Optimal Taxation with Incomplete Markets

This paper characterizes tax and debt dynamics in Ramsey plans for incomplete markets economies that generalize an Aiyagari et al. (2002) economy by allowing a single asset traded by the government to be risky. Long run debt and tax dynamics can be attracted not only to the first-best continuation allocations discovered by Aiyagari et al. for quasi-linear preferences, but instead to a continuation allocation associated with a level of (marginal-utility-scaled) government debt that would prevail in a Lucas-Stokey economy that starts from a particular initial level of government debt. The paper formulates, analyzes, and numerically solves Bellman equations for two value functions for a Ramsey planner, one for t ≥ 1, the other for t = 0.