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Increasing quasiconcave co-radiant functions with applications in mathematical economics. (English) Zbl 1090.90142

Math. Methods Oper. Res. 61, No. 2, 261-280 (2005); erratum ibid. 85, No. 3, 521 (2017).
Summary: 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.

MSC:

90C26 Nonconvex programming, global optimization
91B16 Utility theory
91B38 Production theory, theory of the firm
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