Chapter 6Urban Land RentUrban Land Rent

PurposePurpose

We study how land is allocated We study how land is allocated among the different possible uses.among the different possible uses.

We explore the market forces that We explore the market forces that determine land use pattern.determine land use pattern.

Land UsesLand Uses

Competing land uses:Competing land uses:– AgricultureAgriculture– residentialresidential– ManufacturingManufacturing– OfficeOffice

For each of these uses, there is a For each of these uses, there is a maximum willingness to pay (WTP) in maximum willingness to pay (WTP) in return for using the landreturn for using the land

How is land rent How is land rent determined?determined?

WTP for each use is determined by WTP for each use is determined by how much money can be earned by how much money can be earned by using the land.using the land.

Land will go to the highest bidding Land will go to the highest bidding use or sector.use or sector.

Due to competition, WTP for land Due to competition, WTP for land drives profit to zero.drives profit to zero.

DefinitionsDefinitions

Land rent: periodic payment from Land rent: periodic payment from user to owneruser to owner

Market value: amount paid to take Market value: amount paid to take ownershipownership

In our discussion, we use the term In our discussion, we use the term “price of land” to refer to land rent, “price of land” to refer to land rent, which is a periodic paymentwhich is a periodic payment

Bid RentBid 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 David Ricardo (1881) the price of land is determined by its fertilitydetermined by its fertility

Example: Agricultural landExample: Agricultural land Consider two types of one acre land:

high fertility and low fertility. The price of corn is $10

The bid rent equals the willingness to pay for land since competition between farmers drive profit to zero.

Variation in land fertility generates variation in bid rent

Bid-Rent for ManufacturingBid-Rent for Manufacturing

Desirability of urban land for Desirability of urban land for manufacturing is based on its manufacturing is based on its accessibility.accessibility.

Land closer to highways more desirableLand closer to highways more desirable Maximum WTP for a lot large enough Maximum WTP for a lot large enough

for production facility = Total revenue - for production facility = Total revenue - non-land costsnon-land costs

Bid rent per hectare = WTP / lot sizeBid rent per hectare = WTP / lot size

Manufacturing Bid RentManufacturing Bid Rent

The firm’s freight cost is $20/ mile

Variation in freight cost generates variation in bid rent

Manufacturing Bid Rent Manufacturing Bid Rent CurveCurve

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 DistrictCentral Business District

A B C D E F G

Travel Distance for Information Firms

Travel distance increases at an increasing rateThe median location minimizes the travel

distance

Office Bid Rent

We can calculate the bid rent using We can calculate the bid rent using the left over principle.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 rateSince 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 Bid-Rent with Factor Substitution

Since the price of land increases near Since the price of land increases near the center, people will economize on the center, people will economize on the use of landthe use of land

They use less land space and build tall They use less land space and build tall buildings and thus expanding upwardsbuildings and thus expanding upwards

Tall buildings requires capital to hold Tall buildings requires capital to hold the units on top of one anotherthe units on top of one another

Thus people can substitute between Thus people can substitute between land and capital.land and capital.

Given land rent and capital price, Given land rent and capital price, people choose the building height people choose the building height that minimizes costthat minimizes cost

Example: 4 units of office Example: 4 units of office spacespace

Bid-Rent with Factor Bid-Rent with Factor Substitution Substitution

TallTall MediuMediumm

ShortShort

Land area 0.04 0.25 1

Capital $250 $100 $50

Land cost when rent =$40

Total cost

Land cost when rent =$200

Total cost

Land cost when rent =$1600

Total cost

TallTall MediuMediumm

ShortShort

Land area 0.04 0.25 1

Capital $250 $100 $50

Land cost when rent =$40

1.6 10 40

Total cost 251.6 110 90

Land cost when rent =$200

8 50 200

Total cost 258 150 250

Land cost when rent =$1600

64 400 1600

Total cost 314 500 1650

Substituting between land and Substituting between land and capital saves on building cost.capital saves on building cost.

This leaves firms with positive profit.This leaves firms with positive profit. However, competition and free entry However, competition and free entry

imply that profits will be driven back imply that profits will be driven back to zeroto zero

This takes place as bid rent This takes place as bid rent increases.increases.

Bid-Rent with Factor Bid-Rent with Factor Substitution Substitution

Convex Bid-RentAssume 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.

Capital cost increases to 250, but you only need 0.04 hectaresThe savings in cost raise profit. The higher profit in turn will raise the bid rent to ……..

Housing MarketHousing Market

Model focuses on commuting as key Model focuses on commuting as key location factor:location factor:– Monetary (not time) cost of commutingMonetary (not time) cost of commuting– One member of household commutes to One member of household commutes to

an employment area (CBD or an employment area (CBD or manufacturing area)manufacturing area)

– Non commuting travel insignificantNon commuting travel insignificant– Identical public services, taxes, and Identical public services, taxes, and

amenitiesamenities

Housing Price Curve

A household

has a fixed

amount to spend on housing

and commutin

g. The house price is defined as price per sq ft

How much

?

The cost of commuting is $50/mile per month

Houses are available in standard dwellings of 1000 sq ft.

The slope of the housing price The slope of the housing price curvecurve

Can you derive the slope Can you derive the slope analytically?analytically?

Housing price with Housing price with substitutionsubstitutionWith 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 PatternsLand Use Patterns

We can use the bid rent curves of We can use the bid rent curves of different land users to determine a different land users to determine a city’s equilibrium land use pattern.city’s equilibrium land use pattern.

Three sectors compete for land: Three sectors compete for land: manufacturers, office firms and manufacturers, office firms and residents.residents.

Land Use PatternsLand Use Patterns

Features of urban transportation Features of urban transportation system:system:– Manufacturers use trucks to transport Manufacturers use trucks to transport

output through highwaysoutput through highways– A highway goes through the center of A highway goes through the center of

the metropolitan area and a belt waythe metropolitan area and a belt way– Residents work at the office sector and Residents work at the office sector and

the manufacturing firm travel by the manufacturing firm travel by automobile.automobile.

Bid Rent for the office Bid Rent for the office sectorsector

Bid Rent for Manufacturing Sector

Bid Rent for EmployersBid Rent for Employers

Land Use PatternsLand Use Patterns