On the Optimal Value and Protection of a Patent

In this note, we analyze the behavior of a firm that has a (stochastic) market power due to a patent. For example, we show how to handle the stock aspects of R&D activities (the accumulation of human capital in a firm). In fact, when the R&D stock enters the survival probability of the firm's market power, we do not have a standard optimal control problem. We show how to handle this complication and its implications for the optimal R&D strategy. We also show how to interpret the current value Hamiltonian in terms of the interrest on expected future present value profits. Finally, drawing on resent results on the dynamic envelope theorem, we provide an interpretation of our results in terms of the question whether the market is biased against risky R&D.