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Optimal Dynamic R&D Programs

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Author Info
Gene M. Grossman
Carl Shapiro

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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.

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Publisher Info
Article provided by The RAND Corporation in its journal RAND Journal of Economics.

Volume (Year): 17 (1986)
Issue (Month): 4 (Winter)
Pages: 581-593
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Handle: RePEc:rje:randje:v:17:y:1986:i:winter:p:581-593

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  1. 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. [Downloadable!] (restricted)
  2. Kenneth L. Judd, 1985. "Closed-Loop Equilibrium in a Multi-Stage Innovation Race," Discussion Papers 647, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Harris, Christopher & Vickers, John, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Blackwell Publishing, vol. 52(2), pages 193-209, April. [Downloadable!] (restricted)
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  1. Flavio Toxvaerd, 2004. "Time of the Essence," Discussion Paper Series dp358, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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  2. Ruslan Lukach & Peter M. Kort & Joseph Plasmans, 2007. "Strategic R&D with Knowledge Spillovers and Endogenous Time to Complete," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  3. Bruno Versaevel & Vianney Dequiedt, 2007. "Patent Pools and the Dynamic Incentives to R&D," Working Papers 0703, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure. [Downloadable!]
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  4. Oren Setter & Asher Tishler, 2006. "A Brave Leap Or A Gradual Climb? The Dynamics Of Investment In R&D Of Integrative Technologies," Defence and Peace Economics, Taylor and Francis Journals, vol. 17(3), pages 201-222, June. [Downloadable!] (restricted)
  5. Frank R. Lichtenberg, 1989. "IR&D Project Data and Theories of R&D Investment," NBER Working Papers 2720, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. Kort, P.M., 1996. "Optimal r&d investments of the firm," Discussion Paper 47, Tilburg University, Center for Economic Research. [Downloadable!]
  7. Olivier Cadot & Bernard Sinclair-Desgagné, 1995. "Innovation Under the Threat of Stricter Environmental Standards," CIRANO Working Papers 95s-11, CIRANO. [Downloadable!]
  8. Pindyck, Robert, 1989. "Irreversibility, uncertainty, and investment," Policy Research Working Paper Series 294, The World Bank. [Downloadable!]
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  9. Tien Foo Sing, 2002. "Time to build options in construction processes," Construction Management & Economics, Taylor and Francis Journals, vol. 20(2), pages 119-130, March. [Downloadable!] (restricted)
  10. Jonathan B. Berk & Richard C. Green & Vasant Naik, 1998. "Valuation and Return Dynamics of New Ventures," NBER Working Papers 6745, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  11. 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. [Downloadable!]
  12. 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. [Downloadable!]
  13. Flavio Toxvaerd, 2003. "A Theory of Optimal Deadlines," Discussion Paper Series dp357, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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  14. Robert S. Pindyck, 1993. "Investments of Uncertain Cost," NBER Working Papers 4175, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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