Urban Economics Notes
Econ 155
Homework #1
October 2, 2014
Upload your answers (in PDF format) to the assignments tab on bSpace by 11:55pm on
Thursday, October 9th. Please include your UID in the file name, and in your answers identify yourself both by your full name and UID.
Answer the questions below. There are 25 regular points, and, in addition, there is an optional extra credit question at the end, worth an additional 5 points.
1.
The Bay Area has a history of producing innovations at a much faster rate than other cities in the U.S. Is the Bay Area's population therefore likely "too small", "too big", or "just right", relative to its utility-maximizing size? Why? (4 pts)
2.
Suppose a factory can produce a shirt for the equivalent cost of 3 loaves of bread, and a household can produce a shirt for the equivalent cost of 10 loaves of bread. The factory is located in a rural area with a uniform population density. It costs the equivalent of 0.5 loaves of bread for a household to make a one mile trip to or from the factory (of course they have to travel both directions!)
a.
Assuming the consumer price equals the factory's cost of production, what will be the radius of the factory's market area? (3 pt)
b.
Now suppose the factory develops an innovation that allows it to produce a shirt for the equivalent of 1 loaf of bread. What is the new radius of the factory's market area? (3 pt)
3. A nation has its population of 10 million living entirely within two cities. Initially, migration between the two cities is prohibited. The relationships between population (in millions), daily labor income, and daily commuting costs in each city are given by the two following tables.
Suppose that, initially, City A's population is 4 million and City B's population is 6 million.
Then, the national government allows free migration between the two cities.
a) After migration, what will be the equilbrium population of City A and City B? (8 pts)
b) Will this equilibrium be
Homework #1
October 2, 2014
Upload your answers (in PDF format) to the assignments tab on bSpace by 11:55pm on
Thursday, October 9th. Please include your UID in the file name, and in your answers identify yourself both by your full name and UID.
Answer the questions below. There are 25 regular points, and, in addition, there is an optional extra credit question at the end, worth an additional 5 points.
1.
The Bay Area has a history of producing innovations at a much faster rate than other cities in the U.S. Is the Bay Area's population therefore likely "too small", "too big", or "just right", relative to its utility-maximizing size? Why? (4 pts)
2.
Suppose a factory can produce a shirt for the equivalent cost of 3 loaves of bread, and a household can produce a shirt for the equivalent cost of 10 loaves of bread. The factory is located in a rural area with a uniform population density. It costs the equivalent of 0.5 loaves of bread for a household to make a one mile trip to or from the factory (of course they have to travel both directions!)
a.
Assuming the consumer price equals the factory's cost of production, what will be the radius of the factory's market area? (3 pt)
b.
Now suppose the factory develops an innovation that allows it to produce a shirt for the equivalent of 1 loaf of bread. What is the new radius of the factory's market area? (3 pt)
3. A nation has its population of 10 million living entirely within two cities. Initially, migration between the two cities is prohibited. The relationships between population (in millions), daily labor income, and daily commuting costs in each city are given by the two following tables.
Suppose that, initially, City A's population is 4 million and City B's population is 6 million.
Then, the national government allows free migration between the two cities.
a) After migration, what will be the equilbrium population of City A and City B? (8 pts)
b) Will this equilibrium be