Network Externalities and the Overprovision of Quality by a Monopolist.

• Author: Lambertini, Luca

Luca Lambertini [*]

Raimondello Orsini [+]

We investigate the behavior of a monopolist supplying a vertically differentiated good with network externalities. Assuming a convex unit cost of quality improvements, we show that the presence of network externalities may yield oversupply of quality compared with the social optimum, when partial market coverage emerges at equilibrium. Overall, the incentive to expand output increases in the extent of network externalities, thereby partially counterbalancing the social damage produced by the quality distortion.

1. Introduction

   The increasing relevance of high-tech sectors, such as telecommunication, hardware--software, and audio--video industries, justifies the growing amount of attention devoted to the analysis of markets for goods that generate network externalities (Katz and Shapiro 1985, 1986, 1994; Farrell and Saloner 1985, 1986). An example taken by the audio--video industry is the current discussion concerning the possibility of adopting a new standard for hi-fi equipments, DVD (digital versatile disc) or SACD (super audio compact disc). The network effect consists of the fact that the utility from purchasing equipment characterized by a given standard is positively related to the number of consumers who purchase a compatible equipment, for two reasons. The first is that the larger the number of users of a given standard, the wider the range of software made available for that standard. The second is that a larger network of users is usually associated with more efficient customer service and technical assistance.

   If consumers are sensitive to the size of the market, the producer's choice of the output level can be compared to the provision of product quality, in that allowing consumers to access a larger network is essentially like providing them with a good characterized by a superior quality. Therefore, the existence of network effects in markets where intrinsic quality is endogenous prompts a reassessment of the welfare implications of market power against either perfect competition or social planning.

   To provide a theoretical framework capable of evaluating this issue, we build upon Spence's (1975) seminal paper on vertical differentiation, introducing a network effect into consumer preferences. In the considerable amount of literature stemming from Spence's paper (Sheshinski 1976; Mussa and Rosen 1978; Maskin and Riley 1984), the main question is whether a monopolist supplies the socially optimal quality or distorts it so as to induce self-selection on the part of consumers.

   The earliest contributions (Spence 1975; Sheshinski 1976) deal with a single-product monopolist. Their main conclusions are that (i) for a given output level, quality is over- or under-supplied by the monopolist as compared with social planning, depending on whether the marginal valuation of quality is above or below the average valuation of quality (if they coincide, the monopolist supplies the same quality as the social planner); and (ii) the monopolist under-supplies quality if his output is close to the socially optimal one.

   We adopt a model where a single-product monopolist supplies a good whose production entails a variable cost, which is assumed to be convex in the quality level, and consumers' utility function contains a network externality component. We proceed in two steps. First, we consider the general case where the forms of both the cost function and the consumer distribution are left unspecified, except for the overall features of technology. In this framework, we characterize the role of the interplay between the income distribution of consumers and the network externality in determining the quality choice of a profit-seeking monopolist vis-a-vis a social planner. We find that, for any given income distribution, there may exist a range of network effects such that Spence's conclusions are reversed. As a second step, we investigate in detail a more specific model where we adopt some standard assumptions concerning consumer distribution and technology. In particular, we consider the case of a uniform consumer distribut ion, where it is known that, if network effects were absent, a profit-maximizing monopolist would supply the same quality as a social planner, as long as partial market coverage obtains (Spence 1975). This allows us to describe the behavior of equilibrium prices, qualities, and output levels, as well as to establish the parameter regions where full and partial market coverage alternatively obtains, under both regimes. The main result is that, as long as partial market coverage is observed under both regimes, both equilibrium qualities are decreasing in the amount of network externalities, with the socially optimal quality decreasing faster than the monopoly quality, yielding overprovision of quality by the monopolist. This is driven by the planner's incentive to lower the price so as to increase market coverage as much as possible. As intuition suggests, the number of consumers able to purchase in equilibrium is always larger under social planning. Moreover, in the parameter region where this happens, the dea dweight loss increases in the extent of network externalities. However, this phenomenon tends to disappear as soon as full market coverage emerges at equilibrium under social planning. In the remainder of the parameter range, the deadweight loss is either decreasing or constant with respect to the network effect.

   The paper is organized as follows. Section 2 presents the general model. A specific formulation is introduced in section 3, where we derive both the monopoly equilibrium and the social optimum, which are then compared in section 4. Section 5 concludes.

2. The Model

   Consider a monopoly market for a good whose utility depends both on intrinsic characteristics, which are represented by quality q, and on total consumption x. Consumers are characterized by a parameter [theta], which represents the individual marginal willingness to pay for quality: [theta] is distributed with density f([theta]) over the interval [[theta] - 1,[theta]], with [theta][greater than or equal to]1. The population is normalized to 1. Each consumer buys at most one unit of the good, and the resulting net surplus is

   U = max{[theta]q + [alpha]x - p, 0}

   where p is the price charged by the monopolist, and [alpha] (the same for all the agents) is a positive coefficient representing the weight of the network externality in the utility function. Let [theta]([alpha], p. q, f([theta])) define the marginal willingness to pay of the consumer who is indifferent between buying and not buying:

   [theta]([alpha], p, q, f ([theta])) [equivel] {[theta]: [theta]q + [alpha] [[[integral].sup.0].sub.0]f(z)dx - p = 0}.

   Then, market demand is

   x = [[[integral].sup.0].sub.0]f([theta])d[theta]

   where

   [theta] = max{[theta] - 1, [theta]}.

   When max{[theta] - 1, [theta]} = [theta], partial market coverage (pmc) obtains; when instead max{[theta] - 1 [theta]} = [theta] - 1, full market coverage (fmc) obtains, that is, x - 1. Consumer surplus is

   CS = [[[integral].sup.0].sub.0] U(.)f([theta]) d[theta].

   On the supply side, production involves total costs C = c(q)x, with c', c" [greater than] 0. This amounts to saying that there are constant returns to scale and unit production costs c(q) are convex in quality. The profit function is then

   [[pi].sub.M] = [p - c(q)].[[[integral].sup.0].sub.0]f([theta]) d[theta].

   Social welfare is SW [[pi].sub.M] + CS. Except for the presence of network effects, this setup replicates the model introduced by Spence (1975). In his proposition 1, Spence (1975, p. 419) proves that, for a given output level, the monopolist undersupplies quality compared with the social optimum, iff the marginal willingness to pay of the average consumer is higher than the marginal willingness to pay of the marginal consumer, that is, the poorest consumer who is able to buy. A situation where, for any f([theta]), the average consumer is surely richer than the marginal one is that where full market coverage obtains under both regimes. Therefore

   REMARK 1. Under full market coverage, the monopolist undersupplies quality as compared with the social planner, independently of the consumer distribution and the size of network effects.

   PROOF. See Appendix A.

   Notice that, when the market is fully covered, the size of [alpha] is obviously irrelevant, since the size of the network is given and equal to one. Under partial market coverage, we know from Spence (1975) that the oversupply or undersupply of quality by the monopolist as compared with the social optimum is determined only by the shape of the consumers' distribution, f([theta]). We are going to show below that introducing network effects may drastically modify the acquired wisdom. This is summarized in the following:

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