Chapter 6
Urban Land Rent
Purpose
We study how land is allocated among the
different possible uses.
 We explore the market forces that
determine land use pattern.

Land Uses

Competing land uses:
– Agriculture
– residential
– Manufacturing
– Office

For each of these uses, there is a maximum
willingness to pay (WTP) in return for using
the land
How is land rent determined?
WTP for each use is determined by how
much money can be earned by using the
land.
 Land will go to the highest bidding use or
sector.
 Due to competition, WTP for land drives
profit to zero.

Definitions
Land rent: periodic payment from user to
owner
 Market value: amount paid to take
ownership
 In our discussion, we use the term “price
of land” to refer to land rent, which is a
periodic payment

Bid Rent
Bid rent is the amount that buyers are willing to
offer land owners as rent for a unit of land.
 Due to competition between buyers bid rent
adjusts so as to drive profit to zero.
 To calculate bid rent we use the left over
principle . We need information about revenue
and costs.
 David Ricardo (1881) the price of land is
determined by its fertility

Example: Agricultural land

Consider two types of one acre land: high
fertility and low fertility. The price of corn
is $10
Variation in land fertility generates variation in bid rent
The bid rent equals the willingness to pay for land
since competition between farmers drive profit to
zero.
Bid-Rent for Manufacturing




Desirability of urban land for
manufacturing is based on its accessibility.
Land closer to highways more desirable
Maximum WTP for a lot large enough for
production facility = Total revenue - nonland costs
Bid rent per hectare = WTP / lot size
Manufacturing Bid Rent
The
firm’s
freight
cost is
$20/
mile
Variation in freight cost generates variation in bid rent
Manufacturing Bid Rent Curve
The Bid rent
curve shows
willingness to
pay for land as
a function of
distance from
highway.
The
difference
in land
rent
drives
profit to
zero and
makes
firms
indifferent
between
all
locations
Information Sector

For the City’s Office Sector:
• firms gather, process, and distribute
information
• Face time required in information
exchange
• High opportunity cost of office workers
• Travel for Information Exchange
Central Business District
A
B
C
D
E
F
G
Travel Distance for Information Firms
The median location minimizes the travel
Travel distance increases
distance
at an increasing rate
Office Bid Rent

We can calculate the bid rent using the
left over principle.
The bid rent
curve is
downward
sloping
because as we
move away
from the center
the cost of
travel for
information
increases
The bid rent
curve is
concave
because
travel cost
increases at
an increasing
rate
Since travel
cost increases
at an
increasing
rate, to
maintain
profit at zero
bid rent has
to decrease
at an
increasing
rate
Bid-Rent with Factor Substitution
Since the price of land increases near the
center, people will economize on the use
of land
 They use less land space and build tall
buildings and thus expanding upwards
 Tall buildings requires capital to hold the
units on top of one another
 Thus people can substitute between land
and capital.

Bid-Rent with Factor Substitution
Given land rent and capital price, people
choose the building height that minimizes
cost
 Example: 4 units of office
space

Land area
Capital
Land cost when rent =$40
Total cost
Land cost when rent =$200
Total cost
Land cost when rent =$1600
Total cost
Tall
0.04
$250
Medium Short
0.25
1
$100
$50
Land area
Capital
Land cost when rent =$40
Total cost
Land cost when rent =$200
Total cost
Land cost when rent =$1600
Total cost
Tall
0.04
$250
Medium Short
0.25
1
$100
$50
1.6
251.6
10
110
40
90
8
258
50
150
200
250
64
314
400
500
1600
1650
Bid-Rent with Factor Substitution
Substituting between land and capital
saves on building cost.
 This leaves firms with positive profit.
 However, competition and free entry imply
that profits will be driven back to zero
 This takes place as bid rent increases.

Assume
that at
x=5, the
medium
building is
optimal
At x=1,
land rent
is high so
the tall
building is
most
efficient,
i.e. costs
less.
Convex Bid-Rent
Capital cost
increases to
250, but
you only
need 0.04
hectares
The
savings in
cost raise
profit. The
higher
profit in
turn will
raise the
bid rent to
……..
Housing Market

Model focuses on commuting as key
location factor:
– Monetary (not time) cost of commuting
– One member of household commutes to an
employment area (CBD or manufacturing
area)
– Non commuting travel insignificant
– Identical public services, taxes, and amenities
Housing Price Curve
Houses are
available in
standard
dwellings of
1000 sq ft.
The cost of
commuting
is $50/mile
per month
The house
price is
defined as
price per sq ft
A
household
has a fixed
amount to
spend on
housing and
commuting.
How much
?
The slope of the housing price
curve

Can you derive the slope analytically?
Housing price with substitution
With factor
substitution the
housing bid rent
curve will be
convex as shown
before
Since land price
is more
expensive near
the city center,
the household
consumes less
housing
Land Use Patterns
We can use the bid rent curves of
different land users to determine a city’s
equilibrium land use pattern.
 Three sectors compete for land:
manufacturers, office firms and residents.

Land Use Patterns

Features of urban transportation system:
– Manufacturers use trucks to transport output
through highways
– A highway goes through the center of the
metropolitan area and a belt way
– Residents work at the office sector and the
manufacturing firm travel by automobile.
Bid Rent for the office sector
Bid Rent for Manufacturing Sector
Bid Rent for Employers
Land Use Patterns