Land Use Planning Tools Lecture Notes: Theory of Land Rents

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Ricardo model MC ATC ATC $10 Price determined exogenously by supply and demand in market $ 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. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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 $50 Land rents $110 Close Distance to market Far Austin Troy--Land Use Planning Tools, University of Vermont

18. 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

19. 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

20. 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

21. Bid Rent fn for both farmers Bid rent for flexible farmer Rent/ acre Bid rent for fixed-factor farmer Distance to market U* Austin Troy--Land Use Planning Tools, University of Vermont

22. 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

23. 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

24. 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

25. 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 R2 Distance to market U0 U2 U1 Austin Troy--Land Use Planning Tools, University of Vermont

26. 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

27. Determinants of bid rent slope • Per acre transportation costs. The more weight you produce/acre, the more transport will cost per acre cultivated. E.g. potatoes vs. cotton • 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

28. Bid Rent fn for both farmers Spamelope farm U’= where spamelope farms transition to cotton candy farms Rent/ acre Cotton candy farm U’ Austin Troy--Land Use Planning Tools, University of Vermont

29. 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

30. Corn law debates S Land Rent P2 P P1 R2 d2 d2 d1 R2 d1 C2 C1 C2 Q Q Austin Troy--Land Use Planning Tools, University of Vermont

31. 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