IDEAS home Printed from https://ideas.repec.org/a/wly/soecon/v82y2015i2p408-415.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.4284/0038-4038-2013.202
    Download Restriction: no
    File URL: https://libkey.io/10.4284/0038-4038-2013.202?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
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    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. 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).

    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. repec:wly:soecon:v:82:2:y:2015:p:408-415 is not listed on IDEAS
    2. Stephen K. Layson, 2015. "The increasing returns to scale CES production function and the law of diminishing marginal returns," Southern Economic Journal, Southern Economic Association, vol. 82(2), pages 408-415, October.
    3. Matthew K. Heun & João Santos & Paul E. Brockway & Randall Pruim & Tiago Domingos & Marco Sakai, 2017. "From Theory to Econometrics to Energy Policy: Cautionary Tales for Policymaking Using Aggregate Production Functions," Energies, MDPI, vol. 10(2), pages 1-44, February.
    4. Henningsen, Arne & Henningsen, Geraldine & van der Werf, Edwin, 2019. "Capital-labour-energy substitution in a nested CES framework: A replication and update of Kemfert (1998)," Energy Economics, Elsevier, vol. 82(C), pages 16-25.
    5. Paul E. Brockway & Matthew K. Heun & João Santos & John R. Barrett, 2017. "Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation," Energies, MDPI, vol. 10(2), pages 1-23, February.
    6. Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
    7. Dongya Koh & Raül Santaeulàlia-Llopis, 2017. "Countercyclical Elasticity of Substitution," Working Papers 946, Barcelona School of Economics.
    8. repec:zbw:bofrdp:2016_016 is not listed on IDEAS
    9. Trenczek, Jan & Wacker, Konstantin M., 2023. "Human Capital Misallocation and Output per Worker Differences: Beyond Cobb-Douglas," GLO Discussion Paper Series 1331, Global Labor Organization (GLO).
    10. A. Kamaletdinov Sh. & A. Ksenofontov A. & А. Камалетдинов Ш. & А. Ксенофонтов А., 2018. "Моделирование Доходов Социально-Экономических Систем На Основе Производственной Функции // Modeling Of Income Of Socio-Economic Systems On The Basis Of The Production Function," Финансы: теория и практика/Finance: Theory and Practice // Finance: Theory and Practice, ФГОБУВО Финансовый университет при Правительстве Российской Федерации // Financial University under The Government of Russian Federation, vol. 22(1), pages 118-127.
    11. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    12. Takuma Kunieda & Akihisa Shibata, 2024. "Insurance against Aggregate Shocks," KIER Working Papers 1102, Kyoto University, Institute of Economic Research.
    13. Valeria Costantini & Francesco Crespi & Elena Paglialunga, 2019. "Capital–energy substitutability in manufacturing sectors: methodological and policy implications," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 9(2), pages 157-182, June.
    14. Jakub Growiec & Michał Gradzewicz & Jan Hagemejer & Zofia Jankiewicz & Piotr Popowski & Katarzyna Puchalska & Paweł Strzelecki & Joanna Tyrowicz, 2015. "Rola usług rynkowych w procesach rozwojowych gospodarki Polski," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 2, pages 163-193.
    15. Bretschger, Lucas & Jo, Ara, 2024. "Complementarity between labor and energy: A firm-level analysis," Journal of Environmental Economics and Management, Elsevier, vol. 124(C).
    16. Mangin, Sephorah, 2017. "A theory of production, matching, and distribution," Journal of Economic Theory, Elsevier, vol. 172(C), pages 376-409.
    17. Sebastian Gechert & Tomas Havranek & Zuzana Irsova & Dominika Kolcunova, 2022. "Measuring Capital-Labor Substitution: The Importance of Method Choices and Publication Bias," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 45, pages 55-82, July.
    18. Broadberry, Stephen & Ghosal, Sayantan & Proto, Eugenio, 2017. "Anonymity, efficiency wages and technological progress," Journal of Development Economics, Elsevier, vol. 127(C), pages 379-394.
    19. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2022. "Expectations, self-fulfilling prophecies and the business cycle," Working Papers hal-03923946, HAL.
    20. Kan, Kamhon & Wang, Yong, 2013. "Comparing China and India: A factor accumulation perspective," Journal of Comparative Economics, Elsevier, vol. 41(3), pages 879-894.
    21. Laeven, Luc & McAdam, Peter & Popov, Alexander, 2023. "Credit shocks, employment protection, and growth:firm-level evidence from spain," Journal of Banking & Finance, Elsevier, vol. 152(C).
    22. Kenneth G. Stewart & Jiang Li, 2018. "Are factor biases and substitution identifiable? The Canadian evidence," Canadian Journal of Economics, Canadian Economics Association, vol. 51(2), pages 528-548, May.

    More about this item

    Statistics

    Access and download statistics

    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:wly:soecon:v:82:y:2015:i:2:p:408-415. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)2325-8012 .

    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.