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Does Cost Uncertainty in the Bertrand Model Soften Competition?

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  • Johan N.M. Lagerlöf

    (Department of Economics, Copenhagen University)

Abstract

The answer is no. Although naive intuition may suggest the opposite, uncertainty about costs in the homogeneous-good Bertrand model intensifies competition: it lowers price and raises total surplus (but also makes profits go up). For some economic environments, this is implied by Hansen’s (RAND, 1988) analysis of a procurement auction. However, several authors appear to have overlooked Hansen’s results. Moreover, his results are derived under two assumptions that, if relaxed, conceivably could reverse them. The contributions of the present paper are threefold. First, it clarifies the implications of Hansen’s results for the relationship between uncertainty and competition in the Bertrand model. Second, it shows that his results hold also if drastic innovations are possible. Finally, the paper assumes asymmetric cost distributions and shows, using numerical methods, that then uncertainty lowers price and raises total surplus even more than under symmetry. If the asymmetry is large enough, however, industry profits are lower under uncertainty. This is in contrast to the known results and reinforces the notion that uncertainty intensifies competition rather than softens it.

Suggested Citation

  • Johan N.M. Lagerlöf, 2013. "Does Cost Uncertainty in the Bertrand Model Soften Competition?," Discussion Papers 14-08, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1408
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    References listed on IDEAS

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    1. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
    2. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
    3. Wayne-Roy Gayle & Jean Richard, 2008. "Numerical Solutions of Asymmetric, First-Price, Independent Private Values Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 32(3), pages 245-278, October.
    4. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    5. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    6. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    7. Arozamena, Leandro & Weinschelbaum, Federico, 2009. "Simultaneous vs. sequential price competition with incomplete information," Economics Letters, Elsevier, vol. 104(1), pages 23-26, July.
    8. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    9. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    10. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
    11. Robert G. Hansen, 1988. "Auctions with Endogenous Quantity," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 44-58, Spring.
    12. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
    13. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
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    More about this item

    Keywords

    Bertrand competition; Hansen Spulber model; private information; information sharing; asymmetric firms; asymmetric auctions; boundary value method;

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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