Mathematical Methods of Operations Research

, Volume 61, Issue 2, pp 261–280

Increasing quasiconcave co-radiant functions with applications in mathematical economics

  • Juan Enrique Martínez-Legaz
  • Alexander M. Rubinov
  • Siegfried Schaible
Article

DOI: 10.1007/s001860400405

Cite this article as:
Martínez-Legaz, J., Rubinov, A. & Schaible, S. Math Meth Oper Res (2005) 61: 261. doi:10.1007/s001860400405

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.

Keywords

Abstract convexityDualityCo-radiant functionsQuasiconcave functionsProduction functionsUtility functions

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Juan Enrique Martínez-Legaz
    • 1
  • Alexander M. Rubinov
    • 2
  • Siegfried Schaible
    • 3
  1. 1.CODE and Departament d’Economia i d’Història EconòmicaUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.CIAO and School of Information Technology and Mathematical SciencesUniversity of BallaratBallaratAustralia
  3. 3.A. G. Anderson Graduate School of ManagementUniversity of CaliforniaRiversideUSA