Austin Troy--Land Use Planning Tools, University of Vermont
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?
• 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.
n
tti
RPV0 )1(
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
ATC
MC
Profit=rent>>to landowner
ATC
MC
Profit=rent>>to landowner
160220
ATC
MC
$10
Q=amt of corn
$
“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
Price determined exogenously by supply and demand in market
$8
$4
Austin Troy--Land Use Planning Tools, University of Vermont
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
Bid rent/acre
$50
$300
Close Distance to market Far
Total Cost
Land rents
Total revenue per acre (P*Q; Q/acre does not vary)
$190
$110
$250
Austin Troy--Land Use Planning Tools, University of Vermont
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
Bid rent for flexible farmer
Bid rent for fixed-factor farmer
Rent/ acre
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
Rent/ acre
Distance to market U0
R0
R1
R2
U2 U1
Note that going from u1 to u2 shifts bid rent down in city center because of price effect
Austin Troy--Land Use Planning Tools, University of Vermont
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
U’
Spamelope farm
Cotton candy farm
U’= where spamelope farms transition to cotton candy farms
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
P
Q
d1
d2
C1 C2
P1
P2
Land Rent
Q
d1
d2
S
C2
R2
R2
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
