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A generalized business cycle model with delays in gross product and capital stock

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  • Hattaf, Khalid
  • Riad, Driss
  • Yousfi, Noura

Abstract

In this work, we propose a delayed business cycle model with general investment function. The time delays are introduced into gross product and capital stock, respectively. We first prove that the model is mathematically and economically well posed. In addition, the stability of the economic equilibrium and the existence of Hopf bifurcation are investigated. Our main results show that both time delays can cause the macro-economic system to fluctuate and the economic equilibrium to lose or gain its stability. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the normal form method and center manifold theory. Furthermore, the models and results presented in many previous studies are improved and generalized.

Suggested Citation

  • Hattaf, Khalid & Riad, Driss & Yousfi, Noura, 2017. "A generalized business cycle model with delays in gross product and capital stock," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 31-37.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:31-37
    DOI: 10.1016/j.chaos.2017.03.001
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    References listed on IDEAS

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    1. Riad, Driss & Hattaf, Khalid & Yousfi, Noura, 2016. "Dynamics of a delayed business cycle model with general investment function," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 110-119.
    2. Xiaoqin P. Wu, 2009. "Simple-Zero and Double-Zero Singularities of a Kaldor-Kalecki Model of Business Cycles with Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-29, February.
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    Cited by:

    1. Hartwig, Johannes, 2022. "Semi-endogenous growth dynamics in a macroeconomic model with delays," Structural Change and Economic Dynamics, Elsevier, vol. 62(C), pages 538-551.
    2. Wenjie Hu & Hua Zhao & Tao Dong, 2018. "Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect," Complexity, Hindawi, vol. 2018, pages 1-11, January.
    3. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    4. Aleksander Grzelak & Piotr Kułyk, 2020. "Is Michał Kalecki's theory of investment applicable today? The case study of agricultural holdings in the EU countries," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 66(7), pages 317-324.

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    1. Wenjie Hu & Hua Zhao & Tao Dong, 2018. "Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect," Complexity, Hindawi, vol. 2018, pages 1-11, January.
    2. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.

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