University of Victoria

Economics 312

Urban Land Economics

Martin Farnham

Problem Set #6

Note: Answer each question as clearly and concisely as possible. Use of diagrams, where appropriate, is strongly encouraged. Problem sets are ungraded. However, developing a careful understanding of the problems will, on average, dramatically improve your exam performance. Don’t just look at the answer key and think, from that, that you understand the solution. Force yourself to figure out stuff without help, until you’re sure you can’t do it alone. That’s how you become a good problem solver in life generally.

True/False/Uncertain

For each question, state clearly whether you find the statement to be true, false, or uncertain. Then provide a clear explanation. Answers without explanation will be given zero points.

1) Segregation by income across municipalities arises simply because the rich don’t like to live near the poor.

2) The use of local property taxes to fund local public goods tends to increase residential segregation by income.

3) The use of property taxes to fund provincial expenditures tends to increase residential segregation by income.

4) Segregation by race is efficient if people of different races want to live in separate communities.

Short Answers

Many of these questions involve comparative statics exercises using graphs. When doing such exercises you should always start with a situation in equilibrium, and then illustrate how that situation changes when a particular parameter changes. So your diagram should clearly show the before and the after situations. Do this in a single diagram so it’s clear how curves shift.

Always clearly label your diagrams, including curves and axes.

1) Explain why majority rule does not necessarily lead to efficient provision of local public goods.

2) How does residential sorting potentially improve the social welfare associated with decisions based on majority rule?

3) Consider first a situation where British Columbia funds its schools equally (each school receives the same amount per pupil), through a head tax (an equal lump-sum tax paid by each person). Every person must pay $1000 a year to fund schools. BC contains people with varying willingness to pay for education. Some, if given the choice, would spend nothing for education. Others would spend a lot. Others would spend somewhere in between.

Now consider that BC decides to divide each town into zones. Pro-school zones will raise money from residents via a head tax and set spending levels within their zone at a level decided by the province (assume this is the same level as the province set before). Anti-school zones will not fund schools (and hence raise no school tax).

a) What does “fiscal sorting” predict about residential migration, in response to such a policy change? Who will move to the pro-school zones? Are any assumptions required to support this prediction?

b) In order to maintain per pupil funding at pre-policy-change levels, what will have to happen to head taxes in the pro-school zones? Why?

c) Suppose pro-school zones contain a mix of income levels and that education services are a normal good. This implies that high-income people want to spend more than low-income people on schools. Assuming there are no peer effects in the production of educational services and that wealthy voters decide on the level of per pupil expenditure in the pro-school zones, is there any reason to expect the wealthy to want to segregate themselves from the poor (by forming their own school district)?

d) Is there any reason for the poor to want to isolate themselves from the wealthy?

e) Now suppose that instead of the wealthy deciding on the level of local school spending, it is put to a vote within each pro-school zone. Each pro-school zone contains people from a range of incomes. Once the level of spending is decided, everyone will be assessed an equal head tax to pay for the spending. Is there any reason to expect the wealthy to want to segregate themselves from the poor? Will the poor want to segregate themselves from the wealthy?

f) Now suppose that local schools are funded through a property tax. Will the rich want to segregate themselves from the poor, by forming their own district? Will the poor want to segregate themselves from the rich?

g) With property tax funding of school districts, segregation may break down. What land-use control may be employed to restore segregation. Which group is likely to demand the use of this land-use control?

h) What are the pros and cons of local funding of education, in light of this example?

4) Suppose that people sort over neighborhoods by the “quality” of the neighbors. Let’s assume everyone is shallow and believes that rich neighbors are better than poor neighbors. Consider the income-sorting model presented in lecture. This is the model where we assume a city is divided into two neighbourhoods, each with 100 homes (all homes are the same) and the population consists of 100 rich people and 100 poor people.

a) Assume the rent premium (the extra willingness to pay for a home that’s in a rich neighborhood) is greater for poor than for rich. Illustrate with a diagram the degree of segregation that will occur in this city.

b) Assume the rent premium is greater for rich than for poor. Illustrate with a diagram the degree of segregation that will occur in this city.

c) Suppose that the rent premium curves for the rich and poor cross. Assume that the rent premium curve for the poor is steeper than that for the rich, where they cross. Illustrate with a diagram the degree of segregation that will occur in this city.

d) Suppose they cross, but that the rent premium curve for the poor is flatter than that for the rich, where they cross. Where are the stable equilibria?

5) Consider a local public good for which 3 individuals have the following individual demands:

Person 1: q=50-(1/4)p

Person 2: q=100-(1/4)p

Person 3: q=200-(1/4)p

a) Write the equation for the individual marginal benefit curve for each person, and plot each of these curves in a single graph.

b) Write the equation(s) for the marginal social benefit curve that summarizes the aggregate benefits received by the three people for different levels of the public good. Plot the marginal social benefit curve in your graph from (a).

c) Solve for the efficient level of the public good if the marginal cost of providing the good is $1000 per unit. Show the efficient level in your graph from (a).

d) Solve for the efficient level of the public good if the marginal cost of providing the good is $300 per unit. Show the efficient level in your graph from (a).

e) Suppose that each individual will be charged for 1/3 of the cost of the public good supplied in their community. Assume each person decides on their individually optimal level of the public good by setting their share of the marginal cost equal to their individual marginal benefit. How much of the public good will each person optimally demand if the marginal cost is $300 per unit?

f) Suppose an election were held to decide on the level of the public good that should be provided. If the median voter hypothesis holds, what level would be chosen? Is this efficient?

g) Suppose each person lived in a community with 2 other people with the same marginal benefit curve as them. For each community, how much of the public good would each individual want supplied, assuming they pay 1/3 of the marginal cost?

h) For each community, what is the efficient level of the public good?

i) Would voting lead to efficient provision of the public good in this case? Why or why not?