A Classical Marxian Two-Sector Endogenous Cycle Model

This paper presents a Classical Marxian Two-Sector Endogenous Cycle (CMTSEC) model, merging Dutt's two-sector Classical convergence model with labor dynamics drawn from the Goodwin model and an endogenous labor supply inspired by Harris's interpretation of capitalist dynamics. Empirical support reinforces these assumptions. Utilizing the Hopf bifurcation theorem and numerical simulations, we demonstrate the emergence of persistent and stable limit cycles involving the wage share, employment rate, and sectoral capital distribution, all without relying on specific capital intensity discrepancies between sectors. This result challenges existing two-sector models, particularly Sato's extension of the Goodwin model, in which endogenous cycles either do not exist or vanish over time, even when endogenous labor supply is incorporated. Notably, sectoral profit rates exhibit cyclical fluctuations in the CMTSEC model, suggesting a reevaluation of long-run equilibrium. The findings highlight the role of investment sensitivity to sectoral profit rate disparities in determining cycle stability.