We characterize optimal redistributive taxation when individuals are heterogeneous in their skills and their values of non-market activities. Search-matching frictions on the labor markets create unemployment. Wages, labor demand and participation are endogenous. Average tax rates are increasing at the optimum. This shifts wages below their laissez faire value and distorts labor demand upwards. The marginal tax rate is positive at the top of the skill distribution even when the latter is bounded. These results are analytically shown under a Maximin objective when the elasticity of participation is decreasing in the skill level and are numerically confirmed under a more general objective. Under the Maximin, above approximately $20,000 per year, our model recommends higher marginal tax rates than a comparable competitive setting.h