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)1234689101112

Utility (pounds)32567065554540353025

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 2. What happens next? What is the new equilibrium city size? First, taking into account the information given in the table, it is necessary to construct the utility curve for each of the values given:

(Graphic)

It can be seen that in the initial situation (12 million workers in one city), the utility per worker is 25 £. If the number of cities remains at 2 (A & B), leaving in one of them 11 million workers and 1 million workers in the other one, it can be appreciated in the graphic that the utility per worker in the first city will be 30 £ per worker and 32 £ per worker in the second. The utility curve reaches its maximum with 3 million workers in a city (point M), at this point; the utility per worker maximizes welfare according to city size. Because in this case there is no equilibrium, people will want to move from there in order to get a better welfare level. There are 2 possibilities, to move to city A or to move to city B, as it is shown in the graphic. If workers decide to move to city B, city A would disappear and people would like to come back to the city A to have the anterior level of welfare, because the utility per worker in a city of 1 million workers (32 pounds per worker) is higher than the utility in a city of 12 million workers (25 £ per worker). On the other hand, if workers decide to move from city B to city A, they would not want to come back to the anterior level of welfare because in this case, the utility per worker in a city of 10...

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