Minimum-Distortion Wealth Taxation, I: Information-Theoretic versus Transport-Geometric Optimality on the Proportional Class

Abstract

We characterise minimum-distortion wealth taxation under two contrasting normative criteria within a Fokker-Planck framework on log-wealth: the JKO free-energy gap, an information-theoretic measure aligned with the Mirrleesian decision-distortion tradition, and the squared 2-Wasserstein distance from the no-tax distribution at horizon $T$, a transport-geometric measure aligned with the Saez-Zucman distributional-compression tradition. Restricting to the neutrality-preserving (C1)-(C3) schedule class of a companion paper (Froseth 2026), both optima admit closed forms in the two-dimensional design plane parametrised by the corporate-dividend retention $k=(1-{\tau }_c)(1-{\tau }_d)$ and the proportional wealth-tax rate ${\tau }_w$. The JKO optimum partitions the regime axis into three phases as a function of the dimensionless ratio $\rho ={\Sigma }_0{m}_0/{\sigma }^2$, with $m_0=\mu -{\sigma }^2/2$ the geometric mean log-return: a pure wealth-tax phase at low $\rho$, a mixed-instrument phase at intermediate $\rho$, and a pure flow-tax phase at high $\rho$. The $W_2$ optimum, by contrast, is degenerate in this calibration: it pins to the pure flow-tax corner across the whole regime axis. The criterion contrast admits an economically meaningful reading via a bluntness index $B(m_0)=b/(a{m}_0)$ that measures the wealth-tax channel's mean-displacement-per-revenue overshoot relative to the flow-tax channel; JKO weights $B$ linearly, $W_2$ weights it quadratically, and the two normative traditions correspond to this difference in weighting. Norwegian-flavoured calibrations sit inside the JKO mixed-instrument phase under stock-heavy portfolio volatility but move into the pure flow-tax phase under the realised effective volatility of typical real-estate-heavy households.

41 pages, 3 figures, 2 tables. Companion paper to arXiv:2603.05264, arXiv:2603.05277, arXiv:2603.05283, and arXiv:2607.06153