IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v5y2013i2p440-455d23266.html
   My bibliography  Save this article

Asymptotic Behavior of a Delay Differential Neoclassical Growth Model

Author

Listed:
  • Akio Matsumoto

    (Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo, 192-0393, Japan)

  • Ferenc Szidarovszky

    (Department of Applied Mathematics, University of Pecs, Ifjusag u. 6, H-7624, Pecs, Hungary)

Abstract

A neoclassical growth model is examined with a special mound-shaped production function. Continuous time scales are assumed and a complete steady state and stability analysis is presented. Fixed delay is then assumed and it is shown how the asymptotic stability of the steady state is lost if the delay reaches a certain threshold, where Hopf bifurcation occurs. In the case of continuously distriubuted delays, we show that with small average delays stability is preserved, then lost at a threshold, then it is regained if the average delay becomes sufficiently large. The occurence of Hopf bifurcation is shown at both critical values.

Suggested Citation

  • Akio Matsumoto & Ferenc Szidarovszky, 2013. "Asymptotic Behavior of a Delay Differential Neoclassical Growth Model," Sustainability, MDPI, vol. 5(2), pages 1-16, January.
    • Handle: RePEc:gam:jsusta:v:5:y:2013:i:2:p:440-455:d:23266
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/5/2/440/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/5/2/440/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richard H. Day, 1983. "The Emergence of Chaos from Classical Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 201-213.
    2. 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.
    3. Luciano Fanti & Piero Manfredi, 2003. "The Solow¡¯S Model With Endogenous Population: A Neoclassical Growth Cycle Model," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 28(2), pages 103-115, December.
    4. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    5. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    6. Richard H. Day, 1994. "Complex Economic Dynamics - Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041413, April.
    7. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    8. J. Barkley Rosser Jr. (ed.), 2004. "Complexity in Economics," Books, Edward Elgar Publishing, volume 0, number 2709.
    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. Matsumoto, Akio & Szidarovszky, Ferenc, 2023. "Delay Solow Model with a Normalized CES Production Function," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 305-323.
    2. Ishtiaq Ali & Sami Ullah Khan, 2022. "Asymptotic Behavior of Three Connected Stochastic Delay Neoclassical Growth Systems Using Spectral Technique," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    3. Shaikhet, Leonid, 2023. "Stability of equilibria of exponential type system of three differential equations under stochastic perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 105-117.

    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. Ishtiaq Ali & Sami Ullah Khan, 2022. "Asymptotic Behavior of Three Connected Stochastic Delay Neoclassical Growth Systems Using Spectral Technique," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    2. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    3. Laurent Cellarier & Richard Day, 2011. "Structural instability and alternative development scenarios," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(3), pages 1165-1180, July.
    4. Fabio Tramontana & Viktor Avrutin, 2014. "Complex endogenous dynamics in a one-sector growth model with differential savings," DEM Working Papers Series 078, University of Pavia, Department of Economics and Management.
    5. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    6. Akio Matsumoto & Ferenc Szidarovszky, 2021. "Delay two-sector economic growth model with a Cobb–Douglas production function," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 341-358, June.
    7. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    8. Tramontana, Fabio & Gardini, Laura & Agliari, Anna, 2011. "Endogenous cycles in discontinuous growth models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1625-1639.
    9. repec:ebl:ecbull:v:3:y:2008:i:41:p:1-14 is not listed on IDEAS
    10. Grassetti, F. & Guzowska, M. & Michetti, E., 2020. "A dynamically consistent discretization method for Goodwin model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    11. Juan Sebastián Pereyra & Juan Gabriel Brida, 2008. "The Solow model in discrete time and decreasing population growth rate," Economics Bulletin, AccessEcon, vol. 3(41), pages 1-14.
    12. Rosser, J. Barkley & Rosser, Marina V, 2023. "A conjoined intellectual journey: Richard H. Day and the journal he founded," Journal of Economic Behavior & Organization, Elsevier, vol. 210(C), pages 83-90.
    13. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    14. J. Farmer & Cameron Hepburn & Penny Mealy & Alexander Teytelboym, 2015. "A Third Wave in the Economics of Climate Change," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(2), pages 329-357, October.
    15. Fausto Cavalli & Alessandra Mainini & Daniela Visetti, 2024. "The role of taxation in an integrated economic-environmental model: a dynamical analysis," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(2), pages 597-626, December.
    16. Dohtani, Akitaka, 2010. "A growth-cycle model of Solow-Swan type, I," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 428-444, November.
    17. Matsumoto, Akio & Szidarovszky, Ferenc, 2023. "Delay Solow Model with a Normalized CES Production Function," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 305-323.
    18. Bohm, Volker & Kaas, Leo, 2000. "Differential savings, factor shares, and endogenous growth cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 965-980, June.
    19. Frédéric Lordon, 1991. "Théorie de la croissance : quelques développements récents [Première partie : la croissance récente]," Revue de l'OFCE, Programme National Persée, vol. 36(1), pages 157-211.
    20. Kyoji Fukao & Koichi Hamada, 1989. "The Fisherian Time Preference and the Ebolution of Capital Ownership Patterns in a Global Economy," NBER Working Papers 3104, National Bureau of Economic Research, Inc.
    21. Fausto Cavalli & Alessandra Mainini & Daniela Visetti, 2024. "The role of taxation in an integrated economic-environmental model: a dynamical analysis," Working Papers 530, University of Milano-Bicocca, Department of Economics.

    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:gam:jsusta:v:5:y:2013:i:2:p:440-455:d:23266. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.