Research on the Optimal Path Evolvement of Product Innovation Diffusion model

In this paper a diffusion model of product innovations was firstly formulated on the basis of some important key factors. Then, the Nash equilibrium of optimal time path was obtained by solving the system of product innovations. At last, the output and price of industries based on optimal time paths were studied in equilibrium framework. The paper's conclusion is that all prices in an industry move together at the same rate when all products in the economy are weak gross substitutes, preferences are homothetic, and firms face menu costs; all firms invest in productivity and reduce real prices in the closed loop Nash non-cooperative equilibrium; and in the case of quadratic menu costs, the outputs of industries and the economy go up along S-shaped time paths characteristic of diffusion of innovations.