Strategic R&D investment, competitive toughness and growth

We develop an overlapping generations model, where firms (as consumers) have a two-period life, investing in R&D during the first period and competing in the product market in the second period. The number of firms is endogenously determined and the set of successful firms by a Bernoullian random process. We show the possibility of an inverted-U relationship between innovation and product market competition for an individual industry, based on the possibility for non-successful firms to remain productive. When the relative cost advantage of successful firms is large (large innovation step or small spillovers) this possibility results from the probabilistic nature of the model.