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

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  • Tanaka, Yasuhito
  • Hattori, Masahiko

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.

Suggested Citation

  • Tanaka, Yasuhito & Hattori, Masahiko, 2017. "Convexity, concavity, super-additivity, and sub-additivity of cost function without fixed cost," MPRA Paper 80502, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:80502
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    References listed on IDEAS

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    1. Sen, Debapriya & Stamatopoulos, Giorgos, 2016. "Licensing under general demand and cost functions," European Journal of Operational Research, Elsevier, vol. 253(3), pages 673-680.
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    Cited by:

    1. Tanaka, Yasuhito & Hattori, Masahiko, 2017. "On a strictly convex and strictly sub-additive cost function with positive fixed cost," MPRA Paper 80579, University Library of Munich, Germany.

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    More about this item

    Keywords

    cost function; convexity; concavity; super-additivity; sub-additivity;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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