Taxation, income redistribution and debt dynamics in a seven-equation model of the business cycle

In this paper we investigate the economic dynamics of a seven-equation model of the business cycle. The main distinctive features of the model are related to: (a) the role played by the public sector in redeploying income between workers and capitalists, since it is assumed that the bargaining power of the two classes affects tax rates and transfers levied upon them; (b) the influence that past events have on the agents’ current behavior, with particular regard to consumption patterns; (c) the specification of firms’ investment function, which incorporate Keynesian and Harrodian elements by assuming that investments are a function of both the difference between interest and profit rate and the discrepancy between actual and desired capital to output ratio. Since all these assumptions imply possible balance sheets disequilibrium, particular regard is dedicated to the analysis of macroagents’ debt dynamics. Special emphasis is placed on the analysis of the destabilization of equilibria via Hopf bifurcations, which leads to the emergence of an interesting and rich cyclical dynamics.