On the origin of r-concavity and related concepts

Tamás L. Balogh and Christian Ewerhart

No 187, ECON - Working Papers from Department of Economics - 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.

Keywords: Generalized concavity; r-concavity; ρ-concavity; nonlinear optimization; economic applications (search for similar items in EconPapers)
JEL-codes: C6 D0 Y8 (search for similar items in EconPapers)
Date: 2015-02
New Economics Papers: this item is included in nep-his
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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