Transitions to Chaos in a Seven-Equation Model of the Business Cycle with Income Redistribution and Private Debt

Abstract

In the present paper, we investigate the chaotic implications of a seven-equation model of the business cycle. The main distinguishing features of the model are related to: (a) the role played by the bargaining power in the process of income redistribution; (b) the consideration of hysteresis effects on workers’ consumption demand; (c) the effect of public expenditure on labor productivity. In addition, the role played by the agents’ memory on the actual dynamics of the economic system, with particular regard to their learning-by-doing process, is particularly emphasized. Under all these assumptions, the system exhibits a rich and complex phenomenology, characterized by a number of transitions to chaos (in particular via sequences of period doubling bifurcations), aperiodic behavior, bistability, tristability, etc. We maintain that our analysis takes us another step forward in the building of a more general model of the business cycle. In particular, the model we propose may be of help in the explanation of some peculiar features of advanced capitalist economies, with particular regard to the role played by the State in the determination of agents’ disposable income, to the debt dynamics of the various macroagents, and to the main dilemmas of economic policy. More in general, the main lesson one learns from our investigation is that “disequilibrium paths”, characterized by “complicated” dynamics which, more often than not, takes the form of aperiodic motion, should be considered as the “normal” state of the system.