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Hicks’ trade cycle revisited: cycles and bifurcations

Author

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  • Gallegati, M.
  • Gardini, L.
  • Puu, T.
  • Sushko, I.

Abstract

In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is needed to have non explosive outcome if the equilibrium point is an unstable focus. It will also be shown that when the fixed point is unstable the attracting set has a particular structure: It is a one-dimensional closed invariant curve, made up of a finite number of linear pieces, on which the dynamics are either periodic or quasi-periodic. The conditions under which the model produces periodic or quasi-periodic trajectories and the related bifurcations as a function of the main economic parameters are determined.

Suggested Citation

  • Gallegati, M. & Gardini, L. & Puu, T. & Sushko, I., 2003. "Hicks’ trade cycle revisited: cycles and bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 505-527.
    • Handle: RePEc:eee:matcom:v:63:y:2003:i:6:p:505-527
    DOI: 10.1016/S0378-4754(03)00060-0
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    References listed on IDEAS

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    1. Arnold Heertje & Peter Heemeijer, 2002. "On the Origin of Samuelson's Multiplier-Accelerator Model," History of Political Economy, Duke University Press, vol. 34(1), pages 207-218, Spring.
    2. Hommes, Cars H., 1993. "Periodic, almost periodic and chaotic behaviour in Hicks' non-linear trade cycle model," Economics Letters, Elsevier, vol. 41(4), pages 391-397.
    3. Hommes, Cars H., 1995. "A reconsideration of Hicks' non-linear trade cycle model," Structural Change and Economic Dynamics, Elsevier, vol. 6(4), pages 435-459, December.
    4. James J. Duesenberry, 1950. "Hicks on the Trade Cycle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 64(3), pages 464-476.
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    Cited by:

    1. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
    2. Puu, Tonu & Gardini, Laura & Sushko, Irina, 2005. "A Hicksian multiplier-accelerator model with floor determined by capital stock," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 331-348, March.
    3. Zhusubaliyev, Zhanybai T. & Soukhoterin, Evgeniy & Mosekilde, Erik, 2007. "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 364-377.

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