Intertemporal Price Discrimination, Uncertainty and Introductory Offers

Abstract

Recent analyses of market equilibria have shown that it is possible for price dispersion to exist even in competitive markets for homogeneous goods. The usual departure from the perfectly competitive extreme that leads to the possibility of price dispersed equilibria is the introduction of some form of imperfect information. Salop and Stiglitz (1977; 1982), Braverman (1980), and, Sadanand and Wilde (1982) have all shown that a competitive market may display more than one price in equilibrium. In general these models feature equilibria exhibiting price dispersion because of the assumption that consumers find it costly to obtain full information on prices and/or quality. Although the above models provide better characterisations of actual market structures, they still exhibit a weakness, and this has been highlighted by Varian (1980). He argues that because they model 'spatial' price dispersion it allows some stores to sell their product persistently at a lower price than available elsewhere. This, he argues, ignores the possibility of consumers learning from experience. As an alternative he proposed a model of 'temporal' price dispersion. In his model stores randomly select their price over time so that they can discriminate between the informed and uninformed sectors of the market. At any one moment in time there can exist a price distribution. He argues that the model could be viewed as an explanation of'sales'. However, it is typically the case that sales are predictable, regular, and well advertised, rather than random, and most stores seem to hold sales simultaneously. In a recent paper Sobel (1984) presents a model where stores periodically hold sales. His model displays an equilibrium where stores adopt a cyclical pricing policy, occurring because of known consumer heterogeneity. This heterogeneity enables stores to price discriminate over time by occasionally holding sales in an attempt to capture all of the consumers with a low reservation price. Hence, he argues that consumer heterogeneity may result in price dispersed equilibria over time. In the model considered here there are similarities to those discussed above. We present an intertemporal model where stores hold sales, and these sales take the form of introductory offers. The theme is about consumers who enter a market and choose to purchase a perishable commodity. However, each individual consumer is uncertain about the quality of a match at any store not previously sampled; that is, consumers cannot determine the quality of