ECON 144 University of California Irvine Urban Economics Worksheet


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144A: Urban Economics
Nilopa Shah
Assignment 4 (based on textbook Chapters 4 and 5)
Question 1
Consider a city where all housing is owned by absentee landlords, and the only people who live
in the city are retirees who rent these homes of the same size , regardless of location x . So,
instead of a combination of housing size and housing price, we can have a simple measure
housing rent which is constant through the city at $200. The city’s boundary is defined by a
flowing river and a conserved forest (a beautiful place to retire in!), such that the city exists only
between x = 0 and x = 15, no one lives beyond those edges.
Now, Factory A and Factory B want to locate in this city. The factories are operated by robots
and none of the residents of the city (all retirees) work there. But the factories will emit an
unhealthy amount of carbon monoxide, thus causing air pollution the areas around it. The two
factories can locate anywhere in the city (even at the exact same spot). Each factory will emit a
constant amount of carbon monoxide into the air for 4 miles in each direction.
The pollution from these factories, will have an effect on the housing rent in the city. The
housing rent in the polluted areas is lowered while those in the non-polluted areas increase. If
the areas of pollution by the two factories do not overlap then the housing rent falls by a
constant $25 for each mile in the polluted areas. On the other hand, if a particular spot is
simultaneously affected by pollution from both factories i.e. if the areas polluted by the
factories overlap then the housing rent falls by a total of $40 for each mile. So, instead of
Factory A reducing rent by $25 and Factory B reducing rent by another $25, an overlap of
pollution means their joint effect reduces housing rent by only $40. The housing rent in areas
of the city with no pollution is raised by $10 for each mile.
Let’s draw some graphs representing distance in the city (x = 0 to 15) on the x-axis and housing
rent on the y-axis. Draw separate graphs for each sub-part.
Present a clearly labelled graph of housing rent behavior in the city if Factory A is located
at x = 4 and Factory B is located at x = 13.
Present a clearly labelled graph of housing rent behavior in the city if Factory A is located
at x = 6 and Factory B is located at x = 8.
Department of Economics
University of California, Irvine
Page 1 of 3
144A: Urban Economics
Nilopa Shah
Due to factors beyond control, this town does need to allow the factories to set-up in the city.
However, there is a possible option of enacting a policies restricting the choice of locations for
the factories.
Consider designing a zoning policy under which the factories a required to locate in a
particular region of the city. The location(s) is(are) chosen so as to minimize areas that are
exposed to pollution in the city. What location(s) would you propose for Factory A and
Factory B? [Hint: While designing the policy, recall that both factories can be located at
the same spot.]
While the focus of the policy is to minimize the extent of area polluted, understand that any
policy adopted will also be optimal for maximizing housing rent given pollution or
minimizing the negative impact of pollution on housing rent. Using intuition of the
monocentric city model, explain this claim. (1-2 sentences)
If you have proposed more than one location, pick any one to answer the remaining sub-parts.
Clearly state your proposed policy (which minimizes the area affected and, hence
impact on housing rent) by completing the following sentences:
Factory A locates at x = ________.
Factory B located at x = ________ .
Present a clearly labelled graph for housing rent behavior in the city with the chosen
location(s) for Factory A and Factory B as proposed by the policy.
Explain why the landlords, who do not even live in this city, are not happy about the
factories being located in the city, irrespective of the policy being adopted. (3-5 sentences)
Suppose that the city government (influenced by the landlords) demands tax-payment from
the factories equal to the net change in housing rents in the city (consider both losses and
gains in housing rent due to the factories), depending on their location. Calculate how much
the factories will need to pay if they locate
(1) in part (a) i.e. Factory A at x = 4 and Factory B at x = 13
(2) in part (e) as suggested by the proposed pollution-minimizing policy.
If the city government were to adopt the tax-payment policy as described in (h) above then
will it also have to impose the zoning policy as described in part (c) and specified in part
(e)? Why or why not? Is either policy better? Which and why?
Department of Economics
University of California, Irvine
Page 2 of 3
144A: Urban Economics
Nilopa Shah
Question 2 (similar to Exercise 5.1 from the textbook)
Suppose there are three potential users of a freeway: Andy, Brigit, and Celine.
Alternate Cost (ga)
The cost of the best alternative route for each commuter is
given in the adjoining table.
The average cost AC of using the freeway (i.e., the cost
per car) as a function of traffic volume T is as follows:
Average Cost (AC)
Using this information, answer the following questions: (Note: For this question, do not attempt
to graph the cost or demand curves since here you are dealing with a set of discrete numbers, not
a continuous function as discussed in class.)
Find the equilibrium allocation of traffic between the freeway and alternate routes.
Compute the total commuting cost for all
commuters for the following four allocations of
traffic. Total cost is the cost incurred by
freeway users plus the cost incurred by
commuters who use their alternate routes.
(Hint: Remember the definition of AC, while
carrying out your calculations.)
On Freeway
On Alternate Route
No One
Andy, Brigit, Celine
Brigit, Celine
Andy, Brigit
Andy, Brigit, Celine
No One
Remember that the socially optimal allocation of traffic between the freeway and alternate
routes is the one that minimizes aggregate commuting cost for all commuters in the city.
Based on your answer to (b), which allocation is socially optimal? How does total cost at
the optimum compare to total cost at the equilibrium? (Note: you don’t need to use an MC
curve to get the answer to this question.)
Department of Economics
University of California, Irvine
Page 3 of 3

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urban economics

housing rent

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