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

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  • Anders G Fr{o}seth

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.

Suggested Citation

  • Anders G Fr{o}seth, 2026. "Wealth Taxation as a Drift Modification: A Fokker-Planck Approach to Tax Neutrality," Papers 2603.05283, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2603.05283
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