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1

The figure below shows equilibrium land rent in an open monocentric city, where r is rent, d is distance to the CBD, and b is the boundary of the city.
Suppose that in another city just like this one, the government restricts the geographic size of the city by forbidding development beyond b*. This can be interpreted as a type of growth or city size control.
(a) Draw another diagram showing the equilibrium land rent function in the restricted city, assuming that the reduction in population has no impact on the utility of local residents. Carefully contrast the rent functions in the restricted and unrestricted cities. You may want to refer back to the discussion in the "Congestion and Land Use" section of Chapter 9 to get you started.

(b) Draw another diagram showing the equilibrium land rent function in the restricted city, assuming that the reduction in population has a positive impact on the utility of local residents. Carefully contrast the rent functions in the restricted and unrestricted cities.

(c) Does the restriction cause land prices to increase? Explain.


(a) The key to answering these questions is to recall that the height of the rent function is
determined by the utility level in the city. Higher rents are associated with lower utilities, and
vice versa. Because the utility level in the city does not change, the height of the rent function
will not change either. The rent function in the restricted city will be just like the rent function
shown above, expect that it will stop at b*.

(b) If the restriction has a positive impact on the utility of residents (by reducing congestion, for
example), then rent in this city must rise as well so that the city continues to provide the same
level of utility that is available elsewhere. The rent function in the restricted city will be higher
than, and parallel to, the original rent function and, as in part a., it will stop at b*.

(c) The answers to parts a. and b. suggest that a size restriction on any open city only increases
land prices if the reduction in size has a positive impact on the utility of residents. In other
words, the restriction only raises land prices if it has a positive impact on amenities in the city.

2

In the late 1950's, the city of Urb created a small industrial district around the confluence of several railroad lines near the edge of town. Over time, as Urb's population increased and suburbanized, residential development appeared around the industrial district, and pressure grew for the local government to restrict the scope of suburban industrial development. Urb accomplished this by enacting the following zoning bylaw:
Be it known henceforth to all Urbers that suburban land shall be reserved for residential use, except land that lies within 1 kilometre of the Suburban Confluence Terminal (SCT).
Here is what the area in question looks like today:
Diagram Located R&S Lesson 10
The industrial district is inhabited by identical competitive firms. Each firm produces 20 units of output using 2 units of capital and 1 unit of land. The price (revenue per unit) of output equals $2 per unit; the price of capital also equals $2 per unit. Firms ship all of their output to the SCT at a cost of $0.50 per unit of output per kilometre. In addition, the firms create a noxious odour that keeps Urbers awake at night. The marginal external cost of this olfactory pollution is $0.50 per unit of output. The bid rent for residential land is $26.00 per unit.

a) Find the private (or equilibrium) industrial bid rent function for land, and illustrate the bid rent function in a diagram.

b) What is the socially optimal (or efficient) industrial bid rent function for land?

c) Did the omniscient planners reserve too much, too little, or just the right amount of land for the industrial district? Use a diagram in your explanation.

(a) Profit equals revenue minus the sum of capital costs, transportation costs and land rend.
Symbolically, p = 2(20) - 2(2) - (0.50)20d - R(d). Competition implies that profit must equal zero, which in turn implies
R(d) = 36 10d. The private (or equilibrium) industrial bid rent function is a line with a vertical intercept of 36 and a slope of -10.

(b) To derive the socially optimal (or efficient) bid rent function, we must force the firms to take the costs of the pollution that they create into account. The natural way to do this in the present context is to impose a pollution tax on the firms to internalize the costs associated with the
externalities that they create. The tax should equal marginal external cost, which is $0.50 per unit of output or $10 per firm. If we impose such a tax, the socially optimal (or efficient) bid rent function is R(d) = 36 - 10d - 10 = 26 10d, a line with a vertical intercept of 26 and
a slope of -10.

(c) They reserved too much land. In fact, the industrial district should not exist. As shown in the
figure below, the socially optimal or efficient bid rent function for land is below the residential
bid rent function for land at all locations. Once we properly account for the external costs of
pollution, we see that all of this land should be used for residences.
Diagram on R&D answers Lesson 11 Question 2

3

Consider two communities of equal size that finance the provision of policing through a uniform property tax. Suppose that one community has a higher average income level and a larger property tax base than the other. Let the total market value of the property in the high income community be $10 billion and the total market value of the property in the low income community be $8 billion. Let expenditures on policing in the high income community be $100 million and expenditures on policing in the low income community be $200 million. Finally, suppose that each community must balance its budget, that property is assessed for tax purposes at its market value, and that the crime rate is higher in the low income community.

(a) Find the required (budget balancing) property tax rate in the two communities. Which community has the higher property tax rate and why?

(b) Now suppose that the communities are consolidated and that police provision and finance is controlled by a regional authority. The authority's first act is to levy a uniform property tax on both communities to finance the costs of policing. Find the required (budget balancing) property tax rate in the consolidated community. How do property tax payments in the two communities change as a result of consolidation? Are both communities better off? Explain your reasoning.
How would the property tax equalization program discussed in part (b) affect property values in the two communities? Explain your reasoning.

(c) How would the property tax equalization program discussed in part (b) affect property values in the two communities? Explain your reasoning.

(a) The required property tax rate in the high income community is 1/100= 0.01 or 1% per year. The required property tax rate in the low income community is
2/80 = 0.025 or 2.5% per year. The low income community has the higher rate because it spends more on policing and it’s tax base is smaller.

(b) The required property tax rate is now . 0.0167 or 1.67% per year. The high income community now pays approximately $167 million per year for policing (an increase of 67%), while the low income community pays approximately $133 million (a decrease of 33%). If the
level of services remains the same in both communities, then the high income community must be worse off, and the low income community must be better off.

(c) Higher taxes are associated with lower property values, so property values in the high income community are likely to fall, while property values in the low income community are likely to rise.

4

Why do we need to have a government?

(1) To make and provide for the enforcement of laws.
(2) To promote an equitable distribution of income.
(3) To correct market failure.
(4) All the above are correct.

Answer: (2)
The demand for housing comes from the utility maximizing choices of consumers. Utility maximization
will generally occur at a point where the budget constraint is tangent to the highest possible indifference
curve.

5

Which of the following statements is/are TRUE about pure public goods?

A) Efficient use of a public good is provided when the sum of the marginal benefits to all consumers equals the marginal cost of provision.
B) There is an incentive to become a free rider.
C) People can be excluded from consuming the good.
D) One person's consumption of the good does not detract from another person's consumption.

(1)Only Statement A is true.
(2) Only Statements C and D are true.
(3) Only Statements A, B, and D are true.
(4) All of the above statements are true.

Answer: (4)
Because of adjustment costs, Joanne may be better off staying where she is, even though her preference
for housing has changed. If she stays in her current accommodation, her utility level will be higher than
the highest level she can achieve by moving.

6

What is a key argument made by central city governments in favour of metropolitan consolidation?

1) Central city governments argue for metropolitan consolidation because they want to be in charge of more money.
2) Suburban residents do not pay a tax to use city centre streets and facilities. A unified metropolitan government would internalize these spillovers, resulting in a more efficient public service system.
3) There are scale economies at work when a government is in charge of a large area. Governments are capable of managing a metropolitan area, and should do so to increase efficiency.
4) All of the above are correct.

Answer: (2)
When we say that demand is inelastic with respect to both income and price, this means that the absolute
value of both elasticities is less than one, so Eh,p > -1 and Eh,i

7

Are local governments in the United States and Canada similar?

1) Yes, the structure of local governments in Canada and the United States are exactly the same.
2) No, local governments in the United States are tightly controlled naturally. Local governments are not able to make decisions without first going through the federal government. Local governments in the United States are much more controlled compared to Canada.
3) No, local governments in Canada are tightly controlled by the provinces, and actually have little local autonomy, in comparison to the United States.
4) This question cannot be answered without more information.

Answer: (3)
Each time period, the property owner has to decide how much additional capital to invest in the
property. To maximize the value of his or her holdings, the owner should choose kt, so that the
marginal benefit of investing and the marginal cost of investing are equal. The marginal cost of
investing another unit of capital in the property is simply the opportunity cost. The marginal benefit
of investing is given by the value of the marginal product of structural capital: MB = p × MPk.

8

According to the traditional view, if the supply of land is fixed, who pays the land portion of the property tax?

1) The landowner.
2) The renter. (The tenant now pays the landowner the same rent plus the land tax).
3) It is split equally between the renter and the landowner.
4) It will be split between the renter and the landowner dependent on the slope of the demand curve

Answer: (1)
This implies that in the short-run, the price of housing will be determined by demand conditions, while
the quantity of housing will be determined by supply conditions. Conversely, the general view is that
in the long-run the supply of housing is very elastic. This implies that in the long-run, the price of
housing is determined by cost factors while housing quantity is determined by demand factors.

9

In 1956, what did Charles Tiebout argue?

(1) Charles Tiebout argued that local public goods are supplied efficiently only if consumers are perfectly mobile.
(2) Charles Tiebout argued that local public goods can be supplied efficiently if residents can choose between many different areas which all have different combinations of public spending and taxes.
(3) Charles Tiebout argued that local public goods cannot be supplied efficiently.
(4) Charles Tiebout argued that if residents have sufficient choice among jurisdictions offering different packages of public spending and taxes, they will under-represent the value they place on each jurisdiction.

Answer: (3)
From the equation, change in p = -(t/h*) × change in d, thus, -(65/1,300)(-10) = 0.5. Thus the price of housing at the city border is $0.50 + $1.00 = $1.50 per square foot. The housing price function is a straight line with a slope of
-t/h* = -65/1,300 = 0.05, so it has the form p(d) = a - 0.05d, where a is the vertical intercept. Then p(10) = 1, which implies 1 = a - 0.05(10), a = 1.50, and the housing price function p(d) = 1.50 - 0.05d. When we substitute d = 0 into the housing price function, we get a price per square foot of p(d) = 1.5 - 0.05(0) = $1.50.

10

Consider a community with two types of households, high and low income. The house values are high for the high-income households, Vh , and low for the low-income households, VL . There are Nh high-income households and N - Nh low-income households. Suppose that the annual cost of providing public services is constant C per person, and that the community must balance its budget using a uniform property tax, that is, a property tax levied at the same rate on all property. The required tax rate (assuming market value assessment) is: t = NC/(NL VL + (N - NL )Vh ). L What happens to the tax rate as we increase the number of low-income households and what will the result be on the community's property values?

(1) If we increase the number of low-income households, the property tax rate will increase. An increase in property tax rates will decrease the value of houses in the community.
(2) If we increase the number of low-income households, the property tax rate will decrease. An increase in property tax rates will increase the value of houses in the community.
(3)An increase in the number of low-income households will have no effect on the tax rate because there are still the same number of households in the community, but there will be a decrease in the value of houses in the community.
(4)This question cannot be answered without more information.

Answer: (4)
The profit of a builder who supplies housing at location d is pie = p(d) × h* - pk × k* - r(d) × l*.
Competition forces profits to zero in the long-run and therefore 0= p(d) × h*1 pk × k* - r(d) × l*.
If we substitute in all the variables [p(d) = 1.85,
h* = 1,100, pk = 5, k* = 43, l* = 1,400] into the formula, we have r(d) = ((1.85 × 1,100) - (5 × 43))/1,400, then r(d) = $1.30.

11

Why would a government disrupt a private land market and impose a congestion tax to prevent interactions between conflicting land uses?

(1) It is a quick way for governments to make money.
(2)To place restrictions on congestion and future building improvements.
(3)A private land market places conflicting land uses too close together.
(4)None of the above are correct

Answer: (1)
If households can substitute housing for other goods, they will attempt to reduce their housing
consumption when the price of housing is high (i.e., at locations near the city centre). This will cause
the housing price function to be convex - to be steeper near the city centre than near the boundary of
the city. If builders can also substitute capital for land in housing production, then they will try to
economize on their use of land where the rent on land is high (i.e., at locations near the city centre).
This will cause the land rent function to become convex as well, and will lead to higher population and
structural densities near the city centre than near the boundary of the city.

12

The city of Hampton is inhabited by identical competitive firms. Each firm produces 20 units of output using two units of capital and one unit of land. The price (revenue per unit) of output equals $2 per unit; the price of capital also equals $2 per unit. Firms ship all of their output to the city centre at a cost of $0.50 per unit of output per kilometre. In addition, the firms create a noxious odour that keeps residents awake at night. The marginal external cost of this olfactory pollution is $0.50 per unit of output. The bid rent for residential land is $26.00 per unit.

Find the equilibrium or private industrial bid rent function for land. (Profit is equal to revenue minus capital costs, transportation costs, and rent, and competition implies that profit must equal zero.)

(1) R(d) = 26 - d
(2) R(d) = 36 - 10d
(3) R(d) = 44 - 10d
(4) R(d) = 40 - 100d

Answer: (2)
Hedonic pricing estimates the marginal value or "implicit price" of each characteristic of a property.
This information allows us to construct a measure of the price of housing in different areas or at
different points in time where the characteristics of the houses are held constant. Such "constant quality
price indices" can then be used to make correct inferences about how housing prices vary across space
or over time.

13

The city of Hampton is inhabited by identical competitive firms. Each firm produces 20 units of output using two units of capital and one unit of land. The price (revenue per unit) of output equals $2 per unit; the price of capital also equals $2 per unit. Firms ship all of their output to the city centre at a cost of $0.50 per unit of output per kilometre. In addition, the firms create a noxious odour that keeps residents awake at night. The marginal external cost of this olfactory pollution is $0.50 per unit of output. The bid rent for residential land is $26.00 per unit.

What is the socially optimal point of efficient industrial bid rent function for land? (To derive the socially optimal or efficient bid rent function, you must force the firms to take the cost of the pollution that they create into account.)

1) R(d) = 46 - 20d
2) R(d) = 36 - 20d
3) R(d) = 36 - 10d
4) R(d) = 26 - 10d

Answer: (4)
Filtering has implications for housing policy. The most important implications of filtering for low income
housing policy are that it may be better to let the market supply low-income families with used
housing for them, and that policies that encourage housing construction at higher quality levels may
actually benefit the poor by accelerating the filtering process. Regulations that restrict the supply of
housing in higher-income and higher-quality submarkets may have the perverse effect of worsening
housing conditions in lower quality submarkets, since supply restrictions tend to raise prices, encourage
housing maintenance and improvements, and thus discourage downward filtering.