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

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.