Geography/Planning 379

1

• Geography/Planning 379
• Urban Growth Development
• Lecture 7 Urban Rent and Land Use Theory
• von Thünens Agricultural Land Use Theory
• The Concept of Economic or Bid Rent
• Graphing Bid Rent Lines
• The Negative Exponential Rent Gradient
• Urban Land Uses and Bid Rents
• Amenity versus Location Rent
• Reading
• Required Textbook, Ch. 6, pp. 147-148
• Optional Cadwallader
• 
  PROJECT 1 DUE TUESDAY 1230
• It makes all the difference whether one sees
  darkness through the light or brightness through
  the shadows.
• David Lindsay

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von Thünens Agricultural Land Use Theory

• Modern urban rent theory based on agricultural
  rent theoryas formulated by Johann Heinrich von
  Thünen
• His 1826 book The Isolated State
• Basic idea Agricultural uses conform to
  predictable patterns around cities, which are the
  markets for the farm goods
• Those goods with greatest demand and having the
  highest transport costs should be produced
  closest to the city

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von Thünens Agricultural Land Use Theory

• Where does milk come from?
• Top three dairy states
• 1. Wisconsin
• 2. California
• 3. New York
• Why does milk have high transport costs?
• Perishability

4

• Definition economic rent or bid rent
• The monetary return a farmer can receive for
  growing a particular crop on a unit of land after
  all the costs of production (including
  transportation to the market) are taken into
  account.

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The Concept of Economic or Bid Rent

• Farmers responsible for hauling produce to market
• so economic rent higher for land closer to the
  city
• lower for land farther out
• Economic rent highest price farmer could pay for
  land and break even growing a particular crop
  the maximum rent that could be paid to grow a
  crop
• So it is sometimes called bid rent
• The land may or may not be put into the use
  depending on whether another use can bid more
  for the parcel of land.
• Extensive agriculture (example photo Wheat
  farming)
• Intensive agriculture (example photo Rice
  paddies)

6
Graphing Bid Rent Lines
Assume transporting corn costs 50 cents / mile

• Lets graph some hypothetical bid rents!
• Corn
• PC Market Price 100 (for amount grown on a
  unit of land e.g., one acre)
• SC Spatially Invariant Costs 50 (for
  seed, fertilizer, labor, harvesting)

Assume tomato transport costs 1 / mile
Ri(X)Bid Rent
Whats the Bid Rent right next to the Market?
Rc(x) PC - SC 100 - 50 50
Tomatoes outbid Corn
Whats the Bid Rent 10 miles from Market?
100 - 50 (10 x .50) 45
How far out will it be where Bid Rent is equal to
zero?
60
100 - 50 - .50 Xmax 0
We can now draw in the Bid Rent Line for Corn
50 .50 Xmax
40
Point of Intersection
Xmax 100 miles
Corn outbids Tomatoes
Tomatoes PT Mkt Price 150 ST S.I. Costs
75
20
X, Dist from Mkt

(Miles)
0
Tomato Land
Corn Land
0
10
20
40
30
50
60
70
80
90
100
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The Predicted Land Use Pattern and the Negative
Exponential Rent Gradient

• What would a land use map of our two-crop example
  look like?
• But what if there are other competing land uses?

Market City
Tomatoes
Corn
Dairy
Margin of Cultivation
Grapes
Grazing
Marlboro Country
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The Predicted Land Use Pattern and the Negative
Exponential Rent Gradient

• With more and more competing land uses, what does
  the actual overall rent gradient look like?
• Rent gradient shows the declining value of land
  as you go away from the city land being used for
  the highest and best use
• It is the upper envelope of the bid rent lines
  for all competing land uses
• The gradient takes on a negative exponential
  form decreasing with increasing distance, but
  with a decreasing slope.
• In 3-D It looks kind of like a one-pole circus
  tent!

Ri(X)
R(X) R0 e-bX
X
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Urban Land Uses and Bid Rents

• Urban translation of the definition Economic
  or Bid Rent The monetary return a developer
  can receive for developing a particular land use
  (e.g., apartment buildings, office complex,
  shopping center, single-family homes) on a unit
  of land after all the costs of development are
  taken into account and including the willingness
  of renters/buyers to pay for the level of
  accessibility provided by the location

Office Buildings
BidRent
Multi-family Residential (Apartments)
Single-family Residential
Agriculture
Edge of the Urbanized Area
X (Dist from CBD Center)
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Urban Land Uses and Bid Rents

• The basic von Thünen-style urban economics model
  describes a monocentric city, such as during the
  omnibus, horsecar, and streetcar suburbs eras
• Urban areas now polycentric distance to multiple
  centers matters
• What would a polycentric bid-rent land use map
  look like?

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Amenity versus Location Rent

• How are rents actually determined in the real
  world?
• Lets take the case of yalls slumlords (or
  slumladies)
• How do they go about figuring out how much they
  can gouge you for?
• Rent Location Rent Amenity Rent
• Location Rent Based on accessibility and supply
  and demand factors
• How do supply and demand fit into the basic bid
  rent framework?
• Amenity Rent Amenities may be site-specific or
  externalities externalities can be positive or
  negative

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• Practice Bid-Rent Problem These are the
  bid-rent functions for single-family residential
  land use, R S(x), and multi-family residential
  land use, RM(x), where x is the distance from the
  center of the CBD in kilometers R S(x)
  20,000 2,000 x
• RM(x) 160,000 30,000 x
• Where would we expect to find the boundary
  between multi- and single-family residential land
  use?
• (A) At x 0 km (D) At x 5.333 km
• (B) At x 2 km (E) At x 10 km
• (C) At x 5 km
• Solution Set R S(x) RM(x) and solve for
  x
• 20,000 2,000 x 160,000 30,000 x
• 28,000 x 140,000
• x 140,000 / 28,000 gtgtgtgt x 5 km

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POP QUIZ Name ____________________

• These are bid-rent functions for single-family
  residential land use RS(x) and multi-family
  residential land use RM(x) where x is the
  distance from the center of the CBD in
  kilometers
• RS(x) 20,000 2,000 x
• RM(x) 160,000 30,000 x
• Suppose Agricultural land use can pay 2000 per
  unit of land regardless of how far out it is from
  the center
• R A(x) 2,000
• Find the distance xmax where we would expect to
  find the outer edge of the urbanized area. Show
  your work!

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• QUIZ SOLUTION. These are bid-rent functions for
  single-family residential land use R S(x) and
  multi-family residential land use R M(x) where x
  is the distance from the center of the CBD in
  kilometers
• R S(x) 20,000 2,000 x
• RM(x) 160,000 30,000 x
• Suppose Agricultural land use can pay 2000 per
  unit of land regardless of how far out it is from
  the center R A(x) 2,000
• Find the distance xmax where we would expect to
  find the outer edge of the urbanized area. Show
  your work!

RS(x) RA(x) 20,000 2,000 xmax 2,000 18,000
2,000 xmax xmax 18,000 / 2,000 9 km
150,000
100,000
50,000
0
9
0
2
4
8
6
10