Heterogeneous Returns and Wealth Tax Neutrality: A Fokker--Planck Framework

Anders G Fr{\o}seth

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Abstract: We extend the Fokker--Planck framework of Fr{\o}seth (2026, arXiv:2603.05283) to populations of investors with heterogeneous, persistent return-generating ability. When the drift coefficient in the Langevin equation for log-wealth varies across investors, the proportional wealth tax remains a uniform drift shift but ceases to be neutral in the economic sense: its real incidence differs across ability types, and the stationary wealth distribution changes shape. We derive the extended Fokker--Planck equation on the joint space of log-wealth and ability, characterise the conditions under which the drift-shift symmetry breaks, and identify the consequences for asset prices and portfolio allocations. The analysis connects the neutrality results of Fr{\o}seth (2026, arXiv:2603.05264) and the Fokker--Planck dynamics of Fr{\o}seth (2026, arXiv:2603.05283) to the heterogeneous-returns literature, notably the "use-it-or-lose-it" mechanism of Guvenen, Kambourov, Kuruscu, Ocampo-Diaz and Chen (2023).

Date: 2026-03
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