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.
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Facts Only

* The analysis characterizes minimum-distortion wealth taxation using two criteria: the JKO free-energy gap (information-theoretic) and the squared 2-Wasserstein distance (transport-geometric).
* Both criteria are applied within a Fokker-Planck framework on log-wealth.
* Optima have closed forms when restricted to the neutrality-preserving (C1)-(C3) schedule class.
* The JKO optimum defines three phases based on $\rho = \Sigma0 m0/\sigma^2$: pure wealth-tax, mixed-instrument, and pure flow-tax, depending on the ratio $\rho$.
* The $W2$ optimum is degenerate, pinning to the pure flow-tax corner across the regime axis.
* A bluntness index $B(m0) = b/(a m0)$ measures mean-displacement-per-revenue overshoot for the wealth-tax channel relative to the flow-tax channel.
* JKO weights $B$ linearly, while $W2$ weights it quadratically.
* Norwegian-flavored calibrations fall within the JKO mixed-instrument phase under stock-heavy portfolio volatility but shift to the pure flow-tax phase under realized effective volatility of real-estate-heavy households.

Executive Summary

Minimum-distortion wealth taxation is characterized using two distinct normative criteria within a Fokker-Planck framework applied to log-wealth. The first criterion utilizes the JKO free-energy gap, an information-theoretic measure aligning with Mirrleesian decision-distortion theory. The second criterion employs the squared 2-Wasserstein distance from the no-tax distribution at horizon $T$, representing a transport-geometric measure connected to distributional compression. Both optimization problems yield closed-form solutions when restricted to the neutrality-preserving (C1)-(C3) schedule class of a companion paper. The JKO optimum partitions the regime based on the dimensionless ratio $\rho = \Sigma0 m0/\sigma^2$, yielding three phases: a pure wealth-tax phase at low $\rho$, a mixed-instrument phase at intermediate $\rho$, and a pure flow-tax phase at high $\rho$. In contrast, the $W2$ optimum pins to the pure flow-tax corner across the entire regime axis. A bluntness index $B(m0) = b/(a m0)$ quantifies the wealth-tax channel's mean-displacement-per-revenue overshoot relative to the flow-tax channel, with JKO weighting this linearly and $W2$ weighting it quadratically.

Full Take

The tension between the information-theoretic and transport-geometric approaches reveals a fundamental divergence in how optimality is defined in wealth taxation. The JKO approach recognizes a nuanced, regime-dependent solution space characterized by three distinct phases related to portfolio dynamics ($\rho$), suggesting that the optimal tax structure depends critically on the underlying financial volatility and mean returns. Conversely, the $W2$ approach collapses this complexity, favoring a singular outcome—the flow-tax corner—implying that distributional fidelity via transport geometry inherently smooths out or disregards the richer structural distinctions exposed by information measures.
This contrast is formalized through the bluntness index, which explicitly quantifies the differential sensitivity to taxation across these regimes, showing how linearly versus quadratically weighting this measure aligns with the respective normative traditions. The empirical observation that calibrations shift based on household asset composition (stock-heavy vs. real-estate-heavy) suggests that abstract optimality criteria do not map directly onto observed economic behavior when applied to specific household contexts. The implication is that defining "minimum distortion" requires selecting a framework—information versus geometry—which inherently prioritizes different aspects of wealth distribution, leading to economically meaningful differences in policy outcomes depending on which theoretical lens is adopted.
Bridge Questions: If the JKO phase structure is reflective of achievable market equilibria, what specific economic constraints would force the $W2$ measure to align with this multi-phase reality? How can a single, unified distortion metric be constructed that incorporates both informational and geometric fidelity without collapsing into one normative preference? What are the precise mechanisms by which household asset composition translates into changes in the effective volatility parameter $\rho$?

Sentinel — Human

Confidence

This text exhibits the dense, precise language characteristic of advanced academic research, strongly suggesting human authorship within a specialized field rather than synthetic generation.

Signals Detected

High density of specialized mathematical and theoretical terminology with complex nested relationships, typical of academic exposition.

The argument flows logically from defining two criteria (JKO vs. $W_2$) to applying them via a derived index ($B$), demonstrating internal structural consistency expected in mathematical writing.

Reference to specific theoretical frameworks (Fokker-Planck, JKO, Wasserstein distance) and citations ('Froseth 2026') suggests alignment with existing academic discourse.

The text presents highly specific mathematical results and named optimization criteria. While the content is technical, the presentation style does not exhibit common LLM linguistic artifacts.

Human Indicators

Use of highly specialized nomenclature requiring deep domain expertise.

The nuance in contrasting two specific theoretical optima (JKO vs. $W_2$) and their derived economic interpretation (bluntness index) suggests synthesis by a specialist.