urban economy essay
lqw091123
LectureSlidesChapter43.pptxChapter 4 City Size
Based on Urban Economics by O’Sullivan 8th edition textbook
Cities differ in size and scope
Key Question
How does an increase in city size affect the utility of a worker?
City Sizes Across the U.S.
Table shows that we have very few extremely large cities, some medium sized cities, and many small cities.
Cost and Benefits of Big Cities
Undesirable features of large cities include
Congestion
Longer commute times
Greater density
More pollution
Higher crime
Larger cities benefit from agglomeration economies
Cost savings
Higher productivity
Reflected in higher wages
But, wages increase at a decreasing rate. Why?
Example: Utility of a Worker
Wages increase (@ decr. rate) with city size
Comes from an
8 hour work day
Increases with workforce at an increasing rate
Utility = Labor income - commuting cost
Implies optimal city size = size where utility per worker is maximized
Utility decreases when agglomeration economies weaker than diseconomies from higher commute costs.
utility increases if agglomeration economies stronger than increased commute costs.
Location Choice of Workers
Where will workers choose to live?
Axiom #1 Locational Equilibrium
Locations closer to the city center have lower transportation/commute costs; more desirable
Price of residential land adjusts to make workers indifferent between locations
Cheaper land further away will offset travel/commute costs to the city center
More expensive land near city center must pay for convenience of shorter commute times
Locational Equilibrium
Example: City of 2mill workers where wage = $80, workers own land and each receives an average rental income = $15. The price of land (land rent) adjusts to offset commute cost until total commute cost + rent is equal across locations.
System of Cities
How is the workforce distributed among cities?
What is the equilibrium number of cities?
Is the equilibrium stable?
Consider a region of 6 million workers. Various possibilities include:
Six cities, each with 1 million workers (small)
Three cities, each with 2 million workers (med.)
Two cities, each with 3 million workers (large)
Six Cities
Consider a region where there are 6 cities with 1 million workers in each
Is this an equilibrium? Is it stable? This is marked by point S in figure 4-2.
A
B
C
D
E
F
At point S, utility per worker ($59)
is equal across the six cities.
No worker has an incentive to move to another city
Point S is an equilibrium
Migration of workers will not result in the same equilibrium. Any point on upward sloping portion of the curve results in self-reinforcing migration and is unstable.
Point S is not stable
Growing City
Shrinking City
A
D
Axiom #2: Self-reinforcing effects generate extreme outcomes
Self-reinforcing change: more workers have an incentive to migrate
Extreme outcome: city A disappears
Take-away: Cities cannot be too small because being on the positively sloped portion of utility curve generates unstable equilibrium will not stay there.
A
E
C
D
F
B
Migration from A to D generates higher utility in D
Similarly for B and C
Two large cities
Is point L a stable equilibrium?
Two large cities
Point L is a stable equilibrium
Migration is self correcting. Any point on downward sloping part of utility curve is a stable equilibrium
Cities May Be Too Large, but not Too Small
The 2-city outcome (pt. L, 3mill people)
Migration generates higher utility in shrinking city (moving left of point L)
Migration is self-correcting: migrants regret the move (right from L) and return (back to L)
Lesson: Negatively sloped portion of utility curve generates stable equilibrium. This stability causes inefficiently large cities to exist; because of self-correction never get back to optimal city size.
Questions for Discussion
What is optimal city size?
Is equilibrium stable?
Is it a unique equilibrium?
Implications for policy making?
According to model, what causes city to grow?
What Determines City Size and Scope (mix of products)?
Partly determined by extent of agglomeration (localization and urbanization) economies
The introduction of local goods amplifies differences in size
Specialized and Diverse Cities
Localization economies Specialized cities
Promotes efficient production
Urbanization economies Diverse cities
Promotes innovation
Localization and Urbanization Economies
Differences in city size from differences in agglomeration economies:
workers
Utility/worker
S: small localization
M: large localization
B: large urbanization
There are 10 mill workers total in the region.
Utility must be equal across cities
Each city must be on negative sloped side of utility curve
1
3
6
Role of Local Goods in determining City Size
Export employment: employment in industries where the output is exported to people outside the city Ex: car manufacturer
Local employment: employment in industries where output is sold to people in the city Ex: Pizza shop
Total employment = Export employment + local employment
Role of Local Goods in determining City Size
Local goods (groceries, restaurants, haircuts, auto repair) are ones consumed locally in city
Per-capita demand large relative to scale economies
Some local goods are available only in large cities (e.g. opera, sports, or MRI’s)
Per-capita demand small relative to scale economies
Larger cities have larger consumer base and therefore offer wider variety of consumer products
Rank Size Rule
Describes relationship between the size and rank of a city.
This is a power rule from mathematics also known as Zipf’s Law.
Pr= P1/r where
Pr = population of rth ranked city
P1 = population of largest city (rank 1)
r = city rank
This is a surprisingly stable relationship/pattern. However, does not explain/fit urban giants or primary cities
Urban Giants & Large primary Cities
In many developing countries, the central city, tends to be very large as it has a relatively large population share. Why?
Puzzle of Large Primary Cities
Large economies of scale in trade encourage the development of a single large trading center
In many developing countries a disproportionate share of investment in telecommunication and transportation occurs around the capital city
Role of politics. Ades and Glaeser (1995) suggest that nations run by dictators have larger primary cities. Why?
