Process and Product Innovation: a Differential Game Approach to Product Life Cycle

We investigate the timing of adoption of product and process innovation by using a differential game in which firms may invest in both activities. We consider horizontal product innovation that reduces product substitutability, and process innovation that reduces marginal cost. First, we demonstrate that the incentive for cost-reducing investment is relatively higher than the incentive to increase product differentiation. Second, depending on initial conditions, (i) firms activate both types of investment from the very outset to the steady state; (ii) firms initially invest only in one R&D activity and then reach the steady state either carrying out only such activity or carrying out both; (iii) firms do not invest at all in either type of innovation.