This paper sets up an overlapping generations general equilibrium model with incomplete markets similar to Conesa, Kitao, and Krueger's (2009) and uses it to simulate a policy reform which replaces an optimal at tax with an optimal non-linear tax that is allowed to be arbitrarily age and history dependent. The reform shifts labor supply toward productive households and thereby increases aggregate productivity. This leads to a large increase in per capita consumption and a moderate increase in per capita hours. Under a utilitarian social welfare function that places equal weight on all current and future cohorts, the implied welfare gain amounts to more than 10% in lifetime consumption equivalents.