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The increasing returns to scale CES production function and the law of diminishing marginal returns

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  • Stephen K. Layson

Abstract

This article analyzes the constant elasticity of substitution (CES) production function when there are increasing returns to scale and the elasticity of substitution exceeds 1, which I refer to as the explosive case of the CES. For this explosive case of the CES, the article demonstrates a new and surprising result: marginal and average products of labor and capital approach infinity as either labor or capital approach infinity. Obviously, in this explosive case of the CES, the law of diminishing marginal returns is eventually violated in a dramatic way. Some implications of this result for growth theory are discussed. The article concludes by deriving, for this explosive case of the CES, lower and upper bounds for the capital labor ratio which are consistent with the law of diminishing marginal returns.

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  • Stephen K. Layson, 2015. "The increasing returns to scale CES production function and the law of diminishing marginal returns," Southern Economic Journal, John Wiley & Sons, vol. 82(2), pages 408-415, October.
    • Handle: RePEc:wly:soecon:v:82:y:2015:i:2:p:408-415
    DOI: 10.4284/0038-4038-2013.202
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    1. Szakolczai, Gyorgy & Stahl, Janos, 1969. "Increasing or Decreasing Returns to Scale in the Constant Elasticity of Substitution Production Function," The Review of Economics and Statistics, MIT Press, vol. 51(1), pages 84-90, February.
    2. Keting Shen & John Whalley, 2013. "Capital-Labor-Energy Substitution in Nested CES Production Functions for China," NBER Working Papers 19104, National Bureau of Economic Research, Inc.
    3. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.
    4. Xi CHEN, 2012. "Estimation of the CES Production Function with Biased Technical Change: A Control Function Approach," Working Papers of BETA 2012-20, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
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    Cited by:

    1. Dong, Kangyin & Dou, Yue & Jiang, Qingzhe, 2022. "Income inequality, energy poverty, and energy efficiency: Who cause who and how?," Technological Forecasting and Social Change, Elsevier, vol. 179(C).

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