Product life cycles, product innovation and firm growth

This paper studies research and development (R &D) for product innovation of firms faced with "product life cycles." We represent the concept of product life cycles with bounded revenue and profit functions and describe R &D for product innovation as an activity to control the "birth rate of a new product" (i.e., the probability of product innovation). We then derive the optimal level of R &D, corresponding to the optimal birth rate of a new product, and show that the growth rate of the firm's expected total revenue converges to the optimal birth rate of a new product in the long run.