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Asymptotic Behavior of a Delay Differential Neoclassical Growth Model

Author

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    4. 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.
    5. 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, December.
    6. J. Barkley Rosser Jr. (ed.), 2004. "Complexity in Economics," Books, Edward Elgar Publishing, volume 0, number 2709.
    7. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    8. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
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    Cited by:

    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. 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.
    3. 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.

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