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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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Bibliographic Info

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. Robert E. Lucas, Jr., 1971. "Optimal Management of a Research and Development Project," Management Science, INFORMS, vol. 17(11), pages 679-697, July.
  3. 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.
  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. Kenneth L. Judd, 2003. "Closed-loop equilibrium in a multi-stage innovation race," Economic Theory, Springer, vol. 21(2), pages 673-695, 03.
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Cited by:
  1. Pindyck, Robert S., 1990. "Irreversibility, uncertainty, and investment," Working papers 3137-90., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  2. Lukach, R. & Kort, P.M. & Plasmans, J.E.J., 2007. "Strategic R&D with Knowledge Spillovers and Endogenous Time to Complete," Discussion Paper 2007-38, Tilburg University, Center for Economic Research.
  3. Viju, Crina & Kerr, William A., 2013. "Taking an option on the future: Subsidizing biofuels for energy security or reducing global warming," Energy Policy, Elsevier, vol. 56(C), pages 543-548.
  4. Toxvaerd, Flavio, 2007. "A theory of optimal deadlines," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 493-513, February.
  5. Kenneth Judd & Karl Schmedders, 2002. "Optimal Rules for Patent Races," Discussion Papers 1343, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Dequiedt, V. & Versaevel, B., 2004. "Patent pools and the dynamic incentives to R&D," Working Papers 200412, Grenoble Applied Economics Laboratory (GAEL).
  7. Tannista Banerjee & Stephen Martin, 2013. "Pharmaceutical regulation and innovative performance: a decision-theoretic model," Auburn Economics Working Paper Series auwp2013-21, Department of Economics, Auburn University.
  8. Cozzi, Guido & Galli, Silvia, 2011. "Privatization of Knowledge: Did the U.S. Get It Right? (New Version)," MPRA Paper 29710, University Library of Munich, Germany.
  9. Eymen Errais & Jeffrey Sadowsky, 2005. "Valuing Pilot Project Investments in Incomplete Markets : A Compound Option Approach," Computing in Economics and Finance 2005 73, Society for Computational Economics.
  10. Tannista Banerjee & Ralph Siebert, 2014. "The Impact of R&D Cooperations on Drug Variety Offered on the Market. Evidence from the Pharmaceutical Industry," CESifo Working Paper Series 4567, CESifo Group Munich.
  11. Frank R. Lichtenberg, 1988. "IR&D Project Data and Theories of R&D Investment," NBER Working Papers 2720, National Bureau of Economic Research, Inc.
  12. Dequiedt, Vianney & Versaevel, Bruno, 2013. "Patent pools and dynamic R&D incentives," International Review of Law and Economics, Elsevier, vol. 36(C), pages 59-69.
  13. Olivier Cadot & Bernard Sinclair-Desgagné, 1995. "Innovation Under the Threat of Stricter Environmental Standards," CIRANO Working Papers 95s-11, CIRANO.
  14. Kort, P.M., 1996. "Optimal R&D Investments of the Firm," Discussion Paper 1996-47, Tilburg University, Center for Economic Research.
  15. Marcello Basili & Roberto Renò & Carlo Zappia, 2005. "Production of a New Drug: A Sequential Investment ProcessUnder Uncertainty," Department of Economics University of Siena 453, Department of Economics, University of Siena.

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