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 ? er 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 million people (35? er worker) is higher than the utility in a city of 11 million people (30? per worker).
Moreover, city A will have 2 million workers and will reach a higher level of welfare than before (56 instead of 32? per worker), so workers will not want to come back to the previous level of welfare, as it can be observed in the graphic. As it can be seen in the graphic, after this reallocation of workers, we have a 2 million workers city (A) and 10 million workers city (B). (Graphic) Workers in city B would want to have a higher level of welfare than their actual level.For this reason they would prefer to move to city A, in order to make it real. If doing so, city B would have 9 million workers and its level of utility would be higher than before (40 instead of 35 ? per worker) and city A would get 3 million workers, reaching the maximum point at the utility curve (70 ? instead of 56 ? per worker) as it can be seen in the graphic: (graphic) At this point, during this reallocation, city A has reached the maximum utility per worker (from 32 to 70? per worker) and workers in city B have a better level of welfare than before (from 30 to 40? er worker).
It is considered as the new equilibrium city size, because workers from city A wouldn’t want to change and workers from city B despite they could have a better level of output, are facing a stable situation because the utility curve is negatively sloped. If workers from city B continue moving to city A in order to get a higher level of welfare, they will get it, but workers that actually live in city A will see how their level of welfare will decrease because they will not be anymore at the maximum point of the utility curve.The final equilibrium in this situation would be a region with 2 cities of 6 million workers each one, where the utility level would be 55? per worker, as we can see in the graphic. (graphic) b)Suppose that the government establishes 3 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 4 cities, each with 3 million workers? c)Suppose your objective is to reach the optimum configuration and you establish 3 new cities. What is the minimum number of workers to be placed initially in each of the new cities?