Urban Economics 6th Edition, Arthur O’Sullivan

Chapter 6Urban Land Rent

John William GirsangParamita Estihandayani

5 October 2012

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.

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.

Deriving the Simple Bid-Rent Curve (Agricultural

Land)Price

of Corn

Quantity Produce

d

Total Revenu

e

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.

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.

Manufacturing Sector

Bid Rent Curves for the Manufacturing

SectorDistanc

eTotal

RevenueNonland

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

𝑅𝑒𝑛𝑡 𝑝𝑒𝑟 h𝑒𝑐𝑡𝑎𝑟𝑒=𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒−𝑛𝑜𝑛𝑙𝑎𝑛𝑑𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑐𝑜𝑠𝑡− h𝑓𝑟𝑒𝑖𝑔 𝑡 𝑐𝑜𝑠𝑡

𝐿𝑜𝑡 𝑠𝑖𝑧𝑒(𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑙𝑎𝑛𝑑)

• 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.

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?

Information SectorKeyword: central place, office space

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.

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.

𝑅𝑒𝑛𝑡 𝑝𝑒𝑟 h𝑒𝑐𝑡𝑎𝑟𝑒=𝑇𝑜𝑡𝑎𝑙𝑟𝑒𝑣𝑒𝑛𝑢𝑒−𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑐𝑜𝑠𝑡− h𝑜𝑡 𝑒𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑐𝑜𝑠𝑡− 𝑡𝑟𝑎𝑣𝑒𝑙𝑐𝑜𝑠𝑡

𝐿𝑜𝑡 𝑠𝑖𝑧𝑒(𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑙𝑎𝑛𝑑)

Office Bid-Rent Curves with Factor

Substitution

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

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.

Housing Prices

Housing PricesAssumptions: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 insignificant4. 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.

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)

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.

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 Househol

d (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.

Land Use Patterns

Bid Rent of the Office Sector

Bid Rent of the Manufacturing Sector

Maximum Bid Rent of Employers

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.

Thank You05.05.12