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

Abstract

In economic modelling, a frequent problem is that the generally used deterministic equilibrium models cannot describe the ‘random-looking’ oscillations and irregular motions often observed in real time series. Nonlinear chaotic models offer a way to produce this behaviour without the introduction of stochastic elements. Recently, many publications have dealt with chaos in economic processes, but the majority of them used rather difficult mathematical functions to model these processes. 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 non-linear model of supply and demand of a single product with many producers on the market. N producers operate in the market of a single product; their production technology is described by a quadratic cost function. They produce the amount which maximises their gain considering an expected market price in the next time period. The demand function is d(t) = D∗p(t) + d, a linear function of the p( t) real market price, and the real market price is the value which balances the total supply from the N producers and the total demand in the market. This linear 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 D is tested. As the value of D 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 above 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, in realistic parameter ranges. If parameters have sound meaningful values, then chaotic models can direct the attempts made at price stabilization by describing clearly which is the parameter range the decision maker has to avoid in order to reach a stable or regular behaviour.