On the competitive pressure created by the diffusion of innovations

We consider the decision of a dominant firm to adopt a sequence of potential cost-reducing innovations, where the latest technology adopted diffuses to a competitive fringe at an exogenous rate. With price competition on the product market, the leader optimally spaces apart the adoption dates of successive innovations, so the industry is characterized by Schumpetarian cycles of alternating innovation and diffusion. An increase in the rate of diffusion has ambiguous effects on innovative activity, and, up to a point, hastens the pace of innovation. These results may, however, be reversed in the case of quantity competition.