Consumer heterogeneity, incomplete information and pricing in a duopoly with switching costs

Abstract

It is well known that switching costs may facilitate monopoly pricing in a market with price competition between two suppliers of a homogenous good, provided the switching cost is above some critical level. With heterogeneous consumers and incomplete information about individual consumers’ types, monopoly pricing entails second-degree price discrimination with inefficient contracts for low demand types. We show that introducing consumer heterogeneity may increase the critical switching cost needed to sustain a pure-strategy equilibrium involving monopoly pricing.

Introduction

A wave of privatization and deregulation has rolled over the world in recent years. The old national monopolies—be it railroad services, airlines, telecommunication or electricity provision or distribution—now typically have been forced to share their markets with one or more entrants. This gives rise to numerous interesting issues of competition in general and pricing behavior in particular. A particular problem facing firms is how to escape the Bertrand paradox: they compete in markets for more or less homogeneous goods, with prices as the main strategic variable. In our view, the most compelling solution to the paradox is the existence of switching costs: the fact that even if consumers do not care about which product they start to buy, there may be costs associated with switching suppliers.¹ These costs dampen competition in mature markets in a variety of settings, as shown by Paul Klemperer in numerous articles (see his 1995 survey). Recent efforts to raise barriers for consumers who might consider to switch supplier must be seen in light of this theory.²

Despite the large theoretical literature on the importance of switching costs on pricing in a variety of markets, there are only a limited number of empirical analyses on the measurement of switching costs. Notable exceptions are Elzinga and Mills (1998), who study the wholesale distribution of cigarettes; Kim et al. (2001), who study bank loans; and Chen and Hitt (2002), whose focus is on what they call internet-enabled businesses.³ They all agree that switching costs are an important source of market power.

Another characteristic of some of the industries in question—telecommunications in particular—is the degree of sophistication in pricing behavior: the typical tariff is non-linear, and normally consumers are offered the choice between a variety of schemes, with the purpose of price discrimination between heterogeneous consumers.⁴ The aim of the present paper is to study the interplay between switching costs and pricing behavior in a market where consumers differ in some respect relevant for price discrimination, and where the firms lack information about these consumer differences. In addition to the already mentioned literature on switching costs and non-linear pricing, there are also many contributions studying non-linear pricing in more or less competitive settings. What these contributions have in common, however, is that they model sources of market power other than switching costs. Wilson (1993, Part 12.3) considers Cournot competition, while Stole (1995), Armstrong and Vickers (2001) and Rochet and Stole (2002) are examples of studies based on the assumption that products are differentiated.⁵ Whereas the central focus in all these papers is how market power enables non-linear pricing when firms compete, our focus is different. In a model of imperfect competition based on consumer switching costs we are interested in how consumer heterogeneity affects the critical switching costs needed to sustain non-competitive prices as an equilibrium outcome.⁶

To our knowledge, none has studied the effects of consumer heterogeneity in a homogeneous-good duopoly with switching costs. With homogeneous consumers and linear pricing, Klemperer (1987) shows that monopoly pricing can be achieved if all consumers have (i) strictly positive switching costs and (ii) the switching costs are sufficiently high. We conduct the analysis within a model allowing consumer heterogeneity and non-linear pricing. Our main result is that consumer heterogeneity may increase the critical switching cost, implying that monopoly pricing can be sustained with homogeneous but not with heterogeneous consumers.

To illustrate this result consider a switching cost just high enough to sustain monopoly pricing when all firms have homogeneous consumers of the same type. The critical switching cost is derived from the temptation to offer non-marginal price cuts to the rival’s customers. Suppose then that half of all consumers belonging to each firm experience a drastic reduction in their willingness to pay for the good in question (in fact, so drastic that a monopolist would choose not to serve those consumers). Intuitively, one should think that since the value of each firm’s customer base has been reduced, the temptation to undercut to attract these customers should be reduced and hence the needed switching costs to keep customers from switching could be lower. However, our results show that the opposite may be true. Specifically, in this heterogeneous market, monopoly pricing will no longer be sustainable, in other words the switching cost is no longer sufficient to sustain monopoly pricing as an equilibrium outcome.

The reason for this result is that monopoly pricing with heterogeneous consumers entails inefficient contracts to low-demand types, and that these inefficiencies can be reduced when undercutting your rival, thereby making undercutting more tempting. With homogeneous consumers contracts are efficient, and the temptation to undercut stems solely from the desire to increase the number of customers at a lower price. With heterogeneous consumers, contracts are inefficient to low-demand types to prevent high-demand mimicking low-demand types. When undercutting the rival’s high-demand customers a competitor must offer the high-demand types a more advantageous contract. By doing this it becomes less tempting for high-demand types to mimic low-demand types, and therefore contracts to own low-demand types can be made more efficient. Thus, with heterogeneous consumers the temptation to undercut stems from two sources: (i) increasing the number of customers as before, and (ii) the efficiency gain from less distortion of low-demand customers. When low-demand contracts would be very inefficient in monopoly, the potential for an efficiency gain is larger, and due to this the temptation to undercut may be larger than when consumers are all of the same type.

The present analysis focuses on the existence of a pure strategy equilibrium involving monopoly pricing. There are at least two reasons why firms should be concerned about the existence of such an equilibrium. First, the alternative to the proposed equilibrium is an equilibrium in which each firm draws tariffs from a distribution ranging from competitive pricing to monopoly pricing, with lower profits as an inevitable result. Second, heterogeneity is not entirely exogenous to the firms, but depends on actions taken in earlier periods. Since we advocate homogeneity, we also provide guidelines for firms seeking to affect the prospects of ending up in an equilibrium involving monopoly pricing.⁷

The relevance of the present paper to information economics is two-fold. First, there is the relation between the intertemporal nature of information problems and the existence of switching costs as discussed by von Weizsäcker (1984). von Weizsäcker (1984) argues that problems of incomplete information “intrinsically are problems of intertemporal choice”, where the benefits of acquiring information today may accrue at a later point in time. He uses reputation as an example. Consumers would be unwilling to be ‘locked-in’ to a specific supplier unless the supplier has built a reputation for not fully exploiting his advantage in the future. Thus, incomplete information is a prerequisite for the existence of switching costs. Second, there is the issue of firms having incomplete information about consumers’ types. With perfect information of consumers’ types, firms may offer efficient contracts and fully extract consumers’ surplus. When there is private information about consumers’ types, some kind of inefficiency is needed to induce self-selection.

The paper proceeds as follows. In the next section we present our basic model, we define the key notion of critical switching cost, and we perform some preliminary analysis. In Section 3 we study how consumer heterogeneity affects the critical switching costs under the assumption of non-linear pricing. Some concluding remarks are gathered in Section 4.