Optimal Taxation with Migration

Consider an economy with two sectors H (high-tech) and L (low-tech) and two individuals 1 and 2. Workers in sector H earn an income level of 10 whereas those working in sector L earn an income level of 6 (labor supply is assumed to be inelastic). Type 2 (the high skilled guy) can work in both sectors whereas type 1 (the low skilled type) can only work in sector L. Both types derive utility from income and suffer no disutility from work. The government is considering levying a system of sector-specific lump-sum taxes/transfers on redistributive grounds.

Let T_Hand T_L denote, respectively, the taxes (transfers, if negative) levied on sectors H and L (the after-tax income in sector H is thus given by 10- T_H, whereas that in sector L is given by 6- T_L). The government is seeking to maximize the utility of the least well-off guy, type 1, and is not allowed to run into a fiscal deficit.

a) Formulate the government constrained optimization problem. You should specify the objective function, the revenue constraint and the incentive constraint associated with type 2.

b) Solve for the optimal lump-sum taxes/transfers. [Hint: you first need to show which constraints are binding (satisfied as equality) in the optimal solution for the government problem].

c) Now suppose that type 2 can migrate to another country where her (after-tax) utility level would be given by 0

Remark: Intermediate Public Economics, Jean Hindricds and Gareth Myles, MIT Press, 2006 (Main Textbook)

Guidline to the Assignment:

In Assignment we characterize the optimal system of redistributive occupation (sector-specific) taxes. We also demonstrate how migration possibilities may limit the redistributive capacity of the government.

Notice that the setup in the question is much simpler than the general framework discussed in class for two reasons. First, the choice is confined to the extensive margin (choice b/w sectors H and L), as labor supply by presumption is inelastic. Second, the low skilled agent (type 1) can only work in sector L (and, hence, makes no choices, by presumption).

In part A, you are asked to formulate the government constrained optimization problem. You should specify the objective function, the revenue constraint and the incentive constraint associated with type 2, which requires that type 2 would be weakly better-off working in sector H than moving to sector L.

In part B, you are asked to solve for the optimal solution. Assuming that both the incentive compatibility and the revenue constraints are binding (satisfied as equality), you should obtain a linear system of two equations solved for two unknowns. You may prove that the two constraints are indeed binding in the optimal solution (but this is not required).

In part C, we extend the model by assuming that type 2 can migrate to another country. You need to re-formulate the government constrained maximization program by incorporating the migration decision into the incentive compatibility constraint of type 2. Demonstrate how the presence of migration may limit the redistributive capacity of the government. This would depend on the value ofV(the outside option available to type 2). You should distinguish between two cases: one in which the migration option is a binding constraint and another in which it is non-binding.