4. Consider a region with a workforce of 12 million. The urban utility curve reaches its max- imum with 3 million workers and include the following combinations: Initially, there is a single Table 1: Utility and city size Workers (millions) 1 2 3 4 6 8 9 10 11 12 Utility 32 56 70 65 55 45 40 35 30 25 City with 12 million workers. (For questions a and b) Suppose the government establishes a new city with 1 million Workers, leaving 11 million workers in the old city. (a) Draw the utility curve for these two cities below (or on an attached paper) (5 pts). (b) Assume that the number of cities remains two, What happens next? What's the new equi- librium size? (5 pts) (e) Suppose that the government establishes three new cities instead, each with 1 million work- ers (leaving 9 million in the old city). What happens next? Will the region reach the optimum conguration of four Cities, Each with 3 million workers? (5 pts) (d) Suppose your objective is to reach the optimum conguration and you establish three new Cities. What is the minimum number of workers to be placed initially in each of the new cities? (5 pts. Hint: we want to achieve the optimum relying as much on people's voluntary movement and as little on government initiated migration as possible, so although moving three millions directly to each of the three new cities would suffice, it might or might not be necessary.)