Transcript Land Use and the Monocentric City

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-toface 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
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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:
 x (u )  Px X  C x  t x Xu  Rx (u )
and because of the
leftover principle, the bid
rent function becomes:
$
Slope: txX
Rx (u )  Px X  C x  t x Xu
Distance from Center u
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:
Px X  C x  t x Xu
R x (u ) 
Tx (u )
Convex Bid-Rent
$
Function
Slope: txX/Tx(u)
Distance from Center u
The Bid-Rent Function of Office Firms
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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:
$
 f (u)  Pf F  C f  t f FWu  R f (u)T f (u)
Slope: tfFW/Tf(u)
Slope: txX/Tx(u)
• And the profit bid
function becomes:
R f (u ) 
Pf F  C f  t f FWu
T f (u )
Distance from Center 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:
Slope: tfFW/Tf(u)
Slope: txX/Tx(u)
Distance from Center u
Office
t f WF
T f (u )

tx X
Tx (u )
Manufacturing
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 decreases
b) Price of office output increases
c) 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:
 t h u  Ph H
• The change in commuting costs
due to a change on distance equals
the change in rent paid. Utility is
constant.
$
Housing Price Function
Slope –th/H
u
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  t h u  Ph H can thus be
rewritten as:
 t h u  Ph H (u)
• And the slope of the housing-price function becomes:
Ph
th

u
H (u )
• Multiply by
1
Ph
and we get the Housing Price Gradient:
th
1 Ph

Ph u
Ph H (u )
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:
 h (u)  Ph (u)Q  K  Rh (u)
• And the Residential Bid-Rent Function equals:
Rh (u)  Ph (u)Q  K
• Since Ph is a convex function of u, then the Residential
Bid-Rent Function will also be convex.
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:
Ph (u )Q  K
Rh (u ) 
Th (u )
• Where Th(u) is the size of land and UT  0
• 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.
The Monocentric City in Diagram
$
Office bid rent function
Manufacturing bid-rent function
Residential Bid Rent Function
u
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 tradeoff 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?
Income
Elasticity
Land
>
Income
Elasticity
Commuting
$
MCP
MBP
MCR
MBR
u
Interaction Between Urban and Labor Markets
• Assume Constant Population Density
• Assume a Rectangular City
Labor Supply
$
$
Business Bid-Rent Function
Residential Bid-Rent Function
w*
Labor Demand
d1
d2
u
N*
N
Introduction of a Streetcar System (1)
• Residential Bid-Rent Function expands into
previous agricultural area….
$
$
SL
SL’
DL
d1
d2
d2’
u
N
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)
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What are the main assumptions
Main identification strategy:
Change of transportation technology
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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?