IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/119048.html
   My bibliography  Save this paper

A Note on the Euler Equation of the Growth Model

Author

Listed:
  • Li, defu
  • Bental, Benjamin

Abstract

The neoclassical Euler equation provides the necessary conditions for households to maximize lifetime utility by allocating income between consumption and investment, and is the core equation for solving the steady-state of the neoclassical growth model. The existing textbooks (Barro and Sala-i-Martin, 2004, ch6.3; Acemoglu, 2009, ch13.2, ch15.6; Aghion and Howitt, 2009, ch3.2.2) ignore the premise of this equation and directly apply it to solve the steady state of other growth models, which not only leads to incorrect results but also limits the ability of growth models to analyze the steady-state technological progress direction. This note first points out and rigorously verifies the errors in existing textbooks; Then, by replacing the capital accumulation function with exogenous growth rate with the generalized capital accumulation function considering adjustment costs of investment in the Acemoglu (2009, ch15.6) model, the note put forward the generalized Euler equation and steady-state equilibrium including capital-augmenting technological progress, which reveals the necessary conditions for the neoclassical Euler equation and Uzawa’s (1961) steady-state theorem; Finally, it is pointed out that the possible reasons for the misuse of the neoclassical Euler equation in existing textbooks maybe confuse the rental price of capital and the interest rate of investment.

Suggested Citation

  • Li, defu & Bental, Benjamin, 2023. "A Note on the Euler Equation of the Growth Model," MPRA Paper 119048, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:119048
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/119048/1/MPRA_paper_119048.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    2. Francisco L. Rivera-Batiz & Luis A. Rivera-Batiz, 2018. "Economic Integration and Endogenous Growth," World Scientific Book Chapters, in: Francisco L Rivera-Batiz & Luis A Rivera-Batiz (ed.), International Trade, Capital Flows and Economic Development, chapter 1, pages 3-32, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    5. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    6. Nicholas Kaldor, 1961. "Capital Accumulation and Economic Growth," International Economic Association Series, in: D. C. Hague (ed.), The Theory of Capital, chapter 0, pages 177-222, Palgrave Macmillan.
    Full references (including those not matched with items on IDEAS)

    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. Li, Defu & Bental, Benjamin, 2023. "What determines the Direction of Technological Progress(2023.11.16)?," MPRA Paper 119211, University Library of Munich, Germany, revised 16 Nov 2023.
    2. Li, Defu & Benjamin, Bental, 2021. "Factor Supply Elasticities, Returns to Scale, and the Direction of Technological Progress," MPRA Paper 109920, University Library of Munich, Germany.
    3. 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.
    4. repec:ebl:ecbull:v:2:y:2002:i:1:p:1-15 is not listed on IDEAS
    5. 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.
    6. Li, Defu & Bental, Benjamin, 2019. "A Generalized Growth Model and the Direction of Technological Progress," MPRA Paper 96509, University Library of Munich, Germany.
    7. Ekkehart Schlicht, 2016. "Directed Technical Change and Capital Deepening: A Reconsideration of Kaldor's Technical Progress Function," Metroeconomica, Wiley Blackwell, vol. 67(1), pages 119-151, February.
    8. Roberto Veneziani & Luca Zamparelli & Daniele Tavani & Luca Zamparelli, 2017. "Endogenous Technical Change In Alternative Theories Of Growth And Distribution," Journal of Economic Surveys, Wiley Blackwell, vol. 31(5), pages 1272-1303, December.
    9. Aykut Kibritçioglu, 2002. "On the Smithian origins of "new" trade and growth theories," Economics Bulletin, AccessEcon, vol. 2(1), pages 1-15.
    10. Ekaterina Ponomareva & Alexandra Bozhechkova & Alexandr Knobel, 2012. "Factors of Economic Growth," Published Papers 172, Gaidar Institute for Economic Policy, revised 2013.
    11. Irmen, Andreas & Tabaković, Amer, 2017. "Endogenous capital- and labor-augmenting technical change in the neoclassical growth model," Journal of Economic Theory, Elsevier, vol. 170(C), pages 346-384.
    12. 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.
    13. Li, Defu & Bental, Benjamin, 2016. "What determines the direction of technological progress?," MPRA Paper 71517, University Library of Munich, Germany.
    14. Miguel A León-Ledesma & Peter McAdam & Alpo Willman, 2012. "Non-Balanced Growth and Production Technology Estimation," Studies in Economics 1204, School of Economics, University of Kent.
    15. Pozzolo, Alberto Franco, 2004. "Endogenous Growth in Open Economies - A Survey of Major Results," Economics & Statistics Discussion Papers esdp04020, University of Molise, Department of Economics.
    16. Irmen, Andreas, 2018. "A Generalized Steady-State Growth Theorem," Macroeconomic Dynamics, Cambridge University Press, vol. 22(4), pages 779-804, June.
    17. Jordan Rappaport, 2000. "How does openness to capital flows affect growth?," Research Working Paper RWP 00-11, Federal Reserve Bank of Kansas City.
    18. Gancia, Gino & Zilibotti, Fabrizio, 2005. "Horizontal Innovation in the Theory of Growth and Development," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 3, pages 111-170, Elsevier.
    19. Gene M. Grossman & Elhanan Helpman, 1994. "Endogenous Innovation in the Theory of Growth," Journal of Economic Perspectives, American Economic Association, vol. 8(1), pages 23-44, Winter.
    20. Jakub Growiec, 2008. "A new class of production functions and an argument against purely labor‐augmenting technical change," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 483-502, December.
    21. Frédéric Lordon, 1991. "Théorie de la croissance : quelques développements récents [Deuxième partie : la redécouverte des rendements croissants]," Revue de l'OFCE, Programme National Persée, vol. 37(1), pages 191-243.

    More about this item

    Keywords

    Neoclassical Euler equation; Uzawa’s steady-state theorem; Growth model; the direction of technical change,the rental price of capital; the interest rate of investment;
    All these keywords.

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:119048. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.