The document outlines the factors influencing land prices within cities, emphasizing the relationship between land demand from different sectors—manufacturing, offices, and households—and the resultant land rent dynamics. It explains how bid-rent curves for various sectors are derived, illustrating how competition leads to economic equilibrium where rents adjust to maintain zero profit for producers. Additionally, it discusses consumer and factor substitution effects on housing prices and density, highlighting the significant difference in land use between city centers and suburban areas.

1. John William
GirsangParamita Estihandayani
5 October 2012

2. Chapter Outline
• Explaining why the price of land varies within cities
and show the connection between expensive land
and tall buildings.
• In this chapter, urban economy is divided into 3
sectors—manufacturing, offices, and households—
and see how much each sector is willing to pay for
land in different parts of the city.
• Land usually goes to the highest bidder, so once we
know how much each sector is willing to pay for
land, we can predict what goes where.

3. Introduction to Land Rent
Land rent vs. Market value
• Land rent is the periodic payment by a land user to
a landowner.
• Market value of land is the amount paid to become
the land owner.
• Price of land is land rent, a periodic payment to a
landowner.
• This is sensible because many other economic
variables are expressed as periodic payments,
including household income, firm profits, and
interest payments.

4. Deriving the Simple Bid-Rent
Curve (Agricultural Land)
Price of
Corn
Quantity
Produced
Total
Revenue
Nonland
Cost
WTP for
Land
Bid Rent
for Land
Low Fertility $10 2 $20 $15 $5 $5
High fertility $10 4 $40 $15 $25 $25
• The idea here is that the more fertile
(or productive) land commands a
higher rent
• In farming, productivity is based
primarily on soil quality, but this
location specific, not all places are
equally productive.
• In other industries, productivity may
be based on access to transportation
or other companies in similar business.

5. Describing the Leftover
Principle
• Competition among producers leads to a bidding
process for the land.
• Producers bid more for land that can produce
more.
• This drives economic profits to $0, i.e., all costs are
covered, along with the wages of the producer.
• This means, the land owner gets whatever is ‘left
over’ once all other factors of production are paid.

7. Bid Rent Curves for the
Manufacturing Sector
Distance Total
Revenue
Nonland
Production
Cost
Freight
Cost
WTP for
Land
Production
Site
(hectares)
Bid Rent
(per
hectare)
0 $250 $130 - $120 2 $60
1 $250 $130 $20 $100 2 $50
2 $250 $130 $40 $80 2 $40
3 $250 $130 $60 $60 2 $30
• Price adjust to generate locational equilibrium
• Variations in the bid rent for land make firms indifferent among all
locations. Differences in freight cost are exactly offset by differences in
land rent.

8. Deriving the Simple Bid-Rent
Curve (Manufacturing)
• If we look only at ground
transportation for
manufacturing, we can
develop a bid-rent curve that
declines with distance from a
major highway.
• At each location, rents adjust for
the manufacturer to generate
$0 economic profit.
• According to the graph, what is
the maximum distance away
form a major highway that a
manufacturer will locate?

9. Information Sector
Keyword: central place, office space

10. Bid Rent Curves for the
Information Sector
• In the information sector,
access to other firms in the
sector is important, and
access is determined by
travel distance.
• Firms located at the center
of a region travel less than
those at the edge.
• Firms located away from the
center see costs of travel
increasing at geometric rate.
i.e. not a linear rate.

11. Office Bid-Rent Curve
with a Fixed Lot Size
• As we move away from the
center, travel cost increases at
an increasing rate, so rent
decreases at an increasing rate.
• Differences in the cost of travel
for information exchange are fully
offset by differences in land rent,
so economic profit is zero at all
locations.

12. Office Bid-Rent Curves
with Factor Substitution

13. Building Options: The
Office Isoquant
• An office firm bases its choice of a
building height on the trade-offs
between the costs of land and
capital.
• A firm will use less land as land
becomes more expensive. The will
substitute capital, which is the
same price everywhere and
movable.
• A taller building requires more
capital because it requires extra
reinforcement to support its
concentrated weight, along with
extra equipment for vertical
transportation (elevators).
Tall Medium Short
Land (ha) 0.04 0.25 1.0
Building
Height (floors)
25 4 1
Capital cost
($)
250 100 50

14. Factor Substitution: Choosing
a Building Height
• Factor substitution
increases the slope of
the bid-rent curve
• Land is more expensive
closer to the center, so it
will be rational to
occupy a taller building.
• Because of factor
substitution, the bid rent
decreases by an amount
less than the increase in
travel cost.

16. Housing Prices
Assumptions:
1. The cost of commuting is strictly monetary, a cost of
$t per mile. We ignore the time cost of commuting.
2. One member of each household commutes to a
job in an employment area, either the CBD or a
manufacturing district.
3. Non-commuting travel is insignificant
4. Public services and taxes are the same at all
locations.
5. Amenities such as air quality, scenic views, and
weather are the same at all locations.

17. Linear Housing-Price Curve:
No Consumer Substitution
• A ‘standard’ house is 1,000
SF.
• An average household has
$800 allocated to rent.
• Commuting costs are $50
per mile per month.
• At a distance of 4 miles, a
house will rent for $600 and
commute costs will be 4 x
$50 or $200 for a total $800.
• At a distance of 10 miles, a
house will rent for $300 and
commute costs will be 10 x
$50 or $500 for a total $800.
• There is no utility difference
between locations
(equilibrium).
However, consumers are free to substitute a smaller house as they
move toward the employment center. (cont’d)

18. Consumer Substitution Generates a
Convex Housing-Price Curve
• As the price of housing (i.e., land) per sq feet
rises, people can consume fewer sq feet.
Housing size is not perfectly inelastic.
• This means people near employment
centers consume fewer square feet and
substitute toward other consumer goods with
lower (opportunity) costs.
• The leftover principle still applies here.
Because people use fewer sq feet, they can
now afford to pay more per sq feet.
• So, with factor substitution, price of housing
rises more quickly as you approach the
employment center.
• At a distance of 10 miles, a house will rent for
$300 (3x1000SF) and commute costs will be
10x$50 or $500 for a total of $800.
• At a distance of 5 miles, a house will rent for
$550 (0.8 x approx 687.5 SF) and commute costs
will be 5x$50 or $250 for a total of $800.

19. Residential Density
• Consumer substitution. The price of housing
increases, and households respond by consuming
fewer sq feet.
• Factor substitution. Housing firms respond to higher
land price by using less land per unit of housing.
Housing
(sq feet)
Land per Sq
foot of
Housing
Land per
Household
(sq feet)
Density
(households
per ha)
Suburb 2,000 2 4,000 8
City center 1,000 0.10 100 320
Putting these two factors together, the city-center uses 100 sq feet of
land, while the suburbanite uses 4,000 sq feet. Therefore, this example,
population density is 40 times higher in the central city.

20. Land Use Patterns

21. Bid Rent of the Office Sector

22. Bid Rent of the
Manufacturing Sector

23. Maximum Bid Rent of
Employers

24. Territories of Different Sectors
• Land is occupied by the
highest bidder, and the
intersection of the bid-rent
curves of office firms and
office workers shows the
boundary between the
business and residential area,
x1.
• Boundary between office
workers and manufacturing
workers occurs where the
bid-rent curves of the two
worker types intersect, at x2.
• Manufacturing firms outbid
their workers for locations
between x3 and x5, defining
manufacturing district.
• The area which manufacturing
workers outbid their employers
and a non urban land use
(agricultural), is between x5 and
x6.

25. Thank You
05.05.12