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We explore the suitability of the minimum wage as a policy instrument for reducing emerging income inequality created by new technologies. For this, we implement a binding minimum wage in a task‐based framework, in which tasks are conducted by machines, low‐skill, and high‐skill workers. In this framework, an increasing minimum wage reduces the inequality between the low‐skill wage and the other factor prices, whereas the share of income of low‐skill workers in the national income is nonincreasing. Then, we analyze the impact of an automating economy along the extensive and intensive margins. In a setting with a minimum wage, it can be shown that automation at the extensive margin and the creation of new, labor‐intensive tasks do not increase the aggregate output in general, as the displacement of low‐skill workers counteracts the positive effects of cost‐savings. Finally, we highlight a potential trade‐off between less inequality of the factor prices and greater inequality of the income distribution when a minimum wage is introduced into an automating economy.