This paper examines the dynamic property of a macroeconomic model developed by Matsuyama [Am. Econ. Rev. 97(2007), pp. 503-516] in detail. It is shown that the model can be transformed into a version of the neuron model analysed by Hata [J. Math. Kyoto Univ. 22(1982), pp. 155-173, Chaos in Neural Network Models (in Japanese), Asakura, Tokyo 1998] and that the system can exhibit either periodic fluctuations or non-periodic (chaotic) fluctuations.