Calling vs receiving party pays : market penetration and the importance of the call externality

Calling vs Receiving Party Pays: Market Penetration and the Importance of the Call Externality∗ Tommaso Majer† Universitat Aut`onoma de Barcelona Tommaso.Ma[email protected]t Michele Pistollato‡ Universitat Aut`onoma de Barcelona [email protected] October 21, 2010 Abstract In this paper we study how the access price affects the choice of the tariff regime taken by the network operators. We show that for high values of the access price, that is taken as a parameter by the firms, networks decide to charge only the callers. Otherwise, for low values of the access charge, networks charge also the receivers. Moreover, we compare market penetration and total welfare between the two price regimes. Our model suggests that, for high values of call externality, market penetration and total welfare are larger in Receiving Party Pays regime when the access charge is close to zero. JEL Classification:L96, L50 Keywords: Telecommunications, Mobile termination rates, Calling Party Pays regime, Receiving Party Pays regime, Incomplete Coverage, Call Externality, Market Expansion, Regulation ∗We are grateful to Sjaak Hurkens, Xavier Mart`ınez Giralt, David P´erez Castrillo and Francesc Trillas. †Departament d’Economia i d’Hist`oria Econ`omica, Edifici B, 08193 Bellaterra (Barcelona), Spain. ‡Departament d’Economia i d’Hist`oria Econ`omica, Edifici B, 08193 Bellaterra (Barcelona), Spain. 1 1 Introduction In order to provide interconnection among all users, telecom networks need access to rival’s consumers. Access is provided after the payment of a termination charge (or access price). This charge is a part of the cost of off-net calls and consequently affects the price of calls. Last years in Europe have seen a growing discussion among regulatory authorities about regulation of termination charges or access prices. On the one hand, the European Commission (2008, 2009) recommended to lower termination charges in order to lower average price per minute. On the other hand, some of them (e.g. Ofcom, the UK telecommunications regulator) are worried that this could bring network operators to charge consumers for receiving a call or, in other words, to switch from a Calling Party Pays (CPP) regime, where only callers pay for making a call, to a Receiving Party Pays (RPP) regime, where both caller and receiver pay to join a call. Ofcom has expressed several concerns about the introduction of a RPP tariff regime.1 The main objections of the UK telecommunications regulatory authority are that it would be disruptive to customers, it would meet with consumer resistance and it might also lead to customers turning off their mobile phones. There exist many works about this last concern (e.g. Bomsel et al. (2003), Cadman (2007) and Samarajiva & Melody (2000)) but they are not providing a theoretical background to their analysis. In particular, there is not any model which explain how market penetration and welfare would change switching from one regime to the other. Our intention is to model the two tariff regimes and provide a theoretical framework to compare them. Littlechild (2006) reports some differences between the two regimes. Some data are summarized in Table 1. In RPP countries minutes of usage are more than in CPP countries. To understand the reason of that, it is important to notice that RPP countries usually adopt Bill & Keep (BaK) as interconnection arrangement. This means that network operators pay a price equal to zero (or close to) in order to terminate phone calls. Hence, a BaK policy reduces the marginal costs of traffic and therefore usage prices, leading to higher usage. In 2005 market penetration in US and Canada is far below penetration in EU but in other BaK countries as Hong Kong penetration is above EU average. Other data of 2008 in ERG (2009)2show that US penetration of 87% is lower than EU average of 123%. However, penetration in Hong Kong and Singapore is above EU average. From these data seems that market penetration is lower in BaK countries, but in CPP countries penetration 1See Oftel (2002) and Ofcom (2005). 2See ERG (2009), Next Generation Networks Future Charging Mechanisms / Long Term Termination Issues. 2 Min. of use (per months) Penetration (%, 2005) RPP countries USA 630 61 Canada 359 47 Hong Kong 387 106 Singapore 282 90 CPP countries UK 151 104 Germany 76 87 France 225 74 Italy 120 110 Spain 135 99 Table 1: Mobile market structure in selected countries (2005). might be overstated because of the traditionally greater number of prepaid schemes and multiple SIM cards.3 In this paper we provide a theoretical analysis to show how the choice of the access price determines the retail pricing regime: our model confirms that CPP is a choice of the telecommunications industry in response to access prices above termination cost. Otherwise, for access prices below cost, networks prefer to charge receivers as well. Moreover, we compare our predictions for two regimes with actual data in order to give some indications to the regulator. It turns out that with high call externality, a BaK policy (which is associated to RPP regimes) implies higher usage and higher market penetration. This is because higher usage increases utility of joining a mobile network and consequently more people would like to join a network. Moreover, BaK maximizes social welfare with respect to any other policy. Our model stresses the relevance of the call externality (the utility that consumers 3A report of Analysis Mason (2008, pag. 8) for Ofcom says: While looking at the comparative statics, it is important to note that the standard penetration data [. . . ] measures the number of subscriptions in circulation, and not the number of users who hold mobile subscriptions, which in the case of Hong Kong, Singapore and the UK is much lower [. . . ]. 3 obtain for receiving a call). Indeed, as the European Commission (2008) remarks, the welfare-maximizer policy about the access price may be very different for different values of the call externality. For low values our model suggests that the optimal policy is to set the access price close to the termination cost and, consequently, to induce the industry to adopt a CPP price regime. Otherwise, for high values of call externality, the optimal policy should be BaK (in this case the industry would adopt a RPP regime). The reason is that RPP regimes internalize the call externality by making the receiver paying for receiving the call.4Hence, when this externality is relevant, RPP regimes are more efficient. Related literature. The main contribution to the literature on telecommunications is given by the seminal papers by Armstrong (1998) and Laffont et al. (1998a,b). In their papers they model telecommunications competition between two network operators that compete for consumers that obtain utility only from making calls. Laffont et al. (1998a) analyze network interconnection in an unregulated environment where price discrimination is excluded. They show that for non-linear retail prices, high interconnection tariffs raise final retail prices and reduce social welfare. Gans & King (2001) corrected the above analyses and found that, under price discrimination and non-linear pricing, networks prefer an access price below cost.5 These papers inspired many works. Jeon et al. (2004) extend these models and allow consumers to obtain utility from receiving calls. In the usual setup of two horizontaly differentiated networks with full coverage of the market, they introduce the possibility for operators to charge customers also for receiving a call. Hence receivers may affect volume of the calls by hanging up first. The authors derive equilibrium usage prices under different off-net pricing tariffs. On the one hand, without network based discrimination, networks set prices equal to the perceived marginal cost. On the other hand, in presence of network based discrimination, networks set high off-net prices (for high values of the externality, interconnection breaks down) and on-net prices lower than the marginal cost. To avoid multiplicity of equilibria, they introduce a noise term in the utility of the receiver.6 Cambini & Valletti (2008) use a model where the demand of phone calls between each pair of customers is jointly determined. They show that under certain conditions the connectivity breakdown is eliminated. Moreover, they explain the relationship between 4For a discussion of this topic, see BEREC (2010b). 5For a good survey of the literature, see Armstrong (2002). 6Notice that the hypothesis of full coverage prevents the possibility of analyzing the effects of different access price policy on the market size and their consequences on the welfare. Indeed, in a paragraph the authors study incomplete coverage but they limit their analysis to the definition of the equilibrium usage prices. 4 the access charge and the structure of the retail prices chosen by the network operators (networks choose to charge the receiver only if the access charge is sufficiently low). Lopez (2008) extends Jeon et al. (2004) in another direction. He introduces a random variable also in the utility of the caller. In this framework, networks set prices equal to the perceived marginal cost. Moreover, he shows that firm’s profits do not depend on the access charge. Finally, Hermalin & Katz (2009) allow consumers to obtain utility from receiving calls but, differently from the previous papers, they assume that networks compete on quantities. It turns out that a regulator can not induce efficient off-net prices through the access charge. In this paper we modify the framework described in Jeon et al. (2004) and we incorporate market expansion in the benchmark model to compare equilibrium prices (including the fixed part), market penetration and profits in the two different tariff regimes. Under no network-based discrimination, we consider the case where networks charge a strictly positive charge to the receivers (Receiver Party Pays regime) and the case where networks do not charge consumers for receiving a call (Caller Party Pays regime). In Section 2 we present the model. In Section 3 we characterize the equilibrium prices and quantities in the two tariff regimes. In Section 4 we simulate the equilibrium results and we compare the solutions in the two cases. Section 5 concludes. 2 The Model We generalize the model introduced by Jeon et al. (2004) allowing for market expansion. Networks. We consider two mobile networks i= 1,2 located at two points of an infinite Hotelling line. We normalize to one the distance between the two networks. Mobile networks incur a fixed cost per consumer fand have on-net call cost of c= 2c0+c1, where c0is the marginal cost of originating or terminating a call and c1is the marginal cost of transmitting a call. Let adenote the access charge or termination charge. The marginal cost of an off-net call is therefore c+ (a−c0) for the caller’s network and c0−afor the receiver’s network. Tariffs. Mobile network ioffers a multi-part tariff (pi, ri, Fi) where piis the caller’s usage price (notice that we only consider the case of non network-based discrimination), riis the receiver’s usage price and Fiis the fixed part. 5 Consumers. Consumers are differentiated along the Hotelling line. This line represents the preferences of the consumers over one characteristic of the networks. For instance, consumers may prefer the well know phone operator instead of a new one. A consumer located at xand selecting network iincurs a transportation cost equal to t|x−xi|. The utility of placing a call is u(q), where qdenotes the length of the call. As in Jeon et al. (2004), we assume that the marginal utility that a receiver derives from receiving a call is subject to a noise εwhich introduces uncertainty about the willingness to pay for receiving a call independently on the price she is paying.7For instance, it could be the case that the receiver is unwilling to talk on the phone when she is driving or working and by considering the noise we have a more realistic model. Hence the receiver’s utility is ˜u(q) + εq and we assume that εfollows the distribution function Fwith support [¯ ε, ¯ε], zero mean and density f. For simplicity we consider ˜u(q) = βu(q), with β > 0. The lentgh of calls is determined by the first one who interrupts the conversation. The caller equates her marginal utility to the usage price piand she would hang up when her marginal utility is pi. The receiver equates her marginal utility ˜u′+εto the receiving price ri. Therefore the receiver will solve βu′+ε=rjfor u′and therefore he would hang up when u′is rj−ε β. Hence, the volume of calls is q(max{pi,(rj−ε)/β}). The volume of calls is determined by the pair (pi, rj) and a realized value εof the random variable: D(pi, rj) =h1−F(rj−βpi)iq(pi) + Zrj−βpi ¯ ε qrj−ε βf(ε)dε. (1) This means that with probability [1 −F(rj−βpi)] the caller hangs up first and the call lasts q(pi) minutes. With probability F(rj−βpi) the receiver hangs up first and the call lasts q(rj−ε β) minutes. Therefore network idoes not know a priori who will be the first one to hang up and consequently, who will determine the length of the call. Consider a consumer in network i. Her utility for calling a consumer in network jis: U(pi, rj) =h1−F(rj−βpi)iu(q(pi)) + Zrj−βpi ¯ ε uqrj−ε βf(ε)dε. (2) Her utility from receiving calls from a consumer that joined network jis: ˜ U(pi, rj) = Z¯ε rj−βpih˜u(q(pi)) + q(pi)εif(ε)dε+ +Zrj−βpi ¯ εh˜uqrj−ε β+qrj−ε βεif(ε)dε+ (3) 7This noise results in a positive probability for both the caller and the receiver of hanging up first. 6 Therefore, we can write the net surplus of a consumer that joined network ias follows: wi=v0+niU(pi, ri) + njU(pi, rj) + ni˜ U(pi, ri) + nj˜ U(pj, ri) −pihniD(pi, ri) + njD(pi, rj)i−rihniD(pi, ri) + njD(pj, ri)i−Fi(4) where v0is a subscriber’s utility from other mobile services. The profits of network iare given by: πi=nihni(pi−c)D(pi, ri) + nj[pi−c−(a−c0)]D(pi, rj) + nj(a−c0)D(pj, ri) +riniD(pi, ri) + njD(pj, ri)+Fi−fi(5) where ni(pi−c)D(pi, ri) are the profits per user for making on-net calls, nj[pi−c−(a− c0)]D(pi, rj) are the profits per user for making off-net calls, nj(a−c0)D(pj, ri) are the profits for terminating off-net calls, ri[niD(pi, ri)+njD(pj, ri)] are the profits for receiving calls, Fiis the fixed part of the multi part tariff and fis the cost per costumer. Notice that the expression of the profits takes different forms when the caller or the receiver determines the length of the call. On the one hand, when βpi< rjthe receiver will hang up first and then the length of the call depends only on the price r. On the other hand, when βpi> rjthe caller will hang up first and the length of the call depends only on the price p. But the network does not know who will be the first one to hang up. To model that, Jeon et al. (2004) introduce a noise element in the volume of calls. Therefore, we can maximize the expression of the profits that depends on the noise. In this case the profits are differentiable for all positive prices (pi, ri). 3 The equilibrium In order to analyze market penetration we consider elastic subscriber participation. Explicitly, we model consumer demand as the Hotelling model with hinterlands.8If the two networks offer utilities w1and w2, then network iattracts: ni=1 2+wi−wj 2t+λwi(6) where λ≥0 represents the magnitude of market expansion possibilities. This is one of the novelties we introduce in our model with respect to Jeon et al. (2004) because it allows us to analyze how different values of the access price affect the equilibrium market penetration and the effects of the latter on welfare. In order to have non explosive market 8For more details see Armstrong & Wright (2009). 7 share λmust be small enough.9We impose: λ < min 1 2(Urpp +˜ Urpp −cDrpp),1 2(Ucpp +˜ Ucpp −pcppDcpp).(7) The equilibrium is given by the vector of prices (pi, ri, Fi) that maximize operator i’s profits as defined by equation (5). The only restrictions we impose are the non-negativity of the prices. When the operator is charging strictly positive prices to its users we have a RPP regime. Otherwise, if the receiving price is zero we have a CPP regime.10 Under the assumption of a balanced calling pattern11, we characterize the equilibrium prices given the access charge. 3.1 The case a < c0: the Receiving Party Pays regime Network operators are free to charge customers for making and receiving a call. Therefore, network isets a caller’s usage price piand a receiver’s usage price rithat maximize consumers surplus that will be extracted through the fixed part Fi. Using the usual maximization procedure, the equilibrium retail prices are: Proposition 3.1 (Equilibrium retail prices).The symmetric equilibrium retail prices (p, r, F)are: prpp =c+ (a−c0) rrpp =c0−a Frpp =f+tφ γ(a) + [3 + γ(a)]λt where γ(a)≡1−2λ[Urpp(a) + ˜ Urpp(a)−cDrpp(a)] and φ≡1 + 2λv0−2λf. Proof. See appendix. Notice that, as in the case of inelastic demand described by Jeon et al. (2004), the usage prices are equal to the perceived marginal cost. Moreover, the fixed part is higher 9From equations (15) and (20) the derivatives of the market size with respect to the fixed part are ∂Nrpp ∂F rpp i =−λ γand ∂Ncpp ∂F cpp i =−λ δ. We must have γ > 0 and δ > 0. 10Other cases where prices other than the receiving one are zero can not be an equilibrium. 11This assumption says that the percentage of calls originated and terminated on a given network reflects the market share of this network. 8 than the fixed cost per user as long as φ > 0. Finally, the sum of the usage price is constant and equal to the marginal cost c. The access charge determines the distribution of cost between caller and receiver. Furthermore, notice that γ(a) is an opposite measure of the surplus of joining a call in a RPP regime (Urpp +˜ Urpp −cDrpp), without taking into account the fixed fee: the bigger is γ(a), the lower is this surplus. It is easy to compute the total size of the market and the profits in the symmetric equilibrium: Nrpp =[γ+ (1 + γ)λt] γ[γ+ (3 + γ)λt]φ(8) and πrpp i=N 2hF−fi=γ+ (1 + γ)λt 2γ[γ+ (3 + γ)λt]2tφ2.(9) Notice that, in order to have positive equilibrium quantities, we have to impose: φ > 0⇐⇒ λ > −1 2(v0−f)if v0> f, that is always verified.12 Vanishing noise. As the noise εtends to zero, it can be shown that the caller and the receiver demand the same length of communication when: a=c0−βc 1 + β≡aI. If a > aIthen the caller is determining the length of the call with probability converging to one (caller sovereignty). Given that the equilibrium calling price is increasing in a, by reducing the access price the length of the call increases. Otherwise, if a < aI, the receiver is determining the length of the call (receiver sovereignty). Since the equilibrium receiving price is decreasing in a, by increasing the access price the length of the call increases. Hence, at a=aI, the call is the longest possible. Since the access price ais nonnegative, an equilibrium where both caller and receiver can determine the length of a call exists only if β⩽c0 c−c0 <1, otherwise in equilibrium we can have only caller sovereignty and the longest call happens at a= 0. 12If v0< f, we would have an upper bound for λ: λ < 1 2(f−v0). 9 Length of a call. As usual, the demand function in terms of length of a call, q(·), is a decreasing function of the retail prices (q′<0). Moreover we saw that, as the noise vanishes, the length of the call is determined by the caller with probability converging to one when a > aI. Proposition 4.1 (Length of a call.).Calls last more under RPP regime when calls externality is high enough, i.e.: β≥c0 c. If β < c0/c calls last more under RPP only if the access price is high enough, i.e.: c0−βc < a < c0. Proof. See Appendix. This proposition provides support to some empirical evidences: under RPP regimes the length of calls is significantly longer than under CPP. According with proposition 4.1 calls are longer under RPP if the externality the receivers perceived is high enough. aI c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 Length of the call (a) β= 0.25 aI c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 Length of the call (b) β= 0.5 aI c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 Length of the call (c) β= 0.75 c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 Length of the call (d) β= 1 Figure 3: Length of a call q. Parameter values: c0= 0.01, c= 0.02, t= 1500 and η= 2. 16 We represented the length of a call for different values of βin Fig. 3. From now on, we use a constant elasticity demand function q(p) = p−η(as in Hoernig (2007)) where η > 1 and u(q) = η η−1qη−1 η. The dotted line is still representing the threshold between receiver sovereignty and caller sovereignty while the dashed line separates RPP regime from CPP regime. Notice that the longest length is attained for aI, when caller and receiver want to hang up at the same time. The reason is that in RPP the price of a call is shared between caller and receiver, taking into account the positive externality on the receiver and, therefore, the calls tend to be longer. But this is true only when caller and receiver are eager to hang up more or less at the same time. Otherwise who is bearing the higher price prefers to end the call earlier and, given that in RPP the variation of the retail prices is steeper, the length of the call drops quicker than in CPP. For low values of call externality β, BaK produces shorter calls than values of access charge just above termination cost. For high values of β(Fig. 3c and 3d) access prices close (or equal) to zero imply longer calls in RPP than CPP. Since for higher values of the externality the receiver is eager to pay for receiving a call, the value of athat makes caller and receiver to hang up at the same time shifts towards zero where the associated retail prices are higher for the receiver. This allows the regulator to set zero access price and keeping calls longer than CPP regimes. This confirms the expectation of Ofcom (2009, pag. 37): [. . . ] international comparisons provide evidence that this relationship between termination rates, and take-up and usage, exists. A simple analysis of cross-country data [. . . ] suggests that countries that have, broadly speaking, systems that adopt reciprocity or “bill and keep”-like arrangements – US, Hong Kong and Singapore (and to a lesser degree Canada) have higher usage than countries with “Calling Party’s Network Pays” regimes. Fixed part. Fig. 4 illustrates the comparison between the fixed part in the two price regimes. First, notice that the value of λis chosen according to equation (7). It is worthwhile to notice that at a=aIwe have the highest fixed part in RPP. The reason is straightforward: aImaximizes consumer surplus of joining a call and therefore networks can extract a higher surplus through the fixed part. Indeed this is also the reason why in these graphs higher fixed tariffs are associated to longer calls. For low values of calls externality, the relationship between equilibrium values in RPP and in CPP is not univocally determined. For high values of β, fixed part in RPP is higher than fixed part in CPP. In particular, 17 aI c0 0.000 0.005 0.010 0.015 0.020 a 500 520 540 560 580 600 620 Fixed Part (a) β= 0.25 aI c0 0.000 0.005 0.010 0.015 0.020 a 500 520 540 560 580 600 620 Fixed Part (b) β= 0.5 aI c0 0.000 0.005 0.010 0.015 0.020 a 500 520 540 560 580 600 620 Fixed Part (c) β= 0.75 c0 0.000 0.005 0.010 0.015 0.020 a 500 520 540 560 580 600 620 Fixed Part (d) β= 1 Figure 4: Fixed part F. Parameter values: c0= 0.01, c= 0.02, t= 1500, λ= 0.002, η= 2, f= 0 and v0= 750. BaK determines higher fixed fee than any other value of the access charge. The reason is that, when access charge is below cost, calls last more, therefore the consumers’ surplus that networks can extract is higher. This coincides with many empirical observations. For instance, Ofcom (2009, pag. 37) expects: High termination rates tend to lead to a retail price structure with relatively high off-net call charges (since operators ‘cover’ their wholesale cost of each minute of a call with a corresponding retail charge) and lower subscription charges (since subscribers generate incoming calls that provide call termination revenue). [. . . ] Equally, if termination rates are low, consumers will tend to face higher subscription fees but lower or no charges to make (or receive) calls. Market penetration. Fig. 5 illustrates that there is not a clear relationship between market penetration in the two regimes. For low values of receiver externality, there are values of access charge such that penetration is higher in CPP regimes. Conversely, for 18 high receiver externality, RPP regimes present a high number of subscribers. This indeterminacy is also present in empirical evidence: on the one hand Littlechild (2006) shows how CPP are denoted by higher market penetration, on the other hand Analysis Mason (2008) states that actual data misrepresent true values of penetration by overestimating penetration in CPP countries. Moreover, high penetration is explained through the higher surplus the consumers receive. Once again in RPP we have the highest penetration at a=aI. aI c0 0.000 0.005 0.010 0.015 0.020 a 3 4 5 6 7 8 Subscribers (a) β= 0.25 aI c0 0.000 0.005 0.010 0.015 0.020 a 3 4 5 6 7 8 Subscribers (b) β= 0.5 aI c0 0.000 0.005 0.010 0.015 0.020 a 3 4 5 6 7 8 Subscribers (c) β= 0.75 c0 0.000 0.005 0.010 0.015 0.020 a 3 4 5 6 7 8 Subscribers (d) β= 1 Figure 5: Market penetration N. Parameter values: c0= 0.01, c= 0.02, t= 1500, λ= 0.002, η= 2, f= 0 and v0= 750. Graphics show, once again, that RPP regimes are more sensible to variations of the perceived externality: penetration is increasing in β. 19 4.1 Welfare analysis We compare the welfare in the two regimes in Fig. 6. Total welfare is given by a weighted sum of consumers surplus and industry profits.14 As it is clear, the highest welfare in RPP is attained at a=aI. At this value of the access price, consumer surplus of a call is maximized and the network can obtain the highest profits by extracting it. In CPP the highest welfare is associated to values of the access price close to the termination cost. aI c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 12000 14000 Welfare (a) β= 0.25 aI c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 12000 14000 Welfare (b) β= 0.5 aI c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 12000 14000 Welfare (c) β= 0.75 c0 0.000 0.005 0.010 0.015 0.020 a 2000 4000 6000 8000 10000 12000 14000 Welfare (d) β= 1 Figure 6: Total welfare W. Parameter values: c0= 0.01, c= 0.02, t= 1500, λ= 0.002, η= 2, f= 0 and v0= 750. Notice that as the receiver externality increases, the welfare is getting higher in RPP 14The consumer surplus is given by the net surplus consumers perceive in equilibrium according with equation (4) minus the total amount of the transportation costs: CSrpp =“v0+Nrpp(Urpp +˜ Urpp −cDrpp)−Frpp”Nrpp −"„Nrpp −1 2«2 +1 4#t; CScpp =“v0+Ncpp(Ucpp +˜ Ucpp −pcppDcpp)−Fcpp”Ncpp −"„Ncpp −1 2«2 +1 4#t. 20 regimes. This fact remarks once again the importance for the regulator of having a very precise knowledge of the values of βwhen choosing the access price: very low values of a (accompanied by a RPP regime) are socially optimal only if the receiving externality is high. The European Commission (2008) ends up to the same conclusion: RPP might not be efficient if the calling party values the call highly but the called party does not and, as a result, an efficient call might not be completed. The reverse issue may arise in the CPP system, where an efficient call may not be initiated even if the called party values it highly but the calling party does not. Indeed, if a regulator considers that in its country the externality is very low BaK is not the welfare maximizing policy. Finally, assigning different weights to consumers surplus and industry profits, results do not change qualitatively. 5 Conclusions Regulatory authorities are concerned about reducing mobile termination rates but there is a lack of theoretical analysis that could give them hints about the consequences of such a policy. The European Commission (2008, 2009) proposed a drastic reduction of the mobile termination rates during the next years. This, according to empirical evidence and companies’ previsions, would imply to charge consumers for receiving calls in order to cover the termination cost of a call: the European Commission (2008, pag. 26) noticed that “RPP may evolve after a reduction of the regulated termination charge or as a response to a Bill and Keep system”. Ofcom (2005) warned that RPP regimes could find the opposition of consumers who do not want to be charged for incoming calls. In our paper we provide a theoretical framework that allows to compare the two tariff regimes. We confirm the relationship between interconnection arrangements and retail price structure. It turns out that it does not exist one tariff regime superior to the other other in terms of retail prices, usage, market penetration and overall welfare for all values of the access price. Using realistic values of the industry parameters, we find out that the level of the call externality is crucial. When it takes high values, market penetration and total welfare are higher in a RPP regime with access charges close to zero. This suggests that a BaK policy (which results in the adoption of a RPP regime) should be implemented only once the presence of a high call externality is proven. Otherwise access pricing at the termination 21 cost would be a better policy. Up to our knowledge, there are no estimates of the call externalities. On the one hand, the Body of European Regulators for Electronic Communications (BEREC (2010b)) pointed out that it seems reasonable to assume that the utility of the receiver is lower than that of the caller but that the difference is not very significant. On the other hand, in BEREC (2010a) several phone companies claim that the call externalities are very low or even equal to zero. A Proofs Proof of Proposition 3.1 To find the usage prices we maximize profits with respect to piand rikeeping market share niconstant: max pi,ri πi s.t. pi, ri≥0 We look for the interior solutions where pi, ri>0. For a given ni, the first order derivative of πiwith respect to piwhen r=ri=rjis: q′[1 −F(r−βpi)]{(ni+nj)(u′−c)−nj(a−c0) + ni(˜u′+E[ε|ε⩾r−βpi]) −ni 1 1 + 2tλ(˜u′+E[ε|ε⩾r−βpi]−r)}= 0.(11) Similarly, for a given ni, the first order derivative with respect to riwhen p=pi=pjis: ni(u′−c) + nj(a−c0) + (ni+nj)˜u′+ni 1 1 + 2tλ(u′−p) + E[εq′|ε⩽ri−βp] E[q′|ε⩽ri−βp]= 0.(12) As the noise vanishes, when the caller and the receiver want to hang up at the same time we have that u′=pand ˜u′=r. In a symmetric equilibrium the first order conditions turn out to be: p= (c−r) + 1 2(c+a−c0−c+r) r= (c0−a) + 1 2(c−p−c0+a). Notice that both conditions hold for p=c+a−c0and r=c0−a. To find the fixed part 22 of the two-part tariff, we derive profits with respect to Fi: ∂πi ∂Fi =∂ni ∂Fihni(pi−c)D(pi, ri) + nj(pi−c−(a−c0))D(pi, rj) + nj(a−c0)D(pj, ri) +riniD(pi, ri) + njD(pj, ri)+Fi−fi +nih∂ni ∂Fi (pi−c)D(pi, ri) + ∂nj ∂Fi (pi−c−(a−c0))D(pi, rj) + ∂nj ∂Fi (a−c0)D(pj, ri) +ri∂ni ∂Fi D(pi, ri) + ∂nj ∂Fi D(pj, ri)+ 1i Using equilibrium prices: ∂πi ∂Fi =∂ni ∂Fihni(pi−c)D(pi, ri) + nj(a−c0)D(pj, ri) +riniD(pi, ri) + njD(pj, ri)+Fi−fi +nih∂ni ∂Fi (pi−c)D(pi, ri) + ∂nj ∂Fi (a−c0)D(pj, ri) +ri∂ni ∂Fi D(pi, ri) + ∂nj ∂Fi D(pj, ri)+ 1i =∂ni ∂FihFi−fi+ni= 0 Therefore the fixed part is: Fi=f−ni ∂ni ∂Fi (13) Combining (4) with (6) we find the total size of the market Nand the number of consumers ni: We obtain: N=1−λ(Fi+Fj−2v0) 1−2λ(U+˜ U−cD)and ni=N 2+(Fj−Fi)(1 + λt) 2t(14) Let us write the market size as follows: N=1−λ(Fi+Fj−2v0) γ(15) where γ(a)≡1−2λ(Urpp +˜ Urpp −cDrpp). The derivative of the market share of network iwith respect to Fiis: ∂ni ∂Fi =1 2h∂N ∂Fi −1 + λt ti =−1 2 λt +γ(1 + λt) γt (<0) (16) 23 Substituting (14) and (15) into (13) and looking for the symmetric equilibrium, we have: Fi=f+N 2 2γt λt +γ(1 + λt). Solving for Fwe obtain: F=f+tφ γ+ (3 + γ)λt. Proof of Lemma 3.1 Remember that γ(a)≡1−2λ(Urpp +˜ Urpp −cDrpp). Its derivative is: ∂γ ∂a =−2λh∂U ∂a +∂˜ U ∂a −c∂D ∂a i. Let us first compute the derivative of the volume of calls with respect to the access price. ∂D ∂a =∂D ∂p ∂p ∂a +∂D ∂r ∂r ∂a where15 ∂D ∂p =∂F(r−βp) ∂p βq(p) + [1 −F(r−βp)]q′+q(p)f(r−βp)(−β) = [1 −F(r−βp)]q′ ∂D ∂r =−f(r−βp)q(p) + q(p)f(r−βp) + 1 βZr−βp ¯ ε q′f(ε)dε =1 βEhq′ε≤r−βpiF(r−βp). Hence, we have ∂D ∂a =h1−F(r−βp)iq′−1 βEhq′ε≤r−βpiF(r−βp). The derivative of the utility derived by making calls with respect to the access price is: ∂U ∂a =∂U ∂p ∂p ∂a +∂U ∂r ∂r ∂a where ∂U ∂p =∂F(r−βp) ∂p βu(q) + [1 −F(r−βp)]u′(q)q′+u(q)f(r−βp)(−β) =[1 −F(r−βp)]u′(q)q′ ∂U ∂r =−F(r−βp) ∂r u(q) + u(q)f(r−βp) + 1 βZr−βp ¯ ε u′(q)q′f(ε)dε =1 βEhu′q′ε≤r−βpiF(r−βp). 15Hereinafter q′<0 denotes the derivative of the lenght of a call with respect to the usage price. 24 Hence, we have ∂U ∂a =h1−F(r−βp)iu′q′−1 βEhu′q′ε≤r−βpiF(r−βp). The derivative of the utility derived by receiving calls with respect to the access price is: ∂˜ U ∂a =∂˜ U ∂p ∂p ∂a +∂˜ U ∂r ∂r ∂a where ∂˜ U ∂p =˜u′q′[1 −F(rj−βpi)] + β˜u(q(pi))f(rj−βpi) + q′[1 −F(rj−βpj)] E[ε|ε≥rj−βpi] +βq(pi)(rj−βpi)f(rj−βpi)−β˜u(q(pi)) f(rj−βpi)−βq(pi)(rj−βpi)f(rj−βpi) =˜u′+Ehεε≥r−βpih1−F(r−βp)iq′ ∂˜ U ∂r =−F(r−βp) ∂r ˜u(q) + qf(r−βp)(r−βp) + ˜u(q)f(r−βp) + 1 βZr−βp ¯ ε ˜u′(q)q′f(ε)dε + (r−βp)q(p)f(r−βp) + 1 βZr−βp ¯ ε q′εf(ε)dε =1 βEhq′(˜u′+ε)ε≤r−βpiF(r−βp). Hence, we have ∂˜ U ∂a =˜u+Ehεε≥r−βpih1−F(r−βp)iq′−1 βEhq′(˜u′+ε)ε≤r−βpiF(r−βp). Hence, the derivative of γ(a) is: ∂γ(a) ∂a = 2λn1 βF(r−βp)E[(u′(q) + ˜u′(q) + ε−c)q′|ε≤r−βp] +h1−F(r−βp)ihc−u′(q)−˜u′(q)−E[ε|ε≥r−βp]iq′o. As the noise vanishes we get: ∂γ(a) ∂a = 2λn1 βF(r−βp)hu′(q) + ˜u′(q)−ciq′−h1−F(r−βp)ihu′(q)−˜u′(q)−ciq′o. Notice that when a > aI(a < aI) the caller (the receiver) wants to hang up first and therefore we have ˜u′(q)> r (u′(q)> p). This implies that u′(q) + ˜u′(q)−c > 0. Moreover remember that F(r−βp) denotes the probability that the receiver hang up first: as the noise tends to zero this probability is equal to 1 in receiver sovereignty and equal to 0 in consumer sovereignty. Finally we have: ∂γ ∂a =     2λ βhu′(q) + ˜u′(q)−ciq′<0 if a < aI; −2λhu′(q) + ˜u′(q)−ciq′>0 if a > aI. 25 Samarajiva, R. & Melody, W. H. (2000). Briefing paper. In Fixed-Mobile Interconnection Workshop. available at http://www.itu.int/osg/spu/ni/fmi/workshop/. 32