Convexity, concavity, super-additivity, and sub-additivity of cost function without fixed cost

Yasuhito Tanaka and Masahiko Hattori

MPRA Paper from University Library of Munich, Germany

Abstract: With zero fixed cost, convexity of a cost function implies super-additivity, and concavity of a cost function implies sub-additivity. But converse relations do not hold. However, in addition to the zero fixed cost condition we put the following assumption. (1) If a cost function is convex in some interval, it is convex throughout the domain. (2) If a cost function is concave in some interval, it is concave throughout the domain. Then, super-additivity implies convexity and sub-additivity implies concavity. Subsequently, super-additivity and convexity are equivalent, and sub-additivity and concavity are equivalent.

Keywords: cost function; convexity; concavity; super-additivity; sub-additivity (search for similar items in EconPapers)
JEL-codes: D43 L13 (search for similar items in EconPapers)
Date: 2017-07-31
New Economics Papers: this item is included in nep-mic
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Citations: View citations in EconPapers (1)

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