. Consider a region with a workforce of 12 million. The urban utility curve reaches its maximum with 3 million workers and includes the following combinations:

Workers (millions)	0.5	1	2	3	4	6	8	9	10	11	12
Utility ($)	10	32	56	70	65	55	45	40	35	30	25

Initially, there is a single city with 12 million workers. Suppose the government establishes a new city with 1 million workers, leaving 11 million workers in the old city.

(a) Assume that the number of cities remains at two. What happens next? What will be the new equilibrium city size?

(b) Suppose that the government establishes three new cities, each with 1 million workers (leaving 9 million in the old city). What happens next? Will the region reach the optimum configuration of four cities, each with 3 million workers?

(c) Suppose your objective is to reach the optimum configuration and you establish three new cities. What is the minimum number of workers to be placed initially in each of the new cities.