Anticommons and optimal patent policy in a model of sequential innovation

We present a model of sequential innovation in which an innovator uses several research inputs to invent a new good. These inputs, in turn, must be invented before they can be used by the final innovator. As a consequence, the degree of patent protection affects the revenues and cost of the innovator, but also determines the incentives to invent the research inputs in the first place. We study the effects of increases in the number of required inputs on innovation activity and optimal patent policy. We find that the probability of introducing the final innovation decreases (increases) as the number of inputs increases when inputs are complements (substitutes). We also find that the optimal strength of patents on research inputs is increasing in the degree of substitution between the inputs, but decreasing in the number of inputs for any degree of substitution.