Order and disorder in business cycles

It is shown that a very simple business cycle model of the multiplier-accelerator type can produce chaotic motion. The model uses a cubic approximation of the nonlinear floor–roof type of investment function, and a two-period distributed lag for consumption. It can be cast as a cubic iterative map for income differences, so that chaotic motion for the differences results in Brownian random walk for income itself. The case can be analyzed by means similar to those used in the study of the iterated quadratic mapping. The cubic, except being based on economic principles, has the advantage over the quadratic that it produces cyclical change. In the fast process for income differences the slowly moving income itself becomes a parameter responsible for feedback causing bifurcations between chaotic and ordered behaviour.