Network competition in nonlinear pricing.

Previous research, assuming linear pricing, has argued that telecommunications networks may use a high access charge as an instrument of collusion. I show that this conclusion is difficult to maintain when operators compete in nonlinear pricing: (i) As long as subscription demand is inelastic, profits can remain independent of the access charge, even when customers are heterogeneous and networks engage in second-degree price discrimination. (ii) When demand for subscriptions is elastic, networks may increase profits by agreeing on an access charge below marginal cost (relative to cost-based access pricing). Welfare is typically increased by setting the access charge above marginal cost.

1. Introduction

* Most industrialized countries are engaged in a project to create competition in one of the largest noncompetitive industries of modern economies: local telecommunications. Because of technological advances, the local network has ceased to be a natural monopoly, and competing operators are starting to develop their own local and interurban networks. This is likely to affect considerably the way the industry operates. As customers of different operators want to get in touch with each other, competing networks must be interconnected. This requires a mutual provision of access: each competitor must terminate calls from his rival's customers in exchange for a fee or access charge. Such a two-way access problem differs considerably in its nature from the more familiar one-way access situation in which an (integrated) monopolist controls the local network and is required to interconnect with entrants competing on complementary segments such as long-distance or value-added services. Whereas in the latter case, the economic literature and practice has made clear that regulation is necessary, this is less obvious for the two-way bottleneck situation (see, e.g., Laffont and Tirole, 2000). Should access charges be freely negotiated between operators, with a possible recourse to private arbitration in case of conflict, or should there be a (strong) regulatory involvement? Should private agreements between competitors be trusted to bring about effective competition? No consensus has yet been reached on this point, and the telecommunications industry and regulators are still defining principles for two-way interconnection fees.

Up to now, the economic literature on two-way access charges has advocated the regulatory approach or at least taken a very ambivalent position. In two seminal articles, Armstrong (1998) and Laffont, Rey, and Tirole (1998a) independently warn that competing networks may use a high access charge as an instrument of collusion due to a "raise-each-other's-cost effect": for given market shares, a higher access charge increases each network's average marginal cost and thus induces networks to raise their retail price. The symmetric equilibrium price is therefore increasing in the access charge. (1)

To derive the latter result, however, both articles assume that networks compete in linear pricing. This assumption is not very harmless, as noted by Laffont, Rey, and Tirole (1998a): the collusive power of the access charge disappears completely when networks compete in two-part tariffs and, hence, customers pay a monthly fixed fee in addition to a usage price per call. A higher access charge then still boosts usage prices, but the positive effect from this on retail profits is totally neutralized by a lower fixed fee. Intuitively, nonlinear pricing erodes the fat profits generated by a high access charge, as networks then have an instrument to build market share without inflating their outflow. It seems nevertheless extreme that there is no net effect on profits, in particular since Laffont, Rey, and Tirole obtain their result in a simple model with homogeneous customers. Indeed, the literature on nonlinear pricing has shown that once customers are heterogeneous in volume demand, results under nonlinear pricing typically resemble again those obtained under linear pricing, as firms then try to discriminate implicitly between different types (for example, usage fees are set above marginal cost, some surplus is left to customers). Laffont, Rey, and Tirole (1998a), p. 22, conjecture therefore that the collusive effect of high access charges is likely to be partially restored if one would generalize the model "so as to allow consumers to differ ... in their taste for variable consumption" (see also (Laffont, Rey, and Tirole (1998b), p. 53, and Armstrong (1998), p. 557, for similar statements). Given that nonlinear pricing is prevailing in the industry, the main question the literature tries to answer, whether effective competition between telecommunications networks is possible in a deregulated environment, thus remains open.

The main aim of this article is to provide a more realistic analysis of competition in nonlinear pricing. For this purpose, I shall introduce heterogeneity in volume demand and heterogeneity in subscription demand. This allows me to analyze network competition in the presence of second-degree price discrimination and elastic subscription demand.

* Second-degree price discrimination. Volume demand for calls differs tremendously among customers in the telecommunications industry. I also observe that operators make abundant use of calling plan menus in order to discriminate implicitly between different types of customers. I model this heterogeneity in a straightforward way by assuming that customers are either high-demand or low-demand users, and I allow for a wide range of calling patterns, where high-demand users tend to call more than they are being called and vice versa. I consider both optimal nonlinear pricing and the case where networks are restricted to a menu of two-part tariffs.

* Elastic subscription demand. Customer participation is a significant issue in the telecommunications industry. In the mobile sector, for example, actual penetration rates are currently closer to 50% than 100% in most countries. I allow for an elastic subscription demand by assuming that consumers are heterogeneous in their reservation value for telecommunications services. In equilibrium, some customers then drop out of the market.

I derive two main insights:

(i) Introducing heterogeneity in volume demand is not sufficient to restore the collusive effect of high access charges. Extending the model of Laffont, Rey, and Tirole (1998a) with high- and low-demand customers, I obtain again the result that profits are independent of the access charge, even when differences in demand cannot be perfectly overcome through a menu of calling plans. (2) Intuitively, the main effect of an access markup is that it makes it optimal for both networks to offer lower quantities (i.e., the raise-each-other's-cost effect). With linear pricing, a low quantity of calls is equivalent to a high price and high profits. Once networks compete in nonlinear pricing, however, there is by definition no direct link between the quantities of calls offered to customers and the tariffs that are charged by the operators. If customers are heterogeneous in volume demand, then quantities and tariffs must play an additional role in helping discriminate between customers of different types. The need to meet certain incentive constraints, however, does not reduce a network's incentive or ability to reduce its average tariff in order to build market share. In particular, I show that the benefits of reducing tariffs remain independent of the equilibrium quantities of calls offered to customers. Therefore, unlike under linear pricing, agreeing to offer low quantities to customers--by means of agreeing on a high access charge--does not soften competition for market share.

(ii) If subscription demand is elastic, firms prefer an access charge below marginal cost. As I shall argue, the exact "profit-neutrality" of the access charge relies on some assumptions that are unlikely to be satisfied in more complex settings. In these cases, however, networks may easily prefer an access charge below marginal cost. An important example is elastic subscription demand. If some customers choose not to subscribe in equilibrium, as customers are heterogeneous in their reservation value for a subscription, (3) networks can increase profits by agreeing on an access charge below marginal cost (relative to a cost-based access charge). Intuitively, one consequence of an elastic subscription demand is that the industry exhibits positive network externalities: as customers derive utility from calling other customers, the value of a subscription to one customer is increasing in the total number of subscriptions. Furthermore, these externalities are larger for lower usage fees, as a customer then makes more calls to each additional subscriber. Finally, the larger these externalities, the more each duopolist acts like a monopolist, since a decrease in its tariffs then also benefits his rival's customers. It follows that by agreeing on a low access charge and thus, implicitly, on a low usage fee, networks can increase their equilibrium profits. For example, if for a cost-based access charge two duopolists offer customers a larger net surplus than a monopolist would offer, then a decrease in the access charge results in a decrease in this net customer surplus, a decrease in overall welfare (as market participation decreases), and an increase in profits. Conversely, an increase in the access charge then decreases profits but increases welfare and customer surplus.