Wealth Taxation as a Drift Modification: A Fokker-Planck Approach to Tax Neutrality

TL;DR

This paper models wealth taxation using stochastic dynamics and Fokker-Planck equations, revealing conditions under which taxes are neutral or alter wealth distribution dynamics.

Contribution

It reformulates wealth tax neutrality in the language of physics, identifying symmetry violations that cause non-neutral effects.

Findings

Tax neutrality corresponds to a drift-shift symmetry in the Fokker-Planck equation.

Violations like book-value assessment and market impact break the symmetry.

The framework clarifies when taxes are benign versus when they induce new dynamics.

Abstract

We reformulate the neutral wealth tax framework of Froeseth (2026; arXiv:2603.05264) in the language of stochastic dynamics and statistical physics. Individual wealth under geometric Brownian motion satisfies a Langevin equation with multiplicative noise; the probability density of wealth across a population then evolves according to a Fokker-Planck equation. A proportional wealth tax at market value enters as a uniform reduction of the drift coefficient, preserving the diffusion structure and all relative probability currents. This drift-shift symmetry is the physical content of tax neutrality. Each channel through which neutrality breaks down in practice - book-value assessment, liquidity frictions, forced dividend extraction, migration, and market impact - corresponds to a specific violation of this symmetry: a state-dependent, asset-dependent, or flow-dependent modification of the Fokker-Planck equation. The framework clarifies when wealth taxation is a benign rescaling of the dynamics and when it introduces genuinely new physics.