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.
If government (I think they mean society) enjoys the act of redistribution, or at least place a larger weight on low skill workers than on their higher skill counterparts, and the workers who enjoyed their job the least lose their jobs before the others then I have no doubt that this surgical policy strike could increase social welfare.
I skimmed over the paper and it is well written and classic micro theory, even though it does not pass the reality test. I also didn't see if taxes on high skill labor effected demand for low skill labor, so if someone happens to read it more carefully then I'd appreciate a note in the comments.