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A note on concavity, homogeneity and non-increasing returns to scale

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  • Prada-Sarmiento, Juan David

Abstract

This paper provides a simple proof of the result that if a production function is homogeneous, displays non-increasing returns to scale, is increasing and quasiconcave, then it is concave. If the function is strictly quasiconcave or one-to-one, homogeneous, displays decreasing returns to scale and if either it is increasing or if \mathbf{0} is in its domain, then it is strictly concave. Finally it is shown that we cannot dispense with these assumptions.

Suggested Citation

  • Prada-Sarmiento, Juan David, 2010. "A note on concavity, homogeneity and non-increasing returns to scale," MPRA Paper 27499, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:27499
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    References listed on IDEAS

    as
    1. Bone, John, 1989. "A Note on Concavity and Scalar Properties in Production," Bulletin of Economic Research, Wiley Blackwell, vol. 41(3), pages 213-217, July.
    2. Friedman, James W, 1973. "Concavity of Production Functions and Non-Increasing Returns to Scale," Econometrica, Econometric Society, vol. 41(5), pages 981-984, September.
    3. Ardeshir Dalal, 2000. "Strict concavity with homogeneity and decreasing returns to scale," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 28(3), pages 381-382, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Homogeneity; Concavity; Non-Increasing Returns to Scale; Production Function;
    All these keywords.

    JEL classification:

    • D20 - Microeconomics - - Production and Organizations - - - General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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