Empirical studies have uncovered an inverted‐U relationship between product‐market competition and innovation. This is inconsistent with the original Schumpeterian model, where greater competition always reduces the profitability of innovation and thus the incentives to innovate. We show that the model can predict the inverted‐U if the innovators’ talent is heterogeneous and asymmetrically observable. When competition is low and profitability is high, talented innovators are credit‐constrained, since untalented innovators are eager to mimic them. As competition increases and profitability decreases, untalented innovators become less eager to mimic, and talented innovators can invest more. This generates the increasing part of the relationship. When competition is high and profitability is low, credit constraints disappear, and the relationship is decreasing. Our theory generates additional specific predictions that are well borne out by the existing evidence.