Optimal taxation with persistent shocks

In this paper I study dynamic optimal taxation in a private information economy with continuum of individual productivity shocks that are persistent over time. I formulate the problem recursively and use first order approach to simplify it. I provide full justification of the first order approach. The advantage of the first order approach is twofold. First, as is well known, it simplifies the incentive compatibility constraint. Second, and this is a new feature in this model, it dramatically reduces the state space of the dynamic program. Instead of using the continuation utility function as a state, we use the marginal continuation utility as a state. This feature is extremely useful because it allows us to numericaly implement the dynamic program and solve quantitatively for the optimal allocations