Homework answers / question archive / New York University - ECON 227        Urban Economics Spring 2013   Problem Set #3 Due Monday, Mar 11, 4pm Slip the Problem set under my office door, Econ Dept, 19 W 4th St, Rm 704 Do not put it into any boxes or mailboxes!   Assume the utility functions for two cities are identical and are given by  U=N - 0

New York University - ECON 227        Urban Economics Spring 2013   Problem Set #3 Due Monday, Mar 11, 4pm Slip the Problem set under my office door, Econ Dept, 19 W 4th St, Rm 704 Do not put it into any boxes or mailboxes!   Assume the utility functions for two cities are identical and are given by  U=N - 0

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New York University - ECON 227 

 

Urban Economics Spring 2013

 

Problem Set #3

Due Monday, Mar 11, 4pm

Slip the Problem set under my office door, Econ Dept, 19 W 4^th St, Rm 704 Do not put it into any boxes or mailboxes!

 

1. Assume the utility functions for two cities are identical and are given by  U=N - 0.1*N², where N denotes the city’s population in million. 
   1. What is each city’s utility maximizing population?
   2. If each city had a population of 6.5 million people, how would these cities change their size? Assuming that the total population of 13 million cannot be changed, would there be a smaller and a larger city? Would there be three or more cities? Or would there be no change at all. Explain.  

 

1.  
2. Correct or false? Do not explain
   1. The K=6 principle of the Central Place Theory is reflected in the hexagonal market form (“hexa” in Greek means 6).
   2. In the K=3 principle of the Central Place Theory suggests that each central place serves exactly its own market plus 3 markets of adjacent cities. (c) In the K=4 principle of the Central Place Theory suggests that each central place serves exactly its own market plus 3 markets of adjacent cities.

 

 

3. Innovation and Growth:

Suppose a region’s workforce of 14 million is initially split equally between two cities, X and Y. The urban utility curve peaks at 4 million workers, and beyond that point the slope is constantly -$3 per million workers. The initial equilibrium utility is $60.  Suppose city X experiences technological innovation that shifts its utility curve upward by $12.

1. 1. Draw a pair of utility curves, one for X and one for Y, and label the positions immediately after the innovation (before any migration) as x for city X and y for city Y. Use arrows along the curves to indicate that migration that follows. Show the long-run equilibrium using x’ and y’ respectively.
   2. For the new equilibrium (after migration) calculate the utility and the population in each city.