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An Improvement to Jensen's Inequality and its Application to Mating Market Clearing when Paternity is Uncertain

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  • Dirk Bethmann

    () (Department of Economics, Korea University, Seoul, Republic of Korea)

Abstract

Jensen's inequality can be tightened in the context of binomially distributed random variables. The suggested new inequality coincides with Jensen's inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensen's. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that can not be obtained when relying on Jensen's inequality.

Suggested Citation

  • Dirk Bethmann, 2015. "An Improvement to Jensen's Inequality and its Application to Mating Market Clearing when Paternity is Uncertain," Discussion Paper Series 1506, Institute of Economic Research, Korea University.
  • Handle: RePEc:iek:wpaper:1506
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    File URL: http://econ.korea.ac.kr/~ri/WorkingPapers/w1506.pdf
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    References listed on IDEAS

    as
    1. John Rust & Christopher Phelan, 1997. "How Social Security and Medicare Affect Retirement Behavior in a World of Incomplete Markets," Econometrica, Econometric Society, vol. 65(4), pages 781-832, July.
    2. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey: Part I," Economic Inquiry, Western Economic Association International, vol. 14(2), pages 155-189, June.
    3. Dirk Bethmann & Michael Kvasnicka, 2011. "The institution of marriage," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(3), pages 1005-1032, July.
    4. Eyal Baharad & Benjamin Eden, 2004. "Price Rigidity and Price Dispersion: Evidence from Micro Data," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(3), pages 613-641, July.
    5. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    6. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey," Economic Inquiry, Western Economic Association International, vol. 14(3), pages 347-368, September.
    7. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
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    More about this item

    Keywords

    Expected Utility; Binomial Distribution; Jensen's Inequality; Mating Market; Uncertain Paternity;

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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