Econ 137

Urban Economics
Lecture Notes III

Guillermo Ordonez, UCLA

Questions for Lecture Notes III

„ Is there a land use pattern?

„ What is it like?
„ What determines the price of land?
„ What determines the pattern in the use of land?

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The Leftover Principle
„ From Ricardo

„ From competition (and since land is fixed), households,

manufacturers, offices, etc, would be willing to pay for land
up to the profits of their activities in the land.

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 The Monocentric City
„ City with a Central Business District (CBD)

„ Assumptions:
… 3 type of land uses (offices, manufacturing firms, residential)
… Central Export Node (Railroad terminal)
… Horse drawn wagons (goods from factory to railroad terminal)
… Hub-and-spoke streetcar system (for workers to factory)
… Agglomeration Economies (office industry)

Transport Technology is Key

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The Monocentric City
What determine land prices?

„ Rural sector: Fertility of the land

„ Households: Accessibility to workplaces (i.e. commuting
costs).
„ Manufacturing sector: Accessibility to consumers or
suppliers. (i.e. distance to consumers or suppliers)
„ Information sector: Accessibility to information

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Residential land

Housing
Service Land
Households Owners
Providers

Bid
- Rent for
Residential Land

Price for Housing Land Price and

Land use

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 Housing Prices (without substitution)
„ NO consumer substitution:
… 1000 square
- foot houses
… $300/month budget for typical HH
… Commuting cost = $20/mile per month

Assumed Consumption Pattern

i) Distance to city center (miles) 3 6 9 12 15
ii) Housing consumption (square feet) 1000 1000 1000 1000 1000
iii) Net income/month (300-(i)*20) 240 180 120 60 0
Price per Square-foot (iii/ii) 0.24 0.18 0.12 0.06 0

Linear housing price function [slope = -0.02$/sq. foot]

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 Housing price function (w/o substitution)
Housing Price Function
0.35

0.3

0.25
Price of housin

0.2
Without substitution
0.15

0.1

0.05

0
0 3 6 9 12 15
Distance to center (in miles)

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Housing Prices (with substitution)
„ The household may decide whether to live at:
… A small house (less expensive in land).
… A big house (more expensive in land).

Consumption
Indifference curve

House size

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Housing Pricing (with substitution)

Consumption High relative price of houses

Small house

Big house
Low relative price of house

House size
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 Housing Pricing (with substitution)
„ Consumer substitution
… As the price of land increases, people accept smaller houses.

Assumed Consumption Pattern

i) Distance to city center (miles) 3 6 9 12 15
ii) Housing consumption (square feet) 500 600 750 1000 1000
iii) Net income/month (300-(i)*20) 240 180 120 60 0
Price per Square-foot (iii/ii) 0.48 0.30 0.16 0.06 0

Convex housing price function

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 Housing price functions
Housing Price Function
0.8

0.7

0.6
With substitution
0.5
Price of housin

0.4

0.3

0.2
Without substitution
0.1

0
0 3 6 9 12 15
Distance to center (in miles)
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Residential land – Bid Rents (from
production of houses)
Fixed proportions: Flexible proportions:
Rh (d ) = Ph (d ) H − K Rh (d ) = Ph (d ) H (d ) − K (d )

Rh (d ) = Bid Rent
H = square feet of housing [not land!!]
K = nonland costs (to produce houses)
Ph = price of housing (per squared feet)
d = distance from city center (blocks)
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Housing-Price and Bid-Rent Functions
$
Total Revenue = P(d)H

Cost of non-land inputs (K)

Bid-rent function

d*
Miles to city center

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House production with input substitution
„ The house producer may decide whether to build:
… A tall building (less expensive in land and more expensive
in capital).
… A short building (more expensive in land and less
expensive in capital).
Capital
Isoquant
(let’s say the production of one apartment)

Econ 137 - Summer 2007 Land lot size 15

House production with input substitution

Capital High relative price of land

Tall building

Short building
Low relative price of land

Land lot size

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Consumer density
„ Consumer substitution
… Price of houses is high around the center, so people prefer
smaller houses.

„ Factor substitution
… Producers of houses substitute land by capital (relatively
cheaper), producing tall buildings.

People packed in tall buildings and small apartments !!!

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Important point !!!
„ The big effect is given by lot sizes.

„ If people accept to live in small houses in downtown

(because the price of the houses), then real estate
agents increase even more the price per square feet to
extract all the surplus from the workers !!!!!

Recall we are tracking the price per square feet

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Land for the manufacturing sector
„ Manufacturers
π m (d ) = PmQ − Cm − tQd − Rm (d )

Pm = Price of goods
Q = Quantity produced in one acre
Cm = Production cost (noland inputs) of Q
d = distance from terminal
t = wagon transport cost per unit per mile
Rm (d ) = land rent per acre to bid

„ Fixed Proportions and Constant Returns to Scale

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Land for the manufacturing sector
„ Fixed Proportions and Constant Returns to Scale
„ Profits are zero ( π m (d ) = 0)

Rm (d ) = PmQ − Cm − tQd
∂Rm (d )
= −tQ
∂d

„ Rent is determined by the terminal station location.

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Manufacturing Bid-Rent Curve

Rent (in $)
Linear Bid-Rent Curve

Slope = -tQ

Distance from terminal

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Manufacturing Bid-Rent Curve
Is the Bid-Rent Curve always linear?
Rent (in $) NO if the production is flexible
C(d) such that C’(d)>0

If production function is flexible

This is because, as the factory approach to the center
it saves from distance (freight costs) and saves using
less land and more of other inputs

If production function is fixed

Leontieff

Distance from terminal

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Offices Bid-Rent Curve
„ Travel costs in the information and consulting sector is
subject to agglomeration economies.
„ While the manufacturing sector just has to transport the
production to the terminal (one way), in the information
sector employees have to return to offices (round trip)
„ In this case, the central location minimize total travel
distance, which increases exponentially as the firm
separates from the center.

The median location minimizes total travel distance

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Principle of Median Location
„ Many input or output locations

„ Example: Pizza Delivery

… Ubiquitous inputs (tc=0)
… Pizza price fixed (2 dollars/pizza, 1 pizza/consumer)
… Each pizza sold requires one trip from store to buyer’s
location
… Many markets (differ in size and location)
… Delivery cost per pizza = $2/mile

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 Principle of Median Location
„ Optimal Location?

W X Y Z

Distance from W 0 1 2 9
# of consumers 2 8 1 10
Monetary Weight $4 $16 $2 $20

„ Median Location has ½ of the monetary weight to the left

and ½ to the right. MB of moving to the left or right
(decrease in transport costs) is lower than the MC
(increase in transport costs).

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 Principle of Median Location
„ Optimal Location?

W X Y Z

Distance from W 0 1 2 9
# of consumers 2 8 1 10
Monetary Weight $4 $16 $2 $20

„ Why not move from Y? to X?

… Total TC at X: $4 x1 + $16x0 + $2x1 + $20x8 = $168
… Total TC at Y: $4 x2 + $16x1 + $2x0 + $20x7 = $164
„ What if 4 new consumers move to W?

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Offices Bid-Rent Curve

Rent (in $)
Concave Bid-Rent Curve

Basic assumption:
Standard office

Distance from center

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Offices Bid-Rent Curve
„ The firm may decide whether to locate the office at:
… A tall building (less expensive in land and more expensive
in capital).
… A short building (more expensive in land and less
expensive in capital).
Capital
Isoquant for offices

Econ 137 - Summer 2007 Land lot size 28

Offices Bid-Rent Curve

Capital High relative price of land

Tall building

Short building
Low relative price of land

Land lot size

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 Offices Bid-Rent Curve

Rent (in $) With factor substitution

Close to the center firms not
only have to pay more land
but also more capital
because of tall buildings

Why the two curves coincides here?

Without factor
substitution

Distance from center

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Land Use in the Monocentric City
Land rent per acre

Office bid-rent function

Manufacturing bid-rent function

Residential bid-rent function

Agricultural bid-rent function

u0 u1 u2 Distance to city
center

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Why these slopes?

„ Steeper bid
- rents curves keep the center (more
willingness to pay)
„ Slopes are determined by transport costs.
„ Office steeper because use people (workers walk)
„ Manufacturing use horses and wagoneers (trucks)
„ Resident commute of streetcars (buses or metro), which
represent the lowest cost among the possibilities.

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Land Use in the Monocentric City
Land rent per acre

Office bid-rent function

Manufacturing bid-rent function

Residential bid-rent function

Agricultural bid-rent function

u0 u1 u2 Distance to city center

Office district

Manufacturing district

Residential district

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Relaxing assumptions
„ Time cost of commuting
„ Non
- commuting travel
„ Two
- earner households
„ Spatial Variation in other locational attributes
„ Income differentials
„ Zoning

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Relaxing assumptions
„ How the graph changes if we introduced a beltway?
$

Beltway

Center
Office Office Manufacturing Manufacturing Manufacturing
sector workers workers sector workers
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 Summary Ch. 6 O’Sullivan
„ In the monocentric city, manufacturers export their output in horse-drawn
wagons to a central export node; office workers travel by foot from offices
to a central market area to exchange information; commuters and shoppers
travel to a hub-and-spoke streetcar system.
„ The bid-rent curves are negatively sloped because of transportation cost,
and convex because of factor substitution (and also consumer substitution
in the case of housing).
„ The office sector has higher transportation cost per mile, so its bid-rent
function is relatively steep and office firms occupy the city central area.
„ Employment is concentrated in the CBD because the cost of commuting
from the suburbs to the CBD (via streetcars) is low relative to the cost of
moving output from the suburbs to the city center.
„ The urban land and labor markets are connected because labor demand is
determined by the territory and density of the business sector, and labor
supply is determined by the territory and density of the residential sector.
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 Cities are changing
„ Employers are more dispersed on the metropolitan area.
… In the US, CBD concentrates 20% of total employment in MA
… In the US, CBD concentrates 40% of total offices in MA
… Population (20% in 3 miles around CBD) and commuting

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 General characteristics of centers and
subcenters in US
„ Numerous in both new and old large MAs
„ Jobs dispersed rather than concentrated.
„ Subcenters highly specialized
„ However, centers still important.
„ Density decreases as distance from center increases.
„ Centers still more developed in face2face type of activities.
„ Median workplace of the largest 100 metropolitan areas are
about 7miles from city center

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 Urban density
„ Varies a lot across countries and cities in the US
„ Density gradient: Rate at which population decreases with
distance ∆density
dg = / distance
density
„ For example, 0.1 means the density decreases by 10% per
mile from center.
„ In average the density gradient in the US goes from 0.05 to
0.15

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 Average Density Gradient
Urban density 4 Metropolitan Areas
Year Avg Gradient
1880 1.22
1890 1.06
1900 0.96
1910 0.80
1920 0.69
1930 0.63
1940 0.59
1948 0.50
1954 0.40
1958 0.35
1963 0.31
Baltimore, Milwakee, Philadelphia, and
Rochester. Source, Mills (1972)
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 Subcenters in Los Angeles
„ Conventional view of Los Angeles: “Endless urban sprawl,
with employment and population dispersed throughout”
„ In fact, highly complex space economy characterized by a
system of specialized centers, dispersed but yet strongly
influenced by the pull of LA central area.

„ Up to WWII, metropolitan growth confined to LA county.

„ By 1965 suburbs well extended into Orange County to the
south and San Fernando Valley to the north.
„ By 1980 suburbs well extended to Riverside and San
Bernardino to the east and Ventura County to the western
edge. Econ 137 - Summer 2007 41
 Subcenters in Los Angeles
„ Definition:
… Density at least 25 workers / hectare
… Total employment at least 10,000 workers
„ 32 in 1980 (average 45 workers / hectare), including Downtown
LA, Riverside, Ventura and San Bernardino
„ 23 % of total metropolitan employment
„ 4 largest centers form an arc from Santa Monica through
downtown LA (Wilshire corridor, a giant center 19 miles long)
„ Downtown LA comprises ½ percent of region’s land area but
contains 10% of workers and 31% jobs within centers.
„ Commutes to jobs within the center are longer than outside the
center. Econ 137 - Summer 2007 42
Subcenters in Los Angeles

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Subcenters in Los Angeles

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 Subcenters in Los Angeles
„ 5 types
… Mixed industrial (near a transport node, e.g. airport, port,
marina). (LAX, Orange County Airport, Inglewood, Marina del
Rey, etc.)
… Mixed service (typically an independent center in the past)
(Downtown LA, Santa Monica, Glendale, Santa Ana, Pasadena,
Long Beach, Riverside, Ventura, San Bernardino, etc.)
… Specialized manufacturing (Long Beach Airport, Burbank
Airport, Hawthorne, Lawndale, etc.)
… Service oriented (West LA, East LA, Anaheim, etc.)
… Specialized entertainment (Hollywood and Burbank)
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 The rise of monocentric cities.
„ Improve in transportation technology
„ Rule of thumb: “Radius of a city is the distance that can be
traveled in one hour”
„ Hub and spoke public transit system in the 19th century.
„ Short CBDs
… Before elevators, price of high floors were cheaper because
they were rented at a discount that offset the costs of climbing
four or five floors of stairs.

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 The decline of monocentric cities.
„ Decentralization of manufacturing
… Intercity tucks. Trade off of moving away from center is
between higher freight costs and lower wage.
… Since freight costs decrease, it’s better to move out from
centers.
… From factories close to ports, railroads and city centers to
factories close to highways, beltways and airports

„ Decentralization of offices
… Advance of communications (a reduction in the need for
face2face activities)

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 The decline of monocentric cities.
„ Decentralization of population
… Evidence: Reduction in density gradients
… Rising income and change in consumption bundles (not clear)
… Decrease in commuting costs
… “Jobs follow workers to suburbs and workers follow jobs to
suburbs”
… Others: Old housing at the center, high taxes, crime, low
quality education, etc.

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 Summary Ch. 7 O’Sullivan
„ The median job location is seven miles from the city center and the median
residential location is eight miles.
„ Cities in the US are much less dense than cities in the rest of the world.
„ The key factors in the rise of large monocentric city were innovations in
intraurban transportation that decreased the cost of commuting and
innovations in construction that decreased the cost of tall buildings.
„ The key factors in the decentralization of jobs and people were increases in
income and the development of the truck, the automobile and the highway
system.
„ Between 1950 and 1990, the amount of urban land increased more thn
twice as fast as the urban population.

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Questions for Lecture Notes III

„ Is there a land use pattern?

„ What is it like?
„ What determines the price of land?
„ What determines the pattern in the use of land?

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Practice Exercises - Lecture Notes III
„ O’Sullivan
… Chapter 6: Exercises 2, 3, 4 and 5.
… Chapter 7: All exercises.

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