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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title On the origin of r-concavity and related concepts
Organization Unit
Authors
  • Tamás L Balogh
  • Christian Ewerhart
Language
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 187
ISSN 1664-7041
Number of Pages 26
Date 2015
Abstract Text 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.
Official URL http://www.econ.uzh.ch/static/wp/econwp187.pdf
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Keywords Generalized concavity, r-concavity, ρ-concavity, nonlinear optimization, economic applications, Konkavität, Nichtlineare Optimierung, Anwendung, Ökonometrie