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Article Excerpt
We study access pricing rules that determine the access prices between two networks as a linear function of marginal costs and (average) retail prices set by both networks. When firms compete in linear prices, there is a unique linear rule that implements the Ramsey outcome as the unique equilibrium, independently of underlying demand conditions. When firms compete in two-part tariffs, there exists a class of rules under which firms choose the variable price equal to the marginal cost. Therefore, the regulator can choose among these rules to pursue additional objectives such as increasing consumer surplus or promoting socially optimal investment.
1. Introduction
* Access pricing constitutes the core of the policy issues regarding interconnected networks. More precisely, studying how access prices affect competition between networks and determining the optimal access prices form the central questions of the seminal papers on two-way network interconnection in the telecommunications industry (Armstrong, 1998; Laffont, Rey, and Tirole [LRT, hereafter], 1998a, 1998b) and the papers that followed. 1 Although the papers vary in terms of the retail prices they consider (linear versus nonlinear prices, with or without termination-based price discrimination), the degree of customer heterogeneity, and whether or not they explicitly consider receivers' surplus, all the papers have a common trait in that they consider a fixed (per-minute) access price, which is either negotiated bilaterally between two networks or is set by a regulatory agency. In this article, we make a departure from this standard approach and consider what we call a retail benchmarking approach. In our approach, we study access pricing rules that determine the access price that network i pays to network j as a (linear) function of the marginal costs and the retail prices set by both networks. In a setting without termination-based price discrimination, we first consider the case of competition in linear prices and derive the optimal access pricing rule within the class of linear rules and then consider the case of competition in two-part tariffs and study an adaptation of the optimal rule we discovered in the previous case. It turns out that both rules have some remarkable properties that we explain below.
Although most of the literature on two-way access pricing has moved from linear prices to nonlinear prices, in this article we consider both competition in linear prices and in two-part tariffs, as we think that both are relevant. In particular, in mobile telecommunications markets, it is not uncommon for firms to set linear prices by means of prepaid cards. In 2005, almost half of 40 million mobile phone users in Spain had prepaid cards. Moreover, all mobile operators in Spain offer consumers contracts with a linear price and no subscription fee (but with a minimum amount of 9 euros charged monthly). Such contracts are very much like linear prices. The most recent entrant in the Spanish mobile telecommunications market, Yoigo, in fact only offers uniform linear prices without subscription fees, without minimum consumption requirements, and without termination-based price discrimination.
In the case of competition in linear prices, we consider a set of linear access pricing rules that includes any fixed access price and the well-known efficient component pricing rule (ECPR) as particular rules. We show that within this set, there is a unique rule that implements the Ramsey price outcome as an equilibrium, independently of the underlying demand conditions, as long as there exists at least a mild degree of substitutability between networks' services. Moreover, the Ramsey price outcome is the unique equilibrium outcome under this rule. This optimal rule is such that the mark-up of the access price that network i pays to network j is equal to the mark-up of network i's retail price multiplied by a factor n/(n - 1), where n represents the number of competing networks. This rule promotes competition in retail prices, as network i can decrease its access payment by reducing its retail price. Because access pricing rules are much more general than fixed access prices, it is perhaps not that surprising that some rule is able to implement the Ramsey outcome. What is a very remarkable feature of the optimal access pricing rule is that it does not depend on the demand structure (provided the LRT assumption of full coverage is satisfied) so that the regulator only needs to observe marginal costs and retail prices and does not need to know anything about the demand side. (2) Furthermore, our model and access pricing rules allow for more than two competing networks. (3)
In the case of competition in two-part tariffs, we adapt the access pricing rule that is optimal in the case of linear prices such that the mark-up of the access price above the termination cost that network i pays to network j is equal to network i's average retail price mark-up multiplied by a factor [kappa]. (4) We show that under the adapted rules, each network finds it optimal to charge its variable price equal to the true marginal cost for any market share and for any [kappa] [less than or equal to] 1: in fact, when [kappa] = 0, the access price is equal to the termination cost, and LRT (1998a) show that in this case, the variable price is equal to the marginal cost. When [kappa] = 0, network i's profit is equal to its market share multiplied by profit per customer (net of the fixed cost per customer). Therefore, maximizing network i's profit with respect to its variable price, while maintaining its market share constant, is equivalent to maximizing its profit per customer, which leads to the marginal cost pricing. When [kappa] [not equal to] 0, under our access rule, the access payment per customer that network i makes to its rival networks is equal to a fraction (smaller than one) of its profit per customer (as long as [kappa] [less than or equal to] 1). Therefore, our rule generates the marginal cost pricing as long as [kappa] = does it. We show that this result is robust: for instance, it holds when networks are asymmetric (either in terms of quality of their networks or customer brand loyalty) and when networks face heterogeneous customers and compete with a menu of nonlinear tariffs.
Therefore, the regulator can properly choose [kappa] to pursue another goal while achieving efficient pricing in terms of variable price. Within our framework the profit neutrality result (5) does not hold because a higher [kappa] intensifies competition in fixed fees. Therefore, [kappa] can be chosen at a high level in order to increase consumer surplus at the expense of firms' profits. This also suggests that [kappa] can be chosen to promote penetration in markets where no full coverage equilibrium exists with fixed access charges. Very interestingly, [kappa] can also be chosen at a low level in order to increase firms' profits so as to create incentives for socially optimal investment in network quality (i.e., to achieve static and dynamic efficiency at the same time).
Making access prices depend on retail prices is an old idea in the case of one-way access. The well-known ECPR (6) achieves efficient entry by equalizing the access price that an entrant should pay to the incumbent with the sum of the cost of providing the access and the latter's opportunity cost (i.e., the incumbent's retail price mark-up) when the incumbent's retail price is regulated. However, the ECPR is not good at promoting competition in retail prices when the retail prices are not regulated because the access price that the incumbent receives increases with its retail price. (7) This motivated Sibley et al. (2004) to consider the generalized efficient component pricing rule (GECPR) in which the access price that an entrant pays is, roughly speaking, equal to the sum of the cost of providing the access and the entrant's opportunity cost (i.e., the entrant's retail price mark-up). They find that because the entrant can reduce its access charge payment by lowering its retail price, the GECPR is good at intensifying retail competition.
In the case of two-way access, LRT (1998a) examine various interpretations of the ECPR in a duopoly framework and show that when networks can privately negotiate on a fixed level of access price, the ECPR allows them to collude and achieve the monopoly outcome. More importantly, Mialon (2007) studies the GECPR, considered by Sibley et al. (2004) in one-way access, in LRT's framework of duopoly with linear pricing. (8) Under the GECPR, the mark-up of the access price that network i pays to the rival network is equal to the former's retail price mark-up. We show that there exists a unique rule achieving the Ramsey outcome in the set of linear access pricing rules which includes the GECPR as a special case. Because the optimal rule is different from the GECPR, the GECPR does not achieve the Ramsey outcome. (9)
In practice, there are cases in which access prices (or termination charges) are linked to average retail prices. Some countries use a "retail-minus" approach to set access prices on the basis of a fixed discount off the corresponding retail prices. (See OECD, 2004.) Another example of pegging access price to retail tariffs can be found in the international postal service. For instance, access prices (i.e., what are called "termination dues") among European countries should be set at 80% of domestic tariffs (Ghosal, 2002). In the context of termination charges for mobile phone service, the Australian Competition and Consumer Commission (2001) adopted what they call a "retail benchmarking approach," which means that "access prices for GSM termination will fall at the same rate as retail prices for mobile services provided by a mobile carrier." However, the ACCC retail benchmarking approach is different from ours in several respects. The most important difference is that the ACCC linked the access price charged by an operator to the average retail price of the same operator, similar to what occurs in the ECPR. The ACCC recognized that this could potentially give disincentives to lower retail prices, as we explained above. However, the ACCC relied on the competitive pressure in the retail market to continue retail price reductions observed in previous years, which would then imply access price reductions, which in turn could reinforce lower retail prices. In 2004, the ACCC abandoned its retail benchmarking approach, mainly because retail prices had in fact not decreased in the period 2001-2004. (10) Another difference between the ACCC approach and our proposal is that the ACCC considers intertemporal linkages (access prices in the next six month period depend on retail price reductions in the last six month period), whereas we consider instantaneous linkages. A final difference with our rule is that we propose to benchmark retail and access price mark-ups, whereas the ACCC benchmarks absolute retail and access prices.
Our result in Section 5 that there is a class of access pricing rules which achieve efficiency when networks face heterogeneous consumers and compete in menus of two-part tariffs is interesting in its own right. Previously, Dessein (2003) and Hahn (2004) find that when the access price is equal to the termination cost (i.e., [kappa] = 0), network competition achieves efficiency. However, in this case, access price disappears from the profit function and the profit function becomes the same as the one in a standard Hotelling model without interconnection. This is why they rediscover the efficient two-part tariff result obtained by Armstrong and Vickers (2001) and Rochet and Stole (2002) in the context of competitive price discrimination without interconnection. In other words, in Dessein (2003) and Hahn (2004), efficiency is achieved by making the case with interconnection identical to the case without interconnection. What we show is that in the presence of interconnection, there is a class of access pricing rules which achieve efficiency; interconnection provides additional instruments to achieve efficiency with respect to no interconnection.
Section 2 presents the general model, defines the set of linear access pricing rules, and characterizes the Ramsey outcome. Section 3 considers competition in linear prices: it first establishes the main result, compares different access pricing rules, and discusses the robustness of the result to relaxing the full coverage assumption. Section 4 considers how the rule can be adapted in a context where firms compete in two-part tariffs by benchmarking the access price to the average retail price. Section 4 shows that a whole class of benchmarking rules lead to marginal cost pricing and studies how the regulator can achieve additional goals such as optimal investment by adequately choosing among these rules, and also shows that the marginal cost pricing result holds even for asymmetric networks. Section 5 considers competition in menus of two-part tariffs when there are heterogeneous consumers and shows that the marginal cost pricing result of Section 4 continues to hold. Section 6 concludes. The Appendix gathers omitted proofs.
2. Framework
* The model. We present a general model of n-network competition which includes the duopoly model of LRT (1998a) as a special case. There is a mass one of consumers. We will make the standard assumption of a balanced calling pattern of LRT (1998a), which means that the percentage of calls originating from a given network and completed on another given (including the same) network is equal to the fraction of consumers subscribing to the terminating network.
Individual demand. Let u(q) be the utility that a consumer derives from placing q volume of calls. The utility function u(*) is twice continuously differentiable, with u' > 0, u" < 0, which implies that the demand function is differentiable. Let q(*) denote the demand function, given by u' (q(p)) = p, where p is the variable retail price. When network charges [p.sub.i], the volume of calls placed by a customer of network i is given by q([p.sub.i]). Let [upsilon](p) be the indirect utility function, i.e.,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Let R(p) [equivalent to] (p - c)q(p). We assume that R(p) has a unique maximum at p = [p.sup.m], is strictly increasing when p [p.sup.m]. Therefore, [p.sup.m] denotes the monopoly price. Let [R.sup.m] = R([p.sup.m]). We assume [lim.sub.p[right arrow][infinity] R(p) = 0.
Firm's demand (or market share). The networks (i.e., firms) provide horizontally differentiated services and each network can cover all the consumers. Consider first competition in two-part tariffs: firm i chooses tariff [T.sub.i] = [F.sub.i] + [p.sub.i]q. Given ([p.sub.i], [F.sub.i]), let [w.sub.i] = [upsilon]([p.sub.i)] - [F.sub.i]. Then the utility that a consumer x derives from subscribing to network i is given by
[w.sub.i] - T(x, i),
where T(x, i) denotes consumer x's disutility from not being able to consume her preferred service. (11) Let w [equivalent to] ([w.sub.1], ..., [w.sub.n]) and [w.sub.-i] [equivalent to] ([w.sub.1], ..., [w.sub.i-1] , [w.sub.i+1], ..., [w.sub.n]). Let [[alpha].sub.i]([w.sub.i]; [w.sub.-i]) denote the measure of consumers subscribing to network i. We assume that [[alpha].sub.i] (w) satisfies the following properties:
Property 1 (symmetry). For any vector w with [w.sub.i] = [w.sub.j] for some i and j, we have [[alpha].sub.i] (w) = [[alpha].sub.j] (w).
Property 2 (monotonicity). For any i, j = 1, ..., n and i [not equal to] j, [[alpha].sub.i] ([w.sub.i]; [w.sub.-i]) is differentiable with respect to [w.sub.i] and each [w.sub.j] and increases with [w.sub.i] and decreases with [w.sub.j]; it strictly increases with [w.sub.i] and strictly decreases with [w.sub.j] for [[alpha].sub.i] [member of] (0, 1). (12)
Property 3 (full coverage). [[summation].sup.n.sub.i=1] [[alpha].sub.i]([w.sub.i]; [w.sub.-1]) = 1 for all relevant w [member of] [R.sup.n.sub.t].
Properties 1, 2, and 3 are satisfied by the Hotelling model of LRT (1998a) and the circular city model with n = 2 or 3 (Salop, 1979). For n > 3, our model is more natural than the circular city model because in the latter, a (minor) price change of network i affects only the demands of its direct neighbors (network i - 1 and network i + 1) but does not affect the demands of other networks. In the context of telecommunications markets, all networks compete directly with each other for all customers, and not only with two artificial "neighbors" for a specific subset of consumers. Symmetry and full coverage together imply that [[alpha].sub.i] = 1/n for all i = 1, ..., n if [w.sub.i] = w for all i = 1, ..., n. Regarding the full coverage property, LRT (1998a) assume that each consumer...
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