1. Suppose there are two cities, Eugene and Springeld and 100 identical workers who choose which city to live in. Suppose the indirect utility of living in either city is given by: VjIWj+Mi 'Rj Where Wj is the wage of living in either city j, R is rents and Mi are amenities in city j. Wages in Eugene, WE are given by: WEZZBO. Wages in Springeld, W5 are given by: WSZZOO. Rents in either city are given by the number of workers: RiILj for both cities, where L,- is the number of workers living in either city 1'. Amenities in Eugene, M3 are given by: M320 and amenities in Springfield are given by M5210 a. In equilibrium, how many workers live in Eugene? 2. The government of Eugene is considering a scheme to attract workers to Eugene. The}r want to tax rms $30 per worker that is hired in Eugene. The wage received by the worker then changes to WE:230-30. The tax revenue in Eugene is used to fund local public schools. Suppose that amenities in Eugene can therefore be weitten as a function of tax revenue as: From above, we can see that the government will raise $30 for each worker in Eugene. Everything else is the same as in Problem 1. a. After this scheme is in place, how manyr workers live in Eugene in equilibrium