# 2014 Problem Set 2

**Topics:**Consumer theory, Price elasticity of demand, City

**Pages:**2 (985 words)

**Published:**April 2, 2015

ECO333–Urban Economics

Problem Set 2

Due: 24 October 2014

1. Question 2.1 from Brueckner (p. 250) (book available at http://go.utlib.ca/cat/8842730). 2. (a) Suppose the city fathers in a small Midwestern town, which was started over 100 years ago as a county seat, originally zoned all residential lot sizes in the town to be the same size. All work takes place either at the county seat building on the square in the middle of town or at shops adjacent to the square.

Everyone drives to work at a yearly commuting cost of C per mile. The lot size fixed by the zoning ordinance is L. Construct a graph with yearly rent to land per square foot on the y-axis and distance D from the center of town on the x-axis. Draw the rent schedule showing rent per square foot as a function of distance from the center of town. What is the slope of this schedule? Give the formula for the rent schedule. How does it differ from the schedule in the basic urban model where people are free to choose the size of lot they live on? Explain in common sense terms why the schedule differs. What does the difference tell us about the reason for the shape of the rent curve in the basic urban model? (b) Now suppose that the city council members today (after 100 years of the same fixed lot size for the entire town) consider themselves to be more enlightened. They rule that there can be two lot sizes: a lot size L1 for low income non-managerial workers all of whom earn the same low income Y1 , and another lot size L2 for managers all of whom earn the same high income Y2 . The two groups vote among themselves to decide the uniform lot size that all members of each group must have. Do we expect L1 to be larger than L2 or vice versa? Why?

(c) Assume that the groups segregate according to what their income is. Our problem is to determine which group lives closest to the center of town. Suppose first that the higher income people, being better able than the low income people to...

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