This dissertation contains four essays. The first essay analyzes the role of trade policies in an open economy for income redistribution and shows that tariffs or production subsidies can Pareto-improve welfare when government uses a Pareto-optimal non-linear income tax system under free trade, contrary to the conventional wisdom in the public finance literature (Diamond and Mirrlees, 1971) and the international trade literature (Dixit and Norman, 1980). That is, tariffs and production subsidies complement a Pareto-efficient non-linear income tax system. The second essay analyzes a situation of a closed economy. This essay shows that optimality of uniform commodity taxes under a non-linear income system by Atkinson and Stiglitz (1976), w...