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1

Firms in the software industry seem to be attracted to areas where there is an abundance of highly skilled labour with experience in computer science. Is this an example of an urbanization economy or a localization economy (or neither)? Carefully define urbanization economy and localization economy in your answer

If the strength of an external scale economy is mostly determined by the size of the city, then we say
that there is an “urbanization economy” at work. If the strength of an external scale economy is mostly
determined by the size of an industry in a particular location, then we say that there is a “localization
economy” at work. Since the effect in question is tied to experience in computer science, it seems likely
that the size of the industry is most important, and that this is therefore an example of a localization
economy.

2

The diagram below shows the relationship between utility V and city size N in a city where there is an urbanization economy in production.
Diagram R&D Lesson 3 Question 2

(a) Why does utility initially rise with city size?

(b) Why does utility eventually fall with city size?

(c) Suppose that this is the only city in an otherwise rural economy, where the utility available in the hinterland is V(0). Suppose further that people are free to migrate to the city and that they choose the location that maximizes their utility. What is the equilibrium city size under these conditions? Briefly explain how this equilibrium is determined.

(d) Is the equilibrium city size from part (c) efficient? Why or why not? Identify the efficient city size and discuss its defining characteristic in your answer.

(e) Explain why individual migration generally leads to cities that are too large.

(a) Because the urbanization economy causes wages to increase with city size, and over this range,

wages are rising more quickly than the costs of living.
(b) Because the costs of living, defined broadly to include housing costs, commuting costs and
costs associated with disamenities like congestion and pollution, eventually rise more quickly
than wages.

(c) Individuals migrate to the city so long as the utility that it provides is at least as large as the
utility available in the hinterland. This process stops when utility in the city falls back to V(0).
Thus, N** is the equilibrium city size in this context.

(d) No, N** is not efficient — it is too large. The efficient city size is N* — the size that
maximizes the utility of a typical resident. At this point the marginal benefit and marginal cost
of adding another resident to the city are equal.

(e) The problem is that each new resident considers only his own well-being, and ignores the
impact of his migration decision on others in the city. Although the last migrant is as well off
joining the city as not, the marginal benefit that he brings (by strengthening the urbanization
economy) is not as large as the marginal cost that he imposes (by increasing the costs of living).
Thus, by joining the city population, he is making other residents worse off.

3

Urban and regional economists have noted that the size distribution of cities in some countries tends to follow a simple rule known as the "rank size rule." In its simplest form, this rule states that a city's rank (in terms of population) times its population is a constant. Using the data in Table 4.1(in the text), calculate rank times population for the twenty five largest CMAs in 1996, and plot the results on a graph. What would the graph look like if the distribution did follow the rank size rule? Does the size distribution of cities in Canada seem to follow the rank size rule? Explain

The results are shown on the graph below. If the distribution followed the rank size rule, then the graph
would show a horizontal line whose height was equal to the population of the largest city. However the
actual graph is far from a horizontal line. The size distribution of cities in Canada does not seem to
follow the rank size rule.
Diagram Located R&D answers Lesson 3 Question 3

4

The data in Table 4.2 (in the text) shows that there are very large cities in both rich and poor countries. Using ideas from the discussion of optimum and equilibrium city sizes, explain why there are very large cities in both rich and poor countries. Think about Tokyo on the one hand and Mexico City on the other. Does the explanation for very large city sizes seem likely to differ in the two cases? Briefly explain and use a diagram to illustrate your answer.

In rich countries, it seems likely that very large cities arise from strong agglomeration or external scale
economies. In poor countries, it seems likely that very large cities are a consequence of very low rural
utility levels. This is shown in the following diagram.
Diagram Located R&D answers Lesson 3 Question 4

5

The following statements are related to city formation. Place them in chronological order starting with what comes first.
A. Competition for good accessible locations create differences in land prices.
B. Companies such as specialty vegan stores are introduced into the clustering firms.
C. Economies of scale cause firms to group.
D. There are differences in population density.

(1) C, D, B, A
(2) C, A, D, B
(3) A, D, C, B
(4) D, A, B, C

Answer: (2) First, scale economies cause firms to cluster in space. Competition for accessible locations creates differences in land prices that give rise to differences in population density. Companies such as specialty vegan stores develop last because these specialty stores will only form once the city is big enough to support them.

6

Which of the following statements explain the benefits associated with the clustering of firms?
A) A firm is now able to purchase specialized inputs more cheaply than it can produce them internally.
B) A firm will now have access to a pool of skilled labour that is not available elsewhere.
C) A firm is now able to acquire valuable information from other firms regarding marketing practices.
D) A firm is now able to acquire valuable information from other firms regarding technical innovations.

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

Answer: (4) If a firm locates with many other firms, it will be able to purchase specialized inputs more cheaply than it can produce them internally; it will have access to a pool of skilled labour that is not available elsewhere; and it may acquire valuable information from other firms. Incurring lower transportation cost because of locating within a group is also a benefit associated with the clustering of firms.

7

The demand for products from Alexander's Pastry Shop has sky-rocketed in the last few months and Alexander is making more than he ever has before. His shop is located in a town called Ashcroft. He has finally saved enough money to move his shop to a new city, Kelowna, where he expects his shop will make even more money. Unfortunately, after being in business in Kelowna for 3 months, he goes bankrupt. Alexander says, "there just isn't a large enough industry for hand baked goods in Kelowna. It costs me an arm and a leg to purchase any of my baking materials. In Ashcroft, where there is a large flour mill and many packaging companies, the cost of my inputs are much cheaper." What type of scale economies are at work for Alexander in Ashcroft?

1) Urbanization economies
2) Localization economies
3) Positive economies of scale
4) Negative economies of scale

Answer: (2) Because the external scale economy is mostly determined by the size of the firm’s industry at a particular location, it is a localization economy. When there are localization economies, firms will be more productive when there are many other related firms at the same location. In this case, it is the size of the industry, not the size of the city, that matters.

8

Wesville is a medium-sized city located in Northern Ontario. The city and the standard of living has grown drastically over the last 10 years. What has the trend in wages been over the last 10 years assuming that an external scale economy is present, urbanization has occurred, and the city has not reached its optimum size yet?

1) Over the last 10 years, wages have slowly decreased. 2) Over the last 10 years, wages have increased.
3) Over the last 10 years, wages have stayed approximately the same.
4) The trend in wages cannot be determined with the information given

Answer: (2) If a firm enjoys an external scale economy, then labour productivity will rise with the size of the city. However, in a competitive labour market, wages are tied to labour productivity. More specifically, we know that the wage equals the value of the marginal product of labour in a competitive market. Thus, when there are external scale economies, wages should rise with city or industry size. One of the benefits of living in a larger city, other things being equal, is that wages are higher.

9

At the optimum city size, which of the following statements is TRUE?

1) The cost and the benefit of adding another person to the city is zero.
2) The costs of the concentration curve crosses the benefits of the concentration curve.
3) The marginal benefit of adding another person to the city and the marginal cost of adding another person are equal.
4) The cost and benefit curves are as close as they can possibly be without touching.

Answer: (3) At the optimum city size, the marginal benefit of adding another person to the city and the marginal cost of adding another person to the city are equal. The optimum city size is where the slopes of the costs of concentration curve and benefits of concentration curve, the marginal cost and the marginal benefit, are the same.

10

A city is emerging on the flat lands of Saskatchewan, 400 kilometres north of the Canadian-American border. Residents are beginning to cluster because the utility level that is available in the cluster area is higher than that available in the hinterlands. As more and more residents discover the increased utility they can obtain, they move to the city. Which of the following statements is TRUE?

1) The city will grow until the utility available is equal to the level that is available in the hinterland.
2) The city will grow until the marginal external cost of adding another person to the city equals the marginal cost of adding another person.
3) The city will grow until the utility available is at its highest point.
4) The city will only grow if the utility curve is increasing.

Answer: (1) As the city’s size increases it will eventually reach its optimum size, the peak of the utility curve. The city will not stop growing at this point. The next migrant will be choosing between the utility in the hinterlands and the utility in the metropolitan area, which is slightly lower than at its maximum. They will choose to move to the city. The migration of residents from the hinterland will only stop once the utility in the city is driven all the way down to the utility level that is available in the hinterland. At this point, residents will have no reason to move.

11

Many cities are much bigger than their optimum size. This is because:
A. each additional migrant moves to the city making all residents of the city worse off, while making the individual better off.
B. each additional migrant increases the city's aggregate utility.
C. each individual who migrates to the city ignores the impact that they have on other residents.
D. there is a negative externality that leads to such excessive city sizes.

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

Answer: (3) The equilibrium of cities is very inefficient. Each individual who migrates to the city ignores the impact that he or she has on other residents. Each individual migrant considers only his or her own utility. Once the population of the city passes the optimal size, each additional migrant is making all residents of the city worse off. Thus, there is a negative externality in migration that leads to excessive city sizes.

12

Oliver, the Mayor of Spuzzum, is worried because he thinks that his city's size is far above the optimum level. What can he do to try and reduce the city's size and/or the growth rate? Assume that Oliver cannot directly control individual migration.

1) Oliver can try and raise the utility level of Spuzzum.
2) Oliver can try to raise the utility level of the hinterland.
3) Oliver can try and create more cities.
4) Options (2) and (3) are true.

Answer: (4) Assuming that Oliver cannot directly control individual migration, there are two approaches that might correct the problem of inefficiencies in city size. The first is to raise the utility level that is available in the hinterland. Policies that try to raise rural utility levels to stem migration are common in the developing world. The second is to create more cities, so that even with unrestricted individual migration, all cities are closer to their optimum sizes.

13

As discussed in the text, Henderson argued that _________ will fix the inefficiencies in city sizes by restricting growth past the optimum level. Because every resident in the city will now receive a higher utility there is a profitable opportunity for the __________. People will be willing to pay up to {v(N*) -v(0)} to live in a city of the efficient size, and thus __________ have an incentive to correct inefficiencies in city size.

1) developers, developers, developers
2) large organizations, developers, the government
3) the government, developers, developers
4) the governments, government, large organizations

Answer: (1) Henderson was the first person to carefully consider the role of developers in the process of city formation. Henderson argued that competitive land developers will correct inefficiencies in city sizes. At the city equilibrium, every resident gets the same utility as the residents in the hinterlands. However, if the city size could be restricted to the optimum level, every resident would get a higher utility level. Thus, there is a profit opportunity: people would be willing to pay up to the optimum level of utility minus the level of utility available in the agricultural land in order to live in a city of an efficient size. If a developer can form a new city, he or she can capture at least part of this surplus as profit. In this way, developers have an incentive to correct inefficiencies in city sizes.

14

Is the optimal size of all cities the same?

1) Yes, always.
2) Yes, almost all the time.
3) No, the optimal size depends on the strength of the urbanization and localization economies at work.
4) This question cannot be answered without more information.

Answer: (3) The optimal size of cities is not the same for all cities. It depends on the strength of the urbanization and localization economies at work.