Land Use Planning Tools Lecture Notes Theory of

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--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. 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 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 $ Profit=rent>>t o 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 ATC $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 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 u 1 to u 2 shifts bid rent down in city center because of price effect Rent/ acre R 0 Distance to market R 2 R 1 U 0 U 2 Austin Troy--Land Use Planning Tools, University of Vermont U 1

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 P 2 P P 1 R 2 d 2 d 1 C 1 Q C 2 R 2 d 1 Q C 2 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