An extended Goodwin model with endogenous technical change and labor supply

Abstract

This paper extends the Goodwin model of distributive cycles by incorporating the simultaneous endogeneity of technical change and labor supply within a classical-Marxian framework. It reinterprets induced innovation, suggesting that firms optimize mechanization to maximize cost reduction, obtaining a micro-founded relationship between mechanization and the wage share. Additionally, it assumes a positive relationship between labor supply and the employment rate. The resulting three-dimensional dynamical system includes wage share, employment rate, and capital-output ratio as state variables. The Hopf bifurcation theorem reveals the emergence of limit cycles as the employment rate's effect on labor productivity (reserve-army-creation effect) approximates a critical value from below. Numerical simulations for 10 OECD countries illustrate the cyclical nature of the model and its consistency with empirical patterns. Furthermore, a sensitivity analysis explores the effect of parameters variations, emphasizing the social dimensions of productivity and labor supply as critical factors defining the stability of distributive cycles.