The minimum wage is a politically popular policy instrument meant to improve living standards of the working poor. It has also gained in popularity among economists as a result of new empirical evidence on its mild employment effects. Nevertheless, most theoretical studies have a hard time finding a useful role for the minimum wage alongside the income tax. All of these studies assume a one-to-one correspondence between wages and income. I reconsider the case for the minimum wage when people differ in both wages and preferences for work, such that a given level of income may correspond to different wage rates. This renders the minimum wage unambiguously desirable in a discrete-type labor market à la Stiglitz (1982). But desirability of the minimum wage is ambiguous and subject to a policy trade-off in a continuous-type labor market à la Mirrlees (1971). Compared to the minimum wage, income taxes are less effective in affecting the wage distribution but more effective in redistributing income. The desirability of the minimum wage depends on this trade-off between the "predistributive" benefits of the minimum wage and the "redistributive" benefits of the income tax.
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