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 y = 21, while Pawnee residents have production function 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) 2. 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*, CE*, 1P+, 1E+)? Hint: you will need to maximize the sum of utilities subject to the resource constraint: ye - + yP - OP = 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 wP = 1 and the competitive wages for Eagleton residents is we = 2. (4 points) d. Let T(y) denote the income tax function. Find an income tax function T (y) that implements the socially optimal allocation. Hint: writing out the budget constraints for both Pawnee and Eagleton residents would help. (6 points) A law was passed by Councilman Jeremy Jamm that prohibits the discrimination of Pawnee and Eagleton residents. This law prohibits Leslie from identifying where each individual is from. In essence, she cannot force productive individuals to pro- duce more, because she is no longer even able to identify who is productive. Fur