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This paper studies the optimal redistribution of income inequality caused by the presence of search and matching frictions in the labor market. We study this problem in the context of a directed search model of the labor market populated by homogenous workers and heterogeneous firms. The optimal redistribution can be attained using a positive unemployment benefit and an increasing and regressive labor income tax. The positive unemployment benefit serves the purpose of lowering the search risk faced by workers. The increasing and regressive labor tax serves the purpose of aligning the cost to the firm of attracting an additional applicant with the value of an application to society. Download Paper