Optimal Shadow Prices for the Public Sector in the Presence of a Non-linear Income Tax System in an Open Economy

This study analyzes the optimal shadow prices of inputs to the public sector in the presence of a non-linear income tax system in the standard two-factor Heckscher--Ohlin small open-economy model. In this model, there are two factors of production (unskilled labor and skilled labor) and two tradable goods (skilled labor- and unskilled labor-intensive goods). The two tradable goods are produced in the private sector by using two types of labor. A public good is produced by using the two types of tradable goods and the two types of labor. I show that the optimal shadow prices of the two types of labor in the public sector depend on whether there is a distortion in private production. On the other hand, the optimal shadow prices of tradable inputs do not depend on the presence of distortion in private production. In the second-best allocation, in which the incentive compatibility is binding, there should be distortion in the private sector. Thus, the optimal shadow prices of non-tradable factors of production depend on whether the economy is at the second-best equilibrium or not. On the other hand, the optimal shadow prices for tradable inputs are always equal to the international prices. Thus, for setting the optimal shadow prices in an open economy, it is important to distinguish whether the inputs are tradable goods or non-tradable factors and whether the economy is at the second-best equilibrium or not.