ArXiv paper derives closed-form optima for proportional wealth taxes under JKO versus Wasserstein criteria

The model restricts attention to the (C1)-(C3) neutrality-preserving class and solves the two-dimensional design problem in corporate retention k and wealth-tax rate τw. The dimensionless ratio ρ = Σ0 m0 / σ² governs regime selection under the JKO free-energy gap, producing a pure wealth-tax region at low ρ, a mixed region at intermediate ρ, and pure flow-tax dominance at high ρ. In contrast, the squared 2-Wasserstein distance yields a corner solution at the pure flow-tax vertex for every ρ examined.

Norwegian-calibrated portfolios straddle the mixed-instrument phase when equity volatility is used but shift into the pure flow-tax phase once effective real-estate volatility is substituted. The bluntness index B(m0) = b/(a m0) supplies the economic interpretation: JKO weights the index linearly while W2 weights it quadratically, explaining the divergent instrument recommendations.

The analysis supplies the first explicit mapping between Mirrleesian decision-distortion and Saez-Zucman distributional-compression traditions inside a common Fokker-Planck dynamics. No empirical test of the predicted phase boundaries is reported.