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

Author

Listed:
  • 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
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    File URL: http://www.accessecon.com/Pubs/EB/2024/Volume44/EB-24-V44-I3-P75.pdf
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    More about this item

    Keywords

    chaos; odd period cycle; exchange economy; price dynamics;
    All these keywords.

    JEL classification:

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

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