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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. The value of a research project is convex in its payoff on completion and in the difficulty of the project. 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 the time of the research program. We also show that, for a given level of expected difficulty, a riskier project is always preferred to a safe project. Relaxing (b), we find again that research outlays increase as further progress is made.

Suggested Citation

  • Gene M. Grossman & Carl Shapiro, 1986. "Optimal Dynamic R&D Programs," RAND Journal of Economics, The RAND Corporation, vol. 17(4), pages 581-593, Winter.
  • Handle: RePEc:rje:randje:v:17:y:1986:i:winter:p:581-593
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    References listed on IDEAS

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    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.
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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, pages 1110-1148.
    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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