Summary of chapter 7 of Urban
Economics by Arthur O’Sullivan
Notes by Austin Troy
Austin Troy--Land Use Planning Tools, University of Vermont

• 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

• 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

• 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

PV
 t n 

0
R
( 1
 i ) t
• 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

• 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

• 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

• 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

MC
$
Profit=rent>> to landowner
Profit=rent>> to landowner
ATC
$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
ATC
$10
Price determined exogenously by supply and demand in market

• 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

• 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

• 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

• 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

• 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

• 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

• 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

$300
$250
$190
Bid rent/acre
$110
$50
Total revenue per acre (P*Q; Q/acre does not vary)
Total Cost
Land rents
Close Distance to market
Austin Troy--Land Use Planning Tools, University of Vermont
Far

• 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

• 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

• 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

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

• 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

• Because inflexibility in factor inputs is inefficient, competition for land will eliminate those land users
Austin Troy--Land Use Planning Tools, University of Vermont

• 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

Rent/ acre
Note that going from u1 to u2 shifts bid rent down in city center because of price effect
R
1
R
0
R
2
Distance to market U
0 U
2
Austin Troy--Land Use Planning Tools, University of Vermont
U1

• 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

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

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

• 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

P
2
P
P
1
S
C
1
Q
C
2
Land
Rent d
1 d
2
R
2
R
2
Q
C
2 d
1 d
2
Austin Troy--Land Use Planning Tools, University of Vermont

• 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