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On the origin of r-concavity and related concepts


Balogh, Tamás L; Ewerhart, Christian (2015). On the origin of r-concavity and related concepts. Working paper series / Department of Economics 187, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C6, D0, Y8
Uncontrolled Keywords:Generalized concavity, r-concavity, ρ-concavity, nonlinear optimization, economic applications, Konkavität, Nichtlineare Optimierung, Anwendung, Ökonometrie
Language:English
Date:February 2015
Deposited On:03 Mar 2015 13:59
Last Modified:16 Mar 2022 08:06
Series Name:Working paper series / Department of Economics
Number of Pages:26
ISSN:1664-7041
OA Status:Green
Official URL:http://www.econ.uzh.ch/static/wp/econwp187.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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