Multiple periodicities in an extended Goodwin model with mechanization, independent investment, and disequilibrium: Toward a Marxian-Keynesian synthesis

This paper proposes an extended Goodwin model that synthesizes Marxian and Keynesian dynamics into a unified four-dimensional framework. The model integrates endogenous technical change via mechanization, investment behavior driven by effective demand, and goods market disequilibrium. We develop two three-dimensional closures–a Classical-Marxian and a Keynesian-Kaleckian formulation–each capable of generating persistent endogenous cycles. These are then combined into a Marxian-Keynesian (MK) system, which exhibits complex dynamics including multiple periodicities. This result points to the potential for interacting oscillatory modes and long-run fluctuations even with relatively simple behavioral rules. Numerical simulations suggest that the MK synthesis captures rich endogenous fluctuations without relying on exogenous shocks and may exhibit chaotic dynamics under future extensions. These findings lay the groundwork for a Marx-Keynes-Schumpeter synthesis of capital instability, as suggested in the conclusion section.