We analyze the redistributional (dis)advantages of a minimum wage over income taxation in competitive labor markets, without imposing assumptions on the (in)efficiency of labor rationing. Compared to a distributionally equivalent tax change, a minimum-wage increase raises involuntary unemployment, but also raises skill formation as some individuals avoid unemployment. A minimum wage is an appropriate instrument for redistribution if and only if the public revenue gains from additional skill formation outweigh both the public revenue losses from additional unemployment and the utility losses of inefficient labor rationing. We show that this critically depends on how labor rationing is distributed among workers. A necessary condition for the desirability of a minimum-wage increase is that the public revenue gains from higher skill formation outweigh the revenue losses from higher unemployment. We write this condition in terms of measurable sufficient statistics. Our empirical analysis suggests that a minimum-wage increase is undesirable in nearly all OECD countries. A reduction in the minimum wage, along with tax adjustments that keep net incomes constant, would yield a Pareto improvement.