Chaotic Behavior in a Modified Goodwin's Growth Cycle Model

Claudio Tebaldi
Department of Mathematics, Politecnico of Torino

Giorgio Colacchio
Faculty of Law, University of Lecce

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     Last modified: May 26, 2006

Abstract
The model introduced by Goodwin [1967] in “A Growth Cycle” represents a milestone in the non-linear modeling of economic dynamics. On the basis of few simple assumptions, the Goodwin Model (GM) is formulated exactly as the well-known Lotka-Volterra system, in terms of the two variables “wage share” and “employment rate”. A number of extensions have been proposed with the aim to make the model more robust, in particular to obtain structural stability, lacking in GM original formulation. We propose a new extension that: a) introduces the concept of “learning-by-doing” on the line of Lotka-Volterra models with behavioral adaptation b) considers a new specification, more realistic than “Harrod-neutral”, of technical progress. As a consequence an additional equation appears, the validity of the model is substantially extended and a rich phenomenology is obtained, in particular transitions to chaos via multiple cascades of period-doubling/period halving bifurcations.