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| Tomohiro Uchiyama |
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| ''Characterising the existence of an odd period cycle in price dynamics for an exchange economy'' |
| ( 2024, Vol. 44 No.3 ) |
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| 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. |
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| Keywords: chaos, odd period cycle, exchange economy, price dynamics |
JEL: E3 - Prices, Business Fluctuations, and Cycles: General (includes Measurement and Data)
D5 - General Equilibrium and Disequilibrium: General |
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| Manuscript Received : Feb 21 2024 | | Manuscript Accepted : Sep 30 2024 |
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