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Log-concave functions and transformations thereof

Author

Listed:
  • Dihan Zou

Abstract

I summarize Bagnoli and Bergstrom (2005)'s review on log-concave functions, make several corrections, and augment the discussion with further results that can be useful in obtaining monotone hazard rate. I also provide an application of monopoly pricing, where strict logconcavity of demand curve implies strict concavity of the revenue function.

Suggested Citation

  • Dihan Zou, 2025. "Log-concave functions and transformations thereof," Papers 2512.07768, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2512.07768
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    File URL: http://arxiv.org/pdf/2512.07768
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    References listed on IDEAS

    as
    1. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
    2. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    3. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
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    Cited by:

    1. Jiaming Wei & Dihan Zou, 2025. "Regulating a Monopolist without Subsidy," Papers 2512.06525, arXiv.org, revised Feb 2026.
    2. Hiroto Sato & Ryo Shirakawa, 2025. "Allocating Common-Value Goods," Papers 2512.20001, arXiv.org, revised Apr 2026.

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