Wealth Taxation as a Drift Modification: A Fokker-Planck Approach to Tax Neutrality

Referee: The central claim that drift-shift symmetry is the physical content of tax neutrality is immediate within the chosen SDE dW = (μ − τ)W dt + σ W dB, yet the manuscript does not derive why a real proportional wealth tax must enter solely as a constant drift shift without state-dependent or flow-dependent corrections to either drift or diffusion. The necessity of the symmetry for neutrality therefore remains model-dependent rather than shown to be required by the definition of neutrality itself.

Authors: We agree that the drift-shift symmetry follows directly once the geometric Brownian motion SDE is adopted. The manuscript takes this SDE as the baseline description of wealth dynamics, which is standard in the literature. Under a proportional tax levied continuously at current market value, the tax reduces the instantaneous expected growth rate by a constant τ without altering the multiplicative noise term; this is the modeling step that produces the uniform drift shift. We will revise the manuscript to include an explicit derivation of this SDE modification from the tax rule and a short discussion of the underlying assumptions (continuous proportional levy, no state dependence in the baseline case). We will also clarify that the neutrality result is established within this stochastic framework rather than claimed to follow from a model-independent definition of neutrality. revision: partial

Referee: In the discussion of channels through which neutrality breaks down, the text states that each practical violation corresponds to a specific modification of the Fokker-Planck equation, but no explicit modified operators are supplied for book-value assessment, liquidity frictions, or forced dividend extraction, nor is it demonstrated that those operators necessarily destroy relative-current invariance. This gap leaves the mapping from practice to symmetry violation illustrative rather than rigorous.

Authors: We accept that the current text leaves the mapping illustrative. In the revised version we will add a dedicated subsection that supplies the explicit modified Fokker-Planck operators for each listed channel. For book-value assessment the drift becomes state-dependent, τ(W); for liquidity frictions an additional flow-dependent advection term appears; for forced dividend extraction the diffusion coefficient is altered. For each case we will compute the probability current and show that the relative-current invariance is lost. These additions will make the correspondence between practical violations and symmetry breaking fully explicit and rigorous. revision: yes