Production Substitution of Goods Within and Between Firms in a Multiproduct Duopoly

We consider the product line strategies of duopolistic firms, each of which can supply two vertically-differentiated products under nonnegative output constraints and expectations of their rival's product line reaction. Considering a game of firms with heterogeneous (homogeneous) unit costs for high- (low-) quality products, we derive the equilibria for the game and conduct comparative statics of the equilibria outcomes on the relative superiority of the high-quality product and relative cost efficiency. In two of the equilibria, we find that where the cost-inefficient firm supplies a high-quality good, social welfare can worsen as its unit cost decreases. We also characterize the result using the production substitution of differentiated goods within a firm and the high-quality good between firms. Further, by comparing social welfare in the first-best equilibria with those in the Cournot duopoly equilibria, we find that the social welfare of the market worsens in the multiproduct Cournot duopoly equilibria as the relative superiority of the high-quality good increases.