Remarks on Fenchel-Moreau conjugate in the setting of consumer theory

George H.M. Cunha, Michel A.C. Oliveira, Michel A.C. Oliveira and Wilfredo Sosa Sandoval ()
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George H.M. Cunha: Catholic University of Brasilia
Michel A.C. Oliveira: Catholic University of Brasilia
Michel A.C. Oliveira: Catholic University of Brasilia

Economia, 2016, vol. 17, issue 2, 176_184

Abstract: In thismanuscriptwe considerthe conjugate notion focused fromconsumertheory as an interesting tool.According to us, conjugate notion remained undeveloped in economic theory because Fenchel's conjugate notion was introduced exclusively for proper convex lower semi continuous functions and convexity assumption is not natural in economic theory. Nevertheless, we introduce necessary and sufficient optimality conditions for consumer problem. Also, we consider a particular version of Fenchel-Moreau conjugate notion, for lower semi continuous functions recently introduced in the literature as a generalization of Fenchel's conjugate. Finally, we adapt it to closed functions in order to define a convex dual problem for consumer problem.

Keywords: Convex analysis; Fenchel's conjugate; Economic theory (search for similar items in EconPapers)
JEL-codes: C02 C61 D11 (search for similar items in EconPapers)
Date: 2016
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