Land Use Economics Lecture Notes: Land Rents, Accessibility and Urban Form

1. Land Use Economics Lecture Notes: Land Rents, Accessibility and Urban Form Based on Urban Economics by Arthur O’Sullivan Notes by Austin Troy Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

2. Why do cities exist? • Why not a uniform distribution of people across the landscape? • Comparative advantage • Internal scale economies • Agglomeration economies Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

3. Comparative advantage (CA) • Based not on absolute advantage but on opportunity cost (OC) • Wheat and wool example: west can make 6 cloth or 2 wheat in one hour; east can only make 1 of each in one hour. West has CA in cloth, east in wheat, because for west OC of cloth is 1/3 wheat unit, while OC of east for wheat is 1 cloth, which is better than 3 for west • CA leads to trade in this case based on OC • Trade is beneficial only if offsets transpo costs Output per labor hour OC of Production East West East West Wheat 1 2 1 C 3 C Cloth 1 6 1 W 1/3 W Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

4. Comparative Advantage and Scale Economies in Transportatoin • Scale econ in transpo means trans cost is not independent of volume shipped; cost per unit mile dec. with volume • Otherwise producers/consumers would engage only in direct trade • Cities develop if scale economies in transpo • Then makes sense for trading firms to operate as intermediaries, locating at central places for collection and distribution of goods • Leads to development of market cities • Occurs when: ag productivity is high enough to generate surplus, CA is large enough to offset transpo costs and scale economies in transpo Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

5. Internal Scale Economies in Production • As volume increases, productivity per laborer increases • Arise because of: • Factor specialization: worker skill increases with repetition and spend less time switching between tasks • Indivisible inputs: when certain prod input has minimum indivisible scale; i.e. certain input facilities/equipment can’t be scaled down Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

6. Cost of homemade product Net cost travel cost Factory cost Miles from factory (radius) Market area due to scale economies • Defined as area where factory can underprice home production • Workers live near factory and bid up land price, causing higher density Market area Market area Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

7. Agglomeration Economies in Production (AEP) • Why do most cities have more than one factory/production facility? • AEP: positive externalities allow firms to produce at lower cost per unit because of • Localization economies • Urbanization economies Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

8. AEP: Localization Economies • When production costs of firm in a certain industry decrease as total industry output increases. Due to: • Scale economies in intermediate inputs • Labor market pooling • Knowledge spillovers Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

9. Localization economies: scale economies in intermediate inputs • Firms often cluster because they share inputs from the same supplier if: • Input D of firm is not large enough to leverage the scale economies in input production alone • Transportation costs are relatively high; this is not only because it is costly to transport input but also design/specification of input requires frequent fact to face contact; • Manhattan dressmaking and button makers—requires face to face because designs must be adaptable and producers must supervise input specifications • Corporate headquarters and advertising/marketing firm: need lots of interaction; needs constantly changing • High-tech firm: needs to locate near its suppliers of non-standard parts; interaction in testing and design of parts Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

10. Localization economies: scale economies in intermediate inputs • Business firms often need many services (finance, banking, design, insurance, legal, etc.) so big business clusters develop to exploit scale economies provided by them • Public services also important: areas with good transportation infratructure, services, schools, will attract these clusters of firms Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

11. Localization economies: Labor market pooling • Clustering increases labor efficiency • Facilitates transfer of workers between firms in dynamic industries • Many industries have high mobility between firms, e.g. entertainment • Leads to more stable wage pool, which means wages can be lower in general • Labor pooling is net benefit to firms if wage at isolated site is variable (for good and bad economic times) and wage at cluster is average of those two wages; cluster firm can staff up or downsize more easily than isolated firm Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

12. Localization economies: knowledge spillovers • Rapid exchange of information/technology in cluster • Based partly on the shared pool of workers • Leads to many innovation “corridors” Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

13. Product cycle theory • Incubator process: Often firms cluster when they are in earlier stage of development because production techniques unsettled • As production becomes standardized, often move to lower density areas where land and labor costs are lower Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

14. AEP: Urbanization Economies • Production cost of a firm declines as total output of urban area increases • Occurs for same reasons as localization economies • Different from localization economies in: • Result from scale of entire urban economy • Generate benefits for all firms in city, not just in single industry • Rather than being in one industry, benefits cut across industries • More empirical evidence for localization economies than for urbanization, although Mills points to different results Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

15. Technology and cities • Telecom technology may reduce some advantages from agglomeration economies • However, evidence suggests it is more complement than substitute—actually generates more demand for face to face contact and travel, partly because allows for greater specialization in design/production • Business travel actually increase 50% from 1985 to 1995 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

16. Retail: Agglomerative economies in marketing • Shopping externalities occurs when sales of one store are affected by location of others in same product line • The clustering of similar shops causes sales for all to be higher • Two types of products lead to this: • Imperfect substitutes • Complementary goods Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

17. Imperfect substitutes • Same product type, but subtle differences between product lines; clustering reduces shopping costs by facilitating comparison shopping, attracting more consumers • Attracts new customers (comparison shoppers) who otherwise would not patronize these shops, if isolated • Clothes, jewelry, cars, electronics Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

18. Complementary goods • Items that complement each other and can be purchased on same trip • E.g. new TV and new TV cabinet Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

19. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

20. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

21. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

22. 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. Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

23. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

24. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

25. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

26. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

27. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

28. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

29. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

30. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

31. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

32. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

33. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

34. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

35. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

36. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

37. Bid Rent fn for both farmers Bid rent for flexible farmer Rent/ acre Bid rent for fixed-factor farmer Distance to market U* Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

38. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

39. Two competing land uses • Different land uses (e.g. SPAM factory and grain farm) 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

40. 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 Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

41. Bid Rent fn for both farmers Heavy good U’= where heavy use transitions to light use Rent/ acre Light good U’ Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

42. Multiple land uses in the CBD • Let’s assume a traditional 19th Century city: • Central railroad freight terminal • Central market • Workers travel to center via streetcar • Goods go from factory to railroad via horse cart • Also assume fixed factor production Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

43. Bid Rent of Firms in the CBD • Profit fn looks same as in chapter 7 • = PQ-NC-TC(d)-R(d) • Profit= price*quantity – nonland costs- transport costs (function of distance) – rents (function of distance); • TC(d)= cost/ton/mile* distance*quantity • Then R(d)= PQ-NC-TC(d) Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

44. Freight Costs and Rents • Freight costs decrease with proximity to city center • Through leftover principle, rents increase as transport costs decrease • Hence, there will be a downward sloping bid rent function; it will be linear for fixed factor producers and convex for flexible producers Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

45. Flexible versus fixed producers Fixed: R(d)= P*Q-NC-TC(d) Flexible: = P*Q-NC-TC(d)-R(d)*L(d), Where L(d) is amount of land used at distance d; this results in rent function: R(d)= (P*Q-NC-TC(d))/L(d) Flexible farmer substitutes nonland for land input: spends more on equipment and labor as land gets more expensive Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

46. Flexible versus fixed producers Flexible produce = factor substitution = lower costs* = higher profits By leftover principle, higher profits= higher bid rents Close to city center, land costs are lower; at periphery, freight costs are lower Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

47. Monocentric city firms’ bid rent function flexible producer The flexible firm outbids the fixed factor firm everywhere but point u’’. At u’, the fixed factor producer uses too much land Bid Rent B Fixed-factor producer A u’ u’’ Distance from export hub Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

48. Nonland versus land inputs for the Flexible producer Non-land inputs B flexible producer A Land Amount Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

49. Most central firm type: offices • Office firms: require 1) lots of meetings and face to face contact, 2)ability to gather, process and distribute information quickly and 3)access to services, like printing, lawyers, designers, accountants, etc. • This type of firm will have a steep bid rent function because the travel cost of individuals is very high; travel cost is high because their pay rate is high, since it is generally skilled work Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

50. Land use in CBD • All firms are attracted to center, but only some will be willing to bid enough • Office firms have steepest bid rent fn, and will occupy the most central land • Market allocation is efficient, because the office industry has the most to gain from being in the center; manufacturing could gain too, but not as much, so it’s willing to locate a little further out. Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics