In this paper we characterize the optimal linear and piecewise linear EITC schedule. In the linear framework we demonstrate that in the presence of unemployment, an increase of social inequality aversion and a decrease in labor aversion both derive in a lower optimal EITC. For the piecewise linear schedule, we show that in most cases the optimal schedule is a triangle, which is at odds with actual policy, that is based on a trapezoid. According to our simulation, the use of a trapezoid instead of a triangle implies a substantial loss in terms of Social Welfare. We show that a trapezoid is optimal only when the wage distribution among the working poor is even, with a discrete jump for higher wage groups. After mimicking the wage distribution in different countries, we show that changes in the share of the "very rich" have a lower impact on the optimal EITC compared to changes in the wage variance. Finally, we show that the main impact of an increased minimum wage on the optimal EITC schedule is a more pronounced phasing out.