Progressive taxation in sequential decisionmaking: Deterministic and stochastic analysis

This paper investigates the effect of progressive taxation on sequential decisionmaking. The decision is the archetypical problem of capital theory: determining the optimal cutting time for a tree that grows according to either a deterministic or stochastic process. For the deterministic model, the optimal cutting time is unaffected by proportional taxes, but decreases as taxes become more progressive. For the stochastic model, the major finding is that uncertainty can partially offset the inefficiency induced by progressive taxation; when this result holds the government benefits from increased uncertainty whereas the taxpayer is harmed. One noteworthy example of this is when the tree's growth is governed by Brownian motion.