IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v67y2016icp80-86.html
   My bibliography  Save this article

A note on 2-input neoclassical production functions

Author

Listed:
  • Moysan, Gwenaël
  • Senouci, Mehdi

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

  • Moysan, Gwenaël & Senouci, Mehdi, 2016. "A note on 2-input neoclassical production functions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 80-86.
    • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:80-86
    DOI: 10.1016/j.jmateco.2016.09.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406816301744
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2016.09.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Joan Robinson, 1938. "The Classification of Inventions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 5(2), pages 139-142.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Pierre Barral & Mehdi Senouci, 2018. "Walking on two legs: Growth accounting with labor-saving and capital-saving technical change," Working Papers hal-01709599, HAL.
    4. repec:zib:zbmahj:v:1:y:2021:i:1:p:14-25 is not listed on IDEAS
    5. Saad Labyad & Mehdi Senouci, 2018. "Deriving multiple-input production and utility functions from elasticities of substitution functions ," Working Papers hal-01866275, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gregory Casey & Ryo Horii, 2019. "A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change," ISER Discussion Paper 1051, Institute of Social and Economic Research, Osaka University.
    2. Gene M. Grossman & Elhanan Helpman & Ezra Oberfield & Thomas Sampson, 2017. "Balanced Growth Despite Uzawa," American Economic Review, American Economic Association, vol. 107(4), pages 1293-1312, April.
    3. Danny Givon, 2006. "Factor Replacement versus Factor Substitution, Mechanization and Asymptotic Harrod Neutrality," DEGIT Conference Papers c011_028, DEGIT, Dynamics, Economic Growth, and International Trade.
    4. Manuel García‐Santana & Josep Pijoan‐Mas & Lucciano Villacorta, 2021. "Investment Demand and Structural Change," Econometrica, Econometric Society, vol. 89(6), pages 2751-2785, November.
    5. Gene M. Grossman & Elhanan Helpman & Ezra Oberfield & Thomas Sampson, 2021. "Endogenous Education and Long-Run Factor Shares," American Economic Review: Insights, American Economic Association, vol. 3(2), pages 215-232, June.
    6. Jones, C.I., 2016. "The Facts of Economic Growth," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 3-69, Elsevier.
    7. Pengfei Zhang, 2023. "Endogenous capital-augmenting R&D, intersectoral labor reallocation, and the movement of the labor share," Journal of Economics, Springer, vol. 140(1), pages 1-36, September.
    8. Sriket, Hongsilp & Suen, Richard M.H., 2022. "Sources of economic growth in models with non-renewable resources," Journal of Macroeconomics, Elsevier, vol. 72(C).
    9. Irmen, Andreas, 2011. "Steady-state growth and the elasticity of substitution," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1215-1228, August.
    10. Jakub Growiec, 2019. "The Hardware-Software Model: A New Conceptual Framework of Production, R&D, and Growth with AI," KAE Working Papers 2019-042, Warsaw School of Economics, Collegium of Economic Analysis.
    11. Jakub Growiec & Peter McAdam & Jakub Mućk, 2021. "On the Optimal Labor Income Share," International Journal of Central Banking, International Journal of Central Banking, vol. 17(70), pages 1-52, October.
    12. Nikolaos Charalampidis, 2020. "The U.S. Labor Income Share And Automation Shocks," Economic Inquiry, Western Economic Association International, vol. 58(1), pages 294-318, January.
    13. Dongya Koh & Raül Santaeulàlia-Llopis, 2017. "Countercyclical Elasticity of Substitution," Working Papers 946, Barcelona School of Economics.
    14. Mehdi Senouci & Hugo Mauron, 2020. "A new model of technical change and an application to the Solow model," Working Papers hal-02919860, HAL.
    15. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    16. Fabian Stöckl, 2020. "Is Substitutability the New Efficiency? Endogenous Investment in the Elasticity of Substitution between Clean and Dirty Energy," Discussion Papers of DIW Berlin 1886, DIW Berlin, German Institute for Economic Research.
    17. Manuel A. Gómez, 2020. "Factor substitution, long‐run growth, and speed of convergence in the one‐sector convex endogenous‐growth model," Metroeconomica, Wiley Blackwell, vol. 71(1), pages 2-21, February.
    18. Paul, Saumik, 2019. "A Decline in Labor's Share with Capital Accumulation and Complementary Factor Inputs: An Application of the Morishima Elasticity of Substitution," IZA Discussion Papers 12219, Institute of Labor Economics (IZA).
    19. Basso, Henrique S. & Jimeno, Juan F., 2021. "From secular stagnation to robocalypse? Implications of demographic and technological changes," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 833-847.
    20. Irmen, Andreas, 2018. "A Generalized Steady-State Growth Theorem," Macroeconomic Dynamics, Cambridge University Press, vol. 22(4), pages 779-804, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:80-86. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.