Modelling chaotic behaviour in agricultural pricesusing a discrete deterministic nonlinear price model

Abstract

In economic modelling, the generally used deterministic equilibrium models cannotdescribe the “random‐looking” oscillations and irregular motions often observed in realtime series. Recently, many publications have dealt with chaos in economic processes, butthe majority of them used rather difficult nonlinear mathematical functions. Furthermore,chaotic behaviour emerged most often in parameter ranges that are difficult to interpret aseconomically meaningful values. The present paper analyses the behaviour of a discretedeterministic nonlinear model of supply and demand of a single product with many producerson the market. Market supply is determined by the producers' price expectations, the actualprice is the market clearing price. This linear cobweb model is made a piecewise linear oneby putting a lower and an upper limit on the expected prices and the real market price. Thesensitivity of the model to a wide range of negative values of the price elasticity coefficientis tested. As this value increases, the model produces various types of steady‐state behaviour,such as equilibrium point, periodic behaviour with increasing periods, “quasiperiodic‐like”behaviour, period‐3 cycle, and chaotic behaviour. The model showed that a deterministicprice model without any stochastic component is fully capable of producing irregular oscillations,fluctuations often observed in real price series. Furthermore, it was possible to achievethis behaviour with a simple, piecewise linear cobweb model, with parameters that havestraightforward economic meaning, within realistic parameter ranges. A simple method oflinear coupling is applied to show that price stabilisation can always be achieved by usingtwo control parameters, which can be attributed a sound economic meaning.