Process and product innovation: A differential game approach to product life cycle

We investigate the timing of adoption of product and process innovation using a differential game where 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 in only one R&D activity and then reach the steady state either carrying out only this activity or carrying out both; or (iii) firms do not invest at all in either type of innovation. Comparing R&D investments under Cournot and Bertrand behavior shows that quantity competition entails lower R&D incentives than price competition in both directions.