Is it Possible to Redistribute the Gains from Trade Using Income Taxation?

How does international trade affect income redistribution? We consider a country where the government uses a nonlinear income tax to maximize some redistributive social welfare function, subject to the constraint that it can observe only individual income but not individual characteristics. In autarky, the government is able to partially equalize equilibrium prices and wages by manipulating quantities through the tax system. If borders are open, prices and wages are determined by world markets and the government is deprived of this possibility. This implies that it may be unable to redistribute the gains from trade: opening borders may decrease welfare even after the optimal policy adjustment