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Optimal Dynamic R&D Programs

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  • Gene M. Grossman
  • Carl Shapiro

Abstract

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. 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 1658.

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Date of creation: Jul 1985
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Publication status: published as Grossman, Gene M. and Carl Shapiro. "Optimal Dynamic R&D Programs," Rand Journal of Economics, Vol. 17, No. 4, Winter 1986, pp. 581-593.
Handle: RePEc:nbr:nberwo:1658

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  1. Harris, Christopher & Vickers, John, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Wiley Blackwell, vol. 52(2), pages 193-209, April.
  2. Kenneth L. Judd, 2003. "Closed-loop equilibrium in a multi-stage innovation race," Economic Theory, Springer, vol. 21(2), pages 673-695, 03.
  3. Robert E. Lucas, Jr., 1971. "Optimal Management of a Research and Development Project," Management Science, INFORMS, vol. 17(11), pages 679-697, July.
  4. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
  5. Dasgupta, Partha & Stiglitz, Joseph, 1980. "Industrial Structure and the Nature of Innovative Activity," Economic Journal, Royal Economic Society, vol. 90(358), pages 266-93, June.
  6. Lee, Tom & Wilde, Louis L, 1980. "Market Structure and Innovation: A Reformulation," The Quarterly Journal of Economics, MIT Press, vol. 94(2), pages 429-36, March.
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