Land Use and the Monocentric City

1
Land Use and the Monocentric City

• Chapter 8

2
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

3
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.

4
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.

5
Strategy of todays 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.

6
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.

7
The Bid Rent Function of Manufacturing Firms
(Cont)

• Firms Problem is
• and because of the leftover principle, the bid
  rent function becomes

Slope txX
Distance from Center u
8
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

Slope txX/Tx(u)
Distance from Center u
9
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.

10
The Bid-Rent Function of Office Firms (Cont)

• The firms profit function becomes
• And the profit bid function becomes

Slope tfFW/Tf(u)

Slope txX/Tx(u)
Distance from Center u
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The Bid-Rent Function of Office Firms (Cont)

Slope tfFW/Tf(u)

• The land will be rented to the highest bidder,
  and it will be the office firm as long as the
  cost of workers transportation of the marginal
  office firm is greater than the cost of
  manufactured goods transportation of the marginal
  manufacturing firm

Slope txX/Tx(u)

Distance from Center u
Office
Manufacturing
12
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.

13
Group Discussion (10 minutes)

• Depict graphically the effects of the following
  changes on the division of CDB land between
  office firms and manufacturers
• Unit freight cost decreases
• Price of office output increases
• Opportunity cost of executive travel decreases

14
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.

Housing Price Function
Slope th/H
u
15
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

16
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.

17
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.

18
The Monocentric City in Diagram

Office bid rent function

Manufacturing bid-rent function
Residential Bid Rent Function
u
Office District
Manufacturing District
Residential District
19
Relaxing the Assumptions

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

20
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.

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Income Segregation
Income Elasticity Land
Income Elasticity Commuting

• 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?

gt

MCP
MBP
MCR
MBR
u
22
Interaction Between Urban and Labor Markets

• Assume Constant Population Density
• Assume a Rectangular City

Labor Supply

Business Bid-Rent Function
w
Residential Bid-Rent Function
Labor Demand
u
d1
d2
N
N
23
Introduction of a Streetcar System (1)

• Residential Bid-Rent Function expands into
  previous agricultural area.

SL
SL
DL
u
d1
d2
d2
N
24
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
25
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)

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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

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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?