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

Physics > Physics and Society [Submitted on 8 Jul 2026] Title:Minimum-Distortion Wealth Taxation, I: Information-Theoretic versus Transport-Geometric Optimality on the Proportional Class View PDF HTML (experimental)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. Current browse context: physics.soc-ph References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.