ABSTRACT
Introduction Over the last four decades a significant body of literature has emerged inspired by Goodwin’s (1967, 1972) approach to growth cycle modelling. Vela K. Velupillai (see, for example, Velupillai 1979, 1982a, 1982b, 1983, 2006 and Fitoussi and Velupillai 1987) – in his path to developing an approach to macrodynamic modelling rooted in the Cambridge tradition and in particular in Goodwin’s model and Kaldor’s theory of income distribution and technical progress – has contributed importantly to this literature. With respect to Goodwin’s model, he has among other things concentrated on how to relax the extreme (‘classical’) assumption about savings behaviour originally made by Goodwin and on how to remove from the model the assumption of equilibrium in the goods market (an assumption in contrast with the spirit of previous contributions by Goodwin himself, e.g. Goodwin 1948, 1951). In doing this, he has also strongly emphasised the importance of bifurcation theory – in particular of the Hopf bifurcation theorem – for a qualitative analysis of macrodynamic models with three-dimensional – or higher – dynamical systems. This chapter builds on these basic recurring themes of Vela’s work with the purpose of highlighting their relevance for growth cycle modelling. My purpose is in particular to build a growth cycle model with both differential savings propensities and disequilibrium in the goods market. This is done in order to show (1) that both modifications of the model entail an increase of the dimensionality of the state-space of its dynamical system and (2) that the resulting fourdimensional, nonlinear dynamical system has a structure such that the existence part of the Hopf bifurcation theorem can be easily applied. The remainder of the chapter is organised as follows. In the first section we give a brief overview of the modified version of the model. The next section discusses the dynamics of the model, giving both conditions for limit cycle solutions and some numerical evidence. A few concluding and summarising results are finally given in the last section.
