Frisch Elasticity, Directed Technical Change, and Automation: A Unified Framework for Wage Polarization and Skill Premium Dynamics

This paper examines how labor‐supply responsiveness, captured by the inverse Frisch elasticity, shapes wage inequality in the presence of directed technical change and automation. We develop a dynamic general equilibrium model with task‐based production, heterogeneous labor, and endogenous R&D. The model yields closed‐form expressions for the skill premium and sectoral wage gaps. We show that while the Frisch elasticity does not affect the long‐run growth rate, it plays a critical role in amplifying wage differentials. As labor supply becomes more elastic, small technological or compositional changes lead to disproportionate inequality. Contrary to conventional narratives, automation alone does not generate wage polarization unless combined with highly responsive labour supply and a sufficient mass of routine workers. A calibration based on US data confirms that realistic inequality patterns arise only for moderate values of the Frisch elasticity. The analysis provides new insights on the interaction between supply‐side elasticities and technological change in shaping wage structures.