Question

New Cities Boom or Bust? Consider a region with a workforce of 12 million in a single city. The urban utility curve reaches its maximum with 6 million workers and includes the following combinations (W = workers; U = utility in $):

Suppose the government establishes a new city with 3 million workers, leaving 9 million workers in the old city. Assume that the number of cities remains at two.

a) Immediately following the establishment of the new city, the utility in the small new city is _____ and the utility in the large old city is _____
b) On the utility curve, mark the position of the new city with “N” and the position of the old city (immediately following the formation of the new city) with “D.”

Use arrows to indicate the direction of movement for each city.
c) In the long-run equilibrium, the workforce of the new city = _____ with utility = _____; the workforce of the old city = _____ with utility = _____

Answer 1

ANSWER:

Given

The government establishes a new city with 3 million workers, leaving 9 million workers in the old city. The number of cities remains at two.

a. In the table, we can see that since 3 million workers are relocated to new city, the utility for new city is $43. Old city with 9 million workers will have utility of $40.

So the utility in the small new city is $43 and the utility in the large old city is $40.

b.

c. In the long run the equilibrium will be set up at the maximum point of utility curve as there will be no deviation to move away from the point. The new city will increase other 3 million laborers to arrive at 6 million worker population with utility of $55 and old city will lose 3 million laborers to show up at 6 million laborers too with utility of $55.

In the long-run equilibrium, the workforce of the new city = 6million with utility = 55; the workforce of the old city = 6 million with utility = $55.

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