IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/2423.html
   My bibliography  Save this paper

The Learning Curve and Optimal Production Under Uncertainty

Author

Listed:
  • Saman Majd
  • Robert S. Pindyck

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.

Suggested Citation

  • Saman Majd & Robert S. Pindyck, 1987. "The Learning Curve and Optimal Production Under Uncertainty," NBER Working Papers 2423, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:2423 Note: ME
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w2423.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Shlomo Kalish, 1983. "Monopolist Pricing with Dynamic Demand and Production Cost," Marketing Science, INFORMS, vol. 2(2), pages 135-159.
    4. A. M. Spence, 1981. "The Learning Curve and Competition," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 49-70, Spring.
    5. 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.
    6. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    7. 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.
    8. 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 261-265, March.
    9. 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 331-349, June.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pindyck, Robert S., 1993. "Investments of uncertain cost," Journal of Financial Economics, Elsevier, vol. 34(1), pages 53-76, August.
    2. Matthias Göcke & Svetlana Fedoseeva, 2016. "Optimal Monopolist Export Pricing with Dynamic Demand and Learning Curve Effects," Open Economies Review, Springer, vol. 27(3), pages 447-469, July.
    3. Fernandes, Rui & Gouveia, Borges & Pinho, Carlos, 2013. "A real options approach to labour shifts planning under different service level targets," European Journal of Operational Research, Elsevier, vol. 231(1), pages 182-189.
    4. Pindyck, Robert S, 1991. "Irreversibility, Uncertainty, and Investment," Journal of Economic Literature, American Economic Association, vol. 29(3), pages 1110-1148, September.
    5. Van Robays, Ine, 2012. "Macroeconomic uncertainty and the impact of oil shocks," Working Paper Series 1479, European Central Bank.
    6. Savolainen, Jyrki, 2016. "Real options in metal mining project valuation: Review of literature," Resources Policy, Elsevier, vol. 50(C), pages 49-65.
    7. Emmanuel Petrakis & Eric Rasmusen & Santanu Roy, 1997. "The Learning Curve in a Competitive Industry," RAND Journal of Economics, The RAND Corporation, vol. 28(2), pages 248-268, Summer.
    8. Womer, K. & Li, H. & Camm, J. & Osterman, C. & Radhakrishnan, R., 2017. "Learning and Bayesian updating in long cycle made-to-order (MTO) production," Omega, Elsevier, vol. 69(C), pages 29-42.
    9. Davis, Graham A. & Owens, Brandon, 2003. "Optimizing the level of renewable electric R&D expenditures using real options analysis," Energy Policy, Elsevier, vol. 31(15), pages 1589-1608, December.
    10. Adam B. Jaffe & Richard G. Newell & Robert N. Stavins, 2004. "Technology Policy for Energy and the Environment," NBER Chapters,in: Innovation Policy and the Economy, Volume 4, pages 35-68 National Bureau of Economic Research, Inc.
    11. Gonzalo Cortazar & Eduardo S. Schwartz & Marcelo Salinas, 1998. "Evaluating Environmental Investments: A Real Options Approach," Management Science, INFORMS, vol. 44(8), pages 1059-1070, August.
    12. repec:eee:rensus:v:82:y:2018:i:p3:p:2693-2704 is not listed on IDEAS
    13. Ine Van Robays, 2016. "Macroeconomic Uncertainty and Oil Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(5), pages 671-693, October.
    14. Rupert Way & Franc{c}ois Lafond & J. Doyne Farmer & Fabrizio Lillo & Valentyn Panchenko, 2017. "Wright meets Markowitz: How standard portfolio theory changes when assets are technologies following experience curves," Papers 1705.03423, arXiv.org.
    15. Larson, Bruce A., 1992. "Principles of stochastic dynamic optimization in resource management: the continuous-time case," Agricultural Economics of Agricultural Economists, International Association of Agricultural Economists, vol. 7(2), July.
    16. Nicolas P. B. Bollen, 1999. "Real Options and Product Life Cycles," Management Science, INFORMS, vol. 45(5), pages 670-684, May.
    17. Lukas, Elmar, 2013. "Modeling the transitional dynamics of international joint venture policies: An option pricing approach," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 21-36.
    18. Qin, Ruwen & Nembhard, David A., 2010. "Workforce agility for stochastically diffused conditions--A real options perspective," International Journal of Production Economics, Elsevier, vol. 125(2), pages 324-334, June.

    More about this item

    JEL classification:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:2423. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/nberrus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.