We study the relationship between toughness of competition on the product market, strategic R&D investment and growth. We develop an overlapping generations model, where firms as well as consumers have a two-period life. Firms invest in R&D during the first period and compete on the product market in the second period. The number of firms is endogenously determined through capital market clearing, not through a zero profit condition. We exhibit the non-monotonicity of the relation between the toughness of the competition regime and the incentives to innovate.