Scarcity of ideas and optimal R&D policy

We consider a model of innovation that distinguishes between ideas and innovations. While innovation responds to incentives, ideas are a scarce resource that provide an exogenous constraint on the rate of innovation. We investigate how the optimal reward structure is shaped by the scarcity of ideas. Substitute ideas for innovation in the model arrive to random recipients at random times. By foregoing investment in a current idea, society preserves an option to invest in a better idea for the same market niche but with delay. Because successive ideas may occur to different people, there is a conflict between private and social optimality. The social planner does not observe the arrival of ideas and learns over time about the arrival rate of ideas. We represent the social planner's beliefs using a general continuous density and illustrate that the evolution of beliefs can be tracked by the cumulative hazard function. The reward set by the social planner serves a dual purpose: learning about the arrival rate of ideas and trading off lower delays against lower cost ideas. We show that the optimal reward increases as time passes because the social planner comes to view ideas as more scarce.