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A note on 2-input neoclassical production functions

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  • Gwenaël Moysan

    (Global market solutions)

  • Mehdi Senouci

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

Abstract

In this short note, we show how the space of elasticity of substitution functions maps into the space of 2-input neoclassical production functions. In doing so we derive a general analytical formula for every 2-input neoclassical production function of class C2. We present a simple set of sufficient conditions for the Inada conditions to hold; and prove that the Solow model under capital-augmenting (or investment-specific) technical change is asymptotically balanced if and only if the capital share converges to a non-degenerated limit as the capital-labor ratio tends to infinity.

Suggested Citation

  • Gwenaël Moysan & Mehdi Senouci, 2016. "A note on 2-input neoclassical production functions," Post-Print hal-01383290, HAL.
    • Handle: RePEc:hal:journl:hal-01383290
    DOI: 10.1016/j.jmateco.2016.09.011
    Note: View the original document on HAL open archive server: https://hal.science/hal-01383290
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    References listed on IDEAS

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    1. Brent Neiman, 2014. "The Global Decline of the Labor Share," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(1), pages 61-103.
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    3. Ben R. Craig & William E. Jackson & James B. Thomson, 2004. "On SBA-guaranteed lending and economic growth," Working Papers (Old Series) 0403, Federal Reserve Bank of Cleveland.
    4. Palivos, Theodore & Karagiannis, Giannis, 2010. "The Elasticity Of Substitution As An Engine Of Growth," Macroeconomic Dynamics, Cambridge University Press, vol. 14(5), pages 617-628, November.
    5. H. Uzawa, 1961. "Neutral Inventions and the Stability of Growth Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 117-124.
    6. Greenwood, Jeremy & Hercowitz, Zvi & Krusell, Per, 1997. "Long-Run Implications of Investment-Specific Technological Change," American Economic Review, American Economic Association, vol. 87(3), pages 342-362, June.
    7. Revankar, Nagesh S, 1971. "A Class of Variable Elasticity of Substitution Production Functions," Econometrica, Econometric Society, vol. 39(1), pages 61-71, January.
    8. Charles I. Jones & Dean Scrimgeour, 2008. "A New Proof of Uzawa's Steady-State Growth Theorem," The Review of Economics and Statistics, MIT Press, vol. 90(1), pages 180-182, February.
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    Cited by:

    1. Pierre Barral & Mehdi Senouci, 2018. "Walking on two legs: Growth accounting with labor-saving and capital-saving technical change," Post-Print hal-01709599, HAL.
    2. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    3. repec:zib:zbmahj:v:1:y:2021:i:1:p:14-25 is not listed on IDEAS
    4. Saad Labyad & Mehdi Senouci, 2018. "Deriving multiple-input production and utility functions from elasticities of substitution functions ," Working Papers hal-01866275, HAL.
    5. Pierre Barral & Mehdi Senouci, 2018. "Walking on two legs: Growth accounting with labor-saving and capital-saving technical change," Working Papers hal-01709599, HAL.

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    Keywords

    Production function; Elasticity of substitution; Capital share; Labor share; Solow model;
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