A theory of competitive industry dynamics with innovation and imitation

Empirical evidence on industry life-cycle reveals a pattern in which innovation rates remain fairly stable or are perhaps even higher at early stages, while patenting increases sharply as the industry matures. This increase in patenting in later stages is accompanied by net exit and lower rates of output growth and price decline. In this paper, we develop a dynamic model of a competitive industry with innovation and imitation that is consistent with these stylized facts. We derive an equilibrium growth path, along which leading firms invest in increasing the stock of technological knowledge and choose not to prevent imitation by other firms as long as the industry remains relatively small. As the industry expands including new entry, the leaders' optimal amount of investment gradually declines. We show that under some rather general conditions, there would exist a scale of the industry where innovating firms would choose to start preventing free imitation, bringing further expansion of the industry through new entry to a halt and causing net exit.