, Volume 61, Issue 2, pp 261-280

Increasing quasiconcave co-radiant functions with applications in mathematical economics

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Abstract

We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In particular we identify a small “natural” infimal generator of the set of all coradiant quasiconcave increasing functions. We use this generator to examine two duality schemes for these functions: classical duality often used in microeconomic analysis and a more recent duality concept. Some possible applications to the theory of production functions and utility functions are discussed.

Manuscript received: February 2004/Accepted: June 2004
The research of this author was supported in part by the Ministerio de Ciencia y Tecnología, project BEC2002-00642, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya, grant SGR2001-00162. He also thanks for the support of the Barcelona Economics Program of CREA.
The research of this author was supported by the Australian Research Council.