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Imperfect Competition, Technology Innovation, and Multiproduct Firms

Both horizontal and vertical innovations are studied in this paper, using monopolistic and oligopolistic competition models with multiproduct firms. We consider a two-stage game. In the first stage, all firms simultaneously choose their own number of products. In the second stage, firms make price decisions to maximize the sum of profits for their own products where a compound CES utility function is considered. We assume that the elasticity of substitution across the products produced within the same firm is different from the elasticity of substitution across the products produced by different firms. A firm's innovation level is shown to increase either as income increases or as the firm's entry cost increases. The firm's innovation level decreases either when the elasticity of substitution across products produced by different firms increases or when the marginal cost of innovation increases. In a symmetric equilibrium, firms produce differentiated products with the same level of quality. In contrast to other imperfect competition models with multiproduct firms, the model studied in this paper has the following characteristics: 1) The model is simple and sufficiently general. The model is made easily comparable with the Dixit-Stiglitz (1977) model to increase applicability. 2) The product managers of the same firm behave cooperatively rather than independently. 3) The number of firms is endogenous rather than exogenous, which is determined by a free-entry condition. Since the marginal innovation cost can connected to the usage of human capital and the entry cost can be connected to the investment cost, the model developed in this paper can be easily applied to the studies of labor market, capital market, and technology market. While the corresponding applications in international trade, industrial organization, and macroeconomics may be interesting, they are left for further research.