseansthatfir e has two alternative strategies to enter the arket. The first is alled an aess strategy; itan aess fir s infrastrtre by paying aess harge a set by a reglator. The seond is alled a vertial erger strategy; it an propose a vertial erger to fir. Notethat there exists a third (potential) strategy, alled a bypass strategy; fir e ay se fir s bypass by paying a wholesale prie w set by fir withot vertial erger. This wold or when the aess harge is extreely high and the proposal of vertial erger were rejeted by fir. Then, sing one of the three strategies, fir e an opete with fir 6 The treatent of bypass tehnology in this paper is standard in the aess priing literatre. See Arstrong (00), for exaple. 3

5 in the arket. Let s forlate the sitation speifially. For analytial tratability, we deal with the ase where a representative onser s tility in the arket is desribed by the following adrati fntion. A representative onser s tility is U (, e )( x ) ( sx ) e ( e ) if fir e aesses fir s infrastrtre. Here, i (i, e) is the antity of goods spplied by fir i, x is the level of fir s infrastrtre investent, and s ( [0, ]) represents a spillover to fir e generated by the infrastrtre investent. On the other hand, if fir e ses fir s bypass with (or withot) vertial erger, a onser s tility is desribed by U (, e )( x ) e ( e ) That is, the spillover ors only when fir e aesses fir s infrastrtre. As is well known, this tility fntion yields the linear inverse deand syste as follows. p ( x ) ( e ) and p e ( sx ) ( e ), if fir e aesses fir s infrastrtre, and p ( x ) ( e ) and p e ( e ), if fir e ses fir s bypass with (or withot) vertial erger. 7 One nit of inpt (i.e., the otpt proded pstrea) prodes one nit of otpt downstrea. For sipliity, we asse that the (onstant) arginal aess ost that fir 7 Foros (00) provides the derivation of this type of linear inverse deand with a referene to a broadband interenet deand.

6 owes for fir e s aess is the sae as its arginal prodtion ost pstrea, and the prodtion ost downstrea for eah fir is zero. Fir s (onstant) arginal prodtion ost is denoted by. The prodtion ost of bypass tehnology an be better or worse than that of an inbent s tehnology; < >. The expansion of infrastrtre an be ahieved with soe investent ost inrred by fir, and its expansion has a deandenhaning effet. On the other hand, the expansion of bypass tehnology is ipossible and only one fir (i.e., fir e) an se it. Here, we sppose that the investent ost is represented by a adrati fntion; I (x ) γ (x ) with an investent tehnology paraeter γ (> 0). A reglator deterines the level of aess harge a, and we asse that it is the only poliy instrent available for the reglator. We asse Cornot opetition between fir and fir e in the downstrea arket. 8 Then, fir s profit isforlatedby π [p ] [a ] e γ (x ), if fir e aesses its infrastrtre, and π [p ] γ (x ), if fir e ses fir s bypass with (or withot) vertial erger. Fir e s profit is π e [p e a] e, if it aesses fir s infrastrtre. 8 In a broadband internet arket, Cornot opetition is jstified by the fat that eah of retail ISPs needs regional and global bakbone (i.e., it faes a apaity onstraint). See the disssion in Falhaber and Hogendorn (000) and Foros (00). 5

7 In the ase of vertial erger, the joint profit isdefined by π π e π [p e ] e As entioned before, if aess harge is extreely high and fir e s proposal of vertial erger were rejeted by fir, fir e wold se fir s bypass by paying a wholesale prie w set by fir. 9 In that ase, fir e s profit is π e [p e w] e, and fir s profit is π [w ] e. Sine ost infrastrtre investents are irreversible and the reglator s ability of oitent to an aess harge is liited, we asse that fir invests in infrastrtre prior to the reglator s setting of aess harge. Hene, the tiing of the gae is sarized as follows. First, fir deterines the level of investent x. Seond, given x, the reglator deterines the level of aess harge a. Third, given x and a, fir e hooses one of the two alternative strategies to enter the arket. That is, it deides whether it aesses fir s infrastrtre or offers the proposal of vertial erger to fir by antiipating fir s response to its proposal. If fir rejeted fir e s proposal of vertial erger, it wold set the wholesale prie w and fir e woldseitsbypassby paying w. Moreover,fir and fir e wold do so when fir e neither aesses nor offer a proposal of the vertial erger. Forth, fir and fir e opetes downstrea in a Cornot fashion. 9 In this paper, we asse that fir an nilaterally set the wholesale prie w. Otherforlationof the setting w hanges the profit distribtion nder a vertial-erger proposal, whereas the ain essage of this paper does not hange. 6

8 3 A Preliinary Analysis: The Eilibri Market Strtre with Aess Before analyzing the odel desribed in setion, it is sefl to exaine as a benhark the eilibri of the ase where fir e has only the aess strategy. Indeed, this benhark orresponds to the analyses of Foros (00) and Kotakorpi (006). For analytial tratability, we prepare the following assptions. Assptions (i) Y > ( ), (ii) a, (iii) γ > 9. Assption (i) states that the deand size is sffiiently large relative to the ost differene between fir and fir e. 0 For pratial reason, we pt Assption (ii). Indeed, it is rare for aess harge to be set below the arginal aess ost in the real poliy arena. Assption (iii) garantees the interior soltions for not only fir s profitaxiizing bt also welfare-axiizing investent probles withot any restritions in the following analysis. When aess is the only available strategy for fir e to enter the arket, the level of aess harge a deterines fir e s deision of whether it enters the arket by aess or it reains otside the arket (i.e., the ase of forelosre), given the level of infrastrtre investent x. This sitation orresponds to the ase of "reglated aess harge" analyzed in Foros (00). In the forth stage of the odel, fir and fir e opetes in a Cornot fashion if fir e enters the arket. Table reports the eilibri prodtions and their assoiated profits in all the arket strtres realized in eilibri, inlding the ase where fir 0 Reeber that we allow the ase where > 0. When the bypass tehnology is not available, (i) beoes >3. Foros (00) also onstrained his analysis to the ase where aess harge is at least greater than aess ost. Kotakorpi (006) also deals with this ase, exept that the entrants are opetitive fringe in his odel. 7

9 e has only the aess strategy. See the first row naed "Aess" and the last row naed "Forelosre". When fir e has only the aess strategy, these two arket strtres are possible in eilibri. Of orse, when the profit with aess strategy is positive (i.e., π e A > 0), fir e enters the arket. [Insert Table arond here.] [Insert Figre arond here.] Figre illstrates fir e s deision in ters of the level of aess harge a and that of infrastrtre investent x for s>/. Fro a siple allation, we derive the ritial hyperplane whose eation is given by µ µ s a x () Below (above) the hyperplane (), fir e enters (does not enter) the arket by aessing fir s infrastrtre. That is, when aess harge is low (high), fir e enters (does not enter) the arket. This is an obvios reslt, bease the aess harge is the prodtion ost for fir e when aessing fir s infrastrtre. The effet of infrastrtre investent x needs soe attention for its interpretation. In the ase where s>/, asinfigre,fir e enters the arket with aess strategy as long as a<( ) /. However, when s</, it does not enter the arket even for a low aess harge if the level of infrastrtre investent x is large. In fat, when s</, the ritial hyperplane in Figre beoes a downward sloping line. This eans that when the spillover effet is sall and the level of x is large, fir e does not have an inentive to enter the arket. The reason is explained as follows. In or odel, the infrastrtre investent has a deand-enhaning effet throgh the iproveent of ality of goods. Then, when the spillover effet is sall, the differene of the benefit to onsers between fir s goods and fir e s goods expands, so that fir e annot sell 8

10 its goods to obtain positive profit by entering the arket. Hene, the forelosre ors in that ase. 3 Next, we trn to the seond stage. In the seond stage, the reglator deterines the level of aess harge a, given the level of infrastrtre investent x with the antiipation of the arket strtre downstrea. Sine opetition in the downstrea setor is iperfet (i.e., dopoly or onopoly) in or odel, aess harge shold be set as low as possible in order to orret the distortion of nderprodtion. Hene, with Assption (ii), the reglator sets the soially optial aess harge a sh that the aess harge is eal to the arginal aess ost, i.e., a. Finally, in the first stage, fir deides the level of infrastrtre investent x. Fir deides its profit-axiizing level of infrastrtre investent with the antiipation of a and the arket strtre realized in the downstrea setor. Appendix A gives the proedre of the derivation of the soltion of fir s profit-axiizing investent proble. [Insert Figre arond here.] Figre illstrates the eilibri arket strtres that or throgh fir s infrastrtre investent in (s, γ) plane. Aording to Figre, a "dopoly with aess" arket strtre is ahieved nder the reglated aess harge a in all the regions exept the one where both s and γ are sall. How an we evalate the eilibri arket strtre fro a welfare viewpoint? To do so, it is sefl to derive the soially desirable level of investent and its assoiated arket strtre as a benhark. Let s define the seond-best investent as the investent that the reglator sets in addition to the reglated aess harge a. Also, let s define 3 Notie that when both the spillover effet and the level of infrastrtre investent are large (i.e., when s>/ and x is large), this reasoning an be applied to explain why fir e enters the arket even if the aess harge a is high. 9

11 the seond-best arket strtre as the arket strtre assoiated with that investent. The sketh of the proedre to derive the is given in Appendix B. Then, the oparison of seond-best and eilibri arket strtres are drawn in Figre 3. [Insert Figre 3 arond here.] In Figre 3, we have the region where fir e enters with aess in eilibri whereas it does not enter the arket in the seond best (region III). That is, when fir s infrastrtre investent tehnology is effiient (i.e., γ is sall) and the infrastrtre s spillover effet is sall (i.e., s is sall), exess entry with aess ors in eilibri. We sarize this finding as a proposition. Proposition Sppose an entrant has only the aess strategy to enter a arket. Then, the exess entry with aess ors when an inbent has an effiient tehnology for infrastrtre investent and its spillover effet is sall. The intitive reason for the orrene of the exess entry with aess is explained as follows. In or odel, the iproveent of the alloative effiieny is ahieved by two rotes: one rote is to inrease the prodtion level by introding opetition in the downstrea setor, while the other is to enlarge onser s willingness-to-pay by investing in infrastrtre. When fir (an inbent) has an effiient tehnology for infrastrtre investent and its spillover effet is sall, it is better to invest in infrastrtre and forelose fir e (an entrant) than introding opetition fro an effiieny point of view. However, sine fir does not flly are abot onser s willingness-to-pay, its investent inentive is less than that in the seond best. Therefore, there exists a roo where fir e an enter the arket by aessing fir s infrastrtre. Region I also has the sae reslt as that of region III, exept that fir s deision is indifferent between allowing fir e s entry with aess and forelosre. 0

12 Notie that a rial fator that indes the exess entry with aess is not an entrant s (fir e s) deision, bt an inbent s (fir s) weak inentive for infrastrtre investent. Infat,asobservedbySappington(005),givenaninptprie,anentrant s ake-or-by deision, whih orresponds to its hoie of entry strategy in or odel, an be always effiient fro a welfare viewpoint, irrespetive of the level of aess harge. Hene, a sggestion for opetition poliy shold be ade onerning how to give an appropriate inentive for infrastrtre investent to an inbent. As entioned in setion, Foros (00) dealt with the ase where an entrant has only the aess strategy nder the reglated aess prie. However, he did not exaine how the eilibri arket strtre is evalated fro a welfare viewpoint, sine his ain interest is the oparison of the environents with and withot aess prie reglation. Hene, Proposition has a opleentary role onerning the effet of an inbent s strategi investent pon the eilibri arket strtre in an open aess environent. Fro the intitive reason of Proposition, it sees to be obvios that the level of infrastrtre investent in eilibri is less than that in the seond best. Indeed, the next proposition shows that in eilibri, the nderinvestent reslt ors irrespetive of the inbent s tehnology for infrastrtre investent. Proposition When an entrant has only the aess strategy to enter a arket, an inbent has less inentive to invest in infrastrtre in eilibri than in the seond-best opti, irrespetive of the inbent s tehnology for infrastrtre investent. Proof. See Appendix C. The nderinvestent in eilibri when an entrant has only the aess strategy was also shown in Kotakorpi (006). As seen in the next setion, we will extend the nderinvestent reslt to the ase where the entrant has an opportnity to se the other alternative strategy for entry.

13 The reason why the nderinvestent prevails in eilibri deserves to be larified. Reeber that we define the "seond-best" as the sitation where the reglator sets not only the aess harge a ( ) bt also the level of investent x. In other words, fir e s strategi behavior given a and x still reains in the seond-best. Fro this viewpoint, the nderinvesent reslt in eilibri when opared with the seond-best is not de to the strategi interation between fir and fir e. Rather, the ain driving fore that gives birth to the reslt of nderinvestent in infrastrtre is the fat that fir does not flly are abot the enlargeent of onser s willingness-to-pay generated by infrastrtre investent. Needless to say, when opared with the first-best where the reglator sets not only the level of investent bt also that of prodtion downstrea, the strategi interation between fir and fir e needs to be entioned as a ain fore for nderinvestent. In partilar, Kotarkorpi (006) showed that the spillover effet has a negative ipat on infrastrtre investent bease of their strategi interation (see Proposition 3 in his paper). This point is easily ensred in or fraework as well. 5 The Eilibria with Aess and ertial Merger. Fir e s strategies for entry Let s trn to the odel desribed in setion. In the odel, fir e has three alternative strategies for entry; aess, vertial erger, and bypass. That is, fir e has an opportnity to se fir s bypass tehnology throgh an agreeent of a vertial erger with fir, when it refses the aess to fir s infrastrtre. In addition, as entioned in setion, when a is extreely high and fir e s proposal of vertial erger is rejeted by fir, fir e ay se fir s bypass by paying a wholesale prie w set by fir. Hene, we need to areflly exaine fir e s deision on the hoie of entry strategy. 5 The details of this point will be sent pon reest.

14 In the third stage, fir e deterines its entry strategy, given the level of infrastrtre investent x and the reglated aess harge a. When proposing a vertial erger to fir, fir e needs to antiipate the wholesale prie w set by fir that wold be offered if the vertial-erger proposal were rejeted. Here, we shold notie that the reglated aess harge a an pt soe restrition on w. In Appendix D, we provide the sketh of the proedre to derive fir e s entry deision nder the level of infrastrtre investent x and the reglated aess harge a. (See Appendix D.) Figre - sarizes fir e s hoie of entry strategy in the third stage when s>/. [Insert Figre - arond here.] In the figre, the three pward-sloping straight lines and a vertial line are drawn in addition to (). µ µ s a x. () a sx. (3) µ µ s a x () x x ( ) (5) Eation () indiates whether or not fir anobtainanonnegativeprofit (i.e.,it has an inentive to atally offers the wholesale prie w) when the aess prie reglation is binding for fir s setting its profit-axiizing wholesale prie w. In fat, when the reglated aess harge is low, fir annot set w given by w ( x ) (6) 3

15 Instead, it has to set the binding wholesale prie w given by 6 w a sx. (7) The right hand side of w is interpreted as an "effetive" aess harge. Indeed, the aess to fir s infrastrtre akes the ality of fir e s goods pgrade (i.e., the existene of a spillover effet), so that the wholesale prie w fir offers needs to be lower than the noinal aess harge a. Then, only when w, fir anobtainanonnegative profit. Siilarly, eation (3) represents whether fir has an inentive to offer the binding wholesale prie w (i.e., whether its profit withw is positive or not). Hene, the region enlosed by () and (3) eans that fir wold like to offer w, sine it an gain a positive profit andfir e aepts it if there is not a vertial-erger proposal. Eation () represents whether fir e prefers vertial erger to the other two entry strategies. In addition, the vertial line (5) x x ( ) represents whether fir e aepts the wholesale prie w fir offers when the aess prie reglation is not binding. Now, we ensre several rearkable findings in Figre - when opared to Figre. First, the vertial-erger strategy prevails when the level of aess harge a is high and the level of infrastrtre x is sall. In partilar, there is no roo where the bypass strategy is sed instead of the vertial-erger strategy. Reeber that this finding depends on the opetition ode downstrea and how to deterine the wholesale prie. In fat, as in the setting of Ordover et al. (990), when fir and fir e opetes in prie downstrea and fir an oniate with fir e, itispossibleforthebypass strategy to overoe the vertial-erger strategy in the sense that both fir and fir e 6 Under aess prie reglation, fir s proble is stated as Max w π s.t. π e B π e A w is derived when the onstraint is binding, i.e., π e B π e A.

16 an be better off. In that ase, the bypass strategy an appear in soe part of the region of vertial erger in Figre -. Seond, the region of the aess strategy shrinks when opared to Figre. In partilar, in the region enlosed by () and (3) for x x, fir e takes the vertialerger strategy instead of the aess strategy. As disssed in setion 5, the vertialerger strategy taken by fir e ontribtes to the enhaneent of prodtion effiieny. Third, the region of forelosre beoes saller than in Figre. In fat, when the level of infrastrtre x is sall, fir e has an inentive to enter with the vertialerger strategy even when aess harge is high. In this sense, the existene of the bypass tehnology atally ontribtes to the ahieveent of opetitive environent in network indstries. When x is large, however, fir e givespentry. Thisisbeasethe differene of the ality of goods between fir s and fir e s is large, so that fir e annot fasinate onsers. We ention a final reark in this sbsetion. The alitative featres of fir e s entry deision does not hange even for s /. However,whenfir s strategi opportnity for infrastrtre investent is introded, fir e s hoie of entry strategy in eilibri ay draatially hange aording to the level of s. Hene, we show the figres for the ases where (/) <s (/) and where 0 s (/). [Insert Figres - and -3]. Fir s strategi infrastrtre investent and the eilibri arket strtre In the seond stage, the reglator wold like to set a, bease the iperfetion in the retail arket is prevalent, irrespetive of the level of x. Then, given a and fir e s hoie of entry strategy, fir invests in infrastrtre in order to axiize its profit inthefirst stage. The proedre to derive the optial 5

17 investent is the sae as in setion 3, exept that the lassifiation of the ases we need to hek does not depend only on the level of s. We also need to hek the sign of ost differene and the relationship between the level of fir s arginal ost and the deand size. (See Appendix E for the sketh of the derivation.) In fat, the lassifiation of the eilibri arket strtre aording to these paraeters is as follows. [Insert Figres 5 and 6 arond here.] Case : When / s and 0. Fro Figre -, we ensre that fir e takes only the aess strategy for entry. Hene, the analysis is the sae as in setion 3. That is, a dopoly with aess is realized in eilibri. (See Figre.) Case : When / s and >0. Fro Figre -, we ensre that the aess and the vertial-erger strategies are taken by fir e. The part of s [/, ] in Figre 5 (or Figre 6) applies to this ase. (See Appendix E for the derivation of Figre 5.) Case 3: When / s</ and 0. Fro Figre -, we ensre that fir e takes only the aess strategy for entry. Hene, the analysis is the sae as in setion 3. That is, a dopoly with aess is realized in eilibri. (See Figre.) Case : When / s</ and >0. Fro Figre - and the assption that Y >, we ensre that fir e takes not only the aess strategy bt also the vertial-erger strategy, whih depends on the level of x. The eilibri arket strtre is given in the part of s [/, /) in Figre 5. Case 5: When 0 s / and 0. Fro Figre -3, we ensre that fir e takes only the aess strategy for entry. Hene, the analysis is the sae as in Setion 3. That is, the "dopoly with aess" and 6

18 the forelosre are possible in eilibri. (See Figre.) Case 6: When 0 s / and >0. Note that when 0 s /, wehave ( s) /s. Inthisase,wehaveseveral ases aording to the arket size. Here, we restrit or attention to two illstrative ases, i.e., 0 < (/0) Y and (/0) Y< (/7) Y, whih give a lear ontrast between the eilibri arket strtre and the seond-best arket strtre. The above six ases an be sarized as follows. (i) When 0, the eilibri arket strtre is the sae as in Figre. (ii) When 0 < (/0) Y, the eilibri arket strtre is drawn in Figre 5. (iii) When (/0) Y < (/7) Y, the eilibri arket strtre is drawn in Figre 6. [Insert Figre 7 arond here.] Aording to the paraeter range adopted in the lassifiation of the eilibri arket strtres, the seond-best arket strtres are drawn in Figre 7. Then, oparing Figres 5 and 6 with Figre 7 (in addition to the reslt of Figre 3), we obtain the following proposition. Proposition 3 Sppose that an entrant has not only the aess strategy bt also the vertial-erger strategy and an inbent s aess ost is higher than the prodtion ost of bypass tehnology(i.e., > 0). Then, when the spillover effetofinfrastrtre investent is large and the inbent s investent tehnology is ineffiient, exessive vertial erger and insffiient aess to infrastrtre ors fro a welfare viewpoint. Proposition Sppose that an entrant has not only the aess strategy bt also the vertial erger strategy. Then, if an inbent s aess ost is higher (lower) than the prodtion ost of bypass tehnology(i.e., > (<)0). Then, the exess entry 7

19 with vertial erger (with aess) ors in eilibri when the spillover effet is sall and the inbent s investent tehnology is effiient. Proposition 3 states that in eilibri, fir e adopts the exessive vertial erger strategy when the spillover effet of infrastrtre investent is large. At first glane, this sees to be onterintitive. The reason for the orrene of exessive vertial erger is explained by fir s inentive for nderinvestent in infrastrtre. Sine fir does not flly are abot the benefit to onsers generated by infrastrtre investent, its investent inentive is weak. This gives birth to fir e s inentive for vertial erger, sineitannotenjoythebenefit of aess bease of nderinvestent in infrastrtre. Proposition has a siilar flavor of Proposition. The nderinvestent in the eilibri for any tehnologial environent is also obtained as in setions 3. and 3.. Proposition 5 When an entrant has not only the aess strategy bt also vertial-erger strategy to enter a arket, an inbent has less inentive to invest in infrastrtre in the eilibri than in the seond-best opti, irrespetive of the inbent s tehnology for infrastrtre investent. 5 Disssion: Poliy Ipliations Fro the propositions derived in the previos setion, we an obtain a general essage. Sine fir s (i.e., an inbent s or a network owner s) inentive for infrastrtre investent is weak fro a welfare viewpoint, a arket strtre that reslts fro the relationship between the infrastrtre expansion and fir e s (i.e., an entrant s) entry deision an be also distorted. Notie that if the infrastrtre overage is taken as given, an entrant s ake-or-by deision generates no distortion in prodtion effiieny, irrespetive of the level of the 8

20 reglated aess harge (see Sappington (005)). This point is easy to be verified in or odel. Indeed, when there is no infrastrtre investent, the vertial-erger strategy is taken by fir e, aslongas <(i.e., the vertial interept of a sx in Figre -). Frtherore, even when there is a positive level of infrastrtre investent, the vertialerger strategy is taken by fir e, aslongas <sx (i.e., the nit prodtion ost of bypass is less than the "effetive" nit aess ost that inldes the benefit of spillover effet on the deand). Hene, the driving fore that generates a distortion in the eilibri arket strtre is an inbent s weak inentive for infrastrtre investent. For exaple, when the bypass tehnology is not available for fir e, the exess entry with aess ors in the eilibri. At a first glane, the aess is desirable fro a welfare viewpoint. However, reeber that in or odel, the iproveent of the alloative effiieny an be ahieved by not only inreasing the prodtion level throgh opetition downstrea, bt also enlarging onser s willingness-to-pay throgh the infrastrtre investent. Then, when fir has an effiient tehnology for infrastrtre investent and its spillover effet is sall, it is better to invest ore in infrastrtre and forelose fir e fro an effiieny viewpoint than introding opetition. However, sine fir does not flly are abot onser s willingness-to-pay, its investent inentive is weak, and fir e an enter the arket with aess. Siilarly, when the bypass tehnology is available throgh a vertial erger with fir, the exess entry with vertial erger an or in eilibri. When the spillover effet s is sall, the entrant desires the se of bypass or wants to propose a vertial erger with a fir that has the bypass. However, fro an effiieny viewpoint, the forelosre is better espeially when fir s investent tehnology is good. Again, this is bease the infrastrtre investent an enlarge onser s willingness-to-pay. The reent poliy stane in network indstries has been an introdtion of opetition, and the reglators in any ontries onern abot the existene of an inbent s 9

21 arket power that is sed for the exlsion of potential entrants. Hene, the essage we obtain sees to go into the opposite diretion to the instrtion of opetition poliy in reality. However, this is not the ase. Or essage is rially based on the appropriate setting of aess harge and nonexistene of nonprie exlsionary tools other than the infrastrtre investent. If an inbent has a private inforation on aess ost or the other kinds of nonprie exlsionary tool sh as tying, advertiseent, et., the forelosre shold be areflly onitored. On the other hand, if these isses are appropriately solved in the poliy area, or essage an give a sggestion on the relationship between the level of infrastrtre investent and its assoiated arket strtre. In this sense, the essage derived fro or analysis shold be onsidered to be a opleent to the poliy instrtion in reality. Then, the estion is: how to inde a sffiient inentive for infrastrtre investent? One effetive way to do this is to allow a reglator to obtain an initiative for infrastrtre investent, as long as she nderstands the degree of deand-enhaning effet of infrastrtre investent. 7 In that ase, there ay be a trade-off between a reglator s ability to oit an appropriate vision of infrastrtre projets and the loss generated fro the deterrene of introding opetition in network indstries. 6 Conlding Rearks This paper investigated a fir s inentive for infrastrtre investent in a opetitive environent with open aess. In the odel, we spposed that aess prie reglation is a neessary tool to enhane an alloative effiieny in a retail arket. Given aess prie reglation, we allowed an entrant to has an opportnity to se a bypass tehnology throgh a vertial erger with an pstrea fir. 7 In the fraework of oalition foration to bild an infrastrtre, Mizno and Shinkai (006) also propose the delegation of the initiative for infrastrtre bilding to a reglator, when the ost-reding effet of infrastrtre is large. They, however, insist that, when the effet is sall, a network owner has an appropriate inentive for infrastrtre investent fro a welfare viewpoint, so that the reglator shold not intervene the arket. 0

22 Three ain findings were obtained fro the analysis in this paper. First, we showed that in eilibri, the inbent strategially gives birth to exessive vertial erger and insffiient aess to its infrastrtre fro a welfare viewpoint. Seond, two types of exess entry or in eilibri. In partilar, when the inbent s aess ost is lower than the prodtion ost of bypass tehnology, the "exess entry with aess" ors in the eilibri arket strtre. Otherwise, the "exess entry with vertial erger" ors in eilibri. We also showed the prevalene of nderinvestent in infrastrtre with the eilibri arket strtres, irrespetive of the inbent s tehnology for infrastrtre investent. In an open aess environent, several onrete poliy ideas other than the delegation of the initiative for infrastrtre projets to a reglator an be onsidered for prooting infrastrtre investent. Their effets ay depend on the harateristis of different network indstries. Hene, an iportant researh area fro now on is to investigate the effets of different onrete poliies for the prootion of infrastrtre investent by taking the harateristis of different network indstries into onsideration. Appendix A. Fir s profit-axiizing investent proble with fir e s aess strategy When s /,itisapparentthatfir e aesses fir s infrastrtre for any x nder the reglated aess harge a. Hene, the profit-axiizing investent is x A ( s) Y 9γ ( s), (8) where Y. When s</ and a, there exists a ritial level of x,denotedbyx A,below

23 (above) whih fir e enters (does not enter) the arket. In fat, we have x A Y s. (9) Then, fir s proble an be analyzed by solving the two sbprobles; one sbproble is to hoose the optial investent nder fir e s aess strategy, while the other is to hoose the optial investent with forelosre. When allowing fir e s aess, fir s proble is Max x π A eπ A γ (x ) s.t. 0 x x A Then, fir s axiized profit is represented as follows. π A x A if x A x A, (0) π A x A if x A > x A () Sbstitting () and (5) into x A and x A in the "if" ondition of (6) or (7), we have the ritial hyperplane x A x A.Thatis, γ ( s)( s), () 3 whih is drawn in Figre. Then, we ensre that π A x A (π A x A ) is obtained above(below)thehyperplane(). Siilarly, when forelosing fir e, fir s progra is Max x π F eπ F γ (x ) s.t. x A x

24 Then, fir s axiized profit is represented as follows. π F x F if x F > x A, (3) π F x A if x F x A, () where x F Y γ (5) Sbstitting () and (5) into x F and x A in the "if" ondition of (9) or (0), we have the ritial hyperplane x F x A.Thatis, γ s, (6) whih is also drawn in Figre. We ensre that π F x A (π F x F ) is obtained above(below)thehyperplane(). Now, we an derive the soltion of fir s investent by obining the two sbprobles for the ase where s</. Note that the soltion iplies the deterination of the eilibri arket strtre in eah region. For exaple, onsider the region where γ > ( s)( s) and γ > s. 3 This region orresponds to the ase where x A x A and x F x A.Sineπ A x A π F x A and π A x A > π A x A. fir s profit-axiizing investent is x A, and the eilibri arket strtre in this region beoes dopoly with aess. The profit-axiizing investent and the eilibri arket strtre in other regionsaresiilarlyderived,asisshowninfigre. 3

25 B. The sketh of the derivation of seond-best investent and its assoiated arket strtre with fir e s aess strategy Notie that the differene between the seond-best investent proble and fir s profitaxiization proble exists only on the objetive fntion. Hene, the proedre to derive the seond-best investent is exatly the sae as that of fir s profit-axiization proble. The soial welfare is represented by W A ( x ) A ( sx ) A A e A A e A γ (x ), (7) when fir e aesses fir s infrastrtre. Siilarly, the soial welfare when fir foreloses fir e is represented by W F ( x ) F F F γ (x ). (8) When s /, fir e aesses fir s infrastrtre for any x nder a, so that we have x A (s )Y 9γ (s s ). (9) When s</ and a, the ritial level of x A also applies to the seond-best proble. Hene, the proble is analyzed by the sbprobles of the ases of aess and forelosre, as is fir s profit-axiization proble. In fat, the ritial hyperplane when fir e aesses is given by γ (5 s)( s). (0) 3 That is, in the region above (below) (6), the ondition that x A < (>) x A holds, whih gives W A x A (W A x A )inthatregion.

26 Siilarly, we obtain the ritial hyperplane when fir e is forelosed is given by γ 3 ( s). () Below (7), we have the nonstrained seond-best investent nder the forelosre, whih is given by x F 3Y γ 3, () and the assoiated soial welfare is W F x F. The soial welfare in the above region is W F x A. Coparing W A (.) and W F (.), both of whih are evalated at the assoiated investent levels, we an derive the seond-best arket strtre in eah region when s</. Then, obining the seond-best arket strtre and that in the eilibri, we obtain Figre 3. C. The proof of Proposition Fro () and (5), it is easy to verify that x A <x A. Then, the lai in the text is obtained fro the oparison of the regions in the seond-best and eilibri arket strtres and the fat that x A < x A <x F. D. Fir e s entry deision in the third stage In this appendix, we provide the sketh of the proedre to derive fir e s entry deision in the third stage. First of all, we need to prepare fir s setting of the wholesale prie w nder a reglated aess harge a. Givena, the wholesale prie w shold be aepted by fir e. This onstraint reires π e B (w) π e A (a), whereπ e B (w) is fir e s profit nder a bypass strategy with w, whereasπ e A (a) is its profit nder aess strategy with a. The 5

27 ondition π e B (w) > < πe A (a) is rewritten as w < > a sx w (3) Frtherore, nder w, fir s profit shold be nonnegative; π B (w) 0. Hene, we need to exaine for ases, depending on whether or not fir s profit-axiizing wholesale prie is lower than w (i.e., w > w where < w is the profit-axiizing wholesale prie given by (6)) and whether fir s profit is nonnegative or not (i.e.,π B (w) > 0). < The ondition that π B (w) (<)0 is rewritten as a (<) sx () Using these onditions, we need to exaine fir e s entry deision in all the for ases. Let s trn to fir e s entry deision in the third stage. First, onsider the ase where w w. The ondition that w w is rewritten as µ µ s a x. (5) In this ase, fir needs to offer w if it rejets the proposal of vertial erger. When fir e proposes a vertial erger, the following ondition st be held. π M π B (w) π e B (w) π e A (a) (6) Then, let s exaine the ase where π B (w) < 0. The ondition that π B (w) < 0 is rewritten as a sx <. In this ase, fir doesnothaveaninentivetooffer w. Then, fir e s alternatives are vertial-erger strategy and aess strategy. The ondition that π M π e A (a) is rewritten as a sx, whih ontradits the preise that π B (w) < 0. Hene, when π B (w) < 0, fir e always has an inentive to se the 6

28 aess strategy. In the ase where π B (w) 0, fir e offers a vertial erger if and only if µ µ s a x (7) Seond, onsider the ase where the reglated aess harge does not bind fir s profit-axiizing wholesale prie; w < w. Whenfir e proposes a vertial erger, the following ondition st be held. π M π B (w ) π e B (w ) > π e A (a) (8) In fat, nder Cornot opetition in the resale arket, we ensre that π M > π B (w )π e B (w ). Hene, (3) holds as long as e B (w ) > 0. Sarizing these reslts, we obtain Figre. E. The derivation of Figres 5 and 6: the eilibri investent and arket strtre with aess and vertial-erger strategies As in Figres - to -3, fir e s entry deision depends on the level of s, the sign of ost differene, and the relationship between the level of fir s arginal ost and the deand size. Hene, fir s investent proble shold be exained in all the seven ases stated in the text. Here, the eilibri investent in the vertial-erger arket withot any restrition on x is given by x M (Y ) 9γ 8 (9) The proedre to derive the eilibri investent and arket strtre is the sae as in Setion 3. Hene, we give the analysis of one ase as an exaple. Consider the ase where / s and >0. See Figre -. In this ase, nder a, fir e 7

29 takes vertial-erger strategy if x x M where x M is defined by sx M, i,e., x M /s. Hene, when allowing fir e s vertial erger, fir s proble is Max x π M eπ M γ (x ) s.t. 0 x x M On the other hand, when allowing fir e s aess, fir s proble is Max x π A eπ A γ (x ) s.t. x M x Analyzing these two sbprobles, we an draw the region of the eilibri arket strtre for s [/, ] in Figres 5 and 6. The eations of ritial hyperplanes are γ 8 (Y ) s, (30) 9 9 γ 9 (Y ) s (Y ) s. (3) All the other ases are siilarly exained. One aveat: for s [0, /), we need to lassify several ases aording to the arket size. As entioned in the text, we restrit or attention to two illstrative ases, i.e., 0 < (/0) Y and (/0) Y < (/7) Y. Referenes [] Arstrong, M., 00, "Aess Priing, Bypass, and Universal Servie", Aerian Eonoi Review 9 No., [] Arstrong, M., 00, "The Theory of Aess Priing and Interonnetion", in Cave, M., S. Majdar, and I. ogelsang (eds.) Handbook of Teleoniations Eonois I, Asterda: North Holland. 8

30 [3] Arstrong, M. and Sappington, D. E. M., 006, "Reglation, Copetition, and Liberalization", Jornal of Eonoi Literatre, [] Falhaber, G. R. and Hogendorn, C., 000, "The Market Strtre of Broadband Teleoniations", Jornal of Indstrial Eonois XLIII, [5] Foros,, 00, "Strategi Investents with Spillovers, ertial Integration and Forelosre in the Broadband Aess Market", International Jornal of Indstrial Organization, -. [6] Gthrie, G., 006, "Reglating Infrastrtre: The Ipat on Risk and investent", Jornal of Eonoi Literatre, [7] Kotakorpi, K., 006, "Aess Prie Reglation, Investent, and Entry in Teleoniations", International Jornal of Indstrial Organization, [8] Laffont, J.-J. and Tirole, J., 990, "Bypass and Creaskiing", Aerian Eonoi Review 80, [9] Mankiw, N. G. and Whinston, M. D., 986, "Free Entry and Soial Ineffiieny", Rand Jornal of Eonois 7, [0] Mizno, K., and Shinkai, T., 006, "Delegating Infrastrtre Projets with Open Aess", Jornal of Eonois 88 No.3, 3-6. [] Ordover, J. A., Saloner, G., and Salop, S. C., 990, "Eilibri Market Forelosre", Aerian Eonoi Review 80 No., 7-. [] Sappington, D. E. M., 005, "On the Irrelevane of Inpt Pries for Make-or-By Deisions", Aerian Eonoi Review 95 No.3, [3] Szra, K. and Kiyono, K., 987, "Entry Barriers and Eonoi Welfare", Review of Eonoi Stdies 5,

31 [] aletti, T.M., 003, "The Theory of Aess Priing and Its Linkage with Investent Inentives", Teleoniations Poliy 7, [5] ogelsang, I., 003, "Prie Reglation of Aess to Teleoniations Networks", Jornal of Eonoi Literatre,

32 Fir Fir e Fir ~ π e e π π Aess ( ) ( ) a x s A 3 ( ) ( ) A e A A a ~ π ( ) ( ) a x s A e 3 ( ) A e A e π 0 0 Non- Binding APR ( ) x B ( ) ~ B B π ( ) B e x 6 ( ) B e B e π B e B ( ) B x π Bypass Binding APR ( ) ( ) ( ) a x s A B 3 ( ) ~ B B π ( ) ( ) ( ) a x s A e B e 3 ( ) B e B e π B e B ( ) B e B sx a 3 π Table Eilibri Prodtion and the Assoiated Profits Notes: (i) ~ π represents fir s profit exlding the infrastrtre investent ost. (ii) (Non-)Binding APR represents the ase where aess prie reglation is (not) binding.

33 ertial Merger Forelosre 3 M Fir Fir e Fir ~ ( x ) F ( x ) ~ π π M M ( ) ~ π F F ( ) 3 e M e e ( ) π e e ( x ) π π π π π M e M ( ) Table (Contined) Eilibri Prodtion and the Assoiated Profits Notes: (i) ~ π represents fir s profit exlding the infrastrtre investent ost. (ii) The joint prodtion and its assoiated profit are reported in the vertial erger ase.

34 a Forelosre a s x Aess 0 x Figre Fir e s Entry Deision with Aess: The ase where < s

35 γ Aess 3 9 A or F 0 s Figre Eilibri Market Strtre with Aess Note: A or F represents Aess or Forelosre.

36 5 3 γ Aess vs. Aess Aess vs. A or F Aess vs. Forelosre A or F vs. Forelosre 0 s Figre 3 Coparison of Seond-Best and Eilibri Market Strtres with Aess Notes: (i) A or F represents Aess or Forelosre. (ii) Doble asterisk () represents the seond-best. 3

37 Figre - Fir e s Entry Deision with Aess and ertial Merger: The Case where < s 0 a x x s a Aess Forelosre x s a sx a Merger ertial x s a x sx

38 5 Figre - Fir e s Entry Deision with Aess and ertial Merger: The Case where < s 0 a x x s a Aess Forelosre x s a sx a Merger ertial x s a x sx

39 6 Figre -3 Fir e s Entry Deision with Aess and ertial Merger: The Case where 0 s 0 a x x s a Aess Forelosre x s a sx a Merger ertial x s a x sx

40 γ ertial Merger A or M ( Y ) ( Y ) 3 Aess 9 M or F Y s Figre 5 Eilibri Market Strtre with Aess and ertial Merger: The Case where 0 < Notes: (i) Y, and. (ii) A or M represents Aess or ertial Merger. (iii) M or F represents ertial Merger or Forelosre. 0 Y 7

41 γ ertial Merger A or M 9 Aess Y s Figre 6 Eilibri Market Strtre with Aess and ertial Merger: The Case where Notes: (i) Y, and. (ii) A or M represents Aess or ertial Merger. 0 Y < 7 Y 8

42 γ M or F ertial Merger 5( Y ) 3( Y ) ( Y ) ( Y ) 3 9 Forelosre A or F A or M Aess 0 Y s Figre 7 Seond-Best Market Strtre with Aess and ertial Merger: The Case where 0 < Notes: (i) Y, and. (ii) A or M represents Aess or ertial Merger. (iii) A or F represents Aess or Forelosre. (iv) Doble asterisk () represents the seond best. 7 Y 9