Could you please help with this:

1. Optimal Income Taxation: 60 points After Pawnee and Eagleton merged to become Pawgleton, Leslie Knope was tasked with redesigning the income tax system for Pawgleton residents. Residents from Ea- gleton are more productive than Pawnee residents. Specifically, Eagleton residents have the following production function yE =21, while Pawnee residents have production function y! = 1. In other words, Eagleton residents can produce twice as many output y as Pawnee residents for a given labor input I. The labor market in Pawgleton is perfectly com- petitive. Both Eagleton and Pawnee residents have the same utility function: u (c, 1) = In (c) - 512. Pawnee and Eagleton have the same population. Leslie Knope can identify where each individual is from (Pawnee or Eagleton), and she can also force each agent to produce a certain output. Furthermore, Leslie Knope is utilitarian. a. What is the socially optimal allocation (cP*, cEx, [P*, [E*)? Hint: you will need to maximize the sum of utilities subject to the resource constraint: y - c + yP - cP =0. (8 points) b. What is the utility of Pawnee residents and Eagleton residents at the social optimum? (5 points) c. Suppose that the price of output is 1. Show why the competitive wages for Pawnee residents is w = 1 and the competitive wages for Eagleton residents is w= 2. (4 points)