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Abstract Concavity of Increasing Co-radiant and Quasi-Concave Functions with Applications in Mathematical Economics

Abstract

In this paper, we study nonnegative, increasing, co-radiant and quasi-concave functions over real locally convex topological vector spaces. Such functions have frequently been employed in microeconomic analysis. We next characterize the abstract concavity, the upper support set and the superdifferential of this class of functions by applying a type of duality, which is used in microeconomic theory.

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Acknowledgments

The authors are very grateful to the anonymous referees for their useful suggestions on an earlier version of this paper. The comments of the referees were very fruitful, and these comments have enabled the authors to improve the paper significantly.

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Correspondence to H. Mohebi.

Additional information

Communicated by Constantin Zalinescu.

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Mirzadeh, S., Mohebi, H. Abstract Concavity of Increasing Co-radiant and Quasi-Concave Functions with Applications in Mathematical Economics. J Optim Theory Appl 169, 443–472 (2016). https://doi.org/10.1007/s10957-016-0901-6

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Keywords

  • Abstract concavity
  • Abstract convexity
  • Duality
  • Co-radiant function
  • Quasi-concave function
  • Increasing function
  • Upper semi-continuous function
  • Upper support set
  • Superdifferential
  • Production function

Mathematics Subject Classification

  • 26A48
  • 26B25
  • 90C46