This paper concerns optimal redistributive income taxation and provision of a public input good in a two-type model with a minimum wage policy implemented for the low-ability type, where firms may outsource part of the production process abroad, and where outsourcing is substitutable for domestic low-ability labor. Our results show that the incentives for the government to relax the self-selection constraint and to increase the employment among the low-skilled reinforce each other in terms of marginal income taxation; both of them contribute to increase the marginal income tax rate implemented for the low-ability type and decrease the marginal income tax rate implemented for the high-ability type. The appearance of equilibrium unemployment also constitutes an incentive to implement a tax on outsourcing. Without a direct instrument for taxing outsourcing, the government may reduce the amount of resources spent on outsourcing by increased provision of the public input good, which leads to less wage inequality and increased employment.