Optimal R&D expenditure streams: An empirical view

Are the simple, abstract mathematical models of optimal R&D investment consistent with reality, or even relevant conceptual models of the R&D investment process? In this paper we adduce evidence that suggests the answers to each of these questions is yes. The paper first presents a brief review of the key concept of a convex time-cost tradeoff, which by assumption forms the basis for both static and dynamic models. A dynamic model is presented which determines the optimal expenditure rate and project duration for a profit-maximizing firm as a function of levels of preemptive threat, R&D efficiency, cost of capital, and returns to innovation. Using four different R&D projects, and comparing their expenditures with those predicted by the model, we conclude that the observed behavior is roughly consistent with that expected; the observed behavior implies the existence of a convex time-cost tradeoff when a profit-maximizing firm is assumed and relative efficiencies in converting monetary expenditures into effective R&D effort are consistent with expectations.