An Extended Goodwin Model for Skill-Polarized Economies under Technological Change

We extend Goodwin’s classical growth-cycle model into a five-dimensional integrodifferential system that captures the dynamic competition between high- and low-skilled labor pools under skill-biased technological change. We develop a dynamic optimal framework to stabilize wage-employment cycles, addressing volatility driven by automation and labor market polarization. Mathematically, we establish the existence of endogenous cycles via a supercritical Hopf bifurcation, thereby formalizing Goodwin’s conjecture within a skill-differentiated economy. We derive Hamiltonian conditions for optimal policy intervention, demonstrating how targeted skill subsidies and automation taxes can suppress bifurcations and guide the system toward a stable equilibrium. The model’s prediction accuracy is empirically confirmed using labor market data from Saudi Arabia (2018–2023) and the OECD (2020–2025), particularly in predicting the rebound in high-skilled wages following the 2008 financial crisis. Our results provide a robust mathematical foundation for cost-effective policy tools, such as robotic taxation and workforce retraining, that promote employment stability while sustaining productivity growth. These insights are particularly relevant for economies undergoing rapid transformation, including those aligned with strategic initiatives like Saudi Vision 2030.