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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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  • Bethmann, Dirk

Abstract

Jensen’s inequality can be tightened in the context of discrete 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 cannot be obtained when relying on Jensen’s inequality.

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  • Bethmann, Dirk, 2018. "An improvement to Jensen’s inequality and its application to mating market clearing when paternity is uncertain," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 71-74.
    • Handle: RePEc:eee:matsoc:v:91:y:2018:i:c:p:71-74
    DOI: 10.1016/j.mathsocsci.2017.08.004
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    More about this item

    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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