Modelling chaotic behaviour in agricultural prices using a discrete deterministic nonlinear price model

In economic modelling, the generally used deterministic equilibrium models cannot describe the ‘random-looking’ oscillations and irregular motions often observed in real time series. Recently, many publications have dealt with chaos in economic processes, but the majority of them used rather difficult nonlinear mathematical functions. Furthermore, chaotic behaviour emerged most often in parameter ranges that are difficult to interpret as economically meaningful values. The present paper analyses the behaviour of a discrete deterministic nonlinear model of supply and demand of a single product with many producers on the market. Market supply is determined by the producers' price expectations, the actual price is the market clearing price. This linear cobweb model is made a piecewise linear one by putting a lower and an upper limit on the expected prices and the real market price. The sensitivity of the model to a wide range of negative values of the price elasticity coefficient is 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 deterministic price model without any stochastic component is fully capable of producing irregular oscillations, fluctuations often observed in real price series. Furthermore, it was possible to achieve this behaviour with a simple, piecewise linear cobweb model, with parameters that have straightforward economic meaning, within realistic parameter ranges. A simple method of linear coupling is applied to show that price stabilisation can always be achieved by using two control parameters, which can be attributed a sound economic meaning.