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The Learning Curve and Optimal Production under Uncertainty

  • Saman Majd
  • Robert S. Pindyck

This article 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 the price exceeds a critical level, which is a declining function of cumulative output. We show how the shadow value of cumulative production, the total value of the firm, and the decision to produce depend on the volatility of the price and other parameters. Uncertainty increases the critical price required for the firm to produce, but also increases the value of the firm. Thus, during periods of high volatility, firms facing a learning curve ought to be producing less, but are worth more.

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

Volume (Year): 20 (1989)
Issue (Month): 3 (Autumn)
Pages: 331-343

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Handle: RePEc:rje:randje:v:20:y:1989:i:autumn:p:331-343
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  1. A. M. Spence, 1981. "The Learning Curve and Competition," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 49-70, Spring.
  2. 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.
  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.
  4. 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.
  5. 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.
  6. Shlomo Kalish, 1983. "Monopolist Pricing with Dynamic Demand and Production Cost," Marketing Science, INFORMS, vol. 2(2), pages 135-159.
  7. 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.
  8. 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.
  9. 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.
  10. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-57, April.
  11. 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.
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