Chapter 4
City Size
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.
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)

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.
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
Moving from a
city of 1m to
2m increases
utility of a
typical worker.
The
agglomeration
economies are
stronger than
the
diseconomies
from
commuting.
This implies there is an optimal city
size, the size at which utility per
worker is maximized
Moving from a
city of 2m to
4m decreases
utility of a
typical worker.
The
agglomeration
economies are
weaker than the
diseconomies
from
commuting.
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
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
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

Six cities


Lets consider a situation where there are six
cities each with a population of 1m worker
A
B
C
D
E
F
Is this an equilibrium outcome? Is this outcome
stable?
Six cities: A to F
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
Six cities: A to F
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
Cities Are Not Too Small
Migration from
A to D
generates higher
utility in D
Self-reinforcing
change: more
workers have an
incentive to
migrate
A
D
B
E
C
Extreme
outcome: city A
disappears
F
Similarly for
B and C
Lesson: Positively sloped portion of utility curve generates
unstable equilibrium
Two large cities
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
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
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?
Role of Agglomeration
Economies in Determining City
Size

Differences in city size can be explained partly
by the extent of agglomeration economies.
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.
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
A system of different cities

Equilibrium in cities with differences in
agglomeration economies:
M: large
localization
Utility/worker
B: large
urbanization
Utility must be
equal across
cities
S: small
localization
1
3
6
There are
10 m
workers.
What is the
equilibrium
size of
each city?
workers
Each city has
to be on the
negatively
sloped side of
the utility
curve
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
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.
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%
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