From Gravity to Confinement: Wealth Redistribution as Optimal Drift Design in the Fokker–Planck Framework
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摘要
Wealth taxes reshape the wealth distribution through two channels: a market channel (drift and diffusion in the Fokker–Planck equation) and a fiscal channel (source-sink transfers). A proportional tax acts as a uniform drift shift, leaving the diffusion unchanged and preserving the Gini at all finite times, hence it is non-redistributive via markets but redistributive through public spending. Progressive taxes implement a confining potential (Ornstein–Uhlenbeck dynamics), producing a lognormal steady state with a Gini that declines with the progressivity parameter; transfers and boundaries further shape the distribution, enabling targeted inequality reduction. The analysis frames redistribution as an optimal control problem over the Fokker–Planck equation, balancing policy impact against intervention costs, with general-equilibrium feedback through the production function and diminishing returns to progressivity. The spectral gap governs convergence speed, implying that progressive designs can achieve policy-relevant redistribution within typical political cycles, unlike pure drift shifts which are slow. The framework integrates market and fiscal channels and maps various tax designs to distinct equilibrium outcomes, providing a unified analytic lens for evaluating wealth taxation. [page::0]
