Tax Mechanisms and Gradient Flows

The classical problem of optimal taxation of income, when individual abilities are not known to the policy maker and income reacts to the tax burden, is not fully defined. In order to solve this problem, Steinerberger uses dynamic methods and shows that the adjustments of tax payers to the tax burden follow the heat conduction equation (the propagation of heat through solid objects), and are therefore theoretically determinable. From this it can be deduced that optimal taxation must follow a "fairness" principle and similar incomes should be subject to a similar tax burden.

In his commentary, Simon Loretz first reflected on the goal of maximising tax revenues in classical optimal tax theory. Subsequently, the implicit assumption of the immediate adjustment of income to tax changes was discussed. Regardless of necessary simplifying assumptions, one of the main outcomes is that an optimal tax rate should not have any kinks or discontinuities.