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Urban Development: New Cities' Impact and Equilibrium
Chapter 4, Problem 5(choose chapter or problem)
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 $):
\(\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c|c}
\hline \mathrm{W} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline \mathrm{U} & 23 & 33 & 43 & 48 & 52 & 55 & 50 & 45 & 40 & 35 & 30 & 25 \\
\hline
\end{array}\)
Suppose the government establishes a new city with 1 million workers, leaving 11 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 _____ , so the new city will [shrink, grow] and the old city will [shrink, grow].
b. In the long-run equilibrium, the workforce in the old city _____ .
c. A new city will be viable in the long run if the starting workforce is at least _____ because.
Questions & Answers
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 $):
\(\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c|c}
\hline \mathrm{W} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline \mathrm{U} & 23 & 33 & 43 & 48 & 52 & 55 & 50 & 45 & 40 & 35 & 30 & 25 \\
\hline
\end{array}\)
Suppose the government establishes a new city with 1 million workers, leaving 11 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 _____ , so the new city will [shrink, grow] and the old city will [shrink, grow].
b. In the long-run equilibrium, the workforce in the old city _____ .
c. A new city will be viable in the long run if the starting workforce is at least _____ because.
ANSWER:Step 1 of 3
a. Immediately following the establishment of the new city, the utility in the small new city is $23 (U=23) and the utility in the large old city is $30 (U=30), so the new city will grow and the old city will shrink.
For the small new city with a workforce of 1 million, the corresponding utility is 23. For the large old city with a workforce of 11 million, the corresponding utility is 30.
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Urban Development: New Cities' Impact and Equilibrium
Want To Learn More? To watch the entire video and ALL of the videos in the series:
This video explores urban utility curves, workforce dynamics, and the impact of creating new cities on growth and equilibrium, with a focus on the utility of workers.