1
May 24, 2017
due: June 1, 2017 ECON 146
Urban Economics
Problem Set 4
Since the end of term is an exceptionally busy time with term papers and studying for
finals, I am letting you know in advance which questions will be graded.
The following questions will be graded: 1b), 2c), 3c), 4b), 5a), and 6d).
1. (12) Minimum density restrictions on new construction
In the United States, zoning is done by municipalities, typically with little intervention by
the state or central/federal governments. However, in many other countries, particularly
in Western Europe, the zoning applied by municipalities is subject to state/provincial or
central/federal regulations on land use, which are often strict. Embracing the
sustainability goals of the New Urbanism, the Ontario government has imposed minimum
density regulations on all new "greenfields" (undeveloped land inside the Greenbelt)
development that essentially replace single-family homes at the metropolitan periphery
with townhouses and row houses.
a) (3) What perceived market failures is the policy designed to counter?
b) (3) According to basic microeconomic theory, what are the effects of the minimum
density regulations on urban housing rents and on the market values of existing singlefamily homes?
The policy is accompanied by provincial transportation policies designed to
increase the transit modal share by expanding and improving the transit system and
cutting back the highway budget.
c) (3) What effects do these land use and transportation policies have on average
journey-to-work times?
d) (3) In what ways do the policies help and hurt the urban poor? 2. (8) Mass transit and decreasing average cost
Mass transit exhibits decreasing long-run average cost.
a) (2) Identify one of the sources of decreasing long-run average cost.
b) (2) On a diagram, draw the demand function for mass transit, the long-run average
cost curve, and the long-run marginal cost curve. How is the long-run marginal cost
curve related to the long-run average cost curve?
c) (2) On the same diagram, indicate the optimal level of output (mass transit passengermiles) and the mass transit price consistent with this level of output, and show the loss
made by the transit authority if it produces the optimal level of output and charges this
price.
d) (2) What is the relationship between increasing returns to scale and decreasing
average cost? 2 3. (4) Mass transit and theory of the second best
The first-best policy is the optimal policy taking into account only technological and
resource constraints. The first-best pricing rule is "set price equal to the marginal social
cost".
The previous question asked you to solve for the first-best transit output and price.
In the Real World, there are other constraints that the government takes into account
when deciding on the fare (and hence the mass transit price, which equals the user cost
plus the fare). In class, I discussed several of these other constraints: the "underpricing"
of urban auto travel, the financing of the mass transit deficit with distortionary taxation,
the unionization of mass transit workers (which causes their wage to be approximately
double the wage of workers in the private sector of comparable skill), incentive
constraints for the mass transit system to operate efficiently, and equity considerations
(most mass transit passengers are poor). When the government chooses the fare taking
these additional constraints into consideration, it chooses the second-best fare.
Perhaps the easiest of these constraints to take into account is the equity
constraint. Assume that it is the only additional constraint.
b) (2) In quantity-price space, the equity constraint is considered by taking the marginal
social benefit curve to lie above the demand curve. Why?
c) (2) In quantity-price space, identify the second-best transit fare and output. How do
they differ from the corresponding first-best transit fare and output? 4. (9) Housing
Two of the most important characteristics of housing are its spatial fixity and durability.
These together give rise to filtering and to neighborhood cycles.
a) (2) Define filtering.
A recent paper in the American Economic Review estimated the average annual
rates at which rental and owner-occupied housing filter downward in the income
distribution as they age. It found that the (average) rate of downward filtering is
significantly higher for rental than for owner-occupied housing.
b) (2) The rate of downward filtering is determined by the level of maintenance. What
economic rule does a profit-maximizing landlord follow in choosing the level of
maintenance? What rule does a household follow?
c) (2) Perhaps on the basis of your answer to b), provide one reason why the rate of
downward filtering is lower for owner-occupied than for rental housing.
d) (3) What is the filtering hypothesis? If correct, the hypothesis provides a strong
argument against the construction of public housing as a way of providing affordable
housing for the poor. Indicate briefly why. 3 5. (11) Housing values, Los Angeles vs Riverside.
According to basic urban location theory, there are two sets of factors that account for the
differences in land and property rents and values across locations -- accessibility and
amenity. According to Zillow, the median home value in Los Angeles County in 2015
was $491,000, and the corresponding number in Riverside County was $272,500.
Applying the monocentric city model with fixed lot size, this question asks you to
consider what proportion of the difference in home values can be attributed to Los
Angeles' County better accessibility to the central city and its jobs. You are asked to
reason like a good microeconomist would.
a) (4) Assume, consistent with the basic monocentric model, that all jobs are in the City
of Los Angeles. What would be the approximate annual household commuting cost
savings from living in Los Angeles County compared to living in Riverside County?
Remember that commuting costs include both money and time costs
b) (1) According to the simple von Thunen model, extended to treat urban residential
land use, the annual home accessibility rent premium in Los Angeles County relative to
Riverside County equals the annual housing commuting cost savings from living in Los
Angeles County rather than in Riverside County. According to the theory therefore, what
would be the annual home accessibility rent premium from living in Los Angeles?
c) (2) Now you have to relate the home value accessibility premium to the home rent
accessibility premium. According to economic theory, what is the ratio of home value to
home rent?
d) (2) Apply this rule to estimate the home value accessibility premium of living in Los
Angeles County compared to living in Riverside County.
e) (2) According to your calculations, what proportion of the difference in median home
value between Los Angeles and Riverside Counties can be accounted for by differences
in accessibility (as measured by the basic monocentric theory).
6. (7) Housing vouchers
Consider a housing voucher program that gives a housing voucher to a low-income
household equal to the difference between 50% of the (monthly) rent on its apartment and
30% of its (monthly) income. Let Y be the household's income, H be the quantity of
housing services provided by an apartment, which is measured by its rent R (i.e. H = R),
C be the household expenditure on other goods, and V be the amount of the voucher
( which cannot be negative).
a) (1) Write down the equation for the household's budget constraint without the
housing voucher, and plot the budget constraint in H-C space (similar to Figure 15-4 of
the book).
b) (2) Write down the equation for the household's budget constraint with the housing
voucher, and plot the corresponding budget constraint in the same diagram.
c) (2) On the diagram, using the household's indifference curves, show how the voucher
affects its choice of the quantity of housing to consume.
d) (2) Indicate using the same type of diagram, how the household's budget constraint
affected if the housing voucher is capped at $1000 per month. 4

 

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