cation (c**,c*, 7'*,7+*) in one sentence. (6 points) Leslie is now stumped. Ben Wyatt explains to her that she needs to introduce a new tax system that incentivizes the productive Eagleton residents to voluntarily pro- duce more. Ben suggests to Leslie that she should consider introducing a constant income tax t combined with a universal transfer of T. The Pawgleton government has no external revenue needs, so all of the tax revenue from t will be used to fund the universal transfer. g. Write out the individual's budget constraint. (3 points) h. Derive the labor supply of Pawnee and Eagleton residents as a function of t and T. Hint: you will need to solve the individual's optimization problem. (8 points) i. Without solving for the optimal policy, argue why Ben's proposal is better than the tax system in Part d. Hint: you will need to argue that, despite sacrificing some equality, Ben's proposal is more efficient. (6 points) When Anne saw the problem that Leslie was facing, she immediately recalled her suggestion to Ben for the health insurance problem in Problem Set 2. Anne suggests to Leslie that she should introduce a menu of allocations {(cy). (c",yF)} such that Eagleton residents voluntarily select the allocation (CF,y") while Pawnee residents voluntarily select (cPy). (Notice that Ben has suggested replacing labor supply 1 with output y, because the policy can no longer be based on 1.) j. Rewrite the utilities for both Pawnee and Eagleton residents in terms of con- sumption cand output y. Hint: output is linear in labor supply, sol = marginal productivity (2 points) k. Write out the constraints such that Eagleton residents select (CE,y) while Pawnee residents select (c,y). Hint: check out constraint (2) on page 20 of Week 7 Notes. (2 points) 1. Leslie found that the optimal tax system under Anne's proposal is nonlinear. Without solving for the optimum and comparing the social welfare under both schemes, argue why Anne's proposal is superior to Ben's. (6 points) cation (c**,c*, 7'*,7+*) in one sentence. (6 points) Leslie is now stumped. Ben Wyatt explains to her that she needs to introduce a new tax system that incentivizes the productive Eagleton residents to voluntarily pro- duce more. Ben suggests to Leslie that she should consider introducing a constant income tax t combined with a universal transfer of T. The Pawgleton government has no external revenue needs, so all of the tax revenue from t will be used to fund the universal transfer. g. Write out the individual's budget constraint. (3 points) h. Derive the labor supply of Pawnee and Eagleton residents as a function of t and T. Hint: you will need to solve the individual's optimization problem. (8 points) i. Without solving for the optimal policy, argue why Ben's proposal is better than the tax system in Part d. Hint: you will need to argue that, despite sacrificing some equality, Ben's proposal is more efficient. (6 points) When Anne saw the problem that Leslie was facing, she immediately recalled her suggestion to Ben for the health insurance problem in Problem Set 2. Anne suggests to Leslie that she should introduce a menu of allocations {(cy). (c",yF)} such that Eagleton residents voluntarily select the allocation (CF,y") while Pawnee residents voluntarily select (cPy). (Notice that Ben has suggested replacing labor supply 1 with output y, because the policy can no longer be based on 1.) j. Rewrite the utilities for both Pawnee and Eagleton residents in terms of con- sumption cand output y. Hint: output is linear in labor supply, sol = marginal productivity (2 points) k. Write out the constraints such that Eagleton residents select (CE,y) while Pawnee residents select (c,y). Hint: check out constraint (2) on page 20 of Week 7 Notes. (2 points) 1. Leslie found that the optimal tax system under Anne's proposal is nonlinear. Without solving for the optimum and comparing the social welfare under both schemes, argue why Anne's proposal is superior to Ben's. (6 points)
