Regulating termination charges in asymmetric oligopolies

Information Economics and Policy 32 (2015) 16–28

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Information Economics and Policy journal homepage: www.elsevier.com/locate/iep

Regulating termination charges in asymmetric oligopolies q Dongyeol Lee ⇑ International Monetary Fund, 700 19th St NW, Washington, DC 20431, USA Bank of Korea, 39 Namdaemun-ro, Jung-gu, Seoul 100-794, Republic of Korea

a r t i c l e

i n f o

Article history: Available online 29 July 2015 JEL classifications: D4 K2 L4 L9 Keywords: Termination charges Fixed-mobile substitution Price competition effect Market share effect

a b s t r a c t This paper extends a standard Hotelling model to three firms and analyzes the competitive effect of asymmetric regulation on mobile and fixed termination charges. In the presence of fixed-mobile substitution, above-cost mobile termination charge creates a trade-off on the mobile network’s profit: i.e., (i) reducing retail profit by strengthening competition for subscribers (‘‘price competition effect’’), and (ii) raising termination profit by increasing market shares (‘‘market share effect’’). Our analysis shows that the competitive effect of asymmetric regulation on mobile and fixed termination charges is decided by the interaction between these two effects, which in turn depends on the distribution of customer types. That is, above-cost termination charges are likely to be beneficial to consumers for a sufficiently large fixed-mobile type (i.e., customers choosing between mobile and fixed networks) compared to a mobile type (i.e., customers choosing between mobile networks), while they are likely to be harmful to consumers for a small fixed-mobile type. It would be an important implication for regulatory authorities that there exist various factors to consider in regulating termination charges, including the industry development and market structure. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction In the telecommunication industry, when a caller places a phone call, the receiver’s network imposes a fee on the caller’s network for call termination services, known as ‘‘termination charges’’. There is no general consensus among regulators on the optimal level of termination charge that will maximize the social welfare. For instance, Ofcom, the regulator in the UK, argues that termination charges should be slightly above the cost of termination q This article is a substantially revised version of Chapter 1 of my Ph.D. dissertation at Michigan State University. I am deeply indebted to Jay Pil Choi for his invaluable guidance and support throughout this project. I would also like to thank Thomas Jeitschko, Arijit Mukherjee and Steven Wildman for their thoughtful comments and suggestions. I am also particularly grateful to the very thoughtful comments and suggestions of two anonymous referees. Any remaining errors are mine. ⇑ Address: International Monetary Fund, 700 19th St NW, Washington, DC 20431, USA. E-mail addresses: [email protected], [email protected]

http://dx.doi.org/10.1016/j.infoecopol.2015.07.006 0167-6245/Ó 2015 Elsevier B.V. All rights reserved.

(Ofcom, 2007), while the European Commission recommends that regulators set termination charges at termination cost (European Commission, 2009). Meanwhile, European Commission (2009) stresses the potential competitive distortions from the asymmetric treatment on termination charges and recommends that regulatory agencies adopt symmetric and cost-based termination charge regulations. The recommendation mainly focuses on the competitive effect of termination charges on either mobile markets or fixed markets in isolation, while in the real world, termination rates can have important strategic and competitive implications for the interaction between these two markets. ‘‘Termination markets represent a situation of two-way access where both interconnecting operators are presumed to benefit from the arrangement but, as these operators are also in competition with each other for subscribers, termination rates can have important strategic and competitive implications. Where

D. Lee / Information Economics and Policy 32 (2015) 16–28

17

Fig. 1. Mobile and fixed subscriptions in selected developed countries.

termination rates are set above efficient costs, this creates substantial transfers between fixed and mobile markets and consumers.’’ (European Commission, 2009, p. 67). We also find that, in many developed countries, the recent dramatic increase in subscriptions to mobile networks coincides with a significant decline in subscriptions to fixed networks. Fig. 1 demonstrates that, in the 2000s, mobile subscriptions increased dramatically while fixed subscriptions decreased significantly.1 To capture these regulatory practices and industry developments, this paper introduces competition for subscribers between mobile and fixed networks as well as between mobile networks by extending a standard Hotelling model to three firms: two symmetric mobile networks and one fixed network.2 Departing from Armstrong and Wright’s (2009) duopoly model with hinterlands, our model introduces competition for subscribers between mobile and fixed networks in an explicit way. This paper analyzes how the asymmetric regulation on mobile and fixed termination charges affects the network’s profit and the consumer surplus in the presence of asymmetry between mobile and fixed networks: (i) in the market size (Section 4), and (ii) in the termination cost and fixed utility (Section 5).3 Unlike most existing literature in which mobile and fixed subscribers have been treated as disjointed groups, the novel feature of this paper is to introduce the existence of fixed-mobile substitution in subscription, which results in the endogenous determination of market share. Thus, mobile networks can expand their market shares by penetrating into the fixed market, since the total market size is fixed from the assumption of inelastic demand. This paper demonstrates that the competitive effect of above-cost termination charges mainly depend on the 1 Similar patterns of FTM substitution can be found in other developed countries. Further information is available at http://www.itu.int/en/ITU-D/ Statistics/Pages/stat/default.aspx. 2 In many developed countries, the oligopoly is a typical competition structure in the telecommunication industry. For instance, in the EU countries (e.g., France, Spain, Sweden and the UK), there exist multiple mobile networks and a fixed network having significant market shares. See Armstrong and Wright (2009) for more details. 3 It is commonly observed that termination charges of fixed networks have been more tightly regulated than those of mobile networks in many countries (Hoernig et al., 2015).

distribution of customer types: i.e., above-cost termination charges are likely to be beneficial to consumers for a sufficiently large fixed-mobile type (i.e., customers choosing between mobile and fixed networks) compared to mobile type (i.e., customers choosing between mobile networks), while they are likely to be harmful to consumers for a small fixed-mobile type. In other words, above-cost termination charge raises the consumer surplus if it causes a large increase in market share that offsets an increase in call prices, while it reduces the consumer surplus otherwise.4 The distribution of customer types can be interpreted in terms of the development stage of the telecommunication industry (i.e., mobile-oriented or fixed-oriented). The finding suggests that the asymmetric regulation on mobile and fixed termination charges is likely to be beneficial (harmful) to consumers if the telecommunication industry is fixed-oriented (mobile-oriented). It would be an important implication for regulatory authorities that there exist various factors to consider in regulating termination charges, including the industry development and market structure. This paper contributes to the literature in several respects. First, we present a tractable model representing more realistic competition in the telecommunication industry by extending the circular city model of Salop (1979). Our model incorporates competition among multiple networks in the presence of asymmetry between mobile and fixed networks in both the customer type and the regulation on termination charges. The model is also extended to introduce asymmetry in termination cost as well as in fixed utility between mobile and fixed networks. Second, this paper analyzes the competitive effect of asymmetric termination charge regulation between mobile and fixed markets by departing from the literature which focuses on the competitive effects of asymmetric termination charge regulation in the same market (either mobile markets or fixed markets) between incumbents and entrants (e.g., Peitz, 2005a,b). Lastly, our analysis identifies the important factors in determining the welfare effect of regulation on termination charges. To be specific, the analysis suggests that the symmetric and cost-based regulation on mobile and fixed 4 The outcome is in stark contrast to the welfare effect of above-cost termination charges in Armstrong and Wright (2009), in which competition for subscribers between mobile and fixed networks is not considered and thus the optimal termination rates are always above cost.

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D. Lee / Information Economics and Policy 32 (2015) 16–28

termination charges, which was recommended by European Commission (2009), is more likely to be justified when the fixed market is sufficiently small (i.e., the penetration rate of mobile networks is high).5 The rest of the paper proceeds as follows. A brief literature review is offered in Section 2, and the description of model follows in Section 3. In the presence of competition for subscribers between mobile and fixed networks, Section 4 analyzes the competitive effect of above-cost termination charges in the model of symmetric cost and demand between mobile and fixed networks, while Section 5 extends the analysis to the model of asymmetric cost and demand. Section 6 summarizes and concludes. All proofs are relegated to Appendix A. 2. Related literature There exist substantial disagreements in the literature on the level of termination charges maximizing the social welfare. Some economists insist that the optimal termination charge is above cost (e.g., Armstrong and Wright, 2009; Hurkens and López, 2014; Jullien et al., 2013), while others argue that it is below cost (e.g., Hoernig, 2014; Hurkens and López, 2012). Meanwhile, Hurkens and Jeon (2012) show that the substitutability and the penetration rate of competing networks are the important factors in determining the optimal level of termination charges. Furthermore, the termination charge that networks should prefer is predicted to be below cost when networks compete in two-part tariffs and can offer different prices for on-net and off-net calls.6 In reality, however, networks oppose the attempt by regulatory authorities to reduce termination rate to the cost of termination.7 The literature has proposed several ways to reconcile this paradox by introducing additional realistic features to Laffont et al. (1998b) and Gans and King (2001): e.g., (i) termination profit from terminating fixed-to-mobile (FTM) calls (Armstrong and Wright, 2009), (ii) endogenous formation of calling circles (Hoernig et al., 2014), (iii) heterogeneous usage and elastic participation (Jullien et al., 2013), and (iv) passive rational expectations (Hurkens and López, 2014). Several papers consider fixed-mobile substitution in call and subscription levels to analyze the role of termination charges in determining the market equilibrium. Armstrong and Wright (2009) and Hausman (2012) analyze the role of call substitution between mobile and 5

The result contradicts the argument of networks that reducing termination charges would distort competition and hurt consumers because increased subscription fees would reduce mobile penetration (Ofcom, 2007). 6 The profit-maximizing termination charge critically depends on the assumption about the pricing strategy which networks can choose. Above-cost termination charges can be profitable to networks under linear pricing (Armstrong, 1998; Laffont et al., 1998a), while it is suboptimal under two-part tariffs and termination-based price discrimination (Laffont et al., 1998b; Gans and King, 2001). See Armstrong (2002) for the general review of the literature on termination charges. 7 European Commission (2009) states that ‘‘the absolute level of mobile termination rates remains high in a number of Member States compared to those applied in a number of countries outside of the European Union, and also compared to fixed termination rates generally, thus continuing to translate into high, albeit decreasing, prices for end consumers (p. 67).’’

fixed networks without allowing fixed-mobile substitution in subscription. These authors show that call substitution between mobile and fixed networks brings the termination charges that mobile networks would choose closer to the efficient level while remaining above cost by weakening the competitive bottleneck of call termination. Closest to our paper, Hansen (2006) and Hoernig et al. (2015) develop a model in which substitution between mobile and fixed networks may take place at the subscription level as well as at the call level. In Hansen (2006), the mobile market share expansion by raising mobile termination charges result in an increase of mobile profit, but his model cannot provide any implications on welfare effect of above-cost termination charges. Contrary to the present analysis, though, in his model termination-based price discrimination, which is commonly adopted in practice, is not allowed. Fixed-mobile substitution in both subscription and call is present in Hoernig et al. (2015). Their model focuses on the determination of equilibrium tariffs given that termination charge is set above cost, and thus it fails to capture how networks determine the level of termination charges.8 Building upon recent developments of literature on termination charges, the present paper attempts to provide a tractable model which can be used in the analysis on the effects of asymmetric regulation on termination charges and fills the gap between theoretical analysis and regulatory practice. 3. The model This section introduces the key elements of the model. Additional assumptions or setups will be explained as needed in each section. The model extends a standard Hotelling model to three firms: i.e., two symmetric mobile networks and one fixed network. The model in this paper explicitly generalizes Armstrong and Wright’s (2009) duopoly model with hinterlands to the oligopoly model by adding competition for subscribers between mobile and fixed networks. The model is a special case with three firms of Hoernig’s (2014) multiple networks model as well as a variation of the circular city model of Salop (1979) in which the circular line of circle is replaced by the straight line of triangle.9 3.1. Demand structure Two mobile networks (M 1 and M 2 ) and a fixed network (F) compete for subscribers. The model assumes a balanced calling pattern in which call volumes terminated on each network are proportional to its market share.10 A standard duopoly model is extended to an oligopoly model within a 8 In determining market shares, they use the ‘‘passive belief’’ approach suggested by Hurkens and López (2014), instead of the ‘‘rationally responsive belief’’ approach assumed in the most literature. 9 Similarly, several papers established the network competition model with multiple networks: e.g., the pyramid model of Von Ungern-Sternberg (1991) and the spokes model of Chen and Riordan (2007). 10 The assumption of balanced calling patterns is commonly adopted in the literature. See, for instance, Armstrong (1998), Laffont et al. (1998a), Laffont et al. (1998b), Gans and King (2001) and Armstrong and Wright (2009).

D. Lee / Information Economics and Policy 32 (2015) 16–28

Hotelling framework: i.e., M1 ; M 2 and F are located at each end of a triangle and each line of the triangle corresponds to a Hotelling line between each pair of competing networks. Consumers are uniformly distributed on the Hotelling lines where the length of each line equals 1, and each consumer subscribes to either one of the two networks located at the end of his Hotelling line (i.e., singlehoming).11 As a result, there exist three different customer types according to the consumer’s preference for subscribing to each network12: (i) Mobile type: a proportion of consumers subscribes to M1 or M 2 . (ii) F-M 1 type: ð1  aÞ=2 proportion of consumers subscribes to F or M1 . (iii) F-M 2 type: ð1  aÞ=2 proportion of consumers subscribes to F or M2 . Where a 2 ð0; 1Þ is assumed to ensure the positive fraction of each customer type. The mobile type customer located at s1 from M 1 incurs a transportation cost of ts1 for subscribing to M 1 and tð1  s1 Þ for subscribing to M2 , respectively. In a similar way, the F-M i type customer located at ~si from M i incurs t~si for subscribing to M i and tð1  ~si Þ for subscribing to F. The transportation cost t > 0 measures the degree of product differentiation among networks. 3.2. Cost structure In Section 4, all networks are assumed to be symmetric in the cost structure. Serving a consumer involves a fixed cost f, while per call, each network incurs a marginal cost c ¼ co þ ct where co and ct denote marginal costs for originating and terminating a call.13 Section 5 extends the model to allow the asymmetry in termination costs: i.e., the mobile network’s termination cost (ct ) is assumed to be higher than the fixed network’s termination cost (~ct ).

19

of non-discriminatory termination charges adopted in the EU and the US.15 Accordingly, each network sets a single termination charge which applies to all calls terminating on its own network. Let a1 ; a2 and aF denote the termination charges of M1 ; M2 and F which should be paid by the caller’s network to the receiver’s network for call termination services. The model focuses on the case where mobile networks jointly choose their uniform termination charge (a). The termination mark-up of mobile networks equals m ¼ a  ct , while that of a fixed network is zero (mt ¼ aF  ct ¼ 0). This represents the practice of strictly regulating fixed network termination charges in many developed countries. 3.4. Call prices Both two-part tariffs and termination-based price discrimination, which are commonly observed in practice and adopted in the literature, are allowed in our model.16 ^i ; p ~i g Each mobile network offers two-part tariffs fr i ; pi ; p where r i represents a subscription fee for M i , and pi refers ^i and p ~i denote to a per-minute price for on-net calls, while p call prices for off-net calls to Mj (i – j) and F, respectively. In a similar way, the fixed network offers two-part tariffs ~1F ; p ~2F g where r F denotes a subscription fee for F, while fr F ; pF ; p i ~F refer to call prices for on-net and off-net calls. pF and p Fig. 2 depicts the price competition among mobile and fixed networks. 3.5. Timeline The timing of the game is as follows. In the first stage, mobile networks jointly determine a uniform termination charge, and a fixed network decides termination rates at the termination cost. In stage 2, all networks simultaneously determine their two-part tariffs (subscription fees and call prices). In stage 3, customers make their subscription and call decisions.

3.3. Termination charges The model assumes a uniform termination charge by which networks are not allowed to set different termination charges according to the originating (the caller’s) network.14 The assumption captures the practice of a uniform termination charge and represents the regulatory principle 11 In the real world, there exists a significant proportion of customers subscribing to multiple networks (i.e., multihoming). This paper focuses on the case of singlehoming in order to highlight the competitive effect of fixed-mobile substitution in subscription level by abstracting the call level substitution. 12 The total mass of subscribers is normalized to 1 and the proportion of mobile type and fixed-mobile type customers are given by a and 1  a, respectively. Additionally, fixed-mobile type consumers are assumed to be equally distributed between F-M 1 and F-M 1 types from the symmetry of two mobile networks. 13 Symmetric costs among networks help the analysis to focus on the competitive effect of asymmetric regulation on termination rate. 14 The assumption of uniform termination charges is commonly adopted in the literature. See, for instance, Armstrong (1998), Laffont et al. (1998a), Laffont et al. (1998b), Gans and King (2001) and Armstrong and Wright (2009).

4. Symmetry between mobile and fixed networks This section discusses the competitive effect of regulation on termination charges when the cost and demand structure is symmetric between mobile and fixed networks. We analyze the conditions under which above-cost termination rate is profitable to networks and under which it is beneficial (or harmful) to consumers. The equilibrium concept in this paper is a subgame perfect equilibrium and the game is solved backward. We first analyze how call prices are determined given termination charges and then we check whether termination charges that maximize the network’s profit and consumer surplus are above or below the termination cost. 15 In the EU, Directive 2002/19/EC establishes the principle that termination charges should be non-discriminatory. The US establishes the same principle in Telecommunications Act of 1996. 16 See, for example, Laffont et al. (1998b), Gans and King (2001), Armstrong and Wright (2009), Hurkens and Jeon (2012), Jullien et al. (2013), Hoernig (2014) and Hurkens and López (2014).

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D. Lee / Information Economics and Policy 32 (2015) 16–28

Fig. 2. Price competition among networks.

4.1. Marginal cost pricing Let v ðpÞ denote the consumer surplus associated with a call demand function qðpÞ such that v 0 ðpÞ ¼ qðpÞ. Utilities from subscribing to Mi and F are written as:

^i Þ þ nF v ðp ~i Þ; ui ¼ v 0  r i þ ni v ðpi Þ þ nj v ðp ~iF Þ þ nj v ðp ~Fj Þ þ nF v ðpF Þ: uF ¼ v 0  r F þ ni v ðp where v 0 measures the fixed utility from subscribing to each network and which is assumed to be sufficiently large to ensure the full coverage of markets.17 In addition, ni ; nj and nF represent the market shares of M i ; Mj and F, respectively. Net utilities for the mobile type customer located at si from M i and subscribing to M i and M j are ui  tsi and uj  tð1  si Þ, respectively. Similarly, net utilities for the fixed-mobile type customer located at ~si from M i and subscribing to Mi and F are ui  t~si and uF  tð1  ~si Þ. Then, M i ’s market share on mobile type (si ) and that on fixed-mobile type (~si ) are given by:



M i ’s market share (ni ) equals the sum of its share on mobile type and that on fixed-mobile type, while F’s market share (nF ) consists of only its share on fixed-mobile type:

1a ~si ; 2  1  a nF ¼ 2  ~si  ~sj : 2

ni ¼ asi þ



|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

pF

ð2Þ

It is noteworthy that in our model the market share of each network is no longer constant and the sum of all networks’ market share is fixed at 1 from the assumption of inelastic demand (i.e., ni þ nj þ nF ¼ 1).18 Mobile networks have two sources of profit: (i) the retail profit from providing retail services to its own subscribers, and (ii) the termination profit from providing call termination services to rival networks’ subscribers. However, the fixed network’s profit consists of retail profit only, since in our model the fixed network’s termination rate is assumed to be regulated at its termination cost. The profits of M i and F are written as:

pi ¼ ni ri  f þ ni ðpi  cÞqðpi Þ þ nj ðp^i  c  mÞqðp^i Þ þ nF ðp~i  cÞqðp~i Þ þ ni nj mqðp^j Þ þ ni nF mqðp~iF Þ; retail profit

ð1Þ

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð3Þ

termination profit

n o ~iF  c  mÞqðp ~iF Þ þ nj ðp ~Fj  c  mÞqðp ~Fj Þ þ nF ðpF  cÞqðpF Þ : ¼ nF r F  f þ ni ðp |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð4Þ

retail profit

1 ui  uj þ ; 2 2t 1 u  uF ~si ¼ þ i : 2 2t

Networks set their call prices at the perceived marginal costs while they extract the whole consumer surplus by setting subscription fees. Marginal cost pricing is a

17 In Section 5.2, the model is extended to allow asymmetry in fixed utility between mobile and fixed networks.

18 This feature is the key difference in the model from the literature which allows elastic subscription demands (e.g., Armstrong and Wright, 2009; Hurkens and Jeon, 2012; Jullien et al., 2013). Exceptions are Hansen (2006) and Hoernig et al. (2015) which explicitly consider fixed-mobile substitution in subscription.

si ¼

D. Lee / Information Economics and Policy 32 (2015) 16–28

well-known property in cases firms compete in two-part tariffs.19 The equilibrium call prices are thus given by:

~i ¼ c; pi ¼ pF ¼ p

^i ¼ p ~iF ¼ c þ m: p

In equilibrium, the utilities from subscribing to M i and F are rewritten as:

ui ¼ v 0  r i þ ni v ðcÞ þ nj v ðc þ mÞ þ nF v ðcÞ; uF ¼ v 0  r F þ ni v ðc þ mÞ þ nj v ðc þ mÞ þ nF v ðcÞ: 4.2. Market share and subscription fee This subsection analyzes how subscription fees and market shares are affected by above-cost mobile termination charges. For the sake of conciseness, we focus on the interior solutions such that networks never corner all customers on each customer type. From (1), the market share of M i is given by:

ni ¼

tð1 þ aÞ þ 2aðrj  ri Þ þ ð1  aÞðr F  r i Þ : 4t þ ð1  aÞðv ðc þ mÞ  v ðcÞÞ

tð1 þ aÞ þ ð1  aÞðr F  rÞ n¼ : 4t þ ð1  aÞðv ðc þ mÞ  v ðcÞÞ

ð5Þ

Eq. (5) implies that, at the marginal cost termination charges ( m ¼ 0), the consumer’s subscription decision is determined by the relative size between the mobile and fixed subscription fees. To be specific, in the case of rð0Þ < r F ð0Þ, more consumers are willing to subscribe to a mobile network as the differential between mobile and fixed subscription fees becomes larger.

a

nð0Þ ¼

2 |{z}

mobile type

  1a r F ð0Þ  rð0Þ þ : 1þ t 4 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

pi ¼ nðr  f Þ þ nð1  nÞmqðc þ mÞ; pF ¼ ð1  2nÞðrF  f Þ:

ð6Þ ð7Þ

From the first-order conditions of profit-maximization problem, subscription fees in the symmetric equilibrium are given by:

n

r

rF ¼ f þ

 ð1  2nÞmqðc þ mÞ;

1  2n : r~

~ ¼ ð@nF =@rF ÞðrF =nF Þ where q ¼ ð@n=@rÞðr=nÞ and q denote the elasticities of subscription demand for mobile and fixed networks, respectively. The expressions imply that the mark-up in the mobile subscription fee is composed of two parts: (i) the standard inverse elasticity pricing and (ii) an adjustment term that accounts for termination profits. The negative adjustment is stronger as is the larger m. That is, mobile networks compete more fiercely in subscription fees as termination profits increase. By contrast, the mark-up in the fixed subscription fee depends on the inverse elasticity pricing only from the zero termination profit for the fixed network. Substituting (8) and (9) into (5), the mobile network’s market share is given by:

~g tð1 þ aÞ þ ð1  aÞfmqðc þ mÞ þ 1=r : ~g 4t þ ð1  aÞfv ðc þ mÞ  v ðcÞ þ 2mqðc þ mÞ þ 1=r þ 2=r ð10Þ

Subscription fees and market shares interact with each other and equilibriums are determined by Eqs. (8)–(10). Proposition 1 describes the effects of above-cost termination charges on market shares and subscription fees. Proposition 1. Under two-part tariffs and termination-based price discrimination, the marginal increase in the termination mark-up above 0: (i) raises the mobile network’s market share but reduces the fixed network’s market share; (ii) reduces the subscription fees of both the mobile and fixed networks.

fixed-mobile type

From marginal cost pricing under two-part tariffs, the profits of M i and F, which are given by Eqs. (3) and (4), are rewritten as:

r¼f þ

r  f 1 1  2n mqðc þ mÞ; ¼  r r q rF  f 1 ¼ : rF q~

n¼

In the symmetric equilibrium (ri ¼ r j ¼ r), the mobile network’s market share (ni ¼ nj ¼ n) is written as:

21

ð8Þ ð9Þ

~ ¼ @nF =@r F measure the substiwhere r ¼ @n=@r and r ~ tutability between mobile and fixed networks and r ¼ 2r holds from (5). Eqs. (8) and (9) can be rewritten as:

19 See, for instance, Laffont et al. (1998b), Gans and King (2001), Hurkens and Jeon (2012) and López and Rey (forthcoming) for marginal cost pricing under two-part tariffs.

Proof. See Appendix A. h Above-cost mobile termination charges with regulation of fixed termination charges at cost may have the asymmetric impacts on the market share of mobile and fixed networks, through the asymmetric impacts on call prices and subscription fees. Under two-part tariffs and termination-based price discrimination, above-cost mobile termination rates lead to higher call prices for mobile networks compared to a fixed network, which in turn induces mobile networks to set subscription fees more aggressively.20 The result implies that there exists a negative relationship between termination charges and subscription fees (the ‘‘waterbed effect’’) in the oligopoly model.21 Meanwhile, lower mobile subscription fees make mobile networks more attractive to fixed-mobile type customers, which raises the number of mobile subscribers and reduces the number of fixed subscribers. 20 In equilibrium, above-cost mobile termination charge (m > 0) leads to ~iF ¼ c þ m > c ¼ p ~i ). higher FTM call prices compared to MTF call prices (p 21 See Genakos and Valletti (2011), Genakos and Valletti (2012) and Growitsch et al. (2010) for empirical evidence on the existence of the waterbed effect in the mobile telephone industry.

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D. Lee / Information Economics and Policy 32 (2015) 16–28

4.3. Profitability and welfare analysis As mentioned in the Introduction, the competitive effect of above-cost termination charges is still controversial among regulatory authorities and economists. This section attempts to find a mechanism that gives mobile networks incentives to set termination charges above cost, and analyzes whether the optimal termination charges maximizing the consumer surplus and total surplus are above or below cost. The profits of mobile and fixed networks are given by (6) and (7), while the consumer surplus (CS) and total surplus (TS ¼ CS þ p1 þ p2 þ pF ) are written as:

  CS ¼ v 0  2nr  ð1  2nÞr F þ 2n2  2n þ 1 v ðcÞ þ 2nð1  nÞv ðc þ mÞ  TC;

ð11Þ

  TS ¼ v 0  f þ 2n2  2n þ 1 v ðcÞ þ 2nð1  nÞv ðc þ mÞ þ 2nð1  nÞmqðc þ mÞ  TC:

ð12Þ

where

TC ¼

n o ta t þ ð1  2nÞ2 þ ð1  aÞð2n  aÞ : 4 2ð1  aÞ

ð13Þ

Here TC denotes transportation cost, and r; rF and n are given by (8) and (9) and (10), respectively. The following proposition presents the effects of above-cost termination charges on the mobile network’s profit, consumer surplus and total surplus. Proposition 2. Under two-part termination-based price discrimination:

tariffs

and

(i) the termination charges maximizing the mobile network’s profit are above termination cost; (ii) the termination charges maximizing the consumer sur but at or plus are above termination cost for 0 < a < a  6 a < 1, where a  2 ð0; 1Þ below termination cost for a  3 þ 7a  2 þ 15a   3 ¼ 0; satisfies 5a (iii) the termination charges maximizing the total surplus are at termination cost. Proof. See Appendix A. h The effect of above-cost termination charges on retail profit is ambiguous because above-cost termination charges raise the mobile network’s profit source (n) while they reduce the profit margin (r  f ) (Proposition 1). Contrary to this, above-cost termination charges unambiguously raise the mobile network’s termination profit. Hence, the profitability of above-cost mobile termination charges is decided by the relative importance of these two contrasting effects, which in turn depends on the parameter a characterizing the relative size between mobile type and fixed-mobile type customers. Meanwhile, above-cost mobile termination charges always reduce the fixed network’s profit from the reduction in both the profit source (1  2n) and the profit margin (r F  f ). Proposition 2 shows that the competitive effect of above-cost termination charges mainly depend on the distribution of customer type: i.e., above-cost termination

charges are likely to be beneficial to consumers for a sufficiently large fixed-mobile type compared to a mobile type, while they are likely to be harmful to consumers for a small fixed-mobile type. The market share effect from above-cost termination charges, which is strengthened for larger fixed-mobile types, raises the mobile network’s termination profit. By contrast, the price competition effect, which is independent of the distribution of customer type in the model of symmetric mobile and fixed networks, reduces the mobile network’s profit. In our model, the market share effect outweighs the price competition effect and therefore the profit-maximizing termination rate is above termination cost. When looking at the consumer surplus, above-cost mobile termination rates can be beneficial to consumers due to the decrease in subscription fees, while they can be detrimental to consumers because of the increase in call prices. Our analysis confirms that above-cost termination charge raises the consumer surplus for a sufficiently large fixed-mobile type as it causes a large increase in market share that offsets an increase in call prices. On the other hand, above-cost mobile termination charge reduces the consumer surplus for a small fixed-mobile type as the beneficial market share effect is not large enough to offset the detrimental price competition effect. The distribution of customer type can be interpreted in terms of the development stage of the telecommunication industry (i.e., mobile-oriented or fixed-oriented). In this respect, the finding of this paper suggests that the asymmetric regulation on mobile and fixed termination charges is likely to be beneficial (harmful) to consumers if the telecommunication industry is fixed-oriented (mobile-oriented). In the present model where the total mass of subscribers is fixed and call externality is not present, the total surplus depends exactly on whether calls are priced at marginal costs (welfare related to calls is maximal if the termination charge is set at cost), and on whether transportation costs are minimized. Since networks are completely symmetric with termination rates at cost, the Hotelling lines split in half and transportation costs are minimized. So the total surplus is maximized by setting termination rates at cost.

4.4. Discussion The analysis in this section provides useful insights by raising the issue that the proportion between mobile type and fixed-mobile type plays a central role in determining the competitive effect of asymmetric regulation on mobile and fixed termination charges. The model is set up symmetrically in its cost and demand structure, apart from the asymmetry in market size. Thus, this paper cannot capture some relevant aspects of competition between mobile and fixed networks. In the next section, the assumption on the symmetry in cost and utility between mobile and fixed networks is relaxed and we investigate how the asymmetric cost and utility may change the competitive effect of above-cost termination charges.

D. Lee / Information Economics and Policy 32 (2015) 16–28

It is also noteworthy that the effect of termination charges on the total surplus is based on the assumption that all consumers end up choosing one of three networks and the subscription demand is inelastic. If the subscription demand is elastic, then above-cost termination rates may increase the total number of subscribers, which can intensify the welfare-enhancing effect of above-cost termination charges (Armstrong and Wright, 2009; Jullien et al., 2013).22

23

discrimination, the marginal increase in the termination mark-up above 0: (i) raises the mobile network’s market share but reduces the fixed network’s market share; (ii) reduces the subscription fees of both the mobile and fixed networks. Proof. See Appendix A. h

5. Asymmetry between mobile and fixed networks This section extends the model to allow the asymmetry in termination cost and fixed utility between mobile and fixed networks.23 We analyze whether the main qualitative results in the model of symmetric cost and demand apply to the model of asymmetric cost and demand. 5.1. Asymmetry in termination cost This subsection introduces the asymmetry in termination cost between mobile and fixed networks. Since the marginal cost of mobile networks is observed to be significantly higher than that of fixed networks, our extended model assumes that the mobile network’s termination cost (ct ) is higher than the fixed network’s termination cost (~ct ), which in turn results in the higher marginal cost for the mobile network (i.e., c ¼ co þ ct > ~c ¼ co þ ~ct ). From marginal cost pricing under two-part tariffs, the equilibrium call prices are determined as:

pi ¼ c;

~i ¼ ~c; pF ¼ p

^i ¼ p

~iF p

¼ c þ m:

Note that the lower termination costs for the fixed network make the fixed network’s call prices lower than the mobile network’s on-net call prices. Utilities from subscribing to M i and F differ only in consumer surplus from calls to a fixed network from the symmetric model:

ui ¼ v 0  r i þ ni v ðcÞ þ nj v ðc þ mÞ þ nF v ð~cÞ; uF ¼ v 0  r F þ ni v ðc þ mÞ þ nj v ðc þ mÞ þ nF v ð~cÞ:

As is true in the symmetric model, above-cost mobile termination charges with regulation of fixed termination charges at cost may have the asymmetric impacts on the market shares of mobile and fixed networks, through asymmetric impacts on call prices and subscription fees. In addition, the asymmetric termination cost does not cause any changes in the mobile network’s profit function, while it causes some changes in the functions of the consumer surplus and total surplus. In equilibrium, the mobile network’s profit is given by (6), while the consumer surplus and total surplus are written as:

CS ¼ v 0  2nr  ð1  2nÞr F þ 2n2 v ðcÞ þ ð1  2nÞv ð~cÞ þ 2nð1  nÞv ðc þ mÞ  TC;

ð14Þ

TS ¼ v 0  f þ 2n2 v ðcÞ þ ð1  2nÞv ð~cÞ þ 2nð1  nÞv ðc þ mÞ þ 2nð1  nÞmqðc þ mÞ  TC:

ð15Þ

where TC is given by (13). The following proposition summarizes the competitive effects of above-cost mobile termination charges on the mobile network’s profit, the consumer surplus and the total surplus in the model of asymmetric termination cost between mobile and fixed networks. Proposition 4. Suppose that the mobile network’s termination cost (ct ) is higher than the fixed network’s termination cost (~ct ). Under two-part tariffs and termination-based price discrimination:

where Dv ðcÞ  v ð~cÞ  v ðcÞ > 0. As is the same in the symmetric model, subscription fees and market shares are given by Eqs. (8)–(10), because the changes in the fixed network’s call prices do not have any impact on market shares and subscription fees. Proposition 3 presents the effects of above-cost mobile termination charges on market shares and subscription fees when the mobile network’s termination cost is higher than the fixed network’s.

(i) the termination charges maximizing the mobile network’s profit are above termination cost; (ii) the termination charges maximizing the consumer surplus are:  c but at or (a) above termination cost for 0 < a < a  c 6 a < 1 if below termination cost for a  c 2 ð0; 1Þ satisfies 2Dv ðcÞ < t, where a

Proposition 3. Suppose that the mobile network’s termination cost (ct ) is higher than the fixed network’s termination cost (~ct ). Under two-part tariffs and termination-based price

(b) below termination cost if 2Dv ðcÞ P t; (iii) the termination charges maximizing the total surplus are below termination cost.

 3c þ 7a  2c þ 15a  c  3 þ f2ð1 þ a  c Þð1  a c Þ 5a  ð3  ac ÞDv ðcÞg=t ¼ 0;

Proof. See Appendix A. h 22 For a more complete welfare analysis, the model should be extended to allow for the elastic subscription demand, which is beyond the scope of this paper. 23 Note that, in Armstrong and Wright (2009), above-cost termination charges are profitable without FTM substitution when fixed call demands and termination profit are sufficiently large.

The effect of above-cost termination charges on the mobile network’s profit is not affected by the asymmetry in termination cost, as the mobile network’s profit is determined independently from the fixed network’s termination cost. It is noteworthy, however, that the optimal

24

D. Lee / Information Economics and Policy 32 (2015) 16–28

termination charges maximizing the consumer surplus (or the total surplus) can be affected by the asymmetric termination costs. First of all, as is true in the symmetric model, the termination charge maximizing the consumer surplus is above (below) termination cost if the fixed-mobile type is sufficiently large (small). However, the cutoff value in the  c ), which determines whether the terminamobile type (a tion charge maximizing the consumer surplus is above or below termination costs, is smaller than that in the sym ).24 As the differential in termination cost metric model (a becomes larger, the condition under which above-cost termination charges raise the consumer surplus becomes tighter than in the symmetric model. Secondly, the termination charges maximizing the total surplus are below cost in the model of asymmetric termination cost.25 This result differs from the symmetric model, in which termination charges that maximize the total surplus are determined at termination cost. Since the termination cost is higher for mobile networks than fixed networks, the decrease in the mobile market share by below-cost mobile termination charges will lead to an increase in the total surplus through a decrease in the total termination costs for the whole industry. 5.2. Asymmetry in fixed utility This subsection extends our basic model to introduce the asymmetric fixed utility between mobile and fixed networks. The model assumes that the mobile network’s fixed utility (v 0 ) are larger than the fixed network’s fixed utility ~ 0 ). This assumption represents the convenience of the (v availability of mobile networks as mobile phones can be used both at home and on the move while fixed phones can only be used at home. The asymmetry in fixed utility do not cause any changes in call prices from the symmetric model and thus the equilibrium call prices are the same as in the symmetric model:

~i ¼ c; pi ¼ pF ¼ p

^i ¼ p

~iF p

¼ c þ m:

Note that utilities from subscribing to M i and F differ only in fixed utility from the symmetric model:

ui ¼ v 0  r i þ ni v ðcÞ þ nj v ðc þ mÞ þ nF v ðcÞ; uF ¼ v~ 0  r F þ ni v ðc þ mÞ þ nj v ðc þ mÞ þ nF v ðcÞ: ~ 0 > 0. where Dv 0  v 0  v The market share of mobile networks differs from that in the symmetric model by as much as the differential in fixed utility (Dv 0 ). This fact implies that other things being equal, the mobile network’s market share increases because of the larger fixed utility from subscription to mobile networks. As is the same as in the symmetric model, the subscription fees of mobile and fixed networks 24 By contrast, if the levels of termination cost are opposite to what is assumed in the paper (i.e., the fixed network’s termination cost is larger than the mobile network’s termination cost), the cutoff value will be higher than that in the symmetric model. 25 If the fixed network’s termination cost is larger than the mobile network’s, then the termination charges maximizing the total surplus will be above the termination cost.

are determined by (8) and (9), while the mobile network’s market share is given by:

n¼

~ þ Dv 0 g tð1 þ aÞ þ ð1  aÞfmqðc þ mÞ þ 1=r ~g 4t þ ð1  aÞfv ðc þ mÞ  v ðcÞ þ 2mqðc þ mÞ þ 1=r þ 2=r ð16Þ

Proposition 5 presents the effects of above-cost mobile termination charges on market shares and subscription fees when the mobile network’s fixed utility is larger than that of the fixed network. Proposition 5. Suppose that the mobile network’s fixed utility (v 0 ) is larger than the fixed network’s fixed utility ~ 0 ). Under two-part tariffs and termination-based price (v discrimination, the marginal increase in the termination mark-up above 0: (i) raises the mobile network’s market share but reduces the fixed network’s market share; (ii) reduces the subscription fees of both the mobile and fixed networks. Proof. See Appendix A. h As is true in the symmetric model, above-cost mobile termination charges play a role in raising the mobile network’s market share while they reduce the fixed network’s market share. Meanwhile, the strengthened price competition from above-cost termination charges results in a reduction in mobile and fixed subscription fees. The mobile network’s profit is determined by (6), while the consumer surplus and total surplus are given by:

CS ¼ 2nv 0 þ ð1  2nÞv~ 0  2nr  ð1  2nÞr F   þ 2n2  2n þ 1 v ðcÞ þ 2nð1  nÞv ðc þ mÞ  TC; ð17Þ   TS ¼ 2nv 0 þ ð1  2nÞv~ 0  f þ 2n2  2n þ 1 v ðcÞ þ 2nð1  nÞv ðc þ mÞ þ 2nð1  nÞmqðc þ mÞ  TC: ð18Þ where TC is given by (13). The following proposition presents the competitive effects of above-cost mobile termination charges on the mobile network’s profit, the consumer surplus and total surplus in the model of asymmetric fixed utility between mobile and fixed networks. Proposition 6. Suppose that the mobile network’s fixed utility (v 0 ) is larger than the fixed network’s fixed utility ~ 0 ). Under two-part tariffs and termination-based price (v discrimination: (i) the termination charges maximizing the mobile network’s profit are: ^ v but at or (a) above termination cost for 0 < a < a ^ v 6 a < 1 if below termination cost for a ^ v 2 ð0; 1Þ satisfies 5Dv 20  tDv 0  9t 2 > 0, where a

 2   2   ^ v Þ 2a ^v  a ^ v þ3 þ a ^ v 4a ^ v 3 Dv 0 =tð3þ a ^v Þ ð1þ a   2 ^ v Þð1 a ^ v Þð3a ^ v 5ÞDv 20 =t 2 ð3þ a ^ v Þ ¼ 0; þ ð1þ a (b) above termination cost if 5Dv 20  tDv 0  9t 2 6 0;

D. Lee / Information Economics and Policy 32 (2015) 16–28

(ii) the termination charges maximizing the consumer surplus are:  v but at or (a) above termination cost for 0 < a < a  v 6 a < 1 if below termination cost for a where a v 2 ð0; 1Þ 16Dv 20 þ 4tDv 0  9t2 < 0, satisfies  3v þ 7a  2v þ 15a  v  3 þ fð1 þ a  v Þð1  a v Þ 5a  2    v þ 10a  v  13 Dv 0 =tð3 þ a v Þ  7a n o  2   v Þ2 ð1  a  v Þ2 4a  v þ 11a  v þ 1 Dv 20 =t 2 ð3 þ a  v Þ2 ¼ 0; þ ð1 þ a

(b) at or below termination cost if 16Dv 20 þ 4tDv 0  9t 2 P 0; (iii) the termination charges maximizing the total surplus are above termination cost.

25

asymmetric cost and those of asymmetric utility on the consumer surplus. In reality, the quality of calls may differ between mobile and fixed networks: e.g., fixed connections tend to be at higher speeds and better call quality than mobile connections. This feature may be considered in our model such that fixed networks have higher marginal utility than mobile networks. Another potential extension is to introduce the asymmetry in transportation cost (i.e., the degree of product differentiation) between mobile type and fixed-mobile type. The degree of product differentiation can be smaller between mobile networks than between mobile and fixed networks. Nevertheless, introducing differentiation in marginal utility or transportation cost to our model may make the analysis much more complicated.

Proof. See Appendix A. h When there exists the asymmetry in fixed utility between mobile and fixed networks, both the profitability and welfare effects of above-cost termination charges can differ from the symmetric model. First, above-cost mobile termination charges are not always profitable to mobile networks. If the differential in fixed utility between mobile and fixed networks is small enough, the profit-maximizing termination charges are above cost for a sufficiently large fixed-mobile type, while they are below cost otherwise. Meanwhile, mobile networks always have incentives to set termination rates above cost if the differential in fixed utility is large enough. Second, if the differential in fixed utility is small enough, then the termination rates maximizing the consumer surplus are above cost for a sufficiently large fixed-mobile type, while they are below cost otherwise. Meanwhile, termination charges that maximize consumer surplus are always below cost if the differential in fixed utility is sufficiently large. Lastly, termination charges maximizing the total surplus are above cost when the fixed utility of mobile networks is larger than that of the fixed network. Since the fixed utility is larger for mobile networks than fixed networks, above-cost mobile termination charges lead to the increase in the market share of mobile networks and the total fixed utility, which will raise the total surplus. This fact is in stark contrast to the cases of: (i) the symmetric cost and utility, in which the termination charge maximizing the total surplus is determined at cost and (ii) the asymmetric termination cost, in which the termination charge maximizing the total surplus is below cost. 5.3. Discussion The analysis in this section provides useful insights by exploring the impacts of asymmetric cost and utility on the competitive effects of above-cost termination charges. Though the model of this section introduces the asymmetry in cost and utility in isolation, it is more likely that these asymmetries exist simultaneously in the real world. The analysis implies that the welfare effects of above-cost mobile termination charges are determined by the relative importance between the impacts of

6. Concluding remarks This paper extends a standard Hotelling model to three firms and analyzes the competitive effect of asymmetric regulation on mobile and fixed termination charges. Key finding of this paper is that the competitive effect of above-cost termination charges mainly depend on the distribution of customer type: i.e., above-cost termination charges are likely to be beneficial to consumers for a sufficiently large fixed-mobile type compared to mobile type, while they are likely to be harmful to consumers for a small fixed-mobile type. This paper contributes to the literature in several respects. First, we present a tractable model representing more realistic competition in the telecommunication industry. Our model incorporates competition among multiple networks in the presence of asymmetry between mobile and fixed networks in both the customer type and the regulation on termination charges. Second, this paper investigates the competitive effect of asymmetric regulation on termination charges between mobile and fixed networks and its regulatory implications. Lastly, our analysis suggests that the relative size between mobile and fixed markets is an important factor in determining the welfare effect of regulation on termination charges. We conclude by mentioning some limitations of our simplified model and discussing potential avenues for future research. First, we note that the model in this paper fails to capture some relevant aspects of competition in the telecommunication industry. Our model treats the services offered by mobile and fixed networks as perfectly substitutable (except for horizontal differentiation) to highlight the competitive effect of asymmetric regulation on mobile and fixed networks by abstracting differences in the demand and cost structure. Thus, it would be important to analyze the implications of allowing differentiation in the marginal utility and transportation cost between mobile and fixed networks as well as differentiation in the termination cost and fixed utility (the latter was already analyzed in Section 5). Second, the model can be generalized to analyze the effects of asymmetric regulation on termination charges in other asymmetric oligopoly structures. More specifically, the model can be used for the analysis on the

26

D. Lee / Information Economics and Policy 32 (2015) 16–28

asymmetric competition among three mobile networks, where one mobile network’s termination rate is regulated at cost. This regulation at cost is perhaps due to historical reasons – such as it being the first network authorized by the government – or due to dominance in market share. Our model can also be used to study the competitive effect of asymmetric regulation on termination charges between mobile networks and virtual networks, known as Voice of Internet Protocol (VoIP) (De Bijl and Peitz, 2009). Furthermore, it would be interesting to allow customers to subscribe to multiple networks (Armstrong and Wright, 2009; Hoernig et al., 2015). In the presence of both subscription and call substitutions, the interaction between these two factors will play a central role in determining the competitive effect of regulation on termination charges.

 while it is negative for (23) is positive for 0 < a < a a < a < 1, where a 2 ð0; 1Þ satisfies 5a 3 þ 7a 2 þ   3 ¼ 0. 15a (3) Total surplus: From (12), at m ¼ 0, the first-order derivative of TS with respect to m is always zero from @TS ¼ @TC ¼ 0. h @m m¼0 @m m¼0 Proof of Proposition 4. (1) Mobile network’s profit: See the proof of Proposition 2. (2) Consumer surplus: From (14), at m ¼ 0, the first-order derivative of CS with respect to m is:

 3 @CS 1 ¼ 5a þ 7a2 þ 15a  3 @m m¼0 16ð3 þ aÞ

2ð1 þ aÞð1  aÞð3  aÞDv ðcÞ  qðcÞ: ð24Þ t

Appendix A Proof of Proposition 1 and 3. (1) Market shares: From (10) and r ¼ ð1 þ aÞ= ~ ¼ 2ð1  aÞ= f4t þ ð1  aÞðv ðc þ mÞ  v ðcÞÞg and r f4t þ ð1  aÞðv ðc þ mÞ  v ðcÞÞg, at m ¼ 0, the first-order derivative of n with respect to m is:

@n ð1 þ aÞð1  aÞð3  aÞ ¼ qðcÞ: @m m¼0 16tð3 þ aÞ

ð19Þ

F (19) is positive for 0 < a < 1, and @n < 0 is @m m¼0 straightforward from nF ¼ 1  2n. (2) Subscription fees: From (8), at m ¼ 0, the first-order derivative of r with respect to m is:

@r ð1  aÞð3 þ 2aÞ ¼ qðcÞ: @m m¼0 2ð3 þ aÞ

ð20Þ

(20) is negative for 0 < a < 1. From (9), at m ¼ 0, the first-order derivative of r F with respect to m is:

@r F 3  a2 ¼ qðcÞ: @m m¼0 2ð3 þ aÞ

ð21Þ

(21) is negative for 0 < a < 1. h

(1) Mobile network’s profit: From (6) and (19)–(21), at m ¼ 0, the first-order derivative of pi with respect to m is:

ð25Þ

(25) is negative for 0 < a < 1 from Dv ðcÞ > 0 and @TC ¼ 0. h @m m¼0 Proof of Proposition 5. (1) Market shares: From (16) and r ¼ ð1 þ aÞ=f4tþ ~ ¼ 2ð1  aÞ=f4tþ ð1  aÞðv ðc þ mÞ  v ðcÞÞg and r ð1  aÞðv ðc þ mÞ  v ðcÞÞg, at m ¼ 0, the first-order derivative of n with respect to m is: ( ) 2 @n ð1 þ aÞð1  aÞ ð1  aÞ Dv 0 ¼ a Þð3 þ a Þ þ qðcÞ: ð3  16tð3 þ aÞ @m m¼0 16tð3 þ aÞ

(26) is positive for 0 < a < 1 from Dv 0 > 0, and @nF < 0 is straightforward from nF ¼ 1  2n. @m m¼0 (2) Subscription fees: From (8), at m ¼ 0, the first-order derivative of r with respect to m is:



@r 1a ð1 þ aÞð2  aÞDv 0 qðcÞ: ¼ 3 þ 2a þ @m m¼0 2ð3 þ aÞ tð3 þ aÞ ð27Þ

ð22Þ

(22) is positive for 0 < a < 1. (2) Consumer surplus: From (11), at m ¼ 0, the first-order derivative of CS with respect to m is:

@CS 5a3 þ 7a2 þ 15a  3 ¼ qðcÞ: @m m¼0 16ð3 þ aÞ

@TS @n @TC ¼ 2Dv ðcÞ  : @m m¼0 @m m¼0 @m m¼0

ð26Þ

Proof of Proposition 2.

  ð1 þ aÞ 2a2  a þ 3 @ pi ¼ qðcÞ: 8ð3 þ aÞ @m m¼0

 c while (i) 2Dv ðcÞ < t: (24) is positive for 0 < a < a  c < a < 1, where a  c 2 ð0; 1Þ it is negative for a  3c þ 7a  2c þ 15a  c  3 þ f2ð1 þ a c Þ satisfies 5a  c Þð3  a  c ÞDv ðcÞg=t ¼ 0 and Dv ðcÞ > 0. ð1  a (ii) 2Dv ðcÞ P t: (24) is negative from Dv ðcÞ > 0. (3) Total surplus: From (15), at m ¼ 0, the first-order derivative of TS with respect to m is:

(27) is negative for 0 < a < 1 from Dv 0 > 0. From (9), at m ¼ 0, the first-order derivative of rF with respect to m is: 

@rF 1 2ð1 þ aÞð1  aÞDv 0 qðcÞ: ¼ 3  a2 þ 2ð3 þ aÞ @m m¼0 tð3 þ aÞ

ð28Þ

ð23Þ (28) is negative for 0 < a < 1 from Dv 0 > 0. h

27

D. Lee / Information Economics and Policy 32 (2015) 16–28

@TS @m

Proof of Proposition 6.

m¼0

Proof.

¼

@n @m

(

(1) Mobile network’s profit: From (6) and (26)–(28), at m ¼ 0, the first-order derivative of pi with respect to m is:

@ pi @m m¼0

@TC @m m¼0 m¼0 ð1 þ aÞð1  aÞð5 þ aÞDv 0

¼ 2Dv 0





16tð3 þ aÞ2

) ð1 þ aÞð1  aÞ2 Dv 0 qðcÞ: 3aþ 3þa

8 9 > > > > > >   > > ð1  aÞ a2  4a  3 Dv 0 ð1  aÞð3a  5ÞDv 20 = 1þa < 2 ¼ 2 a  a þ 3 þ þ qðcÞ: 2 |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} > 8ð3 þ aÞ > tð3 þ aÞ t2 ð3 þ aÞ > > > > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} ðþÞ > > : ; ðÞ

ð31Þ

ð29Þ

ðÞ

(i) 5Dv 20  tDv 0  9t2 > 0: (29) is positive for ^ v while it is negative for a ^ v < a < 1, 0
and Dv 0 > 0. (ii) 5Dv 20  tDv 0  9t2 6 0: (29) is positive from Dv 0 > 0. (2) Consumer surplus: From (17), at m ¼ 0, the first-order derivative of CS with respect to m is:

(31) is positive for 0 < a < 1 from Dv 0 > 0. h

References Armstrong, M., 1998. Network interconnection. Econ. J. 108, 545–564. Armstrong, M., 2002. The theory of access pricing and interconnection. In: Cave, M., Majumdar, S., Vogelsang, I. (Eds.), Handbook of Telecommunications Economics. Elsevier Publishers, Amsterdam. Armstrong, M., Wright, J., 2009. Mobile call termination. Econ. J. 119, 270– 307. Chen, Y., Riordan, M.H., 2007. Price and variety in the spokes model. Econ. J. 117, 897–921. De Bijl, P.W., Peitz, M., 2009. Access regulation and the adoption of VoIP. J. Regul. Econ. 35, 111–134.

8 > >   > < ð1 þ aÞð1  aÞ 7a2 þ 10a  13 Dv 0 @CS 1 3 2 ¼ 5a þ 7a þ 15a  3 þ @m m¼0 16ð3 þ aÞ > tð3 þ aÞ >|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} ðþ or Þ : ðþ or Þ 9 > > >   > ð1 þ aÞ2 ð1  aÞ2 4a2 þ 11a þ 1 Dv 20 = qðcÞ: þ 2 > t 2 ð3 þ aÞ > |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}> > ;

ð30Þ

ðþÞ

(i) 16Dv 20 þ 4tDv 0  9t2 < 0: (30) is positive for  v while it is negative for a  v < a < 1, 0
and Dv 0 > 0. (ii) 16Dv 20 þ 4tDv 0  9t2 P 0: (30) is zero or negative from Dv 0 > 0. (3) Total surplus: From (18), at m ¼ 0, the first-order derivative of TS with respect to m is:

European Commission, 2009. Commission recommendation on the regulatory treatment of fixed and mobile termination rates in the EU. Official Journal of the European Union (May 20), L124/67–L124/74. Gans, J.S., King, S.P., 2001. Using ‘bill and keep’ interconnect arrangements to soften network competition. Econ. Lett. 71, 413–420. Genakos, C., Valletti, T., 2011. Testing the ‘‘waterbed effect in mobile telephony. J. Euro. Econ. Assoc. 9, 1114–1142. Genakos, C., Valletti, T., 2012. Regulating prices in two-sided markets: the waterbed experience in mobile telephony. Telecommun. Pol. 36, 360–368. Growitsch, C., Marcus, J.S., Wernick, C., 2010. The effects of lower mobile termination rates (MTRs) on retail price and demand. Commun. Strat. 80, 119–140. Hansen, B., 2006. Termination rates and fixed mobile substitution. mimeo. Hausman, J.A., 2012. 13. Two-sided markets with substitution: mobile termination revisited. In: Faulhaber, G., Madden, G., Petchey, J. (Eds.), Regulation and the Performance of Communication and Information Networks. Edgar Elgar Publishing Limited, Cheltenham.

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D. Lee / Information Economics and Policy 32 (2015) 16–28

Hoernig, S., 2014. Competition between multiple asymmetric networks: theory and applications. Int. J. Indust. Organ. 32, 57–69. Hoernig, S., Inderst, R., Valletti, T., 2014. Calling circles: network competition with non-uniform calling patterns. RAND J. Econ. 45, 155–175. Hoernig, S., Bourreau, M., Cambini, C., 2015. Fixed-mobile substitution and termination rates. Telecommun. Pol. 39, 65–76. Hurkens, S., Jeon, D.S., 2012. Promoting network competition by regulating termination charges. Int. J. Indust. Organ. 30, 541–552. Hurkens, S., López, A., 2012. The welfare effects of mobile termination rate regulation in asymmetric oligopolies: the case of Spain. Telecommun. Pol. 36, 369–381. Hurkens, S., López, A., 2014. Mobile termination, network externalities, and consumer expectations. Econ. J. 124, 1005–1039. Jullien, B., Rey, P., Sand-Zantman, W., 2013. Termination fees revisited. Int. J. Indust. Organ. 31, 738–750.

Laffont, J.J., Rey, P., Tirlole, J., 1998a. Network competition I: overview and nondiscriminatory pricing. RAND J. Econ. 29, 1–37. Laffont, J.J., Rey, P., Tirlole, J., 1998b. Network competition II: price discrimination. RAND J. Econ. 29, 38–56. López, A.L., Rey, P., forthcoming. Foreclosing competition through high access charges and price discrimination. J. Indust. Econ. Ofcom, 2007. Mobile Call Termination: Statement. Ofcom, London. Peitz, M., 2005a. Asymmetric access price regulation in telecommunications markets. Euro. Econ. Rev. 49 (2), 341–358. Peitz, M., 2005b. Asymmetric regulation of access and price discrimination in telecommunications. J. Regul. Econ. 28, 327–343. Salop, S.C., 1979. Monopolistic competition with outside goods. Bell J. Econ. 10, 141–156. Von Ungern-Sternberg, T., 1991. Monopolistic competition on the pyramid. J. Indust. Econ. 39, 355–368.