This paper provides a theoretical analysis of optimal minimum wage policy in a perfectly
competitive labor market. We show that a binding minimum wage – while leading to
unemployment – is nevertheless desirable if the government values redistribution toward
low wage workers and if unemployment induced by the minimum wage hits the lowest
surplus workers first. This result remains true in the presence of optimal nonlinear taxes
and transfers. In that context, a minimum wage effectively rations the low skilled labor
that is subsidized by the optimal tax/transfer system, and improves upon the second-best
tax/transfer optimum. When labor supply responses are along the extensive margin, a
minimum wage and low skill work subsidies are complementary policies; therefore, the
co-existence of a minimum wage with a positive tax rate for low skill work is always
(second-best) Pareto inefficient. We derive formulas for the optimal minimum wage (with
and without optimal taxes) as a function of labor supply and demand elasticities and
the redistributive tastes of the government. We also present some illustrative numerical
simulations.