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Chapter 4

City Size & Growth

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Why Do Cities Vary in Size and Scope?

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City by size and scope in Europe

Own calculation based on the Urban Audit (2004)

3City typogy

A Principal Metropolises

B Regional Centres

C Smaller Centres

D Towns & Cities of the Lagging Regions

Urban Audit (EU)

Urban Audit (non-EU)

Size of circle is relative to population in core city* in 2004

10,000,0001,000,000

500,000100,000

*Paris: Kernel

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• Localization and urbanization economies increase productivity & wage

• Commute time increases with city size, decreasing leisure time

Utility and City Size

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• C: Differences in commute cost offset by differences in land rent

• E: Equal shares of land rent, averaging $15

• Utility = Labor income + rental income - commute cost - rent paid

Locational Equilibrium Within a City

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• Divide fixed number of workers among cities in region

• Six cities, each with 1 million workers

• Three cities, each with 2 million workers

• Two cities, each with 3 million workers

System of Cities in a Region

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Figure 4-2 Cities May Be Too Large

Along the negatively sloped portion of the utility curve, changes in population are self-correcting

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Figure 4-2 Cities Are Not Too Small

Along the positively sloped portion of the utility curve, changes in population are self-reinforcing

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• Two types of cities are complementary

• Many firms start in diverse city, which foster new ideas

• Maturing firms relocate to specialized cities to exploit localization economies

Specialized and Diverse Cities

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• Firm gropes for ideal production process for new product by building prototypes, imitating other firms in the process

• Once ideal process found, firm produces large quantity in a specialized city

• Location for experimentation: Diverse city or series of specialized cities?

• Diverse city: Relatively high prototype cost, given lack of localization economies

• Specialized cities: Move from one city to another until ideal process found

• Diverse city is more profitable if moving costs are relatively large

A Model of Laboratory Cities

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• Early firms were “small, numerous, agile, nervous, and heavily reliant on subcontractors”

• NYC provided a wide variety of intermediate inputs and workers

• Once technology settled, firms relocated to economize on labor cost

Example: The Radio Industry in New York

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• French firms: 7 of 10 relocations from diverse to specialized city

• Most innovative firms have highest frequency of moves from diverse to specialized

Evidence of Laboratory Cities

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• Why do cities differ in size and scope?

• Preview: Differences in localization & urbanization economies

• Introduction of local goods amplifies differences in size

Differences in City Size: Introduction

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• Some local goods (haircuts, groceries, pizza) sold in all cities, large & small

• Per-capita demand large relative to scale economies in production

• Local employment roughly proportional to population

• Some local products (brain surgery, opera) sold only in large cities

• Per-capita demand small relative to scale economies in production

• Local employment concentrated in larger cities

• Larger cities have wider variety: pizzas, haircuts, opera, brainsurgery

Local Goods and City Size

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The Rank-Size Rule (Zipf’s Law)

• Within a region, the size of a city’s population is inversely proportional to its rank on an ordered list: e.g.

•the largest city is #1•the 2nd largest is #2 with ½ the population of #1, •the 3rd largest city is #3 with 1/3 the population of #1

• This relationship applies to large urban systems around the world and over long periods of time.

City of RankPopulation sCity Largest = tionCityPopula '

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The Rank-Size Rule (Zipf’s Law)

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Size-rank of the 135 largest cities in the US (2000) is remarkably linear on a log-log scale (left)

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Size-rank of the 135 largest US cities (2000) has a power law exponent close to 1

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from Human Behavior and the Principle of Least Effort (1949)

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Zipf’s Law

1

communitylargest theof population

communityurban an of population

orderrank

≈

=

=

=

=×

q

K

P

r

KPr q

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R = C / Nb

R: Rank C: Constant

N: Population of city b: scaling exponent

• Rank-size rule holds if b = 1: Rank • N = C

• Empirical results

• Median estimate b = 1.09: Close to rank-size rule, but more even distribution

• Definition of economic city: b = 1.02

The Rank-Size Rule

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Standard Metropolitan Areas (MAs) cover large areas and include non-urban land

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Urbanized Areas include only urban land uses(448 UAs for the lower 48 states shown here)

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Zipf’s exponent for 48 statesWestern ½ = -1.07 Eastern ½ = -1.13

Western cities = 50.3M people Eastern cities = 140.0M people(26% of urban population) (74% of urban population)

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Interpreting Zipf’s graph lines

• Distance from origin = total urban population

• Slope: an integrated scaling factor

• Curves (violate Zipf’s Law)

• concave

• convex

• Tails (a problem for power laws)

• Upper (a few big cities)

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The Puzzle of the Large Primary City

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• Trading and indivisibilities in import/export facilities

• Neglect of intra-national transportation facilities

• Politics: Dictators retain power by bribing likely rebels in large capital city (Roman circus)

Reasons for Large Primary Cities

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• A country’s largest city

• Jefferson’s criteria:

- Always disproportionately larger than the second largest urban center -- more than twice the size

- In Europe, they are esp. expressive of the national culture

- Usually (but not always) the capital

• Examples: Paris, London, Athens, etc

Primate cities in Europe

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Urban Economic Growth (Chapter 5 from A. O´Sullivan)

• Economic growth = increase in per capita income

• Income may not be the best measure of utility

• In this Chapter

• Sources of income and employment growth

• Who benefits?

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Sources of Income Growth

• All sources of income growth do it by way of increasing labor productivity

• Non-geographical sources of income growth• Capital deepening – increase in physical capital per

person

• Increases in human capital

• Technological progress

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Sources of Income Growth

• Geographical source of income growth• Agglomeration economies (Chapter 3)

• Input sharing

• Labor pooling

• Labor Matching

• Knowledge spillovers

Distinguish:

• Change in a city's income level

• Change in a growth rate of income

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City Specific Innovation and Income

• We will use the Utility/City size curve to show the connection tech. progress & Income/capita.

• Suppose two cities in a region with identical utility curve.

• Suppose one city experiences tech progress.

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Results of Innovation

• Workers in both cities benefit from innovations in one city

• Innovations in one city cause that city to grow and the other cities to contract

• Higher wages in one city lead to higher wages in nearby cities

• If workers are mobile the benefits are spread across the region

• If high skilled and low skilled labor are complements, an increase in high skilled labor will increase wages for low skilled labor as well

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• Regionwide Innovation and Income

• Consider next that both cities experience simultaneous upward shift of utility curve

• No utility gap at original populations, so no migration

• Increase in utility in both cities

• Tech innovation ↑ utility and income/capita in a region. The same applies to other sources of higher productivity.

Results of Innovation

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• Increase in human capital increases per-capita income

• Workers are more productive

• Increase in rate of technological progress

• External benefits from increase in human capital

• Labor is complementary across skill levels

• Wage benefits from 1% increase in city's college share: high-school dropouts (1.9%); high-school graduates (1.6%); college graduates (0.4%)

• Proximity to star researchers an important factor in birth of biotechnology firms

Human Capital and Economic Growth

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• Changes in levels of human capital

• From 1980-2000, increase in share of metropolitan residents with degrees

• Variation in college share across metropolitan areas is large and growing

Human Capital and Economic Growth (continued)

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• Export product: sold to people living outside the city

• Local product: sold to local residents

• Related through the multiplier process

• Export workers spend portion of income on local products

• Local workers spend portion of income on other local products

• Employment multiplier: change in total employment per additionalexport job

Export versus Local Employment and the Multiplier

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Labor Demand Curve is negatively sloped:

• Substitution effect of an increase in the wage

• Firms substitute other inputs for relatively expensive labor

• Output effect of an increase in the wage

• ↑W → production cost →↑ in price

• ↓Consumption →↓output → ↓labor demanded

Urban Labor Demand Curve: Negative Slope

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• What causes the labor demand to shift?

• Demand for export goods

• Labor productivity

• Business taxes

• Public services

• Land use policies: accessible and with public services.

Urban Labor Demand Curve: Negative Slope

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• In Fig. 5-2. Increase in exports shift Demand from D1 to D2

• At D2 10.000additional workers are demanded at W=100

• If employment multiplier is 2.1 then:

every export job supports 1.1 local jobs.

So D shifts to the right by an additional 11.000 workers to D3

Total Labor Demand increases by 21.000

Urban Labor Demand Curve: Employment multiplier

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• Simplifying assumptions: • fixed hours per worker;

• fixed participation rate

• Positive slope: Migration in response to wage differences

• ↑ W attracts workers to the city

• Axiom 1: Growing city offer higher wage to offset higher cost of living

Urban Labor Supply Curve: Positive Slope

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• Elasticity of urban living cost, to size of labor force

• %Δ urban living cost / %Δ labor force = 0.20

i.e 10%↑ labor force → ↑ cost of living by 2%

Therefore to keep real wage constant:

• Elasticity of urban wage, to size of labor force

• %Δ wage / %Δ labor force = 0.20

Therefore the inverse will be:

• Elasticity of labor supply to a change in wage

• %Δ labor force / %Δ wage = 0.50

i.e 2%↑ in W → ↑ Labor force by 10%

Urban Labor Supply Curve: Positive Slope

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• What causes the labor supply curve to shift?

• Amenities (such as environmental quality)

• Disamenities (such as crime)

• Residential taxes

• Residential public services

Shifting the Urban Labor Supply Curve

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• In Fig. 5-3. the employment multiplier tells only the horizontal shift of D curve.

• To accurately predicts the Δ in total employment we must know the slopes of D & S.

%ΔW = %ΔD / (Ed + Es)• Ed Elasticity of Supply

• Es Elasticity of Demand (absolute value)

%ΔW = 21% / (2+5) = 3%

• Then by the S elasticity: Es * %ΔW = %Δ labor force5 * 3% = 15%

Urban Labor Demand Curve: Employment multiplier

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• Low-tax city grows faster, ceteris paribus (public services)

• Elasticity (business activity, taxes)

• Intercity location: ε : -0.10 to -0.60 (metropolitan area).

• Intracity location: ε : -1.0 to -3.0 (individual municipality)

• Manufacturers more sensitive to tax differences

• High taxes on capital repels capital-intensive industries

Taxes and Firm Location Choices

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• High-service city grows faster, ceteris paribus (taxes)

• Growth promoted by High tax that supports public services (infrastructure, education, safety)

• Growth inhibited by High tax that supports redistributional programs

Public Services and Location Decisions

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• Tax abatements, guaranteed loans, subsidized land and public services

• Economic development programs have small effects

Subsidies and Incentive Programs

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• What are the benefits of a $150 million stadium?

• Small employment benefits

• Small positive effect in 1/4 of cases; negative effect in 1/5 of cases

• Arizona: 340 jobs for $240 million

• Money spent largely by locals, replacing other local spending

• Other benefits--Civic/tribal pride and cohesion worth the price tag?

Professional Sports, Stadiums, and Jobs

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• Environmental policy decreases labor demand

• Increases production cost of polluting good => increase price

• Increase in price => decrease output and labor demand

• Improvement in environment increases labor supply

• Net effects on total employment logically indeterminate

Tradeoffs from Environmental Policy

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• Both industries (steel and clean) experience lower wages

• Steel: lower wages offset by pollution tax, so decrease employment

• Clean industry: lower wages increase total employment

Pollution Tax and the Distribution of Employment

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• ∆ Total employment = ∆ Export employment • Employment multiplier

• Table 5-1: Employment multipliers for metropolitan area

• Problems with employment-multiplier approach

• Horizontal shift of labor demand, not change in equilibrium employment

• Focuses on jobs rather than income

• Suggests that fate of city in hands of outsiders (export consumers)

Projecting Changes in Total Employment

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Population

• … picture of urban growth in Europe is diverse.

• … urban population in Europe grew from 2001 to 2004.

• …fastest growth in largest and most prosperous urban regions.

• In Principal Metro- polises, growth was high in the outer urban zones.

• Cities in lagging regions have not yet managed to “catch up”.

Urban Trends: Population 71

Own calculation based on the Urban Audit (2001, 2004), 329 obs. (core cities), 294 obs. (LUZ)

Population change by city type 2001 – 2004in %

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Population

• The first component of city growth is migration.

• Northern Europe: city growth corresponds with net migration

• Central Europe: cities lose population due to out-migration

• Western and Southern Europe: diverse picture

• The second component is natural population change.

• low urban birth rates in Northern, Western and Southern Europe, high urban birth rates in Central Europe

• city growth due to birth surpluses in peripheral regions

• cities of Western/Southern Europe and large cities of Central Europe: growth depends on attracting migrants, because there is a surplus of deaths over births.

Urban Trends: Population 72

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Own calculation based on PATSTAT

Patent intensity

10,000,0001,000,000

500,000100,000

above 50

25 - 50

1 - 5

below 1

Size of circle is relative to populationin core city* in 2004

Urban Audit (EU)

Urban Audit (non-EU)

*Paris: Kernel

5 - 25

Patent applications per 100,000 inhabitants, 2004

…innovation and prosperity combine

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74

Own calculation based on the Urban Audit (2004)

Share of foreignersBy city type, 2004 (in %)

The most prosperous cities attract the largest number of immigrants from foreign countries; international migration to peripheral locations is low.

0

10

20

30

40

50

Weighted Average

APrincipalMetro-polises

BRegional Centres C

Smaller Centres Towns & Cities of the

Lagging Regions

D

Urban Trends: Cultural Diversity