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Anders G Frøseth · 2026-07-07
The paper uses a physics model (the Fokker-Planck equation) to describe how wealth spreads across a population, treating a flat wealth tax like a uniform gravitational pull that shifts everyone but doesn't change inequality (the Gini coefficient). It shows mathematically that only progressive taxes or direct transfers actually reshape the wealth distribution and reduce inequality, and it frames choosing the best tax policy as a formal optimization problem accounting for costs like evasion, migration, and distortion.
Why it matters: This is a theoretical macro/policy modeling paper rather than a trading strategy, but it offers a structured way to think about how different tax regimes alter the shape and tails of the wealth distribution over time. Practitioners interested in long-horizon capital allocation, sovereign/policy risk, or the pace at which wealth concentration changes might find the framework useful for scenario thinking.
⚠ This is an abstract mathematical/physics model of policy, not an empirical or tradable result, and rests on strong stochastic-process and equilibrium assumptions.
A proportional wealth tax acts as a uniform gravitational field on the wealth distribution: it shifts the drift of the Fokker-Planck equation without altering the diffusion, preserving the Gini coefficient at all finite times. The same drift-shift symmetry that makes the tax non-distortionary also makes it non-redistributive through the market channel. Redistribution requires breaking this symmetry. A progressive tax (confining potential) replaces the Pareto steady state with a thinner-tailed distribution whose Gini is a closed-form function of the progressivity parameter; source-sink terms (tax-funded transfers) reshape the density directly. We formulate optimal redistribution as a control problem for the Fokker-Planck equation, penalising intervention costs including migration, evasion, and portfolio distortion. In general equilibrium the tax design feeds back through aggregate capital and the production function, yielding a self-consistent McKean-Vlasov equation with diminishing returns to progressivity. The spectral gap of the Fokker-Planck operator determines convergence speed: progressive taxes redistribute within policy-relevant timescales, whereas proportional taxes rely on slow demographic turnover.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.