Dynamic Optimal Non-linear Taxation Under Non-commitment

This paper studies dynamic non-linear taxation in a two-period model without government commitment and a continuum of agents with privately known skill parameters, which are constant overtime. The government is utilitarian but cannot commit at t=1 to the tax scheme that she will propose at t=2. We identify the perfect Bayesian equilibrium of this two period game that maximizes ex-ante payoffs of the government. First, we solve the second period taxation scheme for arbitrary posteriors of the government. Then we show that whenever this posterior has support with gaps this arises from unnatural ways of breaking indifferences. We impose a tie-breaking rule and show then that the only possible equilibria partition types into a countable number of intervals. Hence the optimal taxation scheme in the first period is characterized by two things: 1) a partition of the original type space, that is a sequence of numbers that determine type-cut-offs and 2) a set of tax-consumption pairs, one for each of these sub-intervals. In the second period, the government offers a different tax-schedule for each tax-consumption pair chosen in the first period. We proceed to characterize how the number and the size of partitions at the optimum depend on the discount factor and on the distribution of the skill parameters in the economy