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Characterising the existence of an odd period cycle in price dynamics for an exchange economy

Author

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  • Tomohiro Uchiyama

    (Faculty of International Liberal Arts, Soka University)

Abstract

In this paper, we study a standard exchange economy model with Cobb-Douglas type consumers and give a necessary and sufficient condition for the existence of an odd period cycle in the Walras-Samuelson (tatonnement) price adjustment process. This is a new application of a recent result characterising the existence of a topological chaos for a unimodal interval map by Deng, Khan, Mitra (2022). Moreover, we show that starting from any positive initial price, the price is eventually attracted to a chaotic region. Using our characterisation, we obtain a numerical example of an exchange economy where the price dynamics exhibit an odd period cycle but no period three cycle.

Suggested Citation

  • Tomohiro Uchiyama, 2024. "Characterising the existence of an odd period cycle in price dynamics for an exchange economy," Economics Bulletin, AccessEcon, vol. 44(3), pages 983-989.
    • Handle: RePEc:ebl:ecbull:eb-24-00073
    as

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    References listed on IDEAS

    as
    1. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2022. "Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos," Journal of Economic Theory, Elsevier, vol. 201(C).
    2. Tomohiro Uchiyama, 2023. "Odd period cycles and ergodic properties in price dynamics for an exchange economy," Papers 2309.09176, arXiv.org, revised Apr 2024.
    3. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658, Enero-Abr.
    4. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723, Enero-Abr.
    5. Benhabib, Jess & Day, Richard H., 1980. "Erratic accumulation," Economics Letters, Elsevier, vol. 6(2), pages 113-117.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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