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...

We consider a small set of axioms for income averaging - recursivity, continuity, and the boundary condition for the present. These properties yield a unique averaging function that is the density of the reflected Brownian motion with a drift started at the current income and moving over the...