Transcript Land Use Planning Tools Lecture Notes: Theory of Land Rents

Land Use Planning Tools Lecture
Notes: Theory of Land Rents
Summary of chapter 7 of Urban
Economics by Arthur O’Sullivan
Notes by Austin Troy
Austin Troy--Land Use Planning Tools, University of Vermont
Land Rent vs. Market Value
• Market value: the present value of the
stream of rental income generated by land
• Rental Income: the amount the landowner
charges to use land; equal to income from
land minus costs
Austin Troy--Land Use Planning Tools, University of Vermont
What is Present Value?
• It is the maximum amount an investor would
be willing to pay for something, given that the
investor could safely make i percent returns
on an alternative investment (for instance, a
savings account, or T-bills).
• It equals, the stream of income, discounted
over time
Austin Troy--Land Use Planning Tools, University of Vermont
How is PV discounted?
• PV takes into account the fact that a dollar
earned 5 years from now if worth less to us
now than a dollar earned today
• This is because income put off until later has
opportunity cost associated with it.
• A dollar invested in five years is worth less
than a dollar invested today
• PV takes into account lost opportunity from
that alternative investment
Austin Troy--Land Use Planning Tools, University of Vermont
How is PV calculated?
n
R
PV  
t
t  0 (1  i )
• For $20 yearly stream for 5 years at 10%
PV= $20 +$18.18 + $16.53 + $15.04 + $13.70 = $83.45
• For a constant stream of income into infinity, rule
simplifies to PV= R/i = $20/.1= $200
• Non-constant income example:
• PV= $20 + $24/1.1 + $29/1.21 + $34/1.33…etc.
Austin Troy--Land Use Planning Tools, University of Vermont
Market value of land
• Equals PV of annual maximum rental
payments that the landowner can charge
• For market value to equal PV: given yearly
income R and alternative ROR of i , investor
is indifferent between buying the land and
investing that money elsewhere
• From here out we talk of land rent in place
of price, and assume users of land pay rent
Austin Troy--Land Use Planning Tools, University of Vermont
Land Rent and Productivity
• Value of land, and hence land rent derives
from productivity
• Earliest model of productivity comes from
Ricardo (1821) who looked at land fertility
• Assumptions: fixed inputs/output prices
(price takers), zero profit, 3 levels of fertility,
land to highest bidder, location (transpo
costs) can be ignored, owners are not farmers
Austin Troy--Land Use Planning Tools, University of Vermont
Ricardo model
• On fertile land, a farmer can produce same
amount of corn with fewer inputs
• The price of this type of land is bid up
• All profit accrues to the landowner in the
form of rents
• Payment to farmer is considered a cost
Austin Troy--Land Use Planning Tools, University of Vermont
Ricardo model
MC
ATC
ATC
$
Profit=rent>>
to landowner
Profit=rent>>
to landowner
$8
$4
ATC
MC
MC
Q=amt of
corn
220
160
“A” land
“B” land
“C” land
“A” land has lowest production costs= highest rents
“C” land’s rent is 0 because costs are greater than revenue
Austin Troy--Land Use Planning Tools, University of Vermont
$10
Price
determined
exogenously
by supply and
demand in
market
Ricardo Model
• Competition among farmers for good land bids up
rents on that land until economic profits* =0 for
farmer. All profits on land go to owner.
• Economic profits: greater than “normal” profits
required to pay for time of those doing the work
• Rent for A land= TR-TC= $2200-$880=$1320
Austin Troy--Land Use Planning Tools, University of Vermont
Leftover principle
• In equilibrium, Rent= profits, or revenue over
total nonland costs
• Rent eats up whatever is “left over” because
competition for land bids away any excess
• That is, competition among farmers for land
bids away excess profits until they are zero
and landowner gets all surplus value
Austin Troy--Land Use Planning Tools, University of Vermont
Exceptions to leftover principle
• If there is restrictions on entry or on
competition
– E.g. if farmer (non-owners) owns patent to
farming techniques that reduce costs, landlord
cannot charge additional rents reflecting those
additional profits because noone else would be
willing to pay such high rents
Austin Troy--Land Use Planning Tools, University of Vermont
Who benefits from improvement?
• Example: irrigation project
• If price of corn is fixed (exogenous) the landlord
benefits because competition among farmers for
land will bid away profit
• Winner: land owner; loser: farmer
• However, if the project affects the price of corn
(price is endogenous), consumers gain with lower
prices, while farmer pre rent profits are reduced,
lowering land rents
• Winner: consumer; loser; land owner
Austin Troy--Land Use Planning Tools, University of Vermont
Scale of improvement
• Who benefits is determined by scale of
improvement
• Smaller the area, the more the benefit goes to
landowner; larger the area, more goes to
consumers because of price endogeneity
• Benefits from any improvement are capitalized
into the value of land; a positive capitalization
increases rents, which increases market value
• Negative factors can be capitalized too
Austin Troy--Land Use Planning Tools, University of Vermont
Accessibility
• Now replace fertility of land with location as
the prime determinant of land value--Von
Thunen model (1826)
• No longer assume that transportation is
costless
• This model explains why more “central”
locations command higher rents and have
higher market values than fringe areas
Austin Troy--Land Use Planning Tools, University of Vermont
The Carrot Farmer
• Assume: land is equally fertile, profits are
zero, there is one central market, p is fixed
and farmers use fixed factor production
• Cost is now fn of distance
– Transport Cost= cost/ton/mile*dist*Q
– Profit= P*Q-PC-TC-Rent = 0
– Rent= P*Q-PC-TC
Austin Troy--Land Use Planning Tools, University of Vermont
Carrot Farmer’s bid rent function
Total revenue per acre (P*Q; Q/acre does not vary)
$300
$250
Total Cost
$190
Bid
rent/acre
Land rents
$110
$50
Close
Distance to market
Austin Troy--Land Use Planning Tools, University of Vermont
Far
Carrot farmer’s decision
• Now, market-proximate land replaces fertile
land as the most valuable type
• However, competition for close land bids
away surplus profit so, assuming farmers
are identical, they are indifferent among all
locations, as long as total revenue exceeds
total cost
Austin Troy--Land Use Planning Tools, University of Vermont
The farmer and factor substitution
• What if farmers can be different? Then the
bid-rent function becomes convex.
• Under linear function, fixed amount of land
and non-land inputs, no matter where
• Under convex function, farmers engage in
factor substitution: they increase non-land
inputs (equipment, labor, technology) as
land gets more central and expensive
Austin Troy--Land Use Planning Tools, University of Vermont
Factor substitution
• The farmer in more central land can now
use less land, in exchange for more inputs
• New profit fn: Profit= P*Q-PC=TC-R*T,
where T= acres of land used
• New rent fn: R = (P*Q-PC-TC)/T
Austin Troy--Land Use Planning Tools, University of Vermont
Bid Rent fn for both farmers
Rent/
acre
Bid rent for flexible farmer
Bid rent for fixed-factor
farmer
Distance to market
U*
Austin Troy--Land Use Planning Tools, University of Vermont
Bid rent of flexible farmer
• Flexible farmer will outbid the inflexible
farmer in all locations but u
• That is, land will be used more intensively and,
hence, more efficiently at central locations, and
non-land inputs will be fewer far away
• With inflexible farmers, land is used more
inefficiently
• Rents will still equal profits of highest bidder
Austin Troy--Land Use Planning Tools, University of Vermont
Factor Substitution
• Because inflexibility in factor inputs is
inefficient, competition for land will
eliminate those land users
Austin Troy--Land Use Planning Tools, University of Vermont
Decreases in Transport Costs
• Say a new highway reduces transport costs
• Increases radius of market area for farmers
• Who do benefits go to? Landowner, as long
as price is unaffected
• If scale of supply effect is large enough to
decrease price, TR/acre decreases slightly
• Then, benefits are shared by landowners
and consumers, who get lower prices
Austin Troy--Land Use Planning Tools, University of Vermont
Bid Rent fn for both farmers
Note that going from u1 to u2 shifts bid
rent down in city center because of price
effect
Rent/
acre
R1
R0
Distance to market
R2
U0
U2
Austin Troy--Land Use Planning Tools, University of Vermont
U1
Two competing land uses
• Different land uses (say llama farms vs. ostrich
farms) may have different bid rent functions. The
shapes of those functions will determine who will
locate where
• Steepness of fn determined per unit transport costs
relative to per unit price
• As usual, land goes to highest bidder
• Market allocates land efficiently to usage with the
most to gain from being close to the market
Austin Troy--Land Use Planning Tools, University of Vermont
Determinants of bid rent slope
1. Per acre transportation costs. The more
weight you produce/acre, the more
transport will cost per acre cultivated. E.g.
potatoes vs. cotton
2. Unit transport costs. The more a given unit
weight costs to ship, the higher the
transport costs. E.g. eggs vs. turnips
Austin Troy--Land Use Planning Tools, University of Vermont
Bid Rent fn for both farmers
Rent/
acre
Spamelope
farm
U’= where spamelope farms
transition to cotton candy farms
Cotton candy
farm
U’
Austin Troy--Land Use Planning Tools, University of Vermont
Corn Law Debates
• Is the price of land high because the price of
output high, or vice versa?
• Corn laws restricted imports of grain
• D for domestic corn increased>>P
increased>>Q increased>>D for land
increased, but supply curve for land is
inelastic so price of land went up
Austin Troy--Land Use Planning Tools, University of Vermont
Corn law debates
S
Land
Rent
P2
P
P1
R2
d2
d2
d1
C1
Q
C2
R2
d1
Q
C2
Austin Troy--Land Use Planning Tools, University of Vermont
Corn Laws
• So, price of land is high because the price of
corn is high; landowners will always get
leftovers through competitive bidding
• Same principle applies with housing: price
of land in Silicon Valley is high not because
landlords are more greedy than elsewhere,
but because of demand that allows them to
charge those rentss
Austin Troy--Land Use Planning Tools, University of Vermont