1. Geography/Planning 379
“Urban Growth & Development”
Lecture 7: Urban Rent
and Land Use Theory
1. von Thünen’s Agricultural Land Use Theory
2. The Concept of ‘Economic’ or ‘Bid’ Rent
3. Graphing Bid Rent Lines
4. The Negative Exponential Rent Gradient
5. Urban Land Uses and Bid Rents
6. Amenity versus Location Rent
Reading:
Required: Textbook, Ch. 6, pp. 147-148
Optional: Cadwallader
PROJECT 1 DUE TUESDAY 12:30
“It makes all the difference whether one
sees darkness through the light or
brightness through the shadows.”
– David Lindsay

2. von Thünen’s Agricultural Land Use Theory
• Modern urban rent theory based on:
agricultural rent theory
as 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

3. von Thünen’s 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.

5. 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. Let’s 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…)
Graphing Bid Rent Lines
0 10 20 4030 50 60 70 80 90 100
X, Dist from Mkt
(Miles)
Ri(X)
Bid
Rent
$0
$20
$40
$60
What’s the Bid Rent
right next to the
Market?
Rc(x) = PC - SC = 100 - 50 = $50
Assume transporting corn
costs 50 cents / mile
What’s the Bid Rent
10 miles from
Market?
100 - 50 – (10 x .50) = $45How far out will it be
where Bid Rent is
equal to zero? 100 - 50 - .50 Xmax = $0
50 = .50 Xmax
Xmax = 100 miles
We can now draw
in the Bid Rent
Line for Corn…
Assume tomato transport
costs $1 / mile
Tomatoes:
PT = Mkt Price = $150
ST = S.I. Costs = $75
Point of Intersection
Tomatoes outbid Corn
Corn outbids Tomatoes
Tomato Land Corn Land

7. 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?
Margin of Cultivation
Market City
Tomatoes
Corn
Dairy
Grapes
Grazing
“Marlboro Country”

8. 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)
X
R*(X) = R0 e-bX

9. 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
Multi-family Residential (Apartments)
Single-family Residential
Agriculture
Bid
Rent
X (Dist from CBD Center)
Edge of the
Urbanized Area

10. 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?

11. Amenity versus Location Rent
• How are rents actually determined in the ‘real
world’?
• Let’s take the case of y’all’s 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

12. 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 >>>> x = 5 km

13. 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!
POP QUIZ Name ____________________

14. 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!
150,000
100,000
50,000
0
0 2 4 86 109
RS(x) = RA(x)
20,000 – 2,000 xmax = 2,000
18,000 = 2,000 xmax
xmax = 18,000 / 2,000 = 9 km