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In this paper, we study a standard exchange economy model with Cobb-Douglastype consumers and give a necessary and sufficient condition for the existenceof an odd period cycle in the Walras-Samuelson (tatonnement) price adjustmentprocess. This is a new application of a recent result characterising theexistence 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 ourcharacterisation, we obtain a numerical example of an exchange economy wherethe price dynamics exhibit an odd period cycle but no period three cycle.

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