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This chapter analyzes the effects of introducing a graduated minimum wage in a model with optimal income taxation in which a government seeks to maximize social welfare. It shows that the optimal graduated minimum wage increases social welfare by increasing the low-productivity workers’ consumption and bringing it closer to the first-best. The chapter also describes how the graduated minimum wage in a social welfare optimum depends on important economy characteristics such as the government’s revenue needs, the social welfare weight of low-productivity workers, and the numbers and productivities of the different types of workers.