Optimal Dynamic R&D ProgramsWe 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. 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 that time of the research program. We also show that, for a given level ofexpected difficulty, a riskier project is always preferred to a safe project. Relaxing (b), we find again that research outlays increase as further progressis made. |
Common terms and phrases
amount of progress assume Carl Shapiro comparative dynamics complete the project constant hazard rate control problem deterministic program discount rate discrete distribution distance L₁ dynamic program DYNAMIC R&D PROGRAMS everywhere non-decreasing Expenditure Patterns Figure firm is risk first-order condition Grossman implies intensity investment Kamien and Schwartz L₂-L₁ Lee and Wilde level of effort marginal cost Massachusetts Avenue maximize f(c)/c maximum value function mean preserving spread Model Number Author OPTIMAL DYNAMIC R&D optimal expenditure optimal path optimal program optimal R&D program optimal to increase patent race Path for Prize path of R&D PENNSYLVANIA STATE UNIVERSITY probability density function progress is achieved qualitative properties R&D intensity R&D outlays Reinganum 1981 research effort research program research project risk neutral risky project rV(x saddlepath safe and risky second-order condition Section shutdown point single firm stages stochastic progress success task terminal date Two-Point Distribution unknown difficulty Vi+1 Vp(x