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

Tomohiro Uchiyama ()
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Tomohiro Uchiyama: Faculty of International Liberal Arts, Soka University

Economics Bulletin, 2024, vol. 44, issue 3, 983 - 989

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.

Keywords: chaos; odd period cycle; exchange economy; price dynamics (search for similar items in EconPapers)
JEL-codes: D5 E3 (search for similar items in EconPapers)
Date: 2024-09-30
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