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The Learning Curve and Optimal Production Under Uncertainty

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Author Info
Saman Majd
Robert S. Pindyck

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Abstract

This paper examines the implications of the learning curve in a world of uncertainty. We consider a competitive firm whose costs decline with cumulative output. Because the price of the firm's output evolves stochastically, future production and cumulative output are unknown, and are contingent on future prices and costs. We derive an optimal decision rule that maximizes the firm's market value: produce when price exceeds a critical level, which is a declining function of cumulative output. We show how the shadow value of cumulative production, as well as the total value of the firm, depend on the volatility of price and other parameters. Over the relevant range of prices, uncertainty reduces the shadow value of cumulative production, and therefore increases the critical price required for the firm to begin producing.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 2423.

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Date of creation: Oct 1987
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Handle: RePEc:nbr:nberwo:2423

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Martin B. Zimmerman, 1982. "Learning Effects and the Commercialization of New Energy Technologies: The Case of Nuclear Power," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 297-310, Autumn. [Downloadable!] (restricted)
  2. McDonald, Robert & Siegel, Daniel, 1984. " Option Pricing When the Underlying Asset Earns a Below-Equilibrium Rate of Return: A Note," Journal of Finance, American Finance Association, vol. 39(1), pages 261-65, March. [Downloadable!] (restricted)
  3. Merton, Robert C., 1977. "On the pricing of contingent claims and the Modigliani-Miller theorem," Journal of Financial Economics, Elsevier, vol. 5(2), pages 241-249, November. [Downloadable!] (restricted)
  4. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-49, June. [Downloadable!] (restricted)
  5. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(03), pages 461-474, September. [Downloadable!]
  6. A. M. Spence, 1981. "The Learning Curve and Competition," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 49-70, Spring. [Downloadable!] (restricted)
  7. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," Journal of Business, University of Chicago Press, vol. 58(2), pages 135-57, April. [Downloadable!] (restricted)
  8. Drew Fudenberg & Jean Tirole, 1983. "Learning-by-Doing and Market Performance," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 522-530, Autumn. [Downloadable!] (restricted)
  9. Majd, Saman & Pindyck, Robert S., 1987. "Time to build, option value, and investment decisions," Journal of Financial Economics, Elsevier, vol. 18(1), pages 7-27, March. [Downloadable!] (restricted)
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  10. Marvin B. Lieberman, 1984. "The Learning Curve and Pricing in the Chemical Processing Industries," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 213-228, Summer. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Martzoukos, Spiros H & Zacharias, Eleftherios, 2008. "Real Option Games with R&D and Learning Spillovers," MPRA Paper 12686, University Library of Munich, Germany. [Downloadable!]
  2. Pindyck, Robert S., 1990. "Irreversibility, uncertainty, and investment," Working papers 3137-90., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
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  3. Atsuo Utaka, 2001. "The Learning Curve and Durable-Goods Production," Economics Bulletin, Economics Bulletin, vol. 12, pages 1-8. [Downloadable!]
  4. Ralph Siebert, 2002. "Learning by Doing and Multiproduction Effects over the Life Cycle: Evidence from the Semiconductor Industry," CIG Working Papers FS IV 02-23, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG). [Downloadable!]
    Other versions:
  5. Emmanuel Petrakis & Eric Rasmusen & Santanu Roy, 1995. "The Learning Curve in a Competitive Industry," Industrial Organization 9506001, EconWPA. [Downloadable!]
    Other versions:
  6. Siddiqui, Afzal & Fleten, Stein-Erik, 2008. "How to Proceed with Competing Alternative Energy Technologies: a Real Options Analysis," MPRA Paper 7355, University Library of Munich, Germany, revised 04 May 2009. [Downloadable!]
  7. Robert S. Pindyck, 1993. "Investments of Uncertain Cost," NBER Working Papers 4175, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
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