This paper introduces a model of innovation that explains some of the stylized facts presented in recent empirical literature. In the model, firms choose R&D expenditures that maximize their expected profits under the assumption that R&D expenditures of firms might be constrained by the size of their profits. Optimal decisions of firms generate relationships between profitability and innovation of individual firms that may create the observed patterns at the industry level. In particular, the model is able to explain an inverted-U relationship between profitability and innovation in the industry together with decreasing or flat and concave relationships between profitability and the dispersion of productivity in the industry. Additionally, the paper investigates the parameter space for which the model generates the observed relationships.