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On the origin of r-concavity and related concepts

Author

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  • Tamás L. Balogh
  • Christian Ewerhart

Abstract

In a less widely known contribution, Béla Martos (1966, Hungarian Academy of Sciences) introduced a generalized notion of concavity that is closely related to what is nowadays known as r-concavity in the operations research literature, and that is identical to what is nowadays known as ρ-concavity in the economics literature. The present paper aims at making the original contribution accessible to a wider audience and illustrating its importance from a modern perspective. To this end, we offer a translation of those parts of Martos (1966) that are directly related to generalized concavity. Reviewing the virtues of r-concavity and ρ-concavity, we find a surprisingly short proof of the univariate Prékopa-Borell theorem. We also survey a number of applications of the considered concepts in operations research and economics.

Suggested Citation

  • Tamás L. Balogh & Christian Ewerhart, 2015. "On the origin of r-concavity and related concepts," ECON - Working Papers 187, Department of Economics - University of Zurich.
    • Handle: RePEc:zur:econwp:187
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    References listed on IDEAS

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    More about this item

    Keywords

    Generalized concavity; r-concavity; ρ-concavity; nonlinear optimization; economic applications;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D0 - Microeconomics - - General
    • Y8 - Miscellaneous Categories - - Related Disciplines

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