Land Use and the Monocentric City

Chapter 8

The Monocentric City

• Typical city of the 19th Century. It has a heavy concentration of employment in the central core area

• Key feature is a heavy concentration of employment in the central core area.

• Why study the Monocentric City:– Historical Perspective– Small and Medium are Monocentric

cities– Understand the transition to the

modern city– Many lessons of MC can be expanded to

modern cities

Characteristics of the Monocentric City• Intercity Transportation→ Central Export

Node. A port, or railway station is located at the center of the city. From there the city firms send their production of good x to other cities (Train).

• Intra-City Transportation. Manufacturing firms transport their output a distance u from the plant to the export node, at a cost of per mile (Horse-drawn wagons).

• Workers Commuting Costs. Workers live outside the central district and commute to their place of work (street car).

• Agglomeration Economies. Office industry relies on face-to-face interactions.

The Bid-Rent Function

• The Bid-Rent Function: The Bid-Rent is the hypothetical price that the firm or household would pay for a piece of land for a given level of profits or utility. The difference between Bid-Rent Function and Land Rent is that Land-Rent is derived from the market price and it is observed, while Bid-Rent function is not observed.

Strategy of today’s class:• Calculate the bid-rent function of:

– Manufacturing Firms (Produce a good x)– Office Firms (Produces F consultations)

•They gather, process and distribute information.

•They rely on face to face contact to provide their services.

– Households (Commute to work in central city)• Each of these agents will locate where thay are

willing to pay the highest rent.

The Bid Rent Function of Manufacturing Firms• Fixed Factors of Production. Each firm

uses one acre of land and dollars of non-land inputs, to produce x units of output per time period.

• Output price Px is fixed.

• Competitive Markets, No entry barriers and economic profits are zero.

• Transportation costs per unit of output from plant to export node (distance u) are per mile.

The Bid Rent Function of Manufacturing Firms (Cont)

• Firms Problem is:

and because of the leftover principle, the bid rent function becomes:

)()( uRXutCXPu xxxxx

XutCXPuR xxxx )(

Distance from Center u

$

Slope: txX

Input Substitution

• Remove FFP assumption

• For higher land prices firms will substitute away from land and use other inputs to produce a fixed level of output. And the bid rent function becomes:

Convex Bid-Rent Function

)()(

uT

XutCXPuR

x

xxxx

Distance from Center u

$

Slope: txX/Tx(u)

The Bid-Rent Function of Office Firms

• The office is located u miles from the city center. Each firm produces F units of service or consultations per month.

• Employees travel u miles from the office to the city center to consult with clients in tf minutes. The worker receives a wage W per minute. So the total employee travel cost is: tfWFu .

• The output price is fixed at Pf.• Markets are competitive with free entry

and exit of firms.• There is factor substitution.

The Bid-Rent Function of Office Firms (Cont)

• The firm’s profit function becomes:

• And the profit bid function becomes:

)()()( uTuRFWutCFPu ffffff

)()(

uT

FWutCFPuR

f

ffff

Distance from

Center u

$

Slope: txX/Tx(u)

Slope: tfFW/Tf(u)

The Bid-Rent Function of Office Firms (Cont)• The land will be

rented to the highest bidder, and it will be the office firm as long as the cost of worker’s transportation of the marginal office firm is greater than the cost of manufactured goods transportation of the marginal manufacturing firm:

Distance from Center u

$

Slope: txX/Tx(u)

Slope: tfFW/Tf(u)

)()( uT

Xt

uT

WFt

x

x

f

f

OfficeManufacturing

Residential Land Use• Here the strategy consists of two steps: first to find

the Housing-Price Function (Compensated Demand for Housing Curve, household side), and second to find the Residential Bid-Rent (The Housing Firm side).

a) One member of household commutes to CBD.

b) Non-Commuting travel is insignificant.c) Public services and taxes are the same in

all locations.d) Air quality is the same at all locations.e) All households have the same income and

tastes for housing.f) There is a monetary cost to commuting, but

not a time cost. The opportunity cost of commuting in time is zero.

Group Discussion (10 minutes)• Depict graphically the effects of the

following changes on the division of CDB land between office firms and manufacturers:

a) Unit freight cost decreasesb) Price of office output increasesc) Opportunity cost of executive travel

decreases

Step 1: Household Side• The Housing Price Function

indicates how much a household is willing to pay per square foot in different locations in the city, keeping utility constant.

• Linear Housing-Price Function (No consumer substitution): Here the consumption of housing (H) is fixed. The household will be indifferent as long as:

• The change in commuting costs due to a change on distance equals the change in rent paid. Utility is constant.

HPut hh

$

u

Housing Price Function

Slope –th/H

Household Side Convex Linear-Housing Price Function

• Now housing consumption depends on the price of housing, Consumers obey the law of demand. The equilibrium equation

can thus be rewritten as:

• And the slope of the housing-price function becomes:

• Multiply by and we get the Housing Price Gradient:

HPut hh

)(uHPut hh

)(uH

t

u

P hh

hP

1

)(

1

uHP

t

u

P

P h

hh

h

Residential Bid-Rent Function (Fixed Factors)• Indicates how much producers are willing to

pay for land at different locations in the city. • Because of the leftover principle producers

will be willing to pay a rent that equals the difference between their revenue and their costs:

• And the Residential Bid-Rent Function equals:

• Since Ph is a convex function of u, then the Residential Bid-Rent Function will also be convex.

)()()( uRKQuPu hhh

KQuPuR hh )()(

Residential Bid Function (Factor Substitution)• With factor substitution, as land price falls,

housing firms will use more land. The bid rent function becomes even more convex:

• Where Th(u) is the size of land and • Note that the convexity of the housing-

price function (consumer substitution) and the bid-rent function (factor substitution) makes urban density much greater than suburban density.

)(

)()(

uT

KQuPuR

h

hh

0UT

The Monocentric City in Diagram

$

u

Office bid rent function

Manufacturing bid-rent function

Residential Bid Rent Function

Office District

Manufacturing District

Residential District

Relaxing the Assumptions

• No Time Cost of Commuting• Non-Commuting Travel• Two Earner Households

Group Discussion

• Depict graphically how would the following affect the Housing-Price function:– The quality of air is different in

different parts of the Monocentric city.– The work week is shorten from 5

days to 4 days.– The central node is a cluster for

cultural and recreational activities.

Income Segregation

• Monocentric model predicts that households choose their residential location as a trade-off between commuting costs and land costs.

• Can this model explain why do poor households locate in the CBD area, while the rich on suburban locations?

• Other explanations? u

$

MCR

MCP

MBR

MBP

Income Elasticity Land

>Income Elasticity Commuting

Interaction Between Urban and Labor Markets• Assume Constant Population Density• Assume a Rectangular City

u

$

Residential Bid-Rent Function

Business Bid-Rent Function

$

N

w*

N*

Labor Demand

Labor Supply

d1 d2

Introduction of a Streetcar System (1)• Residential Bid-Rent Function

expands into previous agricultural area….

u

$

d1 d2

$

N

SL

DL

d2’

SL’

Introduction of the Streetcar System (2)• The increase of labor supply will

lower wages• Shift residential bid rent function

downward• Shift the business bid rent function

upward

$

d1 d2’u

$

u

d1’ d2’’

Paradise Lost and Revisited (JUE 1981)• Goal of the paper: Coincide

historical data with the Monocentric City Model using changes in transportation technology (TT).

• Three stages of development of a city:– Paradise: (Common TT, slow)– Paradise Lost: (Rich→Fast TT,

Poor→Slow TT)– Paradise Regained: (Common TT, fast)

Paradise Lost and Revisited (JUE 1981) (2)

• What are the main assumptions • Main identification strategy:

Change of transportation technology

• Walk to omnibus• Omnibus to Commuter Railroad • Commuter Railroad to car

Paradise Lost and Revisited (JUE 1981) (3)

• Further discussion:– How do transportation policy affects

residential segregation– What type of policies would generate a

mixed residential outcome? What type of policies will

generate further segregation? – What role does pollution, congestion and

the free rider problem have on gentrification and residential segregation?