Based on Urban Economics by Arthur O’Sullivan Notes by Austin Troy 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

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% 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 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

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 $ “A” land “B” land “C” land 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

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 $50 Land rents $110 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 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

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

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 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

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

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

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

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 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

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

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= 3min/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 zone 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’ Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Locational choices 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 Residential Zone Manufacturing Zone Office Zone U’ U’’ 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 cost of moving workers Lecture 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

Residential housing price function with consumer substitution $.3 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