J Regul Econ (2012) 42:204–222 DOI 10.1007/s11149-011-9171-2 ORIGINAL ARTICLE Competition with asymmetric regulation of mobile termination charges Edmond Baranes · Cuong Hung Vuong Published online: January 2012 © Springer Science+Business Media, LLC 2011 Abstract The aim of this paper is to explore the effectiveness of asymmetric regulation, which allows a new mobile network operator to set higher termination rates than the incumbent operator We assume that there are two market segments: one in which operators compete on equal terms, with a new technology, and the other in which the entrant is at a disadvantage since the technology it offers is inferior to the incumbent’s Results show that asymmetric regulation can create favorable conditions that allow the entrant to strengthen its market positioning, and enhance consumer net utilities and social welfare This highlights the importance of the degree of network asymmetry and the ways in which consumers are split between the two market segments Lastly, we show that asymmetric regulation can create greater investment incentives for the entrant which could effectively enhance social welfare These findings can provide useful insights for regulatory policy Keywords Access charge · Asymmetry · Network competition · Regulation JEL Classification D43 · L11 · L13 Introduction Since the introduction of competition in the European telecommunications market, business opportunities arisen for a few mobile network operators (MNOs) in each E Baranes (B) Lameta, University Montpellier 1, Montpellier, France e-mail: edmond.baranes@univ-montp1.fr C H Vuong International University, Ho Chi Minh, Vietnam 123 Competition with asymmetric regulation 205 EU Member State Network interconnection and mobile termination rates are crucial for ensuring sustainable competition in this environment Because of the small scale involved in the beginning and to promote competition, regulation allows for asymmetrical treatment of the dominant networks and new entrants whereby new entrants are allowed to set mobile termination rates (MTR) that are relatively higher than those charged by their rivals A recent European Commission recommendation (EC 2009) instructs National Regulatory Authorities (NRAs) on how to regulate MTR The Commission’s recommendations aim at reducing MTRs to reflect the actual incremental costs of providing voice call termination services to third parties The European NRAs have followed and gradually replaced asymmetric MTR regulation by cost-oriented symmetric MTR regulation.1 This opens a discussion on the potential drawbacks and merits of asymmetric MTR regulation as well as the impact of on-net and off-net price discrimination adopted by operators, especially those who have large networks Additionally, asymmetric regulation may become an issue with the launch of new mobile services using next generation technology In Europe, Teliasonera has recently launched 4G commercially in Sweden and Norway There exists then market competition between operators offering mobile services with different technologies, i.e old and new technologies The availability of the new technology allows consumers to access faster mobile broadband connections,2 and provides more choices for Internet users and possibly greater social welfare From a regulatory viewpoint, the key question is how to provide sufficient incentives for all MNOs to upgrade their technologies Despite a large amount of economic literature on access pricing (Laffont and Tirole 2000; Armstrong 2002; Vogelsang 2003; Armstrong and Wright 2009; Harbord and Pagnozzi 2010), there is a relative dearth of economic studies on asymmetric regulation One of the main arguments is that asymmetric regulation could send out the wrong signals, which would cause the new entrant to behave in a rent-seeking manner or to rely solely on the benefits of asymmetric regulation without making any investments to directly compete with the incumbent According to Peitz (2005a,b), although asymmetric MTR regulation can be considered as an appropriate instrument to increase the entrant’s market share, and to compete effectively in the long-run competition, it is not socially desirable in the short-run More specifically, since the incumbent can provide consumers with a relatively higher fixed utility and the implementation of asymmetric regulation, whereby the incumbent is obliged to provide cost-based level whereas the entrant can set an above-cost MTR, the consumer surplus increases thanks to more aggressive pricing strategies adopted by both MNOs Furthermore, the implementation of asymmetric MTRs leads to a distortion of the market structure whereby the entrant acquires too much market share,3 resulting in lower total social surplus A In response to the EC recommendation, there is a growing debat between regulators over alternative approaches to regulating MTRs, including bill-and-keep (ERG 2009) It is entirely possible that the rollouts of 4G mobile networks, and especially investments in Long Term Evolution (LTE) networks, will provide consumers with much higher bandwidth speeds using mobile devices which, in turn, may be considered as a mean to increase competition between wire-less and wire-line providers de Bijl and Peitz (2002) explore the role of reciprocal and asymmetric terminating access prices in a quite similar setting In a dynamic setting, they show that, whereas the entrant’s profits increase and the 123 206 E Baranes, C H Vuong recent paper from Hoernig (2009) examines a fully dynamic model of entry in mobile telephony, taking into account both mobile-to-mobile and fixed-to-mobile termination rates In particular, he concludes that asymmetric termination rates increase the entrant’s market share and profit level.4 This paper will therefore revisit the impacts of asymmetric regulation in a situation in which two MNOs are providing mobile services using different technologies, i.e an old and a new one.5 Our purpose is to determine and to clarify the asymmetrical regulatory impacts on the incentives of the entrants to upgrade their technologies In our model, the incumbent MNO offers the new technology to all consumers while the competitor (the new entrant) can only offer the new technology to some consumers and the old technology to all the others To be more precise, we are considering a situation of two distinct markets: one in which the new entrant offers the same technology (the new technology) as the incumbent, and the other in which the entrant offers an inferior technology (the old technology) This introduces a technology-based asymmetry between mobile networks due to the lower quality of network access provided by the new entrant in the market where it is unable to offer the same new technology as the incumbent Previous studies assume that the mobile network asymmetry is characterized by the fixed value parameter presenting for brand loyalty or switching cost for all customers (see, for example, Peitz (2005a,b), Carter and Wright (2003)) However, customers are often heterogeneous in tastes when choosing mobile networks as documented in Grzybowski (2008), which used UK mobile market data.6 Therefore, in our model, we assume that due to the late entry, the entrant cannot provide as full a range of mobile services as the incumbent can (for instance, the new entrant does not provide the same quality of hot-line services or other non-voice mobile services including mobile broadband mobile technology, or the entrant provides less points of service, lower quality of service infrastructure), or the strategic incumbent’s location is relatively more convenient than the new entrant’s location (in France, the incumbent, Orange, benefits greatly from good distribution channels through the commercial network locations of the historical French telecommunication operator, France Telecom) Consequently, customers find it relatively more problematic to join the entrant’s network than the incumbent’s network These described disadvantages of the entrant are then illustrated in our model by greater unit transportation cost for consumers to subscribe for the entrant’s network,7 eventually leading to the asymmetry between two Footnote continued incumbent’s profits decrease with asymmetric MTRs, the effect on welfare is less easy to analyze and may be negligible In a complementary fashion, and using a simulation model, Hoernig (2010) estimates the impact of a decrease in MTRs in the UK market His findings show that economic welfare in the mobile market can decrease with a reduction in MTR, and that this effect may reverse, especially when call externalities are significant The new technology in this instance could be a 4G mobile technology such as LTE These parameters include sex, age, employment status and household, usage intensity and ways of spend- ing leisure time There exists a number of studies analysing the firm competition in serveral industries accounting for the asymmetric unit transportation costs including Nilssen and Sorgard (1996); Nilssen (1997), and Sun (2010) 123 Competition with asymmetric regulation 207 mobile networks.8 Finally, our work is also related to the literature addressing the role of changes in consumers’ transportation costs in the context of switching cost models9 as discussed in Beggs and Klemperer (1992) Shaffer and Zhang (2000) also assume that loyalty parameters play an analogous role to the usual transportation cost in the Hotelling model Hence, there are some instances in which our assumption, on how asymmetry is modeled, is realistic since it acknowledges a link between the asymmetry and the consumers’ valuation A large literature in marketing has also been developed to study consumer brand preferences and implications for marketing decision A part of this literature aims at analysing consumer heterogeneity in brand loyalty and discusses real-world examples (Villas-Boas and Winer (1999) and more recently Chen et al (2008)) As we will show, asymmetric regulation can have a positive impact on social welfare which depends on the degree of asymmetry between networks and on how consumers are split between the two markets In particular, when asymmetry between networks is sufficiently high, asymmetric regulation improves social welfare if there is a large consumer base in the market in which MNOs compete on equal terms In addition, under asymmetric regulation, we find that the entrant invests to increase its market coverage with the new technology Such investments reduce the entrant’s disadvantage by providing the new technology with higher quality mobile services We will also show that asymmetric regulation can have a mixed effect on the relationship between the new entrant’s profit, investment incentive and the social welfare More precisely, we explicitly show the conditions under which asymmetric regulation can create incentives for the entrant to invest, and thereby increase social welfare in the short-run In the long-term, asymmetric regulation can effectively result in more sustainable competition between infrastructure-owning MNOs, because the new entrant is more firmly established and has a larger market share The remainder of this paper is organised as follows: Section lays out the basic framework and determines prices at equilibrium Section analyses the consequences of asymmetric regulation on firms and social welfare Section explores how asymmetric regulation might provide incentives for the new entrant to invest and improve its track record And, finally, the conclusion provides implications for MTR regulatory policy Most of the proofs for lemmas and propositions are relegated to the Appendix The basic model setting We introduce a model of a telecommunications market, whereby two horizontally differentiated networks compete la Hotelling as in Laffont et al (1998a,b) and Armstrong (1998) The consumers are uniformly located in the segment [0, 1] with a full market coverage while the incumbent (network 1) and the entrant (network 2) are located at x1 = and x2 = respectively It can be easily seen that the symmetry can be considered as a particular case of asymmetry when the perturbation goes to zero See Weitzman (1994) and Hendel and Neiva de Figueiredo (1997) for a general literature on endogeneous disutility 123 208 E Baranes, C H Vuong We assume that there are two technologies, a new and an old technology We then consider two markets, one in which the entrant offers the same technology as the incumbent (the new technology) and the other in which it offers an inferior technology (the old technology) This models a competition with asymmetric networks in which only one network has full market coverage with the new technology, while the other has partial market coverage with the old technology Finally, we assume that consumers are split between the two markets as follows: a fraction ρ of consumers is in the market in which both networks compete on equal terms (market U ), and a fraction − ρ of consumers is in the other market (market R).10 Assume that each network bears a fixed cost normalized to 0, and a same marginal cost c0 at the originating or terminating end of each call whatever the market Then, 2c0 represents the total marginal cost associated with an on-net call For each minute of an off-net call from network i to network j, network i pays the termination charge a j to network j The networks discriminate prices for on-net and off-net calls, and offer two-part tariffs in the retail market Specifically, we denote pi and pi for the on-net and off-net prices respectively, and Fi for the fixed fee for network i On the demand side, given tariff ( pi , pi , Fi ) and under the assumption of balanced calling pattern with αi denoting the market share of network i, the indirect utility from joining network i is wi , where: wi = αi v( pi ) + (1 − αi )v( pi ) − Fi (1) where v( pi ) = u(q( pi )) − pi q( pi ) is the indirect utility associated with pi , q( pi ) is the individual demand of calls and u(q) represents the utility from calling q calls In (1), the first term represents indirect utility, αi v( pi ) which is the utility that a consumer derives from on-net calls while the indirect utility obtained from off-net calls is represented in the second term From market segmentation, we assume for the relative disadvantage of the entrant in the market R due to consumer’s resistance when joining the entrant’s network This introduces an asymmetry between mobile networks based on technology, and reflects a lower quality in network access for the entrant on the market R in which it cannot offer the same, new technology as the incumbent does Let θ denote the consumer’s unit transportation cost when joining the incumbent’s network Without loss of generality, we assume that the unit transportation cost for joining the entrant’s network is θ , where θ = θ (1 + A) with A ≥ The level of A, therefore, measures the degree of asymmetry between networks Given the unit transportation costs θ and θ , the utility for a consumer located at x ∈ [0, 1] from joining the incumbent’s network (network 1) is w1 −θ The consumer’s utility is w2 − θ (1− x), i.e w2 −θ (1− x)−θ A(1− x), if he joins the entrant’s network (network 2), where w1 and w2 are the total indirect utility from joining network and respectively Hence, an entrant’s consumer obviously receives greater total indirect utility if he locates nearer the unity and with a lower value of A 10 This market segmentation can represent regional markets, for example a rual area and an urban area where the asymmetry lies into the deployment of the new mobile technology 123 Competition with asymmetric regulation 209 Explicitly, the marginal consumer’s decision, for consumers in market R, is based on: w1 − θ x = w2 − θ (1 − x) − θ A(1 − x) We note s1 and s2 market shares respectively for network and network in which they compete using different technologies After setting the price vector for both networks, market shares si are determined as follows: s1 = w − w2 (1 + A) + with s2 = − s1 2+ A θ (2 + A) (2) We define the “modified” degree of network substitutability for market R as Hence, from (2) when network services are closely substitutable for moθ (2 + A) bile users (θ is sufficiently low) and by adopting the same price structure, network can gain huge market share compared to network 2.11 Moreover, from a customer’s viewpoint, the higher the asymmetry between networks ( A), the lower the degree of substitutability of the incumbent’s network by the entrant’s network From (2) and setting A = 0, we easily deduce market shares, s1 and s2 , for consumers in market U , in which networks compete on equal terms: s1 = w1 − w2 + with s2 = − s1 2θ (3) Finally, the overall market share for operator i is αi = ρsi + (1 − ρ)si , with α j = − αi By setting two-part tariffs, the profit function for network (respectively for network 2) is equal to: π1 = α1 [α1 ( p1 − 2c0 )q( p1 ) + (1 − α1 )( p1 − c0 − a2 )q( p1 ) + F1 ] + α1 (1 − α1 )(a1 − c0 )q( p2 ) (4) The next section determines the Nash equilibrium prices ( pi , pi , Fi ) for each network for a given set of termination charges, assuming that the incumbent is cost-based regulated Asymmetric termination charges In this section, we examine how asymmetric regulation affects competition between MNOs and whether it can improve consumers’ utilities and social welfare As in Peitz (2005b), we now derive the equilibrium prices ( pi , pi , Fi ) for each operator and show how consumers’ net utilities and welfare move when the entrant is allowed to charge an access mark-up while the incumbent is cost-based regulated 11 By setting the same price structure, total net utility provided by the two network operators are the same and hence we have lim A→∞ α1 = 123 210 E Baranes, C H Vuong Market shares Consumers choose which network to join by comparing a given set of prices ( pi , pi , Fi ) or the net utility offered by the two networks Using (1) and (2), we obtain market shares for the incumbent (network 1) and the entrant (network 2) in market R as follows: s1 = v( p1 ) − v( p2 ) + F2 − F1 + θ (1 + A) and s2 = − s1 v( p1 ) + v( p2 ) − v( p1 ) − v( p2 ) + θ (2 + A) (5) In market U , market shares, s1 and s2 , are simply obtained by setting A to zero in (5) Retail prices and subscription fees We analyze the equilibrium outcome of the market game according to termination charges The MNOs maximise their profits with respect to overall utilities provided and the per unit prices Rewriting (4) and (1), and using the literature on two part tariffs, we easily obtain that on-net and off-net prices are equal to their perceived marginal costs, pi∗ = 2c0 and pi∗ = c0 + a j These classical results are due to Laffont et al (1998a,b) In the setting of network asymmetry, we analyse the impacts of asymmetric regulation in which the incumbent is obliged to set its termination rate at cost-based level (a1 = c0 ), whereas the competitor’s charge can be set at a higher level (a2 ≥ c0 ) Subsequently, equilibrium unit prices are: p1∗ = p2∗ = p2∗ = p ∗ = 2c0 (6) p1∗ = c0 + a2 (7) and Given these equilibrium unit prices and asymmetric regulation, network market shares in both markets (R and U ) become: v( p1∗ ) − v( p ∗ ) + F2 − F1 + θ (1 + A) and s2 = − s1 v( p1∗ ) − v( p ∗ ) + θ (2 + A) ∗ ∗ v( p1 ) − v( p ) + F2 − F1 + θ and s2 = − s1 s1 = v( p1∗ ) − v( p ∗ ) + 2θ s1 = (8) Provided that network i sets usage prices at the perceived marginal costs, its profit can be expressed with respect to subscription fees Fi as: ∗ ( pi , pi∗ , p ∗j , Fi ) = α1 F1 ∗ ∗ ∗ ∗ ( pi , pi , p j , Fi ) = α2 F2 + α2 (1 − α2 )(a2 − c0 )q( p1 ) (9) We now determine the networks’ choice of subscription fee F1 and F2 Expressions (9) show that an increase in subscription fee by network i leads to two opposite effects on network profit: first it raises the direct revenue for i, and, second, it reduces network i’s market share, as consumers are more reluctant to join network i 123 Competition with asymmetric regulation 211 Each network optimally chooses itA subscription fee taking the other network’s fee as given The first order condition for incumbent profit maximization is: ∂π1 ∂α1 = α1 + F1 = ∂ F1 ∂ F1 (10) and the first order condition for the entrant is: ∂α2 ∂π2 = [F2 + (1 − 2α2 )(a2 − c0 )q( p1∗ )] + α2 = ∂ F2 ∂ F2 (11) For an interior equilibrium, we can derive (F1∗ , F2∗ ) from simultaneously solving the system of two Eqs 10 and 11 using (8) (see Appendix A) One can then easily deduce equilibrium market shares (α1∗ , α2∗ ), profits (π1∗ , π2∗ ) and consumer net utilities (w1∗ , w2∗ ) Our analysis is to focus on the impacts of a slight deviation of the entrant’s termination rate from the cost-based level on market equilibrium Specifically, asymmetric regulation affects equilibrium subscription fees as stated in the following Lemma Lemma From the cost-based level, an increase in the entrant’s termination charge: (i) reduces subscription fees and allows the entrant to increase its market share, but (ii) increases the entrant’s profitability if the fraction of consumers in market U is sufficiently high (ρ ≥ ρ) or if the degree of asymmetry between networks is not too large (A ≤ A1 ) Lemma highlights the sizeable consequences of the new entrant’s above-cost MTR on competitive strategies Specifically, by obtaining wholesale revenue, thanks to asymmetric regulation, the entrant can cut its fixed retail price to increase the attractiveness of its network To respond to this, the incumbent, in turn, must also reduce its fixed retail price, resulting in stronger competition in the retail market This first result is the same as the one put forth by Peitz (2005b) Lemma shows that the effects of asymmetric regulation on subscription fees and on the entrant’s market share not depend on the level of asymmetry between networks and how consumers are split between both markets, U and R In other words, a reduction of the entrant’s subscription fee invariably leads to an increase in its market share even if the asymmetry between networks is high However, the impact of asymmetric regulation on the entrant’s profit level depends directly on the trade-off between a low subscription fee, which reduces profit, and the rise of its market share, which has a positive effect on profits When the asymmetry between networks is high, or the fraction of consumers in market R is relatively high (ρ < ρ), the entrant has to charge an attractive subscription fee12 to offset the negative effect of its market disadvantage (inferior technology in market R) Ultimately, this leads to an increase in the entrant’s market share but an overall negative effect on its profit Consumers’ net utilities and social welfare Let us now study how asymmetric regulation affects social welfare which is the sum of consumer surplus and industry 12 We can easily show that ∂ F2 decreases in A ∂a2 a2=c0 123 212 E Baranes, C H Vuong profits We denote W for social welfare and C S for consumer surplus, which is the aggregated consumers’ net utility minus the dis-utility due to the network’s departure from the most ideal location We note S and S for consumer surplus for consumers in market U and market R, respectively: s1 (w1 − θ x)d x + S= s1 = s1 w1 − (w2 − θ (1 − x)d x θ s2 θ s1 + s2 w2 − 2 and, s1 (w1 − θ x)d x + S= (w2 − θ (1 + A)(1 − x)d x s1 θ θ (1 + A) s2 = s1 w1 − s12 + s2 w2 − 2 Hence, at equilibrium, social welfare is: W ∗ = C S ∗ + π1∗ + π2∗ with C S ∗ = ρ S ∗ + (1 − ρ) S ∗ (12) As pointed out in Peitz (2005b), the asymmetric regulatory mode triggers negative impacts on social welfare due to the entrant’s high market share, and because the incumbent’s off-net price is inflated above the cost-based level Arguably, in the Peitz’s framework, from the consumer’s viewpoint, mobile services are differentiated in the sense that the incumbent provides relatively higher total indirect utility than the entrant (w1 > w2 when prices are identically set by both networks) When the entrant’s market share increases due to asymmetric regulation, there is a negative welfare distortion attributable to the change in market structures Since in our model the effect of the entrant’s disadvantage depends on the unit transportation costs and the consumers’ location, thus diminishing this negative effect is diminished The following proposition states the social desirability of asymmetric regulation Proposition When asymmetry between networks is sufficiently high,13 asymmetric regulation around cost-based termination charges (i) always induces greater net utilities for consumers and, (ii) increases social welfare if ρ ≥ ρ ∗ Consumer net utilities increase under asymmetric regulation, as already implied in Lemma 1, which reveals that both networks have to set lower fixed fees, albeit with a slight increase in the entrant’s termination rate Furthermore, although the incumbent’s off-net unit price is higher, our analysis explicitly shows that both the entrant’s and 13 In appendix B, we show that when the asymmetry between networks is low (A < A), asymmetric regulation has a negative impact on the social welfare 123 Competition with asymmetric regulation 213 the incumbent’s consumers are better off under asymmetric regulation When asymmetry between networks increases, both MNOs lower their subscription fees to attract consumers, which, in turn, spurs market competition leading to higher net utilities for consumers (i) Lemma clearly shows that, from the cost-based level, an increase in the entrant’s termination charge leads to a higher market share for the entrant and improves its profit if the network asymmetry is sufficiently small (A ≤ A1 ) Consequently, the incumbent’s market share and profit are dramatically affected under asymmetric regulation In Proposition 1, (ii) reveals that the positive effect of asymmetric regulation on consumer surplus may be sufficiently high to counterbalance the negative effect that such regulation has on the incumbent’s profit, thereby increasing total social welfare This is reinforced by the potential positive effect of asymmetric regulation on the entrant’s profit, when the asymmetry between networks is not so high (i.e., A is lower than A1 ) Finally, Proposition shows that asymmetric regulation intensifies market competition and may enhance overall social welfare That is, asymmetric regulation may be useful from a social perspective by creating favorable conditions for the entrant to strengthen its market position Investment incentives of the entrant This section analyses the impact of asymmetric regulation on the entrant’s incentive to improve its market coverage with the new technology, thus reducing the degree of asymmetry between networks Assume that a fraction ρ0 of consumers is in market U and a fraction − ρ0 in market R The value of ρ0 represents an exogenous fraction of consumers in market U whereby the entrant does not invest in increasing its coverage with the new technology We assume that the entrant can improve its market coverage with the new technology by investing sufficiently to increase the fraction of its consumers in market U More precisely, we assume that with an investment ε, the fraction of consumers in market U becomes ρ(ε), where ρ (ε) > Without investment, the fraction of consumers in market U remains ρ0 , ρ(0) = ρ0 Assuming we only focus hereafter on investment incentives around ρ0 , we assume that investment costs are zero Accordingly, the profit of the entrant is: π2 ( p1 , p1 , p2 , p2 , F1 , F2 ) = α2 (ε)[α2 (ε)( p2 − 2c0 )q( p2 ) + (1 − α2 (ε)) ( p2 − c0 − a1 )q( p2 ) + F2 ] + α2 (ε)(1 − α2 (ε))(a2 − c0 )q( p1 ) (13) where the overall market share for network is α2 (ε) = ρ(ε)s2 + (1 − ρ(ε))s2 Our research questioned whether there is any risk inherent in implementing asymmetric regulation, especially over a long period of time, as the entrant’s business could solely rely on the beneficial effects of the regulation, without making any further investment in new technology to compete with the incumbent Intuitively, there are two opposite effects associated with investment First, the entrant can increase the consumer’s fixed utility by investing to improve its market coverage with the new technology Second, since investment directly affects market shares, it alters the split between on-net and off-net calls and that has an immediate impact on the entrant’s 123 214 E Baranes, C H Vuong short-run profit as well As a result, the entrant would optimise its profit and choose the optimal investment strategy according to, a large extent, the regulated termination rate A complete characterisation of the optimal investment strategy for the new entrant is rather complicated to produce because of the analytical expressions involved In the following, we analyse the incentive for the entrant to provide market coverage for the new technology exceeding ρ0 Proposition Suppose that asymmetric regulation around cost-based termination charge is applied A marginal investment from the entrant: (i) can increase its incentive to invest if A ≤ A, or if A > A and ρ0 ≥ ρ0 ; and, (ii) can strengthen the positive impact of asymmetric regulation on social welfare if A ≤ A, or if A > A and ρ0 ≤ ρ0 Previous results show that asymmetric regulation makes the consumer more valuable from the entrant perspective It is easy to show (see Appendix C) that a higher level of regulatory asymmetry strengthens the entrant’s incentive to invest in increasing its market share whatever the asymmetry between networks However, as investment impacts market shares, it produces additional effects since it affects the balance between on-net and off-net calls Hence, the entrant’s strategy to achieve greater market share and profitability, due to asymmetric regulation, should be subject to sensible justification Whether the investment increases the entrant’s profit and social welfare depends on the exogenous fraction of consumers in market U , which corresponds to the fraction for which the entrant makes no investment (ρ0 ), and on the degree of network asymmetry (A) Accordingly, our analysis dismisses the potential rent-seeking behavior of the entrant by showing that, under asymmetric regulation, the entrant may improve its profit by investing Proposition shows that this could be especially true if the degree of asymmetry between networks is not excessively high or if the exogenous fraction of consumers in market U is sufficiently high, ρ0 ≥ ρ0 Intuitively, this result highlights a potential drawback to asymmetric regulation with respect to the entrant’s market positioning, and its market development strategy Further, Proposition indicates that, for a given level of network asymmetry, greater investment may be required of the new entrant to increase the positive marginal impact of asymmetric regulation on social welfare, provided that the exogenous fraction of consumers in market U is sufficiently low, ρ0 ≤ ρ0 , or the degree of network asymmetry is low Consequently, when asymmetry between networks is relatively high and the previous condition is violated (ρ0 > ρ0 ), then an increase in the entrant’s investment would marginally reduce the total social welfare compared to the case of no investment at all According to Proposition 2, when asymmetric regulation is applied, greater investment by the new entrant could both increase the marginal impact of asymmetric regulation on the entrant’s profit and increase overall social welfare However, the condition on ρ0 on which these results rely, goes in the opposite direction Indeed, the positive effect on the entrant’s profit is obtained when the exogenous fraction of consumers in market U is sufficiently high, whereas the effect on social welfare is positive when there are few consumers in market U What needs to be evaluated, then, is whether the degree to which investment by the entrant improves the impact that asymmetric regulation has on both its profit and social welfare This depends on the combined influence of the level of network asymmetry and the exogenous fraction of consumers 123 Competition with asymmetric regulation 215 in market R In Appendix D, we show that this could indeed be the case, especially when the asymmetry between networks is low or when ρ0 is not too high In particular, this extends the results proved by Peitz (2005), suggesting that asymmetric MTR regulation is not socially desirable Introducing competition between two different technologies, we analyze the potential impact of asymmetric regulation on incentives to invest in the new technology, and show how asymmetric regulation can produce positive effects Finally, this result could provide interesting insights for MTR regulatory policy, suggesting that asymmetric regulation could create incentives for the entrant to compete more vigorously with the incumbent Conclusion Our study shows that asymmetric regulation could have a positive impact on social welfare when operators compete partially using two different technologies This will be particularly true in mobile markets with the launch of 4G Initial results show that asymmetric regulation can enhance long-run competition by increasing the entrant’s market share The impact on the entrant’s profitability depends crucially on the degree of asymmetry between networks and on how consumers are split between the two markets R and U A second set of results shows that asymmetric regulation should result in higher investment made by the entrant, thereby positively affecting the total social welfare Again, this depends on both the degree of network asymmetry and how consumers are split between markets What is particularly interesting to note here is that when asymmetric regulation is applied, it is not always true that the entrant’s marginal investment increases both its profit and social welfare This could lead to a conflict between private incentive of the entrant and social desirability This conflict does not arise, however, when the network asymmetry is limited or when only a relatively small fraction of consumers are served by the market in which networks compete on equal terms This highlights the potential necessity of asymmetric regulation in the European mobile industry, in order to increase market competitiveness and enhance social efficiency—both in the short and the long term thanks to a strengthened market positioning of the entrant Appendix Appendix A: Lemma The equilibrium market share for the entrant under cost-based access prices is A+6 α2∗ a =c = A+ρ 6(2+A) Evaluating the overall market share with (8) and using (10) and (11), we can obtain a system of two equations with two unknown variables (F1 , F2 ) Best responses are ∂π1 ∂π2 implicitly defined by = and = 0, with: ∂ F1 ∂ F2 ∂α1 ∂α2 ∂π1 ∂π2 ∂α2 = α1 + F1 and = α2 + F2 + (1 − 2α2 ) (a2 − c0 )q( p1 ) ∂ F1 ∂ F1 ∂ F2 ∂ F2 ∂ F2 123 216 E Baranes, C H Vuong After tedious calculus, we obtain: F1∗ = (v( p1 ) − v( p1 ) + 2θ )(v( p1 ) − v( p1 ) + 2θ + Aθ ) H1 (v( p1 ) − v( p1 ) + 2θ + ρ Aθ ) H2 H3 /H2 ∗ F2 = (v( p1 ) − v( p1 ) + 2θ + ρ Aθ ) (14) with H1 = q( p1 )(a2 − c0 )(v( p1 ) − v( p1 ) + 2θ + ρ Aθ ) + (v( p1 ) − v( p1 ))(2v( p1 ) −2v( p1 ) + Aθ + 7θ ) + 6θ + Aθ − ρ Aθ H2 = 3(v( p1 ) − v( p1 ))(v( p1 ) − v( p1 ) − Aθ − 4θ ) + 2q( p1 )(a2 − c0 )(v( p1 ) −v( p1 ) + 2θ + ρ Aθ ) + 12θ + 6Aθ H3 = (v( p1 ) − v( p1 ) + 2θ ) (v( p1 ) − v( p1 ) + 2θ + Aθ )[(v( p1 ) − v( p1 ))(v( p1 ) −v( p1 ) + Aθ + 5θ ) + 6θ + 2θ A + ρ Aθ ] + q( p1 )(a2 − c0 )[2θ (v( p1 ) −v( p1 ))2 − (v( p1 ) − v( p1 ))4θ (2 + ρ A) + 2θ (2 + ρ A)2 ] At symmetric cost-based equilibrium, a slight increase in the entrant’s termination rate affects subscription fees as follows: ∂ F1 −28A − 6A3 ρ − ρ A3 (1 − ρ) − 48 − 44ρ A − 4ρ A2 (10 − ρ) = q( p ∗ ) ≤ (15) ∂a2 a2=c0 9(2 + A) (ρ A + 2)2 ∂ F2 −A3 ρ(3 − 2ρ) − 2ρ A3 − 2ρ A2 (13 − 4ρ) − 16ρ A − 20 A − 24 = q( p ∗ ) ≤ ∂a2 a2=c0 9(2 + A) (ρ A + 2)2 (16) Substituting (14) and assuming that unit call prices are set at perceived costs into the operator market shares (8) with a mark-up on the entrant’s MTR, the change of the entrant’s market share evaluate at a2 = c0 is: ∂α2 ∂s2 ∂s2 =ρ + (1 − ρ) ∂a2 ∂a2 ∂a2 ∂s2 ∂ F1 ∂ F2 s2 q( p1∗ ) + = − ∂a2 2θ (1 + A) ∂a2 ∂a2 ∂s2 ∂ F1 ∂ F2 s2 q( p1∗ ) + = − ∂a2 2θ ∂a2 ∂a2 and Finally: ∂α2 8ρ A + ρ A2 (5 − 2ρ) + 12 + A = q( p ∗ ) ≥0 ∂a2 36θ (2 + A)2 and, ∂α2 ≥0 ∂a2 123 (17) Competition with asymmetric regulation 217 At symmetric cost based equilibrium, a slight increase in the entrant’s MTR affects its profit in the following expression: ∂π2∗ ∂a2 a2 =c0 = ∂α2 ∂a2 a2 =c0 F2∗ + α2 ∂ F2 ∂a2 + α2 (1 − α2 )q( p ∗ ) a2=c0 (18) (6 + A + ρ A) (ρ, A) = q( p ∗ ) 108(2 + A)2 (ρ A + 2)2 where (A) = 13ρ A3 − ρ A3 − 6A3 ρ + 26ρ A2 + 10ρ A2 + 56ρ A + 16A + 48 Note that: (0) > and sg√ (A → ∞) = sg(13ρ − ρ − 6ρ) with 13ρ − 145 ρ − 6ρ ≷ iff ρ ≷ ρ = 13 − The derivative of (A) is given by: (A) = A2 ρ[−3ρ + 39ρ − 18] + Aρ[52ρ + 20] + 56ρ + 16 √ We show that ( A) = √ 13ρ +5ρ − ( A) = with A = ρ(1−ρ)(72+193ρ−211ρ and A = 3ρ(ρ −13ρ+6) (0) > We can then deduce that 13ρ +5ρ + 121ρ −404ρ +211ρ +72ρ 3ρ(ρ −13ρ+6) Note that A < for ρ ∈ [0, 1] and ∂π2∗ ≥0 ∂a2 a2 =c0 (2) when ρ < ρ, there exists A1 with A1 > A such that (A1 ) = and if A ≤ A1 ∂π2∗ a2 (resp A > A1 ) then (A) ≥ and ≥ (resp (A) < and ∂ a2 =c0 ∂π2∗ < 0) ∂a2 a2 =c0 (1) when ρ ≥ ρ, (A) ≥ and Finally, note that we can rewrite A as A = 3(ρ2(13ρ+5) −13ρ+6) + ∗ ∂π2 ≥ A → ∞ when ρ → and ∂a2 a2 =c0 121−404ρ+211ρ + 72 ρ 3(ρ −13ρ+6) Hence, Appendix B: Proposition Substituting (14) and (8) into (1) and as analysed in the case of the market shares, we can derive the impacts of asymmetric regulation around cost-based levels on consumer net indirect utility are as follows: 123 218 E Baranes, C H Vuong ∂w1∗ A3 ρ(12 − 5ρ ) − 4ρ A3 + 2ρ A2 (28 − 19ρ) + 32 A + 4ρ A + 24 = q( p ∗ ) ≥ ∂a2 a2 =c0 18(2 + A)(ρ A + 2)2 ∂w2∗ 2ρ A3 + A3 ρ(3 − 2ρ ) + ρ A2 (26 − 8ρ) + 20 A + 16ρ A + 24 = q( p ∗ ) ≥ ∂a2 a2 =c0 9(2 + A)(ρ A + 2)2 Again, using all parameters including fixed fees, market shares and, we can, differentiate and obtain: ∂C S ∗ ∂a2 = a2 =c0 432+ρ(2+ρ)(36−2ρ −25ρ)A4 +4ρ(127−17ρ −56ρ)A3 +(208−404ρ +844ρ)A2 +(240ρ+624)A 108(2+A)2 (ρ A+2)2 ∗ ×q( p ) > The impact of asymmetric regulation can be evaluated aggregately: ∂W∗ ∂a2 a2 =c0 = ∂C S ∗ ∂a2 a2 =c0 + ∂π1∗ ∂a2 a2 =c0 + ∂π2∗ ∂a2 a2 =c0 where ∂π1∗ ∂a2 a2 =c0 = (6+A(4−ρ))(−ρ A3 (7−4ρ)−12 A3 ρ−ρ A2 (94−4ρ)−116ρ A−64 A−120) q( p ∗ ) 108(2+A)2 (ρ A+2)2 ≤0 and, as shown above: ∂π2∗ ∂a2 a2 =c0 3 3 A2 +10ρ A2 +56ρ A+16A+48) = q( p ∗ ) (6+2 A+ρ A)(13ρ A −ρ A −6A ρ+26ρ ≷ (see Lemma 1) 2 108(2+A) (ρ A+2) Tedious calculation yields: ∂W∗ ∂a2 (ρ) = a2 =c0 2 A(1−ρ) (ρ) q( p ∗ ) 108(ρ A+2)2 (2+A)2 (19) = 7ρ A3 + 28ρ A + 2ρ A3 + 44ρ A2 + 52ρ A + 12 A3 ρ − 16A − 48 3 (ρ) = 21ρ A + 56ρ A + 4ρ A + 44 A + 52 A + 12 A > with (0) = −16A − 48 < and Then: (1) = (7A − 4) (A + 2)2 ≷ iff A ≷ A = (1) when A ≥ A, there exist ρ ∗ such that if ρ ≶ ρ ∗ then ∂W∗ ≶0 ∂a2 a2 =c0 ∂W∗ (2) when A < A, then (ρ) < and 0, ∂ α2∗ ∂a2 ∂ε >0 a2 =c0 ε=0 Similarly for (18), ∂ π2∗ ∂a2 ∂ε a2 =c0 ε=0 = Aq( p ∗ ) dρ(ε) dε ε=0 (ρ0 ) 108 (ρ0 A + 2) (2 + A)2 where, (ρ0 ) = −8A + 120ρ02 A2 + 192 + 464ρ0 A + 372ρ0 A2 − 96A2 − 24 A3 + 12 A4 ρ0 − 2ρ04 A4 + 96A3 ρ0 + 12ρ03 A3 + 66ρ02 A3 + 11ρ03 A4 Simple calculations show that (ρ0 ) = 6A2 (ρ A + 2)(20 + A(11 − 4ρ)) ≥ 0, then (ρ0 ) is an increasing function Note that (0) = A(116 + 3A2 + 93A + 24 A2 ) > 0, then (ρ0 ) > and (ρ0 ) is an increasing function in ρ0 We show = 3(7A + 8)(2 + A)3 > and (0) = 8(A + 3)(8 − 3A2 − 3A) ≷ if that (1) √ 1.2 Hence, when A > A3 , there exists ρ0 ∈ [0, 1] such that A ≶ A = 105 − (ρ0 ) ≷ if ρ0 ≷ ρ0 Because ρ (ε) > 0, we conclude that: (i) when A ≤ A, (ii) when A > A, (ρ0 ) ≥ and ∂ π2∗ ∂a2 ∂ε a2 =c0 ε=0 ∂ π2∗ ∂a2 ∂ε a2 =c0 ε=0 ≥0 ≷ if ρ0 ≷ ρ0 123 220 E Baranes, C H Vuong Regarding social welfare, from (19), we have ∂2W ∗ ∂a2 ∂ε a2 =c0 ε=0 = Aq( p ∗ ) dρ(ε) dε ε=0 (ρ0 ) 108 (ρ0 A + 2) (2 + A)2 (21) where, (ρ0 ) = 232 A − 168ρ02 A2 − 256ρ0 A − 132ρ0 A2 + 120 A2 + 96 + 24 A3 + 12ρ0 A4 − 14ρ04 A4 − 84ρ0 A3 − 84ρ03 A3 + 30ρ02 A3 + 5ρ03 A4 Again, we show that: (ρ0 ) = 6A2 (ρ A + 2)(5A − 28 − 28ρ A) ≷ if ρ ≶ ρ = 5A − 28 28A (1, A) ≤ and (ρ) ≤ 0, then (ρ0 ) is a decreasing function Note (0) ≤ 0, that (0) > and (1) ≷ if A ≶ A Hence, when A > A there exists ρ0 ∈ [0, 1] such that (ρ0 ) ≷ if ρ0 ≶ ρ0 Because ρ (ε) > 0, we conclude that: (i) when A ≤ A, (ρ0 ) (ii) when A > A, ∂2W ∗ ∂a2 ∂ε ≥ and a2 =c0 ε=0 ∂2W ∗ ∂a2 ∂ε a2 =c0 ε=0 ≥0 ≷ if ρ0 ≶ ρ0 Appendix D We show here that the entrant has an incentive to increase its reputation which can increase social welfare This occurs in the three following cases: (i) A ≤ A (ii) A ≤ A ≤ (iii) A ≥ √ 105 √ 105 − and ρ0 ≤ ρ0 − 21 and ρ0 < ρ0 < ρ0 when ρ0 < ρ0 From Proposition we can see that a marginal investment from the entrant can increase both its profit and the social welfare The 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regulation 205 EU Member State Network interconnection and mobile termination rates are crucial for ensuring sustainable competition in this environment Because of