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 noting, along Kaldorian–Pasinettian lines, that if workers save, they then 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 cyclic 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.