Periodic, almost periodic and chaotic behaviour in Hicks' non-linear trade cycle model

Abstract

Hicks' non-linear trade cycle model is an unstable multiplier-accelerator model together with an ‘income ceiling’ and an ‘investment floor’. We show that in the simplest, two-dimensional version of the model the income time paths are always regular: either periodic or almost periodic (quasi-periodic) behaviour occurs. When consumption and/or investment is distributed over several time periods, higher dimensional versions of the model are obtained. We show that in the three-dimensional Hicks model irregular, chaotic income time paths may occur.