Optimal Dynamic R&D Programs

We study the optimal pattern of outlays for a single firm pursuing an R&D program over time. In the deterministic case (a) the amount of progress required to complete the project is known and (b) the relationship between outlays and progress is known. In this case it is optimal to increase effort over time as the project nears completion. The value of a research project is convex in its payoff on completion and in the difficulty of the project. Relaxing (a) we find in general a simple, positive relationship between the optimal expenditure rate at any point in time and the (expected) value at the time of the research program. We also show that, for a given level of expected difficulty, a riskier project is always preferred to a safe project. Relaxing (b), we find again that research outlays increase as further progress is made.