This paper investigates the optimal design of income transfer programs at the low end of the income distribution, focusing on the trade-off between equity and efficiency. The author models labor supply responses along two margins: the intensive margin (hours or intensity of work) and the extensive margin (participation in the labor force). The optimal tax formulas are derived based on these behavioral elasticities, the shape of the income distribution, and the government's redistributive preferences. When responses are concentrated along the intensive margin, the optimal program is a Negative Income Tax (NIT) with a substantial guaranteed income and high marginal tax rates. However, when responses are concentrated along the extensive margin, the optimal program is an Earned Income Credit (EIC) with negative marginal tax rates at low income levels and a smaller guaranteed income. Numerical simulations using empirical earnings data show that realistic elasticities lead to a moderate guaranteed income, low tax rates on very low annual earnings, and substantial phasing out of benefits at higher income levels. The paper also discusses the implications of these findings for policy design and highlights the importance of considering both intensive and extensive responses in optimal transfer schemes.This paper investigates the optimal design of income transfer programs at the low end of the income distribution, focusing on the trade-off between equity and efficiency. The author models labor supply responses along two margins: the intensive margin (hours or intensity of work) and the extensive margin (participation in the labor force). The optimal tax formulas are derived based on these behavioral elasticities, the shape of the income distribution, and the government's redistributive preferences. When responses are concentrated along the intensive margin, the optimal program is a Negative Income Tax (NIT) with a substantial guaranteed income and high marginal tax rates. However, when responses are concentrated along the extensive margin, the optimal program is an Earned Income Credit (EIC) with negative marginal tax rates at low income levels and a smaller guaranteed income. Numerical simulations using empirical earnings data show that realistic elasticities lead to a moderate guaranteed income, low tax rates on very low annual earnings, and substantial phasing out of benefits at higher income levels. The paper also discusses the implications of these findings for policy design and highlights the importance of considering both intensive and extensive responses in optimal transfer schemes.