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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, Open Access Journal, 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

    as
    1. Richard H. Day, 1983. "The Emergence of Chaos from Classical Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 201-213.
    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, 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, January.
    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. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
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    More about this item

    Keywords

    neoclassical growth model ; fixed time delay; Hopf bifurcation;

    JEL classification:

    • Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics
    • Q0 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation
    • Q3 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics
    • Q56 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environment and Development; Environment and Trade; Sustainability; Environmental Accounts and Accounting; Environmental Equity; Population Growth
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products

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