Some Illustrations Of Chaos In Commodity Models

This paper develops three commodity models which exhibit chaotic behaviour. The examples chosen are a demand system and two cobweb supply and demand models. The latter differ from the standard forms in that they include risk aversion and a new specification for the formation of price expectations. Simulation of the model highlights three implications of chaos: such systems generate complex time-paths even if the exogenous variables within the model are held constant; the simulated time path is critically sensitive to the starting value of variables, and parameter values; and the average behaviour of the system is critically sensitive to parameter and exogenous variable values. ‘Critically sensitive’ means that very small changes in parameter or starting values leads to substantial changes in the time paths of the variables in the model. These results suggest that if real commodity sectors can be characterised as chaotic systems, then the ability to conduct forecasting and policy analysis of such sectors will be severely curtailed.

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