On the Nature of Competition with Differentiated Products

Abstract

There is an old debate going back to Bertrand (1883) and Edgeworth (1925) about the fragility of market equilibrium when competition arises among a few sellers. It was Hotelling's belief that price instability vanishes when products are differentiated (Hotelling, 1929). Recently attention was drawn to the fact that, even if product differentiation can weaken the forces leading to price instability, it cannot eliminate completely the possibility of price cycles (d'Aspremont et al. 1979). The purpose of this paper is to show that vertical and horizontal product differentiation do not operate in the same manner: a stable market outcome (including an endogenous product specification) arises more frequently with the former than with the latter.' Horizontal product differentiation is rooted in taste differences. More precisely, the potential customers have heterogeneous preferences about the proportion in which the attributes of the product should be combined. A wide range of substitute products can then survive in the same market simply because each of them combines the various attributes of the product in a proportion suitable to a particular segment of customers: between two products in the range the level of some attributes is augmented while that of others is lowered. Each variety has its own circle of customers, exactly as the inhabitants located around a particular shop form its potential market. None the less, competitors can raid these privileged market shares by adequate price cuts. By contrast, vertical product differentiation refers to a class of products which cohabit simultaneously on a given market, even though customers agree on a unanimous ranking between them: between two products in the range the level of all attributes is augmented or lowered. The survival of a low-quality product then rests on the seller's ability to sell it at a reduced price, compensating thereby for the higher a priori attractiveness of a more desirable quality. The seller of a low-quality product will specialise in the segment of customers whose propensity to spend on the corresponding range of products is low, either because they have relatively lower income, or relatively less intensive preferences, than other customers. At the same time, the seller of a high-quality product will enjoy an absolute advantage over his competitor.2 Interestingly, it turns out that price and product competition does not lead to the same results in these two situations, regarding the stability of the market equilibrium. To stress the differences, we have chosen to concentrate on two