We characterize optimal redistributive taxation when individuals are heterogeneous in their skillsand their values of non-market activities. Search-matching frictions on the labor markets createunemployment. Wages, labor demand and participation are endogenous. The government onlyobserves wage levels. Under a Maximin objective, if the elasticity of participation decreasesalong the distribution of skills at the optimum, the average tax rate is increasing, marginaltax rates are positive everywhere, while wages, unemployment rates and participation rates aredistorted downwards compared to their laissez-faire values. Under a general utilitarian objective,numerical simulations suggest that the downward distortions of wages and unemploymentremain. However, the optimal policy then induces upward distortions of participation.