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Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result

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  • John Kennan

    (University of Wisconsin, Madison)

Abstract

The square root function has a unique positive fixed point. This function has the following properties: it is strictly increasing and strictly concave, with f(0)=0, and there are points a>0 and b>0 such that f(b)>a and b>f(b). It is shown that any function from Rn to Rn satisfying these properties has a unique positive fixed point. (Copyright: Elsevier)

Suggested Citation

  • John Kennan, 2001. "Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 893-899, October.
  • Handle: RePEc:red:issued:v:4:y:2001:i:4:p:893-899 DOI: 10.1006/redy.2001.0139
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    More about this item

    Keywords

    fixed points; concavity.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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