NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH
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Stefan Steinerberger

Yale University
Department of Mathematics
10 Hillhouse Avenue
New Haven, CT 06510

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Institutional Affiliation: Yale University

NBER Working Papers and Publications

May 2019Tax Mechanisms and Gradient Flows
with Aleh Tsyvinski: w25821
We demonstrate how a static optimal income taxation problem can be analyzed using dynamical methods. We show that the taxation problem is intimately connected to the heat equation and derive a new property of the optimal tax which we call the fairness principle. The optimal tax at a given income is equal to the weighted by the heat kernels average of optimal taxes at other incomes and income densities. The fairness principle arises not due to equality considerations but represents an efficient way to smooth the burden of taxes and generated revenues across incomes. Just as nature distributes heat evenly, the optimal way for a government to raise revenues is to distribute the tax burden and raised revenues evenly among individuals. We then construct a gradient flow of taxes – a dynamic proc...
 
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