Price Discrimination Based On Imperfect Information: Necessary and Sufficient Conditions

Abstract

Usually, the information a buyer requires in order to obtain the lowest price must be produced at a cost depending on the efficiency with which the buyers gather information. Thus, a suitable price dispersion enables a monopolist to split up the market to permit a more profitable price discrimination. In this paper, necessary and sufficient conditions for the existence of a non-trivial profit maximizing price dispersion are considered. Furthermore, the relationship between statistical properties of the set of consumers' characteristics and this existence problem are studied. This paper takes up again the problem of imperfect information and price originally discussed by Salop (1977) and later by Berninghaus and Ramser (1980). This problem is based on the observation that markets for apparently identical commodities are characterized by dispersion in price and differences in durability and other quality measures. An endogeneous explanation for this kind of price is provided by Salop: The information a buyer requires in order to obtain the lowest price or 'best buy' must be produced at a cost... Consumers' search techniques and the efficiency with which they gather information varies. This heterogeneity leads to differences in optimal information-gathering strategies. Those consumers who are more efficient information-gatherers and searchers obtain better buys on average Hence, price dispersion serves as a device for splitting up the market to permit price discrimination (Salop (1977) p. 393). Salop develops this idea for an economy with a monopolistic producer, selling a homogeneous commodity at different prices to consumers characterized by their information-gathering cost, and a limit price they are willing to pay for this commodity. Under the assumption of a special search behaviour of the consumers, Salop gives necessary conditions for the existence and for the structure of a profit maximizing price dispersion, yielding higher returns for the monopolist than any single price strategy. However, Salop's results are incomplete in that he does not consider sufficient conditions. In their paper, Berninghaus and Ramser take up this point and show for some special cases that Salop's conditions are fulfilled only under restrictive assumptions about the distribution of consumer search costs. Their opinion that . a price dispersion for discriminating uninformed consumers will be rather improbable to be observed (Berninghaus and Ramser (1980), p. 420), is, however, based on these special results. Hence, there is still a need for a general solution of the problem of price