Land Use Economics Lecture Notes Land Rents Accessibility

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

Why do cities exist? • Why not a uniform distribution of people across the landscape? 1. Comparative advantage 2. Internal scale economies 3. Agglomeration economies Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

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 Wheat Cloth Output per labor hour OC of Production East West East 1 2 1 C 1 6 1 W Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics West 3 C 1/3 W

• • • 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

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

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 Cost of homemade product Net cost travel cost Factory cost Market area Miles from factory (radius) Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

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

AEP: Localization Economies • When production costs of firm in a certain industry decrease as total industry output increases. Due to: 1. Scale economies in intermediate inputs 2. Labor market pooling 3. Knowledge spillovers Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

• 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

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

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

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

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 labor costs are lower Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

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

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

Retail: Agglomerative economies in marketing • Shopping externalities occurs when sales of one store 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiple land uses in the CBD • Let’s assume a traditional 19 th 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

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 coststransport 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

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

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

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

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

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

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

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

Office vs. manufacturing • Suppose office firm 1 block from center and manufacturer 5 blocks. If they swapped locations, this would dramatically increase the office firm’s travel cost – Office firm TC= 3 min/block*$4/min*200 meetings/month= $2400 per block/month • So the swap increase TC for office by $9, 600/mo, but only saves the manufacturer $800/month in transportation costs (50 tons * $4/ton/block= $200/block). Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Multiple land use rent gradient Office Bid rent Manufacturing Residential zone Bid Rent Manuf. Bid rent Residential bid rent Office zone U’ U’’ Distance to center Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Locational choices Residential Zone Manufacturing Zone Office Zone U’ U’’ Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Locational choices Residential Zone Manufacturing Zone Office Zone U’ U’’ So workers live on the periphery because they are cheap to transport (i. e. commuting costs are low) relative to cost of moving freight (for manufacturers). For offices, same problem, because of high price of moving executives around for meetings. If office is in suburbs, executive is constantly going to CBD Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Who occupies what? • Activities are arranged according to transport costs; those with the highest costs occupy the most central land • Activity with the highest transport cost will have the highest bid rent curve • All firms have tug-of-war between locating centrally to keep transport cheap, and locating in the suburbs to keep workers’ commute cost lower (and hence pay lower wages) • CBD wins because cost of freight hauling greater than. Lecture cost of moving workers by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Housing price function • In the monocentric model, residents will be attracted towards the center but be outbid by offices and manufacturing. • Assume no factor substitution, identical 1000 sq ft houses, fixed budget of $300/mo for housing+commuting, commute cost (CC)= $20/mi. • WTP for housing = $300 - CC. Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Housing price fuction $. 3 D for housing near center pushes up price until rent= budget-CC. P housing/ sq ft Residents now indifferent among all locations in city $. 18 $. 06 6 mi 12 mi Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Housing price function with consumer substitution • With consumer substitution, residents consume less land as price of land goes up; instead consume more local amenities • Hence, more central homes are smaller • Flexible residents will outbid fixed factor residents everywhere but tangency point • Change in P due to distance= , or negative of (tranpo cost/mi divided by amount of housing consumed) Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

$. 3 Residential housing price function with consumer substitution Price w consumer sub P housing/ sq ft $. 18 $. 06 6 mi 12 mi Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Residential bid rent function and factor subsitution • Residents’ housing price fn with consumer substitution drive producers’ factor substitution • Factor Substitution: Housing producers substitute capital for land as move closer to center; higher density allows residential housing firms to pay the higher cost of land in more central locations. Different from consumer substitution • Producers’ bid rent functions are convex because of consumer substitution in the housing price function Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Density increases towards center because: • Consumer substitution in housing pr fn. – P(housing) goes down away from center, so households consume more housing (i. e. larger dwellings) towards periphery • Factor substitution in producer bid fn – Price of land goes down as move away because of housing price function; housing production firms respond by using more land per unit of housing (less density) towards periphery; towards center they respond with greater density Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Changes to Residential Model • All the following changes in assumptions make cost of commuting greater, and housing price fn/residential bid rent fn steeper: – No time cost to commuting (only monetary cost)>> time cost to commuting (opportunity cost) – Amenities (shopping, recreation) etc. are evenly distributed across city>> Amenities concentrated in the CBD – All households one earner>>two earners commuting to center Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics