Physics-Based Model Shows Proportional Taxes Fail to Redistribute
New research using the Fokker-Planck framework suggests only progressive taxes can shift wealth distributions within policy-relevant timescales.
Proportional wealth taxes do not reduce wealth inequality through market channels because they act as a uniform gravitational field on the distribution. This symmetry shifts the overall drift of the Fokker-Planck equation without altering diffusion, which preserves the Gini coefficient at all finite times.
Effective redistribution requires breaking this symmetry through progressive taxes or tax-funded transfers. Progressive taxes create a confining potential that replaces the standard Pareto steady state with a thinner-tailed distribution. Unlike proportional taxes, which rely on slow demographic turnover, progressive structures redistribute wealth within timescales that matter for policy.
https://arxiv.org/abs/2607.06153
The research treats optimal redistribution as a control problem that accounts for intervention costs such as migration, evasion, and portfolio distortion. In general equilibrium, this design feeds back through aggregate capital and the production function, resulting in a McKean-Vlasov equation that reveals diminishing returns to progressivity.
Convergence speed depends on the spectral gap of the Fokker-Planck operator. This mathematical relationship determines whether a tax regime actually reshapes the density of wealth or merely shifts the existing distribution downward.