Persistent and irregular growth cycles when workers save: a reformulation of Goodwin's model along Kaldorian-Pasinettian lines

The purpose of this paper is to study the influence of workers' savings on the dynamics of Goodwin's growth cycles. This is done by noticing, along Kaldorian-Pasinettian lines, that if workers save, then they hold part of the capital and earn some profits, which vary over the cycle. Thus, a correct specification of such a case requires the consideration of an extra variable - the share of capital held by workers. It is shown that, without having to impose any special condition on the values of the parameters, a Hopf-Bifurcation analysis establishes the possibility of persistent and bounded cyclical paths for the resulting 3-dimensional dynamical system. The paper concludes with an investigation of the possibility of further bifurcations as a route to more complex behaviour