Unbundling the Local Loop time dependent rental path

Unbundling the Local Loop time dependent rental path Marc BOURREAU and P nar DO ¼GAN y November 26, 2001 Abstract Competition for high bandwidth services in the telecommunications industry is studied, with introducing the possibility for the entrant to lease local loops. A pertinent issue for regulatory policy for unbundling is whether unbundling deters or delays the investment in alternative technologies to the traditional copper loops. A main result is that the unregulated incumbent sets a rental scheme which suboptimally retards the new technology adoption. A rental scheme which achieves the optimal adoption date is determined, and a sunset clause is argued to be redundant in improving social welfare. 1 ntroduction n this paper we provide a dynamic model to study the e ect of local loop unbundling on the incentives to adopt new technologies (e.g., wireless local loop, cable networks or ber optic networks). The incumbent sets a rental path for its local loops, and the entrant decides whether to lease loops (to compete on the basis of services) or to adopt a quality improving new technology (to compete on the basis of facilities). We show that an unregulated incumbent sets a rental path for its local loop which suboptimally delays technology adoption. We also characterize a rental path which achieves the socially optimum adoption date, and discuss the role of sunset clauses in attaining socially desirable outcomes. Riordan (1992) studies how price and entry regulations e ect the pattern and timing of technology adoption. Two rms decide if and when to adopt a new technology in a setting where adoption cost declines over time and pro t ows change with adoption patterns. He shows that price and entry regulations tend to slow down technology adoption as they make preemption strategies less attractive. ENST, Paris, FRANCE. E-mail marc.bourreau@enst.fr y GREMAQ, UT-1, Toulouse, France and Public Utility Research Center at UF, Florida U.S.A.; E-mail pinar.dogan@univ-tlse1.fr 1

Similar to Riordan (1992), we consider a new technology, for which the adoption cost declines over time. Furthermore, to the extent that the new technology brings a superior quality, technology adoption alters pro ts ows. However, we consider the entrant as the only rm, who has the option to adopt the new technology. 1 Moreover, the entrant has another option for entry; it can lease the incumbent s local loop and compete on the basis of services prior to any technology adoption. This empowers the incumbent with a strategic tool, rental pricing of the loop, which a ects the opportunity cost -hence, the incentives- of the entrant to adopt the new technology. We show that the incumbent increases the opportunity cost of adoption to the entrant by setting a rental path which is decreasing over time. During the earlier periods in which adoption is too expensive (hence, there is no e ective threat of a new technology), the incumbent sets too high a rental price (or simply refuses to unbundle), and hence protects its monopoly pro ts. As soon as the adoption cost has su ciently declined, so that the entrant is likely to adopt the new technology, the incumbent changes its pricing strategy. Following the fall in the adoption costs, the incumbent lowers the rental price of loops over time so that leasing loops is (or remains as) a better option to the entrant. The incumbent follows this strategy until the time when adoption becomes a better option to the entrant, no matter how low the rental price is. As a consequence, facility based entry is delayed compared to the case in which there is no unbundling. Many policy makers consider facility based competition as an important component of a deregulated competitive telecommunications industry. Therefore, any regulatory policy promoting an unbundled access to the local loop, should be concerned not to undermine the incentives for facility based entry; 2 in words of the EC decision on unbundling the local loop, Pricing rules for local loops should foster fair and sustainable competition, bearing in mind the need for investment in alternative structures, and ensure that there is no distortion of competition, in particular no margin squeeze between prices of wholesale and retail services of the noti ed operator. The possible e ects that unbundling process might have on the build or buy decisions of the entrants are discussed in several policy studies; 3 with the present paper we provide a formal analysis to the issue. The rest of the paper is organized as follows. We begin by describing the model, and computing the pro t ows for service based and facility based com- 1 This situation can be interpreted as one-sided entry regulation in Riordan, except that we consider a single market (market for high bandwidth access) in which old and new technologies compete. 2 See La ont and Tirole (2000) for a discussion on unbundling-based entry and facility-based entry. 3 See Harris and Kraft (1997), EC DG nformation Society Working Document on Unbundled Access to the Local Loop (2000), Polard (1999), Competition in Local Acces; Results of the Public Consultation CP Understanding (2000), ntug Europe position paper on Local Loop Unbundling (2000). 2

petition in Section 2. n Section 3, we compute the equilibrium rental path and the adoption date in the unregulated environment. n Section 4 we characterize the socially optimal adoption date and the rental path. We also determine a sunset clause which achieves socially optimal adoption date. Finally, we conclude. 2 The Model The incumbent rules all the decisions regarding unbundling. f the incumbent decides to unbundle its local loop, it determines a rental path for it. The incumbent has monopoly power in providing high bandwidth services as long as there is no entry. Entry in the high bandwidth services market takes one of the two following forms. Service based entry takes place when the local loop is unbundled and the entrant leases loops. n this type of entry we assume that the incumbent and the entrant provide same quality of service, and di erentiate their products horizontally. A proper interpretation of quality in this context is the size of the bandwidth. On the other hand, facility based entry takes place when the entrant adopts the new technology. The new technology produces a superior quality of service compared to the traditional local loops. We consider this quality improvement to be exogenous. The cost of adopting new technology declines over time, and the entrant can lease loops, prior to the technology adoption if the local loop is unbundled. We assume that the incumbent uses some digital subscriber line (DSL) technology, and is not allowed to invest in an alternative technology. This may be either because of its previous sunk investments in the copper loop, or because of a regulatory ban. Bourreau and Do¼gan(2001)studythesameissuewithtwonotabledi er- ences. First, the incumbent commits to a xed rental price at the initial period. Second, there are two di erent technologies available for adoption, which provide the entrant with a di erent level of quality of service. The reason why we do not consider multiple types of new technologies here is that the entrant may adopt di erent technologies when the local loop is unbundled and when it is not; such a distortion that unbundling may create on the technology choice is out of the focus of this study. Firms The incumbent () has a constant marginal cost of providing high bandwidth services, which is normalized to zero. f it unbundles the local loop it sets the rental path r t ; and receives a marginal revenue of r t per line if the entrant (E) decides to lease lines. To simplify the analysis, we assume that the xed cost of unbundling for the entrant is zero. 4 The quality of service that is provided with the traditional local loop is also normalized to zero, and the new 4 n reality, entrants incur a positive entry cost which is due to co-location and order handling. However, assuming away the xed cost of entry does not change the essence of our analysis. 3

technology brings a superior quality of service, q F E.5 Time is continuous and the time horizon is in nite. The discounted adoption cost of the new technology is A( ) = a 2 2 ; where 2 [0; 1) is the discount factor determined by the adoption date. Here we use the same notation and interpretation of Riordan (1992); =exp( ±t);where ± is a discount rate, and t denotes time. Throughout the paper we will refer to as the adoption date. Note that higher corresponds to an earlier adoption date. We have A 0 ( ) 0; and A 00 ( ) > 0 Furthermore, we normalize ± to 1. Assumption 1. a>4q F E =9. This assumption ensures that the adoption cost is su ciently high, and that adoption never happens at time zero. The entrant weighs the discounted cost of adoption against the bene ts of higher pro t ows, driven by a better quality of service. Firms objective is to maximize discounted pro ts. Consumers Consumers are uniformly distributed on the unit square [0; 1] [0; 1]. Aconsumeroftype(x; µ) has a taste x for variety (its location on the horizontal segment) and a valuation µ for quality (location on the vertical segment), with x; µ 2 [0; 1]. The indirect utility function of a consumer of type (x; µ), who purchases a unit of service from rm i is U = v + µq i (x y i ) 2 p i ; where v>3is the xed utility derived by using high bandwidth services. The horizontal location of rm i on the unit segment is denoted by y i,whereasits price is denoted by p i,withi = ;E The lower bound of v ensures market coverage for all possible cases i) when incumbent operates alone, ii) when rms compete on the basis of services, iii) when rms compete on the basis of facilities. The quality of service provided by the incumbent is q =0 The quality of service provided by the entrant, q E, depends on the technology it uses. f it leases loops and competes on the basis of services q E =0 On the other hand, if it adopts the new technology and competes on the basis of facilities q E = qe F ; where qe F is exogenous and is given in the interval qf E 2 (2; 3) 5 n reality, incumbents can make upgrading investnents which would increase the bandwidth (here the quality) of their local loop. What is essential to our analysis is that the new technolgy brings a su ciently superior quality to the maximum of what can be achieved through the cooper lines. 4

The new technology brings forth vertical dominance in the sense of Neven and Thisse (199). Vertical dominance is determined such that quality di erentiation dominates horizontal di erentiation. This is the case when @µ(x) @x < 1 (1) where µ(x) is the marginal consumer, with µ(x) = (p E p )+ ye 2 y2 2(yE y ) x q E Lower bound on qe F guarantees vertical dominance for any p E, p,andjy E y j 1, as inequality (1) holds for all q>2 On the other hand, the upper bound for qe F ensures the existence of a price equilibrium at the linear part of the demand curve. Note that in this simpli ed setting of Neven and Thisse (199), the demand curve is composed of three parts. n addition to a linear part in the middle, the demand curve has a convex and a concave part, for very high and very low prices, respectively. Through out the paper we focus on the linear part of the demand curve. Considering these non-linear parts would complicate the exposition without substantively enhancing our analysis. To understand the concept of vertical dominance, consider the following situation. Assume that rms achieve maximum horizontal di erentiation (y =0 and y E =1) and that they charge exactly the same price (p E = p ). Now, consider the customer of type (0; 1=2) Clearly, if there were no quality dimension to the service, this customer would purchase access from rm, asx = y =0 However, this customer has a valuation for quality, µ =1=2; and the entrant provides a higher quality of service. Hence, it strictly prefers to purchase the access from rm E; if the quality di erence is su ciently high, i.e., q E > 2 Therefore, for q E > 2, vertical di erentiation dominates horizontal di erentiation. Note that for q E =2; this customer is just indi erent between the services provided by each rm. There is neither vertical, nor horizontal dominance. n this case, the slope of µ(x) is 1, and it passes through the diagonal of the unit square (for p = p E ), and hence the rms share the market equally. Obviously any price di erence would shift µ(x), increasing the market share of the rm with the cheaper service. The Timing The timing of the game is as follows. At the beginning of the game, the incumbent decides whether to unbundle or not. f the incumbent decides to unbundle, it commits to the time dependent rental path r ( ). Ateach time, the entrant decides whether to rent loops if the local loop is unbundled, and compete on the basis of services, or to adopt the new technology. t can compete on the basis of services by leasing lines before it decides to introduce the new technology. Firms obtain pro t ows of ¼ S(r( )); ¼S E (r( )) during the phase of service based competition and ¼ F ;¼F E during the phase of facility based competition. 5

Pro t Flows Let ¼ j i denote the pro t ow of rm i;where j = M;F;S stand for monopoly, facility based competition and service based competition, respectively. The net discounted pro ts will be denoted by j i The incumbent has monopoly power in providing high bandwidth services as long as there is no service based or facility based entry. Since immediate technology adoption is assumed away, this is the case if the rental price is su ciently high (or there is no unbundling) so that the entrant does not lease loops. When the incumbent is the sole provider, it locates at 1=2. Corresponding prices and pro ts are p M = ¼ M = v 1=4 For the rest, pro t ows depend on whether the entrant leases loops (service based competition), or adopts the new technology (facility based competition). Notice that in this setting, the entrant always ends up by adopting the new technology. This follows because there is no xed cost for adopting the new technology (as! 0; we have A( )! 0), and as it will be seen in the following, the entrant obtains a higher pro t ow when it competes with the new technology. There are two possible cases with respect to the entrant s decision. n the following, we compute the payo ows for each case. Case 1 Facility based competition. n this case the entrant has a quality qe F. Then, both rms choose their location on the horizontal line, and then set their prices. While computing the payo ows in this section we assume that y y E, without any loss of generality. Lemma 1 During the phase of facility based competition, the equilibrium is characterized by minimum horizontal di erentiation (y = y E ), the equilibrium prices and pro t ows are p F = q=3, pf E =2q=3, ¼F = q=9, and¼f E =4q=9 Proof. We rst start by deriving the demand function. Marginal consumers are de ned by µ(x) = (p E p )+ ye 2 y2 2(yE y ) x q Let p (0;0) such that µ(x =0)=0for a given p E (µ(x) passes through southwest corner of the unit square, so the superscript (0; 0) stands for (x =0;µ =0)). As @µ=@x < 0; this is the only point where µ(x) touches the unit square. p (0;0) is nd by 0=(p E p )+ ye 2 y 2 ) p (0;0) = p E +(y 2 E y 2 ) 6

Whenever p p (0;0), demand for the incumbent is zero. Similarly, let p (1;1) be such that µ(x =1)=1for a given p E ; so that µ(x) passes through north-east corner of the unit square. 1= (p E p )+ ye 2 y2 2(yE y ) ) q p (1;1) = p E +(ye 2 y) 2 (y E y ) q Whenever p p (1;1) the incumbent has a unit demand (all the market). Similarly, we nd p (0;1) and p (1;0) p (0;1) = p E +(y 2 E y 2 ) q; p (1;0) = p E +(ye 2 y2 ) 2(y E y ) The demand for the incumbent is formed by three segments. Let ex the point where µ(x) touches the lower side of the unit square, i.e., µ(x) =0 We nd ex by 0= (p E p )+ ye 2 y2 2(yE y ) ex ) q ex = (p E p )+ ye 2 y2 2(y E y ) Whenever p 2 (p (1;0) ), wehave ;p (0;0) D 1 = Z ex 0 µ(x)dx; D 1 (pe p )+(ye 2 = y2 ) 2 4(y E y )q On the other hand, for p 2 [p (0;1) ;p (1;0) ), wehavethelinearsegmentofthe demand curve which is de ned by Z 1 D 2 = µ(x)dx; 0 D 2 (pe p )+(ye 2 = y2 ) (y E y ) q Finally, let x such that µ(x) =1so that 1= (p E p )+ ye 2 y2 2(yE y ) x ) q x = (p E p )+ ye 2 y2 q (y E y ) 7

For all p 2 [p (1;1) ;p (0;1) ); Z 1 D 3 = x + µ(x)dx; 2q p +(y D 3 2 = E y 2) q (p +(ye 2 y2 ) 2(y E y )) 2 4(y E y )q The entrant s demand can be nd by DE 1 = 1 D 1 ;D 2 E = 1 D 2 ; and DE 3 = 1 D 3 As mentioned earlier, we focus at the linear segment, D 2 and DE 2.LetDF i denote the demand for rm i, when rms compete on the basis of facility, and let y =(ye 2 y 2 ) (y E y ) Then, we have D F =(p E p + y) =q; and DE F =1 (p E p + y) =q The incumbent and the entrant maximize x ¼ F = p (p E p + y) =q; and ¼E F = p E (1 (p E p + y) =q) ; respectively. f it exists, the Nash equilibrium of this price game yields p F = (q + y) =3 and p F E = (2q y) =3 We have DF = (q + y) =3q; and DE F = (2q y) =3q; and corresponding pro ts are ¼ F =(q + y)2 =9q; and ¼E F =(2q y)2 =9q Now, it remains to show that the price equilibrium exists. The price equilibrium exists if p F and p F E are valid in the linear part of the demand, i.e., p F 2 [p(0;1) ;p (1;0) ) We know that p (0;1) = p F E 1; and p(1;0) = p F E +1 Furthermore, p F E =(2q y) =3. Thus, the price equilibrium exists if (q + y) =3 2 [(2q y) =3 1; (2q y) =3+1) t is easy to verify that given q E 2 (2; 3) by our assumption, price equilibrium does exist. The equilibrium horizontal locations are y E = y =1=2;as for p F =(q + y) =3 and p F E =(2q y) =3; and maximization of ¼F and ¼F E yields y E = y =1=2 Case 2 Service based competition.

As already stated, when rms compete using the same infrastructure, i.e., the traditional local loops, quality of service provided by both rms is the same, and is normalized to zero. The rms obtain maximum horizontal di erentiation. Without loss of generality, let y =0and y E =1 Lemma 2 During the phase of service based competition, equilibrium prices and pro t ows depend on r; and are the following < 1+r if r 2 [0;v 5=4) p S (r) = v 1=4 if r 2 [v 5=4;v 3=4) (2v + r) =3 1+2 p ; (v r) =3 if r 2 [v 3=4;v] < p S E (r) = >< ¼E S (r) = > 1+r if r 2 [0;v 5=4) v 1=4 if r 2 [v 5=4;v 3=4) (2v + r) =3 if r 2 [v 3=4;v] 1=2 if r 2 [0;v 5=4) (v 1=4 r)=2 if r 2 [v 5=4;v 3=4) ³2 p 3(v r) 3=2 =9 if r 2 [v 3=4;v] ; ; and < 1=2+r if r 2 [0;v 5=4) ¼ S(r) = (v 1=4+r)=2 if r 2 [v 5=4;v 3=4) r 1+ p 3(v r) 2 p 3(v r) 3=2 =9 if r 2 [v 3=4;v] Proof. See Appendix A. Lemma 3 At any time t, the incumbent prefers service based competition (to lease its loops to the entrant) instead of facility based competition. Proof. Pro t ows are determined in Lemma 1 and Lemma 2. When the entrant adopts a new technology, the incumbent obtains a pro t ow of ¼ F = qf E =9 On the other hand, service based competition yields ¼ S (r) =1=2 +r for r 2 [0;v 5=4) ; and ¼ S(r) =(v 1=4+r)=2 for r 2 [v 5=4;v 3=4) As qf E =9 < 1=2; ¼ F <¼ S(r) holds for all r 2 [0;v 5=4) Furthermore, we have qf E =9 < (v 3=4) as v>3; thus ¼ F <¼S (r) holds for all r 2 [v 5=4;v 3=4) Finally, for r 2 [v 3=4;v),we have ¼ S(r) =r 1+p 3(v r) 2 p 3(v r) 3=2 =9; and the rental price which maximizes the pro t ow is r = v 3+3 p 3=2; which yields ¼ S(r) =v 3+3p 3 t is easy to check that v 3+3 p 3 >qe F =9; as v>3 The di erence between ¼ S(r) and ¼F measures the rents protected by preventing the entrant s adoption when setting an attractive rental price for the loops. Up till now, we have looked for the equilibrium pro t ows, for given entry decision of the entrant. n the next section we study the optimal date of adoption, both for the cases with and without unbundling. 9

3 The Equilibrium We begin with solving the equilibrium for the unregulated environment. n Section 4 we introduce a social welfare maximizing regulator, and analyze the relevant regulatory policies for achieving socially desirable outcomes. The adoption date changes with the entrant s incentives to lease loops, hence, with the rental path. ndeed, we show that when the entrant leases loops prior to its technology adoption, the adoption date is retarded compared to the case in which local loop is not available for lease (or is too expensive). This follows mainly because of the replacement e ect which has been mentioned in several other studies. t has been introduced in the R&D literature by Arrow (1962); an incumbent rm has less incentives to invest in R&D, because by increasing its R&D investment, it hastens its own replacement. 6 The replacement e ect in our model is very similar to the replacement e ect considered in the licensing literature (for example, see Gallini (194)). ndeed, by licensing its technology, the incumbent reduces the entrants incentives to innovate. 3.1 NoUnbundlingoftheLocalLoop f the local loop is not unbundled, the only way of entry for the entrant is to adopt the new technology. The entrant maximizes its discounted pro ts net of the adoption cost, hence solves the following problem max n ¼ F E a 2 2o The optimal adoption date is determined by the rst order condition = ¼E F =a; (2) where ¼E F is de ned in Lemma 1. Therefore for all 2 ( ; 1) the entrant does not enter the market, and for all 2 [0; ] competition is facility based. The discounted net pro t of the entrant is F E = ¼ F 2 E =2a On the other hand, for all 2 ( ; 1) the incumbent operates alone, and earns monopoly pro ts. From on, it earns pro ts from facility-based competition, hence, its discounted pro ts are F ( )=(1 ) ¼ M + ¼ F 6 See Tirole (19). 10

3.2 Unbundled Local Loop We begin with computing the adoption date when the entrant leases loops prior to technology adoption. Assume that the entrant starts leasing lines at 2 [0; 1), and adopts the new technology later at. b Let S+F E denote the entrant s discounted pro ts net of adoption cost. The entrant s problem is the following max S+F E b max b Z b ¼ S E (r(x))dx + b ¼ F E A( b ) (3) Replacing ¼E S (r) with the values determined in Lemma 2, we nd the entrant s net discounted pro t function, ³ >< b =2+ b ¼ E F A( b ) if r ( ) 2 [0;v 5=4) S+F E (r ( )) = > R b ((v 1=4 r(x)) =2) dx + b ¼ E F A( b ) if r ( ) 2 [v 5=4;v 3=4) R ³ b 2 p 3(v r) 3=2 =9 dx + b ¼ E F A( b ) if r ( ) 2 [v 3=4;v) Remark that if the rental price at is set such that r ( ) 2 [0;v 5=4) ; the pro t ow of the entrant does not depend on r ( ) ; and the optimal adoption date for this range is b 1 = ¼F E 1=2 (4) a f r ( ) 2 [v 5=4;v 3=4) ; the optimal adoption date is b (r ( )) = 1=4+2¼F E + r ( ) v (5) 2a Notice that (r b ( )) is increasing in r ( ) ; which implies that at ; ahigher r ( ) leads to an earlier adoption. Thus, the earliest adoption in this range of rental price occurs when r ( ) is set at r ( ) = v 3=4 ²; and is at ¼ F E 1=4 =a ²; with ² very small. On the other hand, the rental price r ( ) = v 5=4 triggers the earliest adoption in this range, which occurs at b 1 Therefore, for r ( ) 2 [v 5=4;v 3=4) ; we have (r b h ( )) 2 b 1; b 2, where b 2 = ¼F E 1=4 a Finally, when r ( ) 2 [v 3=4;v), the optimal adoption date is b (r ( )) = ¼F E 2p 3(v r ( )) 3=2 =9 (6) a Again, (r b ( )) increases with r ( ) ; and any rental price set such that r ( ) 2 [v 3=4;v) leads to technology adoption at (r b h ( )) 2 b 2 ; ; where is determined in (2). Therefore any r ( ) v; yield the same adoption date as if the local loop was not unbundled. 11

Note that the order b 1 < b 2 < implies that the earliest possible adoption date in this game is ; and the latest b 1 Having de ned the optimal adoption function for all r ( ) ; we now study the entrant s strategy with respect to entry for a given rental path set by the incumbent. To do so, we distinguish between the phases in which the entrant s optimal adoption function changes. For each phase, we determine the optimal adoption strategy, given that no adoption has occurred prior to that phase. Optimal Entry Strategy Phase 1 to This is the initial phase with respect to the time line. We know that in this phase adopting the new technology is too expensive, and is not optimal for the entrant. During this phase the only possibility for entry is by leasing loops. Furthermore, as adoption is not optimal, the rental price does not a ect any adoption decision during this phase. Therefore, for a given r ( ) at 2 ( ; 1] the entrant leases loops and competes on the basis of services if ¼E S (r ( )) > 0; which also implies that S E ( ) > 0 We know that the entrant obtains a positive pro ts ow from service based competition if r ( ) 2 [0;v) Hence at all 2 ( ; 1] ; the entrant leases loops if r ( ) 2 [0;v); does not enter if r ( ) 2 [v; +1) Phase to b 2 During this phase the ³ entry idecision depends on the rental path set by the incumbent. At all 2 b 2 ; ; the entrant leases loops if r ( ) 2 [0;v 3=4) ; adopts new technology if r ( ) 2 [v; +1) Furthermore, at any at this phase, given any r ( ) 2 [v 3=4;v), the entrant adopts the new technology if it is optimal to do so. Given the adoption function for this range in (6), this is true if = ¼ E 2 p 3(v r) 3=2 =9 ; a which implies that adoption is optimal at if µ 3 r ( ) = v q12 p 3 2 ¼ FE a =4 (7) µ q 3 Note that the entrant adopts the new technology at if r ( ) v 12 p 2 3(¼ E a) =4, as any r ( ) greater than the one determined in (7) implies and earlier op- 12

timal adoption date than. Therefore, for all 2 [v 3=4;v) ;the entrant ³ b 2 ; i ; if r ( ) 2 µ q 3 leases loops if r ( ) < v 12 p 2 3(¼ E a) =4; µ q 3 adopts new technology if r ( ) v 12 p 2 3(¼ E a) =4 Phase b 2 to b 1 We have already shown that when r ( ) 2 [0;v 5=4) ; the entrant optimally adopts the new technology at b 1 Therefore at any > b 1 (at any date before than b 1), the entrant does not adopt the new technology, and leases loops if r ( ) 2 [0;v 5=4) On the other hand, if the rental price is su ciently high, i.e., r ( ) 2 [v 3=4;v] ; the entrant adopts the new technology, as we know that rental price in this range yields an adoption date between b 2 and Hence, at any < b 2 (at any date later than b 2), the entrant ³ adoptsi the new technology if r ( ) 2 [v 3=4;v] To summarize, at all 2 b 1 ; b 2,theentrant leases loops if r ( ) 2 [0;v 5=4) ; adopts new technology if r ( ) 2 [v 3=4;v] and for r ( ) 2 [v 5=4;v 3=4), similar argument we had for the phase to b 2 applies, and the rental ³ price above i which the entrant leases loops at is nd from (5). For all 2 b 1 ; b 2 ; if r ( ) 2 [0;v 5=4) ;the entrant leases loops if r ( ) <v 1=4+2¼ F E 2 a; adopts new technology if r ( ) v 1=4+2¼ F E 2 a Phase b 1 to 0 We have already showed that whatever the rental price is, the adoption occurs at latest at b 1 The entrant adopts new technology at b 1; for any given r ( ) ³ Hence, for all 2 0; b 1 competition is facility based. Equilibrium Rental Path We now determine the strategy of the incumbent for the pricing of its local loop. To do so, we study each of the following phases separately, in which the entrant has di erent optimal adoption functions. Phase 1 to We have already showed that whether there is unbundling or not, it is not optimal for the entrant to adopt the new technology, as the adoption cost is still too high. Therefore, only the pro t ows matter for the incumbent s strategy. f the incumbent denies unbundling -or equivalently sets 13

a very high rental price so that the entrant does not lease lines (r ( ) v)- it earns monopoly pro ts ¼ M = v 1=4. On the other hand, if it leases its loops, the maximum pro t ow it can obtain is ¼ S (r = v 3+3 p 3=2) = v 3+3 p 3; and hence, max ¼ S (r) <¼M ; which implies that the incumbent charges r ( ) 2 [v; +1) for 2 ( ; 1] without loss of generality we determine the rental path in this phase with r ( ) = v. Phase to b 2 The incumbent changes its pricing strategy in this phase. This is because r ( ) = v triggers immediate technology adoption. We have already showed with Lemma 3 that at each time, the incumbent obtains a higher pro t ow with service³ based competition i than with facility based competition. Therefore, for all 2 b 2 ;, the incumbent is better o by charging r ( ) such that at each ; the entrant prefers to lease loops to adopt the new technology. This implies that the incumbent sets the rental price r ( ) that maximizes its pro t ow, under the constraint that the entrant leases its loops. As we have mentioned, given the entrant leases loops, the incumbent s pro t ow is maximized with r ( ) = v 3+3 p 3=2 At this rental price, the entrant does not adopt technology at if (r b ( )) Replacing r ( ) in equation (6), we nd that the incumbent charges this price for all such that Hence, > ¼F E 3 p 3 5 =2 a = b 3 r ( ) = v 3+3 p ³ 3=2 for 2 b 3; i However for all b 3; the rental price r ( ) triggers immediate adoption. One can show that the pro t ow of the incumbent under service based competition increases with r for r r ( ). Therefore, the incumbent charges the maximum µ 3 rental rate such that r ( ) <v q12 p 3 2 ¼ FE a =4; so that the entrant leases loops. Hence, µ 3 r ( ) = v q12 p 3 2 ³ ¼ FE a =4 ² for all 2 b 2 ; b i 3 ; where ² is very small. 14

Phase b 2 to b 1 We know that during this phase the entrant has the following strategy for entry it leases loops if r ( ) 2 [0;v 5=4) ; and it adopts the new technology if r ( ) 2 [v 3=4;v] And for r ( ) 2 [v 5=4;v 3=4) the entrant leases loops if r ( ) <v 1=4+2¼E F 2 a; and adopts technology otherwise. One can observe from Lemma 2 that the incumbent s pro t ow under service based competition is increasing in r; for all r 2 [0;v 3=4) Furthermore, we know that any rental price r 2 [0;v 5=4) yields the same adoption date, which is b 1 = ¼E F 1=2 =a This means that the incumbent can not delay adoption further than b 1. We also know that r ( ) = v 5=4 achieves the same adoption date, ³ b 1 i This implies that for 2 b 1 ; b 2 the incumbent sets the maximum r ( ) such that the entrant leases its loops, i.e., ³ i r ( ) = v 1=4+2¼E F 2 a ² for 2 b 1; b 2 ; where ² is very small. Phase b 1 to 0 As we mentioned before, the entrant adopts the new technology at date b 1 at the latest, and stops leasing loops. Therefore, rental price in this phase is irrelevant. The incumbent sets any rental price after b 1 on. With the following we summarize the optimal rental path for the unregulated incumbent, and drop the term ² for expositional simplicity. v for 2 ( ; 1] v 3+3 p ³ i 3=2 for 2 b 3 >< µ ; r 3 ( ) = v q12 p 3 2 ³ i ¼ FE a =4 for 2 b 2 ; b 3 () ³ i v 1=4 2¼E F +2a for 2 b 1; b 2 h i > any rental price for 2 0; b 1 The incumbent has the following strategy with an incentive to protect its monopoly pro ts, the incumbent begins with -and keeps- charging an unattractive rental price, r ( ) = v, during the time when there is no e ective threat of entry due to high adoption costs. When there is no unbundling (or the rental price is too high), the entrant adopts the technology at This is the very moment the incumbent changes its strategy. t charges a rental price which is decreasing by time, as the adoption cost of the new technology is decreasing by time. t makes sure that at each time the entrant leases -or continues to lease- its lines, instead of adopting the new technology. This follows because the incumbent obtains a higher pro t ow when it leases its loops (competes service based) than when it competes against a superior facility. Then, when the adoption cost has su ciently declined, so that adopting the new technology becomes a better option to the entrant, no matter how low the rental price is. Hence the rental price becomes irrelevant. 15

Proposition 1 Unbundling delays technology adoption. Proof. Following the unregulated rental path determined in () the entrant adopts the new technology at b 1 = ¼F E 1=2 a = q=9 1 2a as opposed to = ¼E F =a =4q=9a when there is no unbundling. The adoption is delayed by b 1 = 1 2a t is intuitive that, the higher the adoption cost for the new technology, i.e., the higher a, the lower the delay unbundling introduces for adoption. ndeed, the incumbent has an incentive to delay the adoption of the new technology only if it represents an e ective threat. 4 The Social Optimum and Regulatory Tools n this section, a social welfare maximizing regulator is introduced to compare the unregulated and the socially e cient outcomes. The regulator maximizes the social welfare which is de ned by the sum of consumers s surplus and industry pro ts. n the following, we consider regulation of the rental path as the only regulatory tool. Hence, we assume that the regulator does not control nal prices. We also investigate the case for sunset clauses as a regulatory tool to achieve desirable outcomes. Webeginwithstudyingtheoptimalrentalpathforconsumers. Lemma 4 Consumer surplus maximizing rental path is r cs ( ) = 0 for 2 [1; ),andr cs ( ) v for 2 ( ; 0) Proof. When the entrant leases loops prior to technology adoption, the discounted consumer surplus is S S+F (r ( )) = s S (r ( )) 1 S F (r ( )) + s F S F (r ( )) ; where s S (r ( )) and s F denote consumer surplus ows under service based competition and facility based competition, respectively, and >< v 13=12 r ( ) if r ( ) 2 [0;v 5=4) s S (r ( )) = ³ 1=6 if r ( ) 2 [v 5=4;v 3=4) > 2 v r ( ) + 1 p 3 p v r ( ) =3 if r ( ) 2 [v 3=4;v) ; s F = v 1=12 q=9 16

When the entrant does not lease loops, discounted consumer surplus which is denoted by S F is S F = s M (1 )+s F ; where s M denotes consumer surplus under monopoly, and s M =1=6 Computations for consumer surplus ows can be nd in Appendix B. One can verify that s M s S (r) <s F ; for all v>3, andq 2 (2; 3) This implies that the consumers always prefer immediate adoption. We know that entrant adopts the new technology at earliest (if the local loop is not unbundled, or if the rental price is too high). Prior to, i.e., during the phase in which adoption is never optimal for the entrant, consumers prefer the lowest possible rental price as @s S (r ( )) =@r ( ) 0 Hence for all >, consumers prefer the rental price which is set at the marginal cost of the loops, r cs ( ) = 0 From that date on, they prefer a high rental price (any price above or equal to v) that would give the entrant incentives to adopt the new technology immediately. Note that consumers do not take into account the high cost of adoption which is incurred at early adoption dates. This is the reason why consumers favor a suboptimally early adoption. n the following, we study the socially optimum adoption date. Let w M ;w S and w F denote welfare ows under monopoly, service based competition and facility based competition, respectively. Welfare ows are w M = v 1=12, ( v ³ 1=12 if r ( ) 2 [0;v 3=4) w S (r ( )) = 2v + r ( ) 1+ p 3 p v r ( ) =3 if r ( ) 2 [v 3=4;v) ; w F = v 1=12 + 4q=9, and are computed as shown in Appendix C. t is easy to verify that w S (r ( )) w M <w F ; as @w S =@r 0 when r 2 [v 3=4;v) and w S (v 3=4) = w M. w S (r ( )) = w M if r ( ) 2 [0;v 3=4]. Note that Lemma 5 The socially optimal adoption date is w =. Proof. When r ( ) 2 [v 3=4;v], whatever the adoption date is, the society is better o by no service based competition prior to facility based entry, as w S (r) <w M When r ( ) 2 [0;v 3=4], the service based competition and the monopoly cases yield the same welfare ow, v 1=12. Therefore, welfare maximizing adoption date is nd by maximizing W =(1 w )(v 1=12) + w w F A( w ) 17

The socially optimal adoption date is w = w = w F w M a (v 1=12 + 4q=9) (v 1=12) ; a w = 4q 9a = Proposition 2 Adoption date in the unregulated environment is suboptimally late. hence, Proof. We have b 1 = 4q=9 1=2 ; a b 1 > w The socially optimum adoption date is earlier than the adoption date of the entrant in an unregulated environment, and is later than the date preferred by the consumers, i.e., b 1 < w < cs =1 Corollary 1 A social welfare maximizing rental path is the following r w ( ) = ½ 0 if 2 [ ; 1] v if 2 [0; ] Note that this rental path correspond to the optimal rental path for consumers. However, it is not the unique rental path which achieves the maximum social welfare. For instance, when < ; the social welfare maximizer takes only into account the welfare ows, as in this phase there is no entry at all. Due to the speci cation of our model in which price changes are translated to simple transfers between consumers and the industry, any rental price in the interval [0;v 3=4] achieves maximum welfare. Notice that in this phase, there is no trade o between static and dynamic e ciency, and hence the regulator may set the rental price at r ( ) = 0 in order to maximize the consumer surplus. At the socially optimal adoption date, ; in order to induce the entrant to adopt the new technology, the regulator sets the rental price up to a point where leasing loops is not anymore an attractive option. Any price above v serves this purpose. Finally, from b 1 on, the rental price is irrelevant, as the entrant adopts never leases loops after b 1. 1

v v 3+(3) 1/2 /2 r (!) unregulated rental path regulated rental path any rental path 0! ^ ^ 1! ^ 2! 3!* 1 Figure 1 Regulated and unregulated rental path Sunset Clauses Another important supply condition is the timing of introduction of local loops for leasing. Sunset clauses specifyexanteaperiodoftime after which the incumbent s facilities are no longer regulated. Sunset clauses have been speci ed in the unbundling regulations in Canada and in the Netherlands. For example, Opta, the Dutch regulatory authority, has speci ed a veyear period after which the incumbent operator, KPN Telecom, would be in principle, free to set a tari on a commercial basis. 7 Similarly, Canadian Radio- Television and Telecommunications Commission issued a decision (CRTC-97-), which stated that following a ve-year mandatory unbundling, the incumbent s services and components that are deemed to be essential facilities (including local loops in certain areas) would not be subject to mandatory unbundling and the rental rate would not be regulated any longer. n March 2001 CRTC has extended this sunset period without specifying a termination date. The motivation behind these sunset clauses is to provide the entrants with incentives to build their own facilities. n this respect, deregulating the rental rate is assumed to render leasing lines an unattractive option to the entrant and lead the entrant to install its own facilities. We show that in our setting, sunset clauses do not enhance incentives of the entrant to build its own infrastructure. To see this, consider a regulator who commits to the following rental path r ( ) = 0 until > e (where 7 See Guidelines on access to the unbundled loop, March 1999. See Order CRTC 2001-14. 19

e w = ), and then no regulation on rental price from date e on (therefore the sunset clause is determined by ). e This path does not yield the socially optimum adoption date, which is w. ndeed, as it is optimal for him to do so, the incumbent will charge its optimal rental scheme, which delays adoption up to b 1. This implies that the regulator cannot stop regulating the rental rate before the entrant has adopted the new technology. Otherwise stated, the regulator should regulate the rental price until adoption has occurred. 5 Conclusion We have demonstrated how unbundling the local loop may suboptimally delay technology adoption in the absence of regulatory control. The unregulated incumbent has an incentive to increase the opportunity cost of adoption of the entrant by lowering the rental price of its loops when it faces an e ective threat of facility based entry. Our model also explains the fact that the incumbent operators have a tendency to resist the unbundling of their loops. We argue that this would occur in the earlier periods when an alternative technology is too expensive to adopt, and hence, the incumbent can protect its monopoly pro ts by denying access to its loops (or setting too high a price for it). We claim that as soon as new technologies are available at reasonable costs, the incumbent would promote the lease of its loops, in particular if the prospective technology brings a superior quality. n this paper we have considered an exogenous quality improvement brought forth by the new technology. Certainly, in reality rms can choose from a variety of technologies. Our previous study shows that unbundling may not only distort the timing of the adoption, but also the type of the technology to be adopted. The distortion on the type of technology gives rise to complications for welfare analysis, in particular when the incumbent sets a time dependent rental path. Furthermore, although we do not consider any possibility of deterred entry of the new technology, the analysis can be easily extended in that direction with a slight modi cation in the adoption cost function. There are other issues worth studying. For example, entry via unbundling may reduce the adoption of cost a new technology due to learning economies. Or it may provide the entrant with an information about the demand in the industry. Such a learning e ect would operate in the opposite direction of the replacement e ect, and hence may hasten technology adoption. References [1] Arrow, K. (1962), Economic Welfare and the Allocation of Resources for nvention, in NBER Conference, The Rate and Direction of nventive Activity Economic and Social Factors, Princeton University Press, Princeton. [2] Bourreau, M., and Do¼gan P., (2001), Unbundling the Local Loop, mimeo. 20

[3] Competition in Local Access, Results of the Public Consultation CP Understanding (2000), www.icp.pt/interligocao/uk/relatorio-oll-ng42.doc [4] Bourreau, M., and Do¼gan P., (2001), nnovation and Regulation in Telecommunications ndustry, Telecommunications Policy, Vol.25. [5] Decision CRTC 97-, http//www.crtc.gc.ac/archive/eng/decisions/1997/dt97-.htm, May 1997. [6] EC DG nformation Society Working Document on Unbundled Access to the Local Loop (2000), NFSO A/1. [7] EC Regulation No. 27/2000 on unbundled access to the local loop, O cial Journal of EC, December 2000, L. 336/4-. [] Guidelines on Access to the Unbundled Local Loop, OPTA, March 1999. [9] Harris, R. G. and Kraft, C.J. (1997), Meddling Through Regulating Local Telephone Competition in the United States, The Journal of Economics Perspectives,Vol.11(4),p.93-112. [10] ntug Europe Position Paper on Local Loop Unbundling (2000), ntug 2000/04/E, www.intug.net/views/europe/local_loop_recommendation.html. [11] La ont, J.J., and Tirole J., Competition in Telecommunications, MT Press, 2000. [12] Neven, D. and Thisse, J-F., (199), Choix des Produits Concurrence en Qualité et en Variété, Annales D Economie et Statistique, No.15/16. [13] Pollard, C. (1999), Unbundling - is it really necessary?, ntercai Mondiale White Paper, www.intercai.co.uk/papers_loop.htm. [14] Riordan, M. H., (1992), Regulation and Preemptive Technology Adoption, RAND Journal of Economics, Vol. 23(3), p. 334-349. [15] Tirole, J. (199), The Theory of ndustrial Organization, MT Press, 199. A Appendix Computations for Service Based Competition. We proceed in three steps. We rst derive the pro t functions. Then, we determine the reaction functions. And nally, we solve for the Nash equilibrium of the game. 21

Step One We start by deriving the pro t function of rm i 2f;Eg for any price charged by rm j 6= i, ¼ i (p i j p j ). Notice that the demands for the two rms overlap only when p i 2 (p j 1;p j +1). First, assume that p j v, then ¼ i (p i j p j ) is independent of p j,as rmj serves no consumer. Second, assume that p j <v;then, the marginal consumer is de ned by x =(p E p +1)=2. The marginal consumer obtains a positive surplus if and only if p i p i (p j ) p j 1+2 p v p j f p i > p i (p j ), rmi and j get the following local monopoly pro ts ¼ M (p ;p E )=p p v p + r p v p E ; and ¼E M (p ;p E )=(p E r) p v p E f p i < p i (p j ), rmi and j get the following duopoly pro ts ¼ D (p ;p E )=p D + rd E ; and ¼ D E (p ;p E )=(p E r) D E ; where < 0 if x 0 D = (p E p +1)=2 if x 2 (0; 1) 1 if x 1 and D E =1 D. ; Step Two Now, we can determine the reaction functions of the rms. The reaction function of rm i is de ned as the optimal choice of p i given p j. Let p M i and p D i denote the prices that maximize ¼i M and ¼i D, respectively. We nd p D i (p j )=(p j +1+r) =2, p M = v 1, and p M E = ½ (2v + r) =3 if r v 3 v 1 if r<v 3 We start by deriving the reaction function of rm. cases. The optimal price for rm is We have four possible 1. p M if p (p E ) p M, 2. p D (p E) if p (p E ) >p M, pd (p E) < p (p E ) and p E 1 <p D (p E) p E +1, 3. p E 1 if p (p E ) >p M, pd (p E) < p (p E ) and p D (p E) p E 1, 4. p (p E ) if p M < p (p E ) <p D (p E). 22

To begin with, consider case (1). We nd that p (p E ) p M if p E >v. Now, consider cases (2) to (4). First, we look for the conditions for case (2). We nd that p D (p E) < p (p E ) if and only if p E <r 5+4 p v r +1 and that p D (p E) >p E 1 if and only if p E <r+3. Wehavetocomparethese two conditions. The comparison yields that r 5+4 p v r +1 r +3if and only if r v 3. Firm gets positive demand when it charges p D (p E) if and only if p D (p E) p E +1, which is satis ed if p E r 1. When p E <r 1, rm prefers rm E to serve all customers and to pay r for leasing lines than to charge a retail price lower than r. This analysis shows that when r v 3, the optimal price for rm is p D (p E) if p E 2 [r 1;r+3] and p E 1 if p E >r+3. When r > v 3, the optimal price for rm is p D (p E) if p E 2 r 1;r 5+4 p v r +1 and p (p E ) if p E >r 5+4 p v r +1. To summarize, we have two cases. f r 2 (0;v 3), then r if p >< E 2 [0;r 1) (p R (p E )= E +1+r) =2 if p E 2 [r 1;r+3) p > E 1 if p E 2 [r +3;v) v 1 if p E 2 [v; 1) f r v 3, then r if p E 2 [0;r 1) >< (p R (p E )= E +1+r) =2 if p E 2 r 1;r 5+4 p v r +1 p > (p E ) if p E 2 r 5+4 p v r +1;v v 1 if p E 2 [v; 1) We proceed the same way to derive the reaction function of rm E. The only di erence is that when r>v 3, rme does not serve all customers when it charges its monopoly price, p M E =(2v + r) =3. When r>v 3, rm E can charge its monopoly price if M E > p E (p ), which is satis ed if and only if p > (2v + r) =3 1+2 p v r= p 3. To summarize, we have two cases. f r 2 (0;v 3), then >< R E (p )= > r if p 2 [0;r 1) (p +1+r) =2 if p 2 [r 1;r+3) p 1 if p 2 [r +3;v) v 1 if p 2 [v; 1) f r 2 [v 3; 1), then r if p 2 [0;r 1) >< (p +1+r) =2 if p 2 r 1;r 5+4 p v r +1 R E (p )= p > E (p ) if p 2 r 5+4 p v r +1; (2v + r) =3 1+2 p v r= p 3. (2v + r) =3 if p 2 (2v + r) =3 1+2 p v r= p 3; 1 Step Three Now, we can determine the equilibrium of the game. First, for all r 2 (0;v 3), p S = p S E = 1 + r is an equilibrium and it is the unique equilibrium. Second, let us assume that r v 3. The competitive equilibrium 23

(1 + r; 1+r) exists if and only if 1+r 2 r 1;r 5+4 p v r +1,whichis satis ed if r < v 5=4. There is an equilibrium such that rm charges its monopoly price, v 1, onlyifv 1 <r 1, i.e., r>v. When r 2 (v 5=4;v 3=4), there is a corner equilibrium such that the marginal consumer gets zero surplus, i.e., p S = ps E = v (1=2)2 = v 1=4. ndeed, we nd that v 1=4 >r 5+4 p v r +1 if and only if r>v 5=4. Besides, we nd that v 1=4 < (2v + r) =3 1+2 p v r= p 3 if v 27=4 <r< v 3=4. Finally, when r 2 (v 3=4;v), there is an equilibrium such that rm E charges its monopoly price, p M E =(2v + r) =3 and rm charges p p M E. ndeed, when r>v 3=4 and rm charges p S = v 1=4, theoptimalprice for rm E is p M E =(2v + r) =3. p The best p response of rm is then to charge p p M E =(2v + r) =3 1+2 v r= 3. We check that R p M E = p p M E, as (2v + r) =3 >r 5+4 p v r +1 when r>v 21=2+3 p 10 ¼ v 101 < v 3=4. We also check that R E p p M E = p M E,asp p M E =(2v + r) =3 1+2 p v r= p 3. To summarize, for r v 5=4 we have a competitive equilibrium; for r 2 (v 5=4;v 3=4), we have a corner equilibrium; for r 2 (v 3=4;v), wehavea quasi-monopolistic equilibrium. Equilibrium prices and pro ts are < p S = < p S E = < ¼E S = 1+r if r 2 [0;v 5=4) v 1=4 if r 2 [v 5=4;v 3=4) (2v + r) =3 1+2 p v r= p 3 if r 2 [v 3=4;v) 1+r if r 2 [0;v 5=4) v 1=4 if r 2 [v 5=4;v 3=4) (2v + r) =3 if r 2 [v 3=4;v) 1=2 if r 2 [0;v 5=4) (v 1=4 r)=2 if r 2 [v 5=4;v 3=4) 2 p 3(v r) 3=2 =9 if r 2 [v 3=4;v) and < 1=2+r if r 2 [0;v 5=4) ¼ S = (v 1=4+r)=2 if r 2 [v 5=4;v 3=4) r 1+ p 3 p v r 2 p 3(v r) 3=2 =9 if r 2 [v 3=4;v) B Appendix Computations for consumer surplus When the incumbent is a monopolist consumer surplus ow is Z 1=2 ³ s M =2 v (x 1=2) 2 (v 1=4) dx; hence, 0 s M =1=6 24

When the rms compete on the basis of services, and if r 2 [0;v 3=4) consumer surplus ow is Z 1=2 s S (r) =2 v x 2 p S (r) dx; where p S (r) =p S = ps E Hence, When r 2 [v 3=4;v), Z p (v r)=3 s S (r) = 0 0 s S (r) =v 1=12 p S (r) v p S E (r) x 2 dx+z 1 p (v r)=3 ³ v p S (r) (1 x) 2 dx; where p S E (r) =(2v + r) =3 and ps (r) =(2v + r) =3 1+2p v r= p 3. Hence, s S (r) = 2 ³ v r +1 p 3 p v r ; 3 < v 13=12 r if r 2 [0;v 5=4) s S (r) = 1=6 if r 2 [v 5=4;v 3=4) p p 2 3 v r +1 3 v r if r 2 [v 3=4;v) When the rms compete on the basis of facilities, consumer surplus ow is s F = Z 1=3 Z 1 0 0 ³ Z 1 v (x 1=2) 2 q=3 dxdµ+ 1=3 Z 1 0 ³ v + µq (x 1=2) 2 2q=3 dxdµ; hence, One can verify that as v>3 and q 2 (2; 3) s F = v 1=12 q=9 s M s S (r) <s F ; C Appendix Computations for social welfare Social welfare ow is the sum of consumer surplus ow and industry pro t ows. When the incumbent is a monopolist, social welfare ow is w M = v 1=12; as w M = s M + ¼ M =1=6+v 1=4 When the rms compete on the basis of services, and if r 2 [0;v 5=4) social welfare ow is w S (r) =v 1=12, 25

as w S (r) =s S (r)+ ¼ S (r)+¼ S E (r) = v 1=12 (1 + r)+(1+r) f r 2 [v 5=4;v 3=4) social welfare ow is as w S (r) =v 1=12, w S (r) =s S (r)+ ¼ S (r)+¼s E (r) = v (v 1=4) 1=12 + (v 1=4) When r 2 [v 3=4;v), social welfare ow is w S (r) = 2 3 w S (r) =s S (r)+ ¼ S (r)+¼ S E (r), ³ v r +1 p 3 p ³ v r + r 1+ p 3 p v r, Hence, w S (r) = 2v + r 1+p 3 p v r. 3 w S (r) = ½ v 1=12 if r 2 [0;v 3=4) 2v + r 1+ p 3 p v r =3 if r 2 [v 3=4;v) When the rms compete on the basis of facilities, social welfare ow is w F = v 1=12 + 4q=9; as w F = s F + ¼ F + ¼ F E = v 1=12 q=9+5q=9. 26