Number of Firms and Price Competition - Bagwell, Kyle (Institutional Knowledge at Singapore Management University, 2014)
The relationship between the number of firms and price competition is a central issue in economics. To explore this relationship, we modify Varianís (1980) model and assume that firms are privately informed about their costs of production. Allowing that the support of possible cost types may be large, we show that an increase in the number of firms induces lower (higher) prices for lower-cost (highercost) firms. We also characterize the pricing distribution as the number of firms approaches infinity, finding that the equilibrium pricing function converges to the monopoly pricing function for all but the lowest possible cost type. If demand is inelastic, an increase in the number of firms raises social welfare. If in addition the distribution of types is log concave, then an increase in the number of firms raises aggregate consumer surplus and lowers producer surplus. We identify conditions, however, under which uninformed consumers are harmed, and informed consumers are helped, when the number of firms is larger. By contrast, when the number of firms is held fixed, a policy that increases the share of informed consumers benefit informed and uninformed consumers. Finally, we confirm that results previously obtained in Varianís (1980) complete-information model can be captured in our model as a limiting case when the support of possible cost types approaches zero.