摘要翻译：
我们演示了如何用动态方法分析静态最优所得税问题。具体地说，我们表明税收问题与热方程密切相关。我们的第一个结果是最优税收的一个新性质，我们称之为公平原则。任何收入的最优税收在其他收入的最优税收的适当调整的高斯平均（热核）族下是不变的。也就是说，给定收入的最优税收等于其他收入和收入密度的最优税收的热核平均值加权。此外，这种平均发生在相互紧密联系的每个尺度上，为所有收入范围提供了统一的加权方案。公平原则的产生并不是出于平等的考虑，而是代表了一种有效的方式，以减轻税收负担和各种收入产生的收入。就像自然希望平均分配热量一样，政府增加收入的最佳方式是将税收负担和增加的收入平均分配给个人。然后，我们构造了一个税收梯度流--一个按照税收增加的方向改变现有税收制度的动态过程--并表明它采取了热方程的形式。公平原则也适用于梯度流的短期渐近性，即对当前税收进行平均。我们所考虑的梯度流可以看作是一个非线性所得税表改革的连续过程，从而将变分税收法和最优税收法统一起来。我们给出了梯度流的其他几个特征，重点讨论了梯度流的光滑特性。
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英文标题：
《Tax Mechanisms and Gradient Flows》
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作者：
Stefan Steinerberger, Aleh Tsyvinski
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  We demonstrate how a static optimal income taxation problem can be analyzed using dynamical methods. Specifically, we show that the taxation problem is intimately connected to the heat equation. Our first result is a new property of the optimal tax which we call the fairness principle. The optimal tax at any income is invariant under a family of properly adjusted Gaussian averages (the heat kernel) of the optimal taxes at other incomes. That is, 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. Moreover, this averaging happens at every scale tightly linked to each other providing a unified weighting scheme at all income ranges. The fairness principle arises not due to equality considerations but rather it represents an efficient way to smooth the burden of taxes and generated revenues across incomes. Just as nature wants to distribute 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 process changing the existing tax system in the direction of the increase in tax revenues -- and show that it takes the form of a heat equation. The fairness principle holds also for the short-term asymptotics of the gradient flow, where the averaging is done over the current taxes. The gradient flow we consider can be viewed as a continuous process of a reform of the nonlinear income tax schedule and thus unifies the variational approach to taxation and optimal taxation. We present several other characteristics of the gradient flow focusing on its smoothing properties.
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PDF链接：
https://arxiv.org/pdf/1904.13276