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A large exclusion from the labor market or an important unemployment of lowskilled workers is observed in numerous countries that set a minimum wage. Unemployment benefit or subsidizing low-skilled job policies can be mixed to deal with this situation. We introduce a matching model where (i) co-exist classical and frictional unemployments, (ii) the labor market is dual. Low-skilled jobs pay the minimum wage, while high-skilled wages result from bargaining. High-skilled unemployed can apply for both types of jobs, while opportunities for low-skilled ones are limited to low-skilled jobs. In this set-up, increasing low-skilled job subsidies with a balanced budget does not necessarily reduce low-skilled unemployment or unemployment spells. The model is calibrated for the French labor market. Classifications JEL: H21, H23, J41