1. (20 points) Utility. Suppose we have two cities, 1 and 2. Assume every individual has the same utility function, given by: u (wjr;) = 4 * wj - 0.75 * r; where / = 1,2. Furthermore, for all parts of the problem, assume the population is fixed at 100 and wages in each city are given by: W1 = 150 W2 = 120 a. (3 points) What is the utility from each choice if ri = 200 and re = 120. Is this an equilibrium? How do you know? b. (4 points) For the rest of the problem, assume that rents are increasing in the population of each city. Specifically, assume r, (L1) = 4 * L1 and r2(L2) = 8 * Ly. Compute the equilibrium population of each city, the equilibrium rents, and equilibrium utility.. {2 points) Suppose the government decides to implement an income tax of 510 on all workers. What are the new equilibrium populations levels of the city? d. {2 points) Now suppose the government decides to implement a flat income tax of 10% on all workers. What are the new equilibrium population levels of the city? e. (4 points) Now the government levels the 10% income tax on only people in city 1. What are the new population levels in each city? Compare your answer to part . How did it change? Why? f. {3 points] Let's say instead that the government imposes a progressive tax system. Mare spacifically, suppose the tax system is given by _ (0% w