ABSTRACT
The contribution of Goodwin (1951) is reconsidered in this study. Goodwin developed a nonlinear accelerator business cycle model and showed that it could generate a stable limit cycle when a stationary point was locally unstable. Considerable effort has been devoted to investigate the dynamic structure of Goodwin’s model since then. However, in the existing literature, not much has yet been revealed with respect to the circumstances under which the stationary point is locally stable. In particular, it is not yet known whether cyclical global dynamics may appear in the stable case. We draw attention to this unexplored case and exhibit the coexistence of multiple limit states, namely a stable stationary point, an unstable limit cycle and a stable limit cycle. Since very few explorations have been made in the global dynamics of the stable case, this study is intended as an investigation of an unexplored aspect of Goodwin’s nonlinear business cycle model.
