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Optimal Dynamic R&D Programs


  • Gene M. Grossman
  • Carl Shapiro


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.

Suggested Citation

  • Gene M. Grossman & Carl Shapiro, 1985. "Optimal Dynamic R&D Programs," NBER Working Papers 1658, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:1658
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    References listed on IDEAS

    1. Kenneth L. Judd, 2003. "Closed-loop equilibrium in a multi-stage innovation race," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 673-695, March.
    2. Dasgupta, Partha & Stiglitz, Joseph, 1980. "Industrial Structure and the Nature of Innovative Activity," Economic Journal, Royal Economic Society, vol. 90(358), pages 266-293, June.
    3. Tom Lee & Louis L. Wilde, 1980. "Market Structure and Innovation: A Reformulation," The Quarterly Journal of Economics, Oxford University Press, vol. 94(2), pages 429-436.
    4. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 193-209.
    5. 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.
    6. Robert E. Lucas, Jr., 1971. "Optimal Management of a Research and Development Project," Management Science, INFORMS, vol. 17(11), pages 679-697, July.
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    Cited by:

    1. Korok Ray, 2007. "Performance Evaluations and Efficient Sorting," Journal of Accounting Research, Wiley Blackwell, vol. 45(4), pages 839-882, September.
    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. Tannistra Banerjee & Stephen Martin, 2015. "Pharmaceutical Regulation and Innovative Performance: A Decision‐theoretic Model," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 36(3), pages 177-190, April.
    4. 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.
    5. Dequiedt, V. & Versaevel, B., 2004. "Patent pools and the dynamic incentives to R&D," Working Papers 200412, Grenoble Applied Economics Laboratory (GAEL).
    6. Tannista Banerjee & Ralph Siebert, 2013. "The Impact of R&D Cooperation on Drug Variety Offered on the Market: Evidence from the Pharmaceutical Industry," Auburn Economics Working Paper Series auwp2013-20, Department of Economics, Auburn University.
    7. Pindyck, Robert S, 1991. "Irreversibility, Uncertainty, and Investment," Journal of Economic Literature, American Economic Association, vol. 29(3), pages 1110-1148, September.
    8. By Kenneth L. Judd & Karl Schmedders & Şevin Yeltekin, 2012. "Optimal Rules For Patent Races," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 23-52, February.
    9. 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.
    10. Olivier Cadot & Bernard Sinclair-Desgagné, 1995. "Innovation Under the Threat of Stricter Environmental Standards," CIRANO Working Papers 95s-11, CIRANO.
    11. Dutta, Prajit K., 1997. "Optimal management of an R&D budget," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 575-602.
    12. Toxvaerd, Flavio, 2007. "A theory of optimal deadlines," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 493-513, February.
    13. Toxvaerd, Flavio, 2006. "Time of the essence," Journal of Economic Theory, Elsevier, vol. 129(1), pages 252-272, July.
    14. Kaies Samet, 2010. "The creative intelligence," Working paper serie RMT - Grenoble Ecole de Management hal-00512539, HAL.
    15. repec:ipg:wpaper:2014-362 is not listed on IDEAS
    16. Kort, P.M., 1996. "Optimal R&D Investments of the Firm," Discussion Paper 1996-47, Tilburg University, Center for Economic Research.
    17. 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.
    18. Frank R. Lichtenberg, 1988. "IR&D Project Data and Theories of R&D Investment," NBER Working Papers 2720, National Bureau of Economic Research, Inc.
    19. 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.
    20. 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.

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