Law of Motion for Economic Inequality: An Analogy to Newtonian Mechanics

This paper demonstrates that the dynamics of economic inequality follow a law of motion closely analogous to Newtonian mechanics. Within this framework, specific types of inherent household heterogeneity generate continuous "forces" that persistently exacerbate inequality, thereby necessitating government intervention as an essential counterforce. This study formally models how the force-based aggravation of economic inequality aligns with classical Newtonian laws—specifically the principles of inertia, acceleration, and action and reaction. Furthermore, the underlying real interest rate is identified as the primary point of application for these forces, where the interest-bearing period determines the transient deformation, or softness, of the economic system. Finally, the force driving inequality is conceptualized as a dynamic interaction among heterogeneous households. These findings provide a novel mathematical foundation for understanding and controlling the persistent widening of economic inequality.