Firm Growth by Product Innovation in the Presence of the Product Life Cycle

In this paper, we present a model which enables us to look into the process of research and development (R&D) for product innovation in the presence of the product life cycle and the resultant firm or economic growth. Specifically, we describe R&D for product innovation as an activity to control the birth rate of a new product, which measures the probability of product innovation; derive the optimal birth rate of a new product, which determines the size of R&D expenditure; and examine the growth rate of the (representative) firm('s expected total revenue) along the optimal R&D plan. We then find that the growth rate of the firm converges to the optimal birth rate of a new product in the long run.