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.

a) Let TH and TL 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-TH, whereas that in sector L is given by 6-TL). 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