Patentability, R&D direction, and cumulative innovation

We present a model of cumulative innovation where firms can conduct R&D in both a safe and a risky direction. Innovations in the risky direction produce quality improvements with higher expected sizes and variances. As patentability standards rise, an innovation in the risky direction is less likely to receive a patent that replaces the current technology, which decreases the static incentive for new entrants to conduct risky R&D, but increases their dynamic incentive because of the longer duration---and hence higher reward---for incumbency. These, together with a strategic substitution and a market structure effect, result in an inverted-U shape in the risky direction but a U shape in the safe direction for the relationship between R&D intensity and patentability standards. There exists a patentability standard that induces the efficient innovation direction, whereas R&D is biased towards (against) the risky direction under lower (higher) standards. The optimal patentability standard may distort the R&D direction to increase the industry innovation rate that is socially deficient.