Third degree price discrimination in linear-demand markets: effects on number of markets served and social welfare

Southern Economic Journal, Oct, 2008 by Victor Kaftal, Debashis Pal

1. Introduction

Does monopolistic third degree price discrimination reduce social welfare? The question has continued to intrigue economists and policy makers for more than half a century. The seminal work of Robinson (1933) shows that if a monopolist with a constant marginal cost sells in two distinct and independent markets having linear demands, then welfare falls with third degree price discrimination. Almost half a century later, Schmalensee (1981) reexamines Robinson's result and demonstrates that for any number of markets with linear demands, third degree price discrimination lowers welfare. Schmalensee (1981) also establishes, more generally, that price discrimination increases welfare only if it increases aggregate output. Subsequently, using ingenious duality approaches, Varian (1985) and Schwartz (1990) generalize the results for correlated demands and nonlinear marginal costs. (1)

It is, therefore, well known that for linear market demands and constant marginal costs, monopolistic third degree price discrimination indeed lowers welfare. It is important to note, however, that the welfare reducing effect of third degree price discrimination is derived under a crucial assumption. It is assumed that if the monopolist is forced to charge the same price in all markets (uniform pricing), the monopolist would sell a positive quantity in each market. In a recent article, Cowan (2007) considers various forms of nonlinear demands and presents the necessary and sufficient and/or sufficient conditions for price discrimination to reduce welfare.

Cowan (2007), however, also assumes that all markets are served under uniform pricing. Yet, when this assumption does not hold, the welfare effects of monopolistic third degree price discrimination turn out to be significantly more intricate.

Observe that when all markets are not served under uniform pricing, price discrimination may increase welfare because price discrimination may serve markets that would not be served under uniform pricing. Thus, relative to uniform pricing, price discrimination has two countervailing effects on welfare. Aggregate welfare goes down in those markets that are originally served under uniform pricing; whereas, welfare goes up in those markets that are not served under uniform pricing. Therefore, the additional welfare from the "new markets" under price discrimination may offset any loss of welfare in the markets that are originally served under uniform pricing.

The point is strongly emphasized in Schmalensee's (1981) seminal work. In the context of prescription drugs, an identical sentiment is recently echoed in Varian (2000). In the context of two markets, the possibility of price discrimination opening up "new markets" is first analyzed (graphically) by Battalio and Ekelund (1972). Layson (1994) also considers two markets but includes nonlinear demands and presents conditions for "opening of new markets" based on endogenous features, such as elasticities. In the context of patent policy, "opening of new markets" by price discrimination is explicitly incorporated by Hausman and MacKie-Mason (1988). Using two markets, they show that price discrimination by a patent holder is socially desirable in many cases because it allows the patent holder to "open new markets."

There is a related literature in spatial economics, beginning with Greenhut and Ohta (1972) and Holahan (1975), that deals with spatial price discrimination and market opening with linear demand. The issue is whether all consumers should face a mill price plus transportation costs (no discrimination), or the firm should be allowed to set delivered pricing that is discriminatory but serves more consumers. This strand of literature bears some resemblance to our analysis with a continuous distribution of markets (see section 5 in this paper), though our analysis is more general because we allow both market size and demand intercept to vary.

Given the abundance of examples where all markets are not served by a single price monopolist and the interests that researchers have placed on analyzing this issue, it is somewhat surprising that no necessary and sufficient conditions for the direction of welfare change have been established. The objective of the present paper is to fill this gap.

We consider several markets with linear demands and characterize each demand by two exogenous parameters: the price intercept of the demand curve and the size of the market as measured by the area under the demand curve. Based on these exogenous parameters, we establish the necessary and sufficient conditions to determine the number of markets to be served under uniform pricing and whether welfare goes up or down under third degree price discrimination. We also establish sufficient conditions to determine the direction of welfare change based on either demand intercepts or market sizes. In particular, we demonstrate that even if some markets are ignored under uniform pricing, price discrimination increases welfare only in limited scenarios. It increases welfare only if both the price intercept of the demand and the market size are significantly lower in some markets.