When firms have different R&D productivities, it may be welfare increasing to differentiate patent lives across inventions. The reason is that any uniform patent life provides excessive incentives to do R&D to the low productivity firms and insufficient incentives to the high productivity firms. Such a differentiated scheme is implementable through renewal fees, which endogenously determine an optimal pattern of patent lives. We characterise the optimal pattern of patent life-spans and show how it depends on key features of the economic environment, such as the degree of heterogeneity in R&D productivity across firms, the ability of patentees to appropriate the potential rents generated by R&D and the learning process about the value of the...