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Quasi-Concavity

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Abstract

A real function f defined on a convex subset C of a linear space E is said to be quasi-concave if

$$ x, y\in C, t\in \left[0,1\right]\Rightarrow f\left( tx+\left(1- t\right) y\right)\ge \mathrm{M}\mathrm{i}\mathrm{n}\left[ f(x), f(y)\right]. $$

A function g is said to be quasi-convex if – g is quasi-concave. Concave functions are quasi-concave, convex functions are quasi-convex.

This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume

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Bibliography

  • An important and up to date discussion of quasiconcavity and related topics with their applications for economics as well as for mathematical programming can be found in Generalized concavity in optimization and economics, a collection of papers by several authors edited by S. Schaible and W.T. Ziemba (New York: Academic Press, 1981).

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  1. http://link.springer.com/referencework/10.1057/978-1-349-95121-5

    J.-P. Crouzeix

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  1. J.-P. Crouzeix
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    Crouzeix, JP. (2008). Quasi-Concavity. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_1863-2

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    • DOI: https://doi.org/10.1057/978-1-349-95121-5_1863-2

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    • Publisher Name: Palgrave Macmillan, London

    • Online ISBN: 978-1-349-95121-5

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    Chapter history

    1. Latest

      Quasi-Concavity
      Published:
      13 March 2017

      DOI: https://doi.org/10.1057/978-1-349-95121-5_1863-2

    2. Original

      Quasi-Concavity
      Published:
      30 November 2016

      DOI: https://doi.org/10.1057/978-1-349-95121-5_1863-1

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