1. Chapter 4
City Size

2. Why do cities differ in size and scope?
In this Chapter we explore the economic forces responsible for the development of cities with different sizes.

4. Determinants of City Size
The following factors will determine the size of a city:
Localization or urbanization economies
Congesting factors
Migration from neighboring cities
Creation of local employment
Political economy considerations (democracy vs. dictatorship)

5. Benefits and Costs of Big Cities
Larger cities benefit from agglomeration economies reflected in higher wages.
However, large cities have several undesirable features, e.g. congestion, longer commuting times and pollution.

6. Utility of a Typical Worker
Commuting cost increases with workforce at an increasing rate
Wages increase with city size
Labor income assuming 8hrs work day
Utility = Labor income -commuting cost

7. Moving from a city of 1m to 2m increases utility of a typical worker
Moving from a city of 1m to 2m increases utility of a typical worker. The agglomeration economies are stronger than the diseconomies from commuting.
Moving from a city of 2m to 4m decreases utility of a typical worker. The agglomeration economies are weaker than the diseconomies from commuting.
This implies there is an optimal city size, the size at which utility per worker is maximized

8. A Side on Locational Equilibrium
Locations closer to the city center are more desirable as they result in lower transportation costs
Locational equilibrium implies that the price of residential land will adjust to make workers indifferent among all locations

9. Rental Price Adjusts
For example, in a city of 2m workers where the worker is paid $80, the price of land adjusts to achieve locational equilibrium.
Rent adjusts so that the total commute cost and rent is the same for all locations
Workers own land, each receives rental income equals to the average rent paid
Utility =D+E-B-C

10. A System of Cities Consider a region of 6 million workers
How will the region’s workforce be distributed among cities?
What is the equilibrium number of cities? Is this equilibrium stable?
We start by considering different possibilities
Six cities, each with 1 million workers
Three cities, each with 2 million workers
Two cities, each with 3 million workers

11. Six cities
Lets consider a situation where there are six cities each with a population of 1m worker
Is this an equilibrium outcome? Is this outcome stable? A B C F D E

12. Six cities: A to F Point S is an equilibrium
At point S, the utility per worker is equal across the six cities.
No worker has an incentive to migrate to a different city
Point S is an equilibrium

13. Six cities: A to F Point S is not a stable outcome
However, the migration of a group of workers will not give us back the same equilibrium. Any point on the upward sloping part of the utility curve is not a stable equilibrium
Point S is not a stable outcome

14. Cities Are Not Too Small
Migration from A to D generates higher utility in D
Extreme outcome: city A disappears A B C
Self-reinforcing change: more workers have an incentive to migrate F D E
Similarly for B and C
Lesson: Positively sloped portion of utility curve generates unstable equilibrium

15. Two large cities Point L is a stable equilibrium
Migration is self correcting. Any point on the downward sloping part of the utility curve is a stable equilibrium
Point L is a stable equilibrium

16. Cities May Be Too Large Start with 2-city outcome
Migration generates higher utility in the shrinking city
Migration is self-correcting: migrants regret the move and return
Lesson: Negatively sloped portion of utility curve generates stable equilibrium

17. Questions for Discussion
What is the optimal city size?
Is it a stable equilibrium?
Is it a unique equilibrium?
What are the implications for policy making?
According to this model, what causes a city to grow?

18. Role of Agglomeration Economies in Determining City Size
Differences in city size can be explained partly by the extent of agglomeration economies.

19. Extent of Agglomeration Economies
The extent of localization economies differs across cities. Consider cost saving from knowledge spillovers
The cluster exists, because the co-location of firms cut the expenses of identifying, accessing and transferring knowledge. Some studies have emphasized how firms will cut the costs of interacting if located in a cluster characterized by trust and other features of social capital (Maskell, 2000) that help reduce malfeasance, induce reliable information to be volunteered, cause agreements to be honored, enable employees to share tacit information, and place negotiators on the same wave-length.

20. Extent of Agglomeration Economies
However for other industries, trust-levels are insignificant, like, for instance, in Silicon Valley where “nobody knows anybody else’s mother”, and where no deep history or complex familial ties exist (Cohen and Fields, 1999: 2).
Finally, the extent of knowledge spillovers varies by industry type and age and by geographic region, and is influenced by structural and institutional factors, by culture [social or business] and by public policy

21. A system of different cities
There are 10 m workers.
What is the equilibrium size of each city?
Equilibrium in cities with differences in agglomeration economies:
M: large localization
B: large urbanization
Utility must be equal across cities
Utility/worker
Each city has to be on the negatively sloped side of the utility curve
S: small localization 1 3 6
workers

22. Role of Local Goods in determining City Size
Local goods are those consumed locally within a city
Some local goods are available only in large cities, e.g. opera or Peruvian restaurants.
That is because demand in small cities is not large enough to make it profitable for sellers to produce them

23. Local Goods and City Size
When producing local goods for which economies of scale exit, sellers are more likely to locate in larger cities, creating new employment opportunities.
Thus, Larger cities will create more employment opportunities than smaller ones.
Self Reinforcing effect: Larger cities are more likely to grow than smaller ones.

24. Large Primary Cities
In many developing countries, the central city tends to be very large as it has a relatively large population share
Metropolitan Area
Share of National population
New York metropolitan area
6.5 %
Tokyo
15.8%
Buenos Aires
35.5%
Mexico City
21%
Montevideo, Uruguay
39.4%

25. Puzzle of large primary cities
In many developing countries a disproportionate share of investment in telecommunication and roads occurs around the capital city (Why?)
Ades and Glaeser (1995) suggest that nations run by dictators have larger primary cities.
The dictator transfers resources to the primary city to satisfy the people who are most likely to overthrow him
This creates incentives for the rural dwellers to migrate to the city which gets even larger