Product selection by quantity-setting firms

Abstract

Hotelling suggested that competition between oligopolistic sellers would result in consumers with inelastic demands being offered products with an excessive sameness. Smithies extended the Hotelling result to the case of elastic demand. While these results are intuitively appealing, it has subsequently been shown that both the two-stage and simultaneous price-location games suffer from fundamental non-existence problems when firms do not price discriminate. In this paper we investigate the Smithies analysis assuming that firms compete in quantities rather than prices. We show that a tendency to agglomeration is characteristic of quantity-location competition. But when locations and quantities are chosen simultaneously, problems of non-existence of equilibrium do not arise and the principle of minimum differentiation does not hold. By contrast when firms play a two-stage game, choosing locations in the first stage and quantities in the second stage, the non-existence problems that characterize price-location games (whether simultaneous or two-stage) extend to the two-stage quantity-location game for certain parameter values.