Optimal patent length and breadth in an economy with creative destruction and non-diversifiable risk

In this paper, I examine the optimal patent shape in an economy in which R&D firms innovate and imitate, households face non-diversifiable risk and there is externality in production and R&D. With non-diversifiable risk, a household's consumption and investment decisions are interlinked. This economy contains industries of two kinds: monopoly industries with an innovator only, and duopoly industries with an innovator and an imitator. I define patent length as the expected time in which an innovation is imitated, and patent breadth as the innovator's profit share in an industry after a successful imitation. The government can control patent length by the requirements for accepting a substitute for a patented good, and patent breadth by imposing compulsory licensing and royalties for the patentee after a successful imitation. I show that the stronger the externality in production relative to R&D is, the slower the optimal growth rate, the larger the optimal proportion of duopoly industries, and the longer and narrower the optimal patent.