144A: Urban Economics Nilopa Shah
Assignment 4 (based on textbook Chapter 4)
Question 1 (Exercise 4.1 from textbook)
Suppose that landowners have the power to restrict , the distance to the edge of the city, in order
to increase the land rent they earn. Suppose that, with no restriction, the urban land function is
given by r = 100 − x, where x is distance in blocks to the CBD. Suppose that agricultural land
rent rA is equal to 20.
a) Compute in the absence of any restriction by landowners. Show your result in a clearly
labelled diagram showing the urban land-rent function and city size. [Note: You will be using
this graph to add a few other lines as well as calculate some areas, while working through
sub-parts (b) through (e). So, draw a large clear graph about half an A4-size sheet.]
Now suppose that landowners can restrict to a value of 65 blocks. When they impose this
restriction, the urban land rent curve shifts up. (Take a minute to understand why.)
b) With restricted to 65 blocks, the new rent function given by r = 105 − x. Clearly show this
new land-rent curve in your diagram, and indicate the area corresponding to the land-rent
loss from the restriction (label it ‘Loss in Rent’), as well as the additional area showing the
gain in land-rent (label it ‘Gain in Rent’).
c) Compute the sizes of these areas, and compute the net gain or loss in land-rent from
imposing the restriction = 65. Is the restriction beneficial to the landlords? Will it be
imposed? [Hint: the area corresponding to the land-rent gain is a parallelogram. If you have
forgotten, you can look up the formula and then make a simplistic calculation: consider the
horizontal length of this parallelogram as measured in terms of distance i.e. our x-axis and
then multiply it by the corresponding height from the y-axis.]
Now suppose that the landowners can impose a further restriction, with set equal to 50 blocks.
When this restriction is imposed, the urban land-rent curve shifts further up.
d) With restricted to 50 blocks, the new rent function given by r = 110 − x. Repeat parts (b)
and (c) to show this the new land-rent curve on the graph and calculate again the net gain or
loss in land-rent.
e) Relative to the original x̄ restriction of 65, is this further restriction beneficial to the
landlords? Will it be imposed?
f) If your answer is different from before, explain intuitively why a difference emerges.
x¯
x¯
x¯
x¯
x¯
x¯
x¯
Department of Economics University of California, Irvine
Page 1 of 3
144A: Urban Economics Nilopa Shah
Question 2
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 . 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 and , 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 ( 0 to 15) on the x-axis and housing
rent on the y-axis. Draw separate graphs for each sub-part.
a) Present a clearly labelled graph of housing rent behavior in the city if Factory A is located
at and Factory B is located at .
b) Present a clearly labelled graph of housing rent behavior in the city if Factory A is located
at and Factory B is located at .
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.
x
x = 0 x = 15
x =
x = 4 x = 13
x = 6 x = 8
Department of Economics University of California, Irvine
Page 2 of 3
144A: Urban Economics Nilopa Shah
c) 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.]
d) 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 more than one proposed location, pick any one of the proposals to answer the
remaining sub-questions.
e) Clearly state your proposed policy (which minimizes the area affected and, hence the
impact on housing rent) by completing the following sentences:
(1) Factory A locates at _____________ .
(2) Factory B located at _____________ .
f) 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.
g) 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)
h) 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 and Factory B at
(2) in part (e) as suggested by the proposed pollution-minimizing policy.
i) 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?
x =
x =
x = 4 x = 13
Department of Economics University of California, Irvine
Page 3 of 3