Transcript Slide 1

Basic Urban Economics
 Primary Factors of Production
 Land
 Labor
 Capital
 Raw

Materials
Note:
Mobility
Euler’s Theorem
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Location & Residual Land Value
 Value of land is based on..
 “Land”
 Land
=
as Derived Demand
 Residual
David M. Harrison, Ph.D.
Texas Tech University
Theory of Land Value:
Real Estate Investments
Consider a Clothing Factory
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Residual Land Valuation
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Competition in the Land Market
 Demand Side:
 Supply Side:
 Equilibrium under “perfect competition” –


David M. Harrison, Ph.D.
Texas Tech University
Pareto Optimality
“Highest & Best Use” (HBU)
Real Estate Investments
Highest & Best Use Example
 Two Potential Land Uses:
 The
previous clothing factory
 A grocery store
 Two Available Land Sites:
 Site
1 is the previously-described site for the
clothing factory
 Site 2 is closer to most residences, but farther
from highways
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
HBU Example Continued
Site 1
Site 2
Clothing
Factory
Grocery
Store
Clothing
Factory
Grocery
Store
$10,000,000
$4,600,000
$10,000,000
$5,000,000
Mobile Factor
Costs
9,900,000
4,550,000
9,990,000
4,625,000
Residual (Land
Rent)
100,000
Revenues
David M. Harrison, Ph.D.
Texas Tech University
50,000
10,000
Real Estate Investments
375,000
Land Rents and Transport Costs
 Land Rent  HBU Residual  Transport Costs
 Transport costs include:





Cost to move “inputs”.
Cost to move “outputs”.
Trans.Costs directly borne by “seller” on site.
Trans.Costs indirectly borne by “buyers” on site.
Value of travelers time (& inconvenience) spent traveling
to/from site.


David M. Harrison, Ph.D.
Texas Tech University
Site 1 minimized transport costs for factory
Site 2 minimized transport costs for grocery store (considering
customers travel costs).
Real Estate Investments
Bid-Rent Curve
 “Bid-Rent” = Maximum land rent a potential user would
be willing to pay for a given site (location). (Equals
residual value.)
 “Bid-Rent Curve” shows how a potential user’s bid-rent
changes as a function of distance from some central
point.
 The “central point” is the point at which transport costs
are minimized (bid-rent maximized) for the given use.
 Each potential use has its own bid-rent curve (and
central point).
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Bid-Rent Example
 Consider our Factory:
 Central
Point = highway entrance
$100,000
$10,000
1 Mi.
David M. Harrison, Ph.D.
Texas Tech University
4 Mi.
Real Estate Investments
Bid-Rent Curve w/Multiple Uses
Land Rent
A
B
C
Center
Zone of Use B
Distance from Center
Use A: Most productive use, Most sensitive to transport costs.
Use C: Least productive use, Least sensitive to transport costs.
Each use prevails where its bid-rent curve is highest.
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Monocentric City Model
 Consider a city in which:



Everyone must commute to one central point
Only one use (housing) for urban land
Topography is infinitely devlopable in all directions –
i.e., a “featureless plain”
“Circlopolis”
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Characteristics of Circlopolis
 All households must commute to the central point
(CBD) every day to earn the income they need to pay
for housing, transportation, and all other consumption
goods that make them healthy and happy citizens.
 Transportation costs are proportional to the distance the
good citizens must travel.
 Circlopolis has constant density at any given time within
the city.


Population = 1,000,000
Density = 2 persons/acre
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Urban Economics of Circlopolis
 What is the physical size (sq. miles) of Circlopolis?
 What is the physical extent (radius) of Circlopolis?
 What is the annual property rent at the edge of the city?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Determining Edge Rents
 Agricultural (or no-urban use) Opportunity Value

$500/Yr/Acre
 Construction Cost Rent

$10,000/Yr/Acre
Property Rent =
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Determining Intra-Urban Rents
 In Equilibrium:

The sum of annual housing rent + annual commuting
cost must be the same for all residents, no matter
where they live in Circlopolis. Why???

Therefore:
The slope of the bid-rent curve for housing in Circlopolis equals
the transportation cost per mile per acre. This slope is called
the “rent gradient”. It tells you how much land rents decline per
mile of additional distance from the city center, in equilibrium.
The land rent gradient equals the transportation cost per
mile per person times the number of people per acre.
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Land Rent Gradient for Circlopolis
 Transport costs = $250/Yr/person (round-trip
commuting costs).
 One person lives in each house (a city of loners!).
 Density is 2 houses (2 inhabitants) per acre (1280/Mi2).
 Land Rent Gradient =

What will be the monthly rent, 1 mile inside the city edge?

What will be the montly rent at the city center?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Location Rents
 Rent = Opportunity Cost + Construction Cost + Location

Opportunity Cost and Construction Cost Rents…

Location Rent = (Rent Gradient) x (Dist. From Edge)

David M. Harrison, Ph.D.
Texas Tech University
Note: Everyone in Circlopolis pays $9,250/Yr for the
Real Estate Investments
Land Rents in Circlopolis
Exhibit 4-3: A Cross-Section of Land Rents in Circlopolis and
Agricolia . . .
L
L
C
C
A
A
B
CBD
B
A = Agricultural Rent = $500/ac
C = Construction Rent = $10000/ac
L = Location Rent = from $0 to $8000/ac
CBD = Circlopolis Central Business District
B = Circlopolis Urban Boudnary (16 mi radius)
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Equilibrium Rents in Circlopolis
 What is the property rent (per acre) four miles from the
urban boundary, 12 miles from the CBD?
 What are the transportation costs for residents at this
distance from the center?
 What are the total costs, per person of locating at this
site?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Monocentric City Model
 Strengths:



 Limitations???
 What happens when population changes?
 What happens when income changes?
 What happens when transportation costs change?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Changes in City Population
 Population Growth with Constant Density:
 Rent
at the periphery (edge) must be the same
as before.
 Rent Gradient Must also be the same as before.
HENCE…
 Principle #1:
“Other things equal, larger cities will have higher
average rents.”
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Population Growth: Constant Density
Effect of Population Growth with Density and Transport Cost
Constant . . .Why???
L
L
C
C
A
B
David M. Harrison, Ph.D.
Texas Tech University
A
CBD
Real Estate Investments
B
Urban Economics of Population Growth
 Suppose Circlopolis’ Population Increases by 10%

Holding Density Constant:
Area must increase by:
Thus, the city’s extent/radius must increase by:
New Urban Boundary:

Location Rents:
At Periphery:
At City Center
• Conclusion:
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Population Growth w/ Constant Area
 Density must



!
Transport cost per acre
Land Rent Gradient
Land rent at boundary


Land rent increases everywhere, but proportionately more in center
HENCE…
 Principle #2:
“If a city grows by increasing area rather than density, property rent
growth will be relatively greater closer to the periphery, but if a city
grows by increasing density instead of area, property rent growth
will be relatively greater the closer to the center of the city.”
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Population Growth: Constant Area
Exhibit 4-5: Effect of Population Growth with Area Constant . . .
L
L
C
C
A
A
B
David M. Harrison, Ph.D.
Texas Tech University
CBD
B
Real Estate Investments
Transport Cost Reduction
 Typically results in an increase in land rents
near the periphery, and a decrease in land
rents near the center of the city. Why???
L
L
C
C
A
A
B
David M. Harrison, Ph.D.
Texas Tech University
CBD
B
Real Estate Investments
Transport Cost Reduction
 Principle #3:
“Declining transport costs (per person, per
mile or per year) holding population &
income constant, will always reduce the
value of land rent in the center of the city;
the effect on the land rent near the
periphery is generally ambiguous,
depending on changes in density.”
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Growth in Per Capita Income
 Two Typical Effects on Urban Form:


People choose to spend some of their extra income consuming
more urban land, thereby decreasing density:  Reduction in
rent gradient.
People have higher value of time, thereby increasing transport
cost:  Increase in rent gradient.
 Conclusion:
L
L
C
C
A
A
B
David M. Harrison, Ph.D.
Texas Tech University
CBD
B
Real Estate Investments
Urban Economics of Income Growth
 Principle #4:
“Increasing real income per capita (holding
population constant), will tend to decrease rent
gradients, with a possible result of absolute
reductions in land rent at the center of the city,
though a secondary transport cost increase effect
(and/or increasing open space reservation) due to
higher incomes may mitigate this result or even
reverse it, especially if the spatial expansion of the
city is constrained.”
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments