Fixed-Mobile Substitution and Termination Rates

Transcription

1 Fixed-Mobile Substitution and Termination Rates Steffen Hoernig, Marc Bourreau, Carlo Cambini 27 February 2014 Abstract We model substitution between fixed and mobile calls and access when consumers differ in the benefits of mobility. Call prices are affected by substitution possibilities if and only if this leads to price discrimination between heterogenous consumers. Our simulations show that high mobile termination rates increased adoption of mobile telephony, while low fixed termination rates led to reduced fixed access, and that this termination rate structure likely increased social welfare. Keywords: Network competition; fixed-mobile substitution; termination rates. JEL: L51, L92. 1 Introduction The Issues at hand. New technologies and innovative service providers are often challenging the provision of traditional services. One of the most striking phenomena is the advent of mobile telephony and its impact on the traditional telephony service over fixed lines. Only three decades ago, fixed-line operators provided all communications needs over their respective Corresponding author. Nova School of Business and Economics, Universidade Nova de Lisboa; CEPR, UK. shoernig@novasbe.pt. Postal address: Nova SBE, Campus de Campolide, Lisboa, Portugal. tel , fax Acknowledges funding through grant PTDC/EGEECO/100696/2008 of the Ministry of Science and Technology. Telecom ParisTech, Department of Economics and Social Sciences, and CREST-LEI, Paris. marc.bourreau@telecom-paristech.fr. Politecnico di Torino, DIGEP; EUI - Florence School of Regulation. carlo.cambini@polito.it. 1

2 networks, but in the last 20 years mobile telephony has significantly disrupted the historical market structure. All over the world, wireless services have recorded substantial growth in terms of subscribership, revenue, and usage, and despite the recent economic crisis, the number of mobile subscribers and usage have continued to grow. Much of the enormous success of the mobile sector is due to intermodal competition, or more specifically to fixed-mobile substitution. Major technological advances and cost reductions have enabled mobile carriers to decrease the difference between fixed and mobile pricing levels, which has allowed them to become strong competitors to traditional fixed providers. At the same time, both fixed and mobile telephony have been subject to regulatory intervention, but to different degrees: While fixed telephony operators retail and wholesale prices (i.e. termination rates) tended to be strongly regulated at cost, for mobile operators only termination rates were eventually regulated, and until recently at values far above marginal cost. Empirical studies have attempted to quantify fixed-mobile substitution (see the survey by Vogelsang, 2010, as well as our review in the next paragraph), but there is a lack of theoretical investigation on how to model consumers mobility preference and its effect on access and call substitution away from fixed networks. This paper tries to fill this gap. We are well aware that there is a variety of factors that are considered as potential causes of fixedmobile substitution, and believe that none on its own provides a suffi cient explanation. In this paper we consider the potential role of asymmetric regulation of termination rates on fixed and mobile network as a contributing factor. In particular, we consider a model with three independent but interconnected operators, one fixed and two mobile networks. Our key novelty is the construction of the demand side. Consumers have variable mobility needs, i.e. a different probability that they are on the move. Depending on their mobility, consumers choose whether to single- or multihome, i.e. whether to subscribe to a fixed or a mobile network, or to both. Moreover, in our paper, differently from previous work, fixed and mobile telephony are simultaneously substitutes and complements: They are complements because even owners of a fixed line benefit from having a mobile subscription, by being able to make calls when they are not at home; they are substitutes because when both networks are available only the cheaper type of call will be used. These assumptions are particularly realistic and in line with recent evidence from the market. The association of European Telecom Regulators (BEREC, 2011) reported that although the share of mobile-only households increased and that of fixed-only households decreased, having both is now the most common situation in Europe (62% of households, on average) and 2

3 is not declining. 1 In a recent report, the OECD (2012) also concluded that fixed and mobile networks are both complements and substitutes. First we find that the possibility of call and access substitution affects call pricing only if consumers are heterogeneous and firms want to price discriminate. More specifically, we find that mobile-to-fixed prices are distorted downward from cost in order to make more consumers forgo a fixed connection, which raises termination profits. The main aim of our paper, though, is to analyze the impact of varying levels of termination rates on consumers subscription decisions. The key question is whether the different regulatory treatments of termination on fixed and mobile networks affect the development of fixed and mobile subscription decisions. Performing numerical simulations, we find that each (fixed or mobile) termination rate has a strong positive effect on the take-up of the corresponding service, via the well-known waterbed effect. A higher fixed termination rate is also found to lower the number of mobile subscriptions, while a higher mobile termination rate has almost no effect on fixed subscriptions. The latter is caused by call substitution, since consumers who hold both a fixed and a mobile phone do not make fixed-to-mobile calls, on which the effect of mobile termination rates is strongest. We also show that these shifts are stronger when consumers are more heterogeneous in their benefits of mobility. We also consider the socially optimal combination of termination rates: Fixed termination rates should be set at cost, and mobile termination rates above cost. The interests of mobile operators and the different consumer groups do not coincide, though. Both mobile operators and mobile-only consumers prefer a fixed termination rate at cost, consumers who hold both a fixed and a mobile subscription prefer an intermediate level of fixed termination rates, and fixed-only consumers prefer a high termination rate. On the other hand, consumers agree on a level of mobile termination rates below the social optimum, while mobile operators would like to set them at a higher level. Thus our model implies that high mobile and low fixed termination rates led to an additional shift of subscriptions from fixed to mobile networks. Furthermore, we also find that this structure of termination rates tends to 1 Based on the 2011 E-communication household survey, the number of households having at least one mobile subscription is rather high and homogeneous from 82% to 96% (average 89%) across Europe. On the other hand, fixed-line penetration is extremely heterogeneous: It is very high in countries such as Sweden (98%), the Netherlands (89%) and France (87%), whereas no more than 17% of the Czech households are connected. Mobile-only households range from 2% to 81%, while those with both range from 15% to 94%. 3

4 be socially optimal in the initial phase of the market. Literature Review There exists a sizeable economic literature on the relationship between fixed and mobile telephony and on the role of fixed-tomobile termination charges. Wright (2002) considers fixed-to-mobile calls with a focus on mobile termination rates, while others (e.g. Valletti and Houpis, 2005) analyze how socially optimal mobile termination charges would depend on the magnitude of network externalities, the intensity of competition in the mobile sector, and the distribution of customer preferences. These papers however does not consider the role of fixed-mobile substitution. Armstrong and Wright (2009) and Hausman (2012) analyze the role of call substitution and discuss voluntary vs. regulated setting of termination rates. Both papers show that substitution between fixed- and mobile-originated calls weakens the competitive bottleneck of call termination and brings the rate that firms would choose closer to the effi cient level. Hence, the welfare gains from regulating mobile termination rates are smaller, while private incentives do not imply excessively high levels. Hausman s setup is similar to ours, but we depart from these papers by analyzing substitution of access and all types of calls, and subscription decisions are affected by both mobile and fixed termination rates. [sh: Baake/Mitusch 2011] Closest to our paper is Hansen (2006), who also investigates fixed-mobile access substitution in a model with competition in the mobile market and subscribers with varying mobility. Contrary to our analysis, though, in his model varying mobility implies heterogeneity in the access surplus (as in Hausman 2012) and does not interact with the calls that a consumer can make (e.g., we assume that while not at home no fixed calls can be made). Moreover, he does not analyze most realistic and thus most practically relevant market structure that we focus on, with the simultaneous presence of mobile-only, fixed-only, and fixed-mobile subscribers. User mobility is also present in Valletti (2003) but in a mobile-only model with consumers moving from an urban to a rural area and seeking access to mobile services conditional on the mobile operators coverage. Though applied to a different setting, the game-theoretic structure of our paper is similar to de Bijl and Peitz (2009), who analyze the effect of access and retail price regulation on the adoption of voice over IP telephony. In both models, consumers first choose which technology to adopt. Firms then compete in the respective markets, given these adoption decisions. On the policy side, Bomsel et al. (2003) study the simultaneous impact of fixed and mobile termination rates on fixed-to-mobile or mobile-to-fixed 4

5 traffi c. The authors show that the transfer from fixed networks and their customers, as a result of high mobile termination rates, has amounted to 19 billion Euros in France, Germany and the UK over 1998 to According to these authors, the effect of this transfer has been to injure fixed customers and their operators, is likely to have damaged competition in the fixed market, and distorted competition between fixed and mobile operators. Our paper is theoretical, but it is important to review also the relevant empirical evidence on fixed-mobile substitution (see the surveys by Woroch, 2002; and Vogelsang, 2010). These papers consider different geographical areas, with different histories, and look at the market at very different points in time, so their results are not always comparable. The evidence to date for fixed-mobile substitution is rather mixed, but indicates that both call and access substitution is increasing over time. For example, Rodini et al. (2003), using data from US, show that households subscription to second fixed lines and mobile service are access substitutes, while Ward and Woroch (2005 and 2010) find substantial substitutability between fixed and mobile subscriptions. More recently, new studies provide much stronger evidence on fixed mobile call substitution. Briglauer et al. (2011) find that, at least for Austria, fixed and mobile calls are strong substitutes while access substitution is rather weak. Ward and Zheng (2012), using panel data from China, find that fixed and mobile telephony services have become fairly strong substitutes both for usage and subscriptions. Barth and Heimeshoff (2012a,b), using panel data on EU27 countries, show modest substitution effects on fixed and mobile subscriptions, while the estimated cross-price elasticity of the mobile price on fixed line call demand is relatively large compared to previous studies. Finally, Grzybowski (2012) analyses substitution between access to fixed-line and mobile telephony in the European Union and finds that decreasing prices for mobile services increase the share of mobile-only households and decrease the shares of fixed-only and fixed-plus-mobile households which suggests substitution between fixed-line and mobile connections. Note that none of these empirical studies present evidence on the impact of fixed and mobile termination rates on consumers subscription decisions. Hence our paper provides new testable predictions for future empirical work on fixed-mobile substitution. 5

6 2 Model and Pricing Equilibrium 2.1 Setup Consumers and firms. In our basic setting, there are two mobile networks and one monopoly fixed network. The latter is regulated such that its call prices are set at cost and its total profits are zero. This setting is intended to capture the first phase of the development of mobile markets, with a monopoly fixed network and high mobile termination rates. There is a total mass 1 of consumers, who can subscribe to some mobile network and / or the fixed network. We denote them correspondingly as mobile-only (M), fixed-mobile (FM) and fixed-only (F) subscribers. All consumers have the same mobility λ (0, 1), i.e. λ is the probability that a given consumer is on the move, where he only has access to his mobile phone and can neither make nor receive calls via a fixed line. On the other hand, with probability 1 λ he is at home, where he has access to a fixed and / or a mobile phone, and chooses whichever is cheaper if he has both. Consumers are on the move or at home independently of each other, 2 and calling patterns are balanced. Consumers are heterogenous in their fixed benefit from mobility and, independently, in their preferences for the two mobile networks, as specified below. We further assume that when consumers choose the type of subscription they know their benefit from mobility but not yet their network preference. 3 For i = 1, 2, mobile network i s numbers of M- and FM-clients, respectively, are µ m i and µ mx i, and thus its number of subscribers is µ i = µ m i + µ mx i. The numbers of all M- and FM-clients are µ m = µ m 1 + µ m 2 and µ mx = µ mx 1 + µ mx 2, with total number of mobile subscribers µ = µ m + µ mx and F-clients µ x. We assume that both consumers and firms take µ m, µ mx and µ x as given, while the firms take into account that µ m i and µ mx i are affected directly by the tariffs on offer. 4 Mobile networks have a fixed cost per subscriber f, marginal costs of origination and termination c o and c t, and on-net costs c = c o +c t. The mobile termination rate, applied regardless of whether calls originate on mobile or fixed networks, is a. The fixed network, on the other hand, has fixed cost f x, 2 [sh: check with correlation? Also, what happens if consumers can wait to make a cheaper call (intertemporal substitution)?] 3 This timing assumption implies simple expressions for market shares and keeps the analysis technically feasible. It can be justified by considering the choice of having a mobile phone as a more long-run decision than that whether to subscribe to one or the other mobile operator. 4 [sh: we have model with elastic subscription numbers that shows that equilibrium is qualitatively similar, though very complicated.] 6

7 marginal costs c xo and c xt, on-net costs c x = c xo + c xt, and termination rate a x. We assume the following ordering of the marginal costs of calls: c x < c o + a x < c o + c t + a 2 < c xo + a. (1) Given that marginal costs and termination rates on fixed networks tend to be far below those of mobile networks, the only actually restrictive assumption is the last one, i.e. that mobile termination rates are so high that calls from fixed to mobile networks have higher perceived marginal costs than mobileto-mobile calls, i.e. a > c t + 2 (c o c xo ). 5 Tariffs and surplus. Mobile network i charges a tariff (F i, p i, p ix ), where F i is a monthly fixed fee, and p i and p ix are the mobile-to-mobile and mobileto-fixed per-minute call prices. 6 The fixed network offers a tariff (F x, p x, p xm ), where F x is its monthly fixed fee, p x is its on-net price, and p xm is the fixed-tomobile per-minute call price. For now we also postulate (and later confirm), that the following ordering of prices holds: p x < p ix < p i < p xm. (2) Note that (2) is consistent with all or most of equilibrium prices being equal to marginal cost, ordered by assumption (1). If the price of a call minute is p k for k {x, ix, i, xm}, the caller s indirect utility from this call is v k = v (p k ) with call duration q k = v (p k ). Apart from the surplus related to calls, subscribers obtain different amounts of access surplus depending on what they subscribe to. If they only subscribe to a mobile network or the fixed network, the common part of their subscription surplus is A m or A x, respectively; if they subscribe to both the fixed and a mobile network, it is A mx. When an FM-subscriber of network i is on the move, the above ordering of prices implies that it is cheaper to make mobile-to-fixed calls instead of mobile-to-mobile calls when receivers are at home (p ix < p i ), thus mobile-tomobile calls are only made when receivers are themselves on the move. 7 When at home, the same subscriber can use both the fixed and mobile phones. He uses his fixed phone to call other users at home (p x < p ix ) and his mobile 5 Historically correct, but not in the future, maybe. Thus Extension section: low MTR, so that FTM calls are cheaper than MTM calls. 6 We assume a uniform MTM call price, ruling out tariff-mediated network effects, in order to concentrate on the effects of interconnection between fixed and mobile networks. 7 We can imagine that the caller first tries the receiver s fixed line and then calls him on his mobile if he is not at home. [sh: As Marc said, this tends to be the other way round, but this cannot be explained in this model. See FTM4.] 7

8 phone to call others on the move (p i < p xm ). The resulting expected surplus of both subscribing to the fixed network and to mobile network i is w mx i = A mx F i F x + ρ m v i + ρ x [λv ix + (1 λ) v x ], (3) where we have denoted the number of receivers on mobile phones by ρ m = µ m + λµ mx, and those on fixed phones by ρ x = (1 λ) (µ mx + µ x ). First we have subscription surplus minus fixed fees, then the surplus of calling M-clients and FM-clients when the latter are on the move, and the surplus of calling FM- and F-clients when they are at home, either calling from the road with probability λ or from home with probability 1 λ. The last term implies substitution to cheaper fixed on-net calls. An M-client makes all calls with his mobile phone, with corresponding surplus w m i = A m F i + ρ m v i + ρ x v ix. (4) Similarly, an F-client obtains surplus w x = A x F x + (1 λ) (ρ m v xm + ρ x v x ). (5) The latter is the only group that makes fixed-to-mobile calls, and contrary to the other customers only has access to a phone when they are at home. Subscription decisions and market shares. As mentioned above, consumers differ in their preferences for mobile networks and learn these preferences after deciding whether to take up a mobile subscription (but before actually choosing a subscription from a specific network). As such they will base the former decision on the expected surplus of having a mobile subscription, while the latter decision is based on comparing individual tariffs. For given tariffs (F i, p i, p ix ) and resulting surpluses wi m and wi mx, we assume that mobile operator i s market shares in the respective subscriber groups are given by µ m i = y ( w m i w m j ) µ m, µ mx i = y ( w mx i ) wj mx µ mx, where y is a function y : R [0, 1] with y (0) = 1/2, y > 0 and y (0) = σ > 0. 8 On the other hand, when consumers choose whether to subscribe to a mobile or fixed network, they base their decision on the expected surplus. 8 An often-used special case is the Hotelling model with y (x) = 1/2 + σx (over the relevant range). 8

9 We assume that consumers correctly anticipate that the mobile market equilibrium is symmetric and that they will adhere to either network with probability 1/2. 9 Introducing an expected disutility κ > 0 from not obtaining a perfect match in their operator choice, 10 subscribers expected surpluses are w m = 1 2 (wm 1 + w m 2 ) κ, w mx = 1 2 (wmx 1 + w mx 2 ) κ, and for notational convenience also w x = w x. We capture consumer heterogeneity in the benefits of mobility by the following assumption: The utility of consumer l of taking subscription decision k {m, mx, x} is given by U lk = w k + ε lk, where ε lk is a random term. 11 For these utilities, the numbers of consumers in each segment k {m, mx, x}, are given by µ k = P k ( w m, w mx, w x ), (6) where P k is the probability of choice k, P k / w k > 0, P k / w l 0 for l k, and P m + P mx + P x 1. Profits. Similar to the above we define the number of call receivers on mobile network i = 1, 2 as ρ m i = µ m i + λµ mx i and let j i. The profits of mobile operator i are given by { π i = µ i Fi f + [ ρ m (p i c) ρ m j (a c t ) ] } q i +ρ m i ρ x (p ix c o a x ) q ix (7) +ρ m i (a c t ) [ µ j q j + (1 λ) µ x q xm ]. On the first line we have the profits due to fixed fees and calls to other mobiles, on the second line the profits from calls to the fixed network, and on the last line termination profits. For the fixed network, profits are π x = (µ x + µ mx ) (F x f x ) + (ρ x ) 2 (p x c x ) q x + (1 λ) µ x ρ m (p xm c xo a) q xm (8) +ρ x (a x c xt ) (ρ m 1 q 1x + ρ m 2 q 2x ). 9 In the absence of network effects, which could give rise to multiple equilibria, this assumption is without loss of generality. 10 In the Hotelling framework we have κ = 2 1/2 0 x/ (2σ) dx = 1/(8σ). 11 The distribution of the ε lk is not relevant for the determination of equilibrium tariffs, but in our simulations below we make a specific assumption. 9

10 Again, subscription profits are on the first line, together with those from on-net calls. On the second line we have calls to mobiles, and termination profits are on the last line. Expected consumer surplus is given by CS = µ x w x + µ mx w mx + µ m w m, and total welfare is W = CS + π 1 + π 2 + π x. (9) 2.2 Equilibrium Tariffs and Subscriber Numbers We now solve for the (symmetric) equilibrium in the mobile market, taking consumers decision of buying a mobile phone and / or adhering to the fixed network as given. The standard procedure of maximizing networks profits over call prices while holding subscriber numbers constant fails because of composition effects : Fixed fees and mobile-to-fixed prices enter µ m i and µ mx i with different relative weights. Thus adjusting F i to hold, say, µ m i constant after a change in p ix does not annul the changes in µ mx i. The correct procedure, as applied in the proof of the following result, is to maximize simultaneously over the whole tariff (F i, p i, p ix ). Proposition 1 Symmetric mobile equilibrium tariffs are given by: 1. A mobile-to-mobile call price equal to average marginal cost, p i = c (a c t) ; (10) 2. a mobile-to-fixed call price below marginal cost if and only if the mobile termination rate is above cost, where 3. fixed fees equal to p ix = c o + a x (a c t ) µq i + (1 λ) µ x qxm ρ x qix q ix / (11) (2σΦq ix ), Φ = µm + λ 2 µ mx ρ m ρm µ > 0; Fi = f + t ρm ρ x µ (p ix c o a x ) qix (12) ( ) q ρ m (a c t ) i (1 λ) µx + qxm. 2 µ 10

11 Equilibrium profits are π i = µ 4σ. (13) Profits and the mobile-to-mobile call price p i have the standard form for uniform tariffs in the Hotelling model, i.e. "transport cost" 1/2σ times the subscriber number, and perceived average marginal cost, respectively (Armstrong 1998 and Laffont, Rey and Tirole 1998a). On the other hand, the mobile-to-fixed call price p ix is set below marginal cost and the fixed fee is increased. 12 This pricing structure allows mobile networks to charge more to its infra-marginal customers, while compensating its marginal ones through a lower call price. It is precisely these mobile-only subscribers that then receive a larger compensation via a lower mobile-tofixed call price, since they have no opportunity to substitute toward fixedto-fixed calls. On the other hand, they receive more incoming calls, and therefore are relatively more valuable to have on one s own rather than the rival s network when a > c t. This is borne out by the fact that the distortion in p ix disappears when mobile termination is set at cost, i.e. a = c t. Thus we find that the combination of call substitution and customer heterogeneity gives rise to a distorted usage pricing structure. For a regulated monopoly fixed network, cost-based call pricing and a zero-profit constraint imply, given a symmetric equilibrium in the mobile market, p x = c x, p xm = c xo + a, F x = f x ρx ρ m µ x + µ mx (a x c xt ) q ix. (14) 3 The Effects of Mobile Termination Rates 3.1 Fixed-Mobile Substitution In this section we will consider the effect of both fixed and mobile termination rates on subscription decisions. In particular, we are interested in whether higher termination rates raise or lower subscriber numbers, and whether there are cross-effects. Due to the complex expressions for fixed fees and mobile-tofixed prices, we have to take recourse to numerical simulations, independently of the subscription demand model. In the following we solve for the subscriber numbers (6), using the equilibrium tariffs derived above. We have made the following assumptions: Individual tastes for mobility are described by ε lx = 0, ε lmx = λb, and ε lm = B, where B is uniformly 12 [sh: the fact that we get exactly the same result with an arbitrary choice framework implies that it has nothing to do with M-subscribers only substituting to the FM-offer] 11

12 distributed on [ 1/2b, 1/2b] for some b > 0, where larger b indicates more consumer heterogeneity. Mobility is λ = 1/2 and mobile market differentiation is σ = 1/2. Call demand is q (p) = 1 p, and marginal costs are c o = c t = 0.2, c xo = c xt = 0.1. Fixed costs and common components of access surpluses are f = f x = A x = 0 (wlog normalized to zero), A m = A mx = 1.16, and σ = 0.5. Varying the termination rates a x c xt = 0.1 and a c t + 2 (c 0 c xo ) = 0.4), we find the following results as summarized in Table 1. b = 1 b = 4 a\a x ,54 57,52 60,50 58,66 81,52 95, ,57 57,55 60,53 58,76 82,60 96, ,58 57,55 61,53 58,81 82,63 97, ,57 57,55 60,53 58,80 82,61 96,39 Table 1: Shares of fixed and mobile subscribers for low and high heterogeneity in mobility surplus. Each cell contains (µ mx + µ m, µ m + µ mx ). We obtain two main results, concerning the levels of termination rates and the role of consumer heterogeneity. First, a higher fixed (mobile) termination rate increases the total number of fixed (mobile) subscribers, as one might expect. These are instances of the waterbed effect, where higher profits from the termination of cross-network calls are handed on to consumers via lower subscription fees in (12) and (14). These lower subscription fees then make the marginal M-(F-)client subscribe to both services. More precisely, we obtain and w mx i w x = A mx A x f t + ρ m vi + λρ x vix (1 λ) ρ m vxm (15) ( ( )) ρ m ρ x µqi + (1 λ) µ x qxm q + (a c t ) µ ρ x qix q ix / (2σΦq ix )q ix + ρ m i (1 λ) µx + qxm 2 µ wi mx wi m = A mx A m f x + (1 λ) ρ x (vx vix) ρ x ρ m + (a x c xt ) µ x + µ mx q ix. (16) We see that wi mx w x, which determines the total number of mobile subscribers, increases directly in the termination charge a, while wi mx wi m, which defines the number of fixed subscribers, increases directly with a x. 13 Still, if mobile termination rates get too high then mobile subscriptions are 13 There are also indirect effects and feedback loops via call quantities and subscriber numbers, of course. 12

13 decreased, due to declining termination profits (beyond the monopoly termination rate) and the adverse effect of higher mobile-to-mobile call prices. We also take from Table 1 that increasing the fixed termination rate decreases the total number of mobile subscribers, while changing the mobile termination rate has very little effect on the total number of fixed subscribers. The first effect can be explained by looking at (15): A higher fixed termination rate a x reduces wi mx w x, via lowering the quantity of and surplus from mobile-to-fixed calls, v ix and qix, and thus makes marginal MF-clients drop their mobile subscription. On the other hand, since MF-clients do not make fixed-to-mobile calls anyway (they substitute them via cheaper mobileto-mobile calls), the mobile termination rate affects wi mx wi m in (16) only via changes in subscriber numbers, whose affect is not straightforward. The second main result is that consumer heterogeneity matters quite a bit. The left-hand side of Table 1 contains values for more homogeneous consumers (b = 1), while the right-hand side contains the corresponding value for more heterogeneous consumers (b = 4). We can see that for more heterogeneous consumers both total numbers of fixed and mobile customers increase, i.e. a significantly larger share of the population hold both a mobile and a fixed phone. Second, the effects of termination rates on subscriber numbers are much larger with more heterogeneity. The reason is that any given difference in surplus between the three options makes a larger number of customers switch when heterogeneity is larger. These simulation results indicate that the regulatory policy in effect during the last decade furthered fixed-mobile access substitution through two separate channels: High mobile termination rates significantly increased takeup of mobile services, while low (cost-based) fixed termination rates encouraged some customers to drop their fixed connection and other to take up mobile services in the first place. 3.2 Optimal Termination Rates Since we have determined that fixed and mobile termination rates have an effect on subscriber numbers, the question arises which combination of the former would have led to the highest welfare. Computing total welfare (9) at equilibrium tariffs for both scenarios depicted in Table 1, we find the results in Table 2. 13

14 b = 1 b = 4 a\a x Table 2: Total welfare for low and high heterogeneity in mobility surplus. Thus for the above values of termination charges, a clear picture emerges: Welfare is highest at the first fixed termination rate level and at the third level of mobile termination rates. Searching for the actual maximum, using a fine grid, reveals that indeed welfare is maximized if fixed access is costbased, and if a = 0.57 (b = 1) and a = 0.63 (b = 4). While these values are not the outcome of a calibrated model (and thus should not be taken literally), they indicate that it in the early phase of the market was indeed a socially optimal policy to set a fixed termination rate at cost and allow a mobile termination rate significantly above marginal cost. It is interesting to decompose welfare in its components. The surplus of the different consumer segments turns out to be maximized at different combinations of termination charges. All consumers prefer mobile termination rates somewhat below the social optimum but M-, MF- and F-clients prefer cost-based, medium and high fixed termination rates, respectively. On the other hand, mobile networks prefer mobile termination rates somewhat above the social optimum and cost-based fixed termination rates. 14 Thus no group of actors prefers exactly the social optimum to be implemented, while mobile networks and mobile-only subscribers agree that fixed termination rates should be set at the socially optimal level. 4 Fixed-Market Competition and low termination rates. To be written up. 5 Conclusions Mobile telephony has been a tremendous success in the last two decades, making large inroads into the fixed telephony market. Subscribers in many countries now use their mobiles more than their fixed lines, and quite often 14 Remember that by definition the fixed network s profits are zero in this scenario. 14

15 disconnect the latter. We have presented a model that captures this development and substitution at subscription and call level. In a rather general framework, our results show that call substitution does not change retail pricing incentives unless customer heterogeneity makes it worthwhile to discriminate between customers with different substitution possibilities. We then performed numerical simulations in order discern the effects of mobile termination rate regulation, in a setting where the fixed network s tariff is regulated as to exactly cover its costs. Termination rates do have an effect on subscription substitution and fixed disconnection, but in more specific manner than is usually postulated. More precisely, a higher mobile termination rate increases the number of mobile subscribers, while a lower fixed termination rate does the latter while also leading to fewer fixed subscribers. On the other hand, the mobile termination rate as such has little effect on the number of fixed subscribers, due to call substitution. We also found that these effects are stronger if consumers are more heterogeneous in their benefits from mobility. Lastly, we found that socially optimal fixed termination rates are indeed set at cost, a level which mobile operators and mobile-only customer prefer (but not the customers of fixed networks). On the other hand, socially optimal mobile termination rates are above marginal cost, with consumers (firms) preferring levels below (above) the socially optimal level. This indicates that the termination rate structure prevalent in early mobile markets tended to increase social welfare. Future research will contemplate the transition to cost-based mobile termination and competition in the fixed market. References [1] Armstrong M. & J. Wright (2009). Mobile Call Termination, Economic Journal, 119(538), F270-F307. [2] Barth, A.-K. & U. Heimeshoff (2012a). Does the growth of mobile markets cause the demise of fixed networks? Evidence from the European Union, DICE Discussion Papers 42, January. [3] Barth, A.-K. & U. Heimeshoff (2012b). How large is the magnitude of fixed-mobile call substitution? Empirical evidence from 16 European countries, DICE Discussion Papers 49, April. [4] BEREC (2011), BEREC report on impact of Fixed-Mobile substitution in market definition, (11) 54, December. 15

16 [5] Bomsel, O., M. Cave, G. Le Blanc & K.-H. Neumann (2003). How mobile termination charges shape the dynamics of the telecom sector, WIK-Consult, July. [6] Briglauer W., A. Schwarz & C. Zulehner (2011). Is fixed-mobile substitution strong enough to de-regulate fixed voice telephony? Evidence from the Austrian markets, Journal of Regulatory Economics, 39(1), [7] de Bijl, P. & M. Peitz (2009). Access regulation and the adoption of VoIP, Journal of Regulatory Economics, 35(2), [8] Grzybowski, L. (2012). Fixed-to-Mobile Substitution in the European Union, University of Cape Town, Working Paper 271, March. [9] Hansen, B. (2006). Termination Rates and Fixed Mobile Substitution, April. [10] Hausman J. A. (2012), Two Sided Markets with Substitution: Mobile Termination Revisited. In: Faulhaber, G.R., G. Madden & J. Petchey (Eds.), Regulation and the Performance of Communication and Information Networks, Edward Elgar Publishing Limited, Cheltenham, UK. [11] Hoernig, S., M. Bourreau & C. Cambini (2013a). Fixed-Mobile Integration, CEPR Discussion Papers 9361, London, February. [12] Hoernig, S., M. Bourreau & C. Cambini (2013b). Fixed-Mobile Bundling, July. [13] OECD (2012). Fixed and Mobile Networks: Substitution, Complementarity and Convergence, OECD Digital Economy Papers, No. 206, OECD Publishing. [14] Rodini, M., M.R. Ward & G.A. Woroch (2003). Going mobile: substitutability between fixed and mobile access, Telecommunications Policy, 27(5-6), [15] Valletti, T. (2003). Is Mobile Telephony a Natural Oligopoly?, Review of Industrial Organization, 22(1), [16] Valletti, T., & G. Houpis (2005). Mobile Termination: What is the Right Charge? Journal of Regulatory Economics, 28(3),

17 [17] Vogelsang, I. (2010). The relationship between mobile and fixed-line communications: A survey, Information Economics and Policy, 22(1), [18] Ward, M.R. & G.A. Woroch (2005). Fixed-Mobile Telephone Subscription Substitution in the U.S., mimeo. [19] Ward, M.R. & G.A. Woroch (2010). The effect of prices on fixed and mobile telephone penetration: Using price subsidies as natural experiment, Information Economics and Policy, 22, [20] Ward, M.R. and S. Zheng (2012). Mobile and Fixed Substitution for Telephone Service in China. Telecommunications Policy, 36(4), [21] Woroch, G. (2002). Local Network Competition. In: Cave, M., Majumdar, S. & Vogelsang, I. (Eds.), Handbook of telecommunications economics. Amsterdam: Elsevier Publishing. [22] Wright, J. (2002). Access pricing under competition: an application to cellular networks. Journal of Industrial Economics, 50, Appendix Proof of Proposition 1: Firm i s profits are { π i = µ i Fi f + [ ρ m (p i c) ρ m j (a c t ) ] } q i ( ρ x (p ix c o a x ) q ix + (a c t ) [ ]) µ j q j + (1 λ) µ x q xm. +ρ m i We will need the following derivatives, all originating from µ k i = y ( ) wi k wj k µ k, for j i and k {m, mx}: wi m = A m F i + ρ m v i + ρ x v ix wi mx = A mx F i F x + ρ m v i + ρ x [λv ix + (1 λ) v x ] µ m i µ m i = σµ m, = σµ m ρ m q i, = σµ m ρ x q ix, F i p i p ix µ mx i = σµ mx µ mx i, = σµ mx ρ m µ mx i q i, = σλµ mx ρ x q ix. F i p i p ix µ m i 17

18 Thus we have, with ρ λ = µ m + λ 2 µ mx, µ i µ = σµ, i = σµρ m µ q i, i = σρ m ρ x q ix, F i p i p ix ρ m i = σρ m ρ m i, = σ (ρ m ) 2 ρ m i q i, = σρ λ ρ x q ix, F i p i p ix while the derivatives of µ j and ρ m j are identical apart from having the opposite sign. The first-order conditions for maximizing profits π i over p i, p ix and F i, can be written as follows, for symmetric µ i = µ/2 and ρ m i = ρ m /2, and letting ( T 1 = F i f + ρ m p i c a c ) t q i, 2 ( µ ) T 2 = ρ x (p ix c o a x ) q ix + (a c t ) 2 q i + (1 λ) µ x q xm. For F i, 0 = π i F i = µ 2 σ (µt 1 + ρ m T 2 ), from which we obtain directly For p i, 0 = π i p i = π i = µt 1 + ρ m T 2 2 { [ ( µ 1 + p i c a c t 2 2 = µ 4σ. ) ] q i q i } σ (µt 1 + ρ m T 2 ) ρ m q i Combining these two first-order conditions leads directly to p i = c + a c t. 2 Solving the first-order condition for the fixed fee then yields Finally, 0 = π i p ix = { ρ m 2 F i = f + 1 2σ ρm µ T 2. [ ] 1 + (p ix c o a x ) q ix σ ( ) } ρ m T 1 + ρ λ T 2 ρ x q ix q ix σ ρm µ 2 Φ (a c t) q i ρ x q ix 18

19 with Φ = ρλ ρ m ρm µ > 0, where the latter inequality follows from λ < 1 and µ m, µ mx > 0. Combining the conditions for p ix and F i, using T 1 = F i f leads to the following outcome: p ix = c o + a x (a c t ) µq i + (1 λ) µ x q xm ρ x q ix q ix / (2σΦq ix) 19