This paper characterizes the optimal redistributive taxation when individuals are heterogeneous in two exogenous dimensions: 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. The government only observes wage levels. Under a Maximin objective, if the elasticity of participation decreases along the distribution of skills, at the optimum, the average tax rate is increasing, marginal tax rates are positive everywhere, while wages, unemployment rates and participation rates are distorted downwards compared to their laissez-faire values. A simulation exercise confirms some of these properties under a general utilitarian objective. Taking account of the wage-cum-labor demand margin deeply changes the equity-efficiency trade-off.