To redistribute or to predistribute? The minimum wage versus income taxation when workers differ in both wages and working hours

I consider the case for the minimum wage alongside (optimal) income taxes when workers differ in both wages and working hours, such that a given level of income corresponds to multiple wage rates. The minimum wage is directly targeted at the lowest-wage workers, while income taxes are at most targeted at all low-income workers, regardless of their hourly wage rates. This renders the minimum wage unambiguously desirable in a discrete-type model of the labor market. Desirability of the minimum wage is a priori ambiguous in a continuous-type model of the labor market. Compared to the minimum wage, income taxes are less effective in compressing the wage distribution but more effective in redistributing income. Desirability of the minimum wage depends on this trade-off between the "predistributional advantage" of the minimum wage and the "redistributional advantage" of the income tax. I derive a desirability condition for the minimum wage and write it in terms of empirical sufficient statistics. A numerical application to the US suggests a strong case for a higher federal minimum wage - especially if social preferences for the lowest-wage workers are relatively strong and the wage elasticity of labor demand relatively small.