Price and quantity competition in a differentiated duopoly

• Two classical models in the theory of oligopoly are those of Coumot (1838) and Bertrand (1883). In both models the equilibrium concept is the noncooperative equilibrium of Nash (1950). In the former firms set quantities. In the latter prices are the strategy variables. In a duopoly situation where firms produce a homogeneous good and marginal costs are constant and equal for both firms, the Bertrand price equals marginal cost and the Coumot price is above it. With differentiated products, Bertrand prices are above marginal cost. In this case Coumot competition is still viewed as more "monopolistic" than Bertrand competition.' We consider first a differentiated duopoly proposed by Dixit (1979). The demand stmcture is linear and allows the goods to be substitutes or complements. Firms have constant marginal costs and there are no fixed costs and no capacity limits. In this setup Coumot and Bertrand equilibria are unique. We show that Bertrand competition is more efficient than Coumot competition, in the sense that in equilibrium consumer surplus and total surplus are higher in the former regardless of whether the goods are substitutes or complements. Furthermore, profits are larger, equal, or smaller in Coumot than in Bertrand competition, according to whether the goods are substitutes, independent, or complements.