Week 2: The Urban Land Market, location, rents, prices.Empirical Studies of Location and Land Prices (e.g. Waddell) Sometimes the relationships are complicated. Components of Housing Rent dashed line: rent without development at the edge = rent for the lotExpansion of Housing Rent as the city grows in population and the border moves from b0 to bt.The components of Land PricesNumerical ExampleTransportation: the real explanation for Historic appreciation (or lack thereof). Expansion of Housing Rents as population growth expands the border, but technology improves transportation.Housing Rents and Land Use Competition with 2 Household types [1,2]MIT OpenCourseWare http://ocw.mit.edu 11.433J / 15.021J Real Estate EconomicsFall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.MIT Center for Real Estate Week 2: The Urban Land Market, location, rents, prices. • Ricardian Rent with Commuting in a radial city. • Land Supply and Urban Comparative Statics. • Spatial capitalization of Ricardian Rent. • Multiple land users, market competition, “highest use” segmentation.MIT Center for Real Estate Empirical Studies of Location and Land Prices (e.g. Waddell) Sometimes the relationships are complicated. Land or Housing Price Positive Value of Access Negative Value of Proximity Distance from HighwayMIT Center for Real Estate 1). R(d) = R(b) + k(b - d) : “Housing Rent” d = any “interior” location b = Most “marginal or farthest location 0 = “Best”, most central location k = annual commuting cost [inc. time] per mile from “best” or central location 2). R(b) = “replacement” cost [annualized] = Ra + c Ra = “Agricultural” rent for a lot c = annual “rent” for constructionMIT Center for Real Estate 3). r(d) = [R(d) – c]/q “Land Rent=a residual” q = lot size, acres 4). r(d) = ra + k[b – d]/q ra = Ra/q, land price per acre 5). b = [Nq/πV]1/2 N = # households [population] V = fraction of land within circle available for developmentW.C.W1 MIT Center for Real Estate Components of Housing Rent dashed line: rent without development at the edge = rent for the lot Housing rent R(d) Location Rent: k [ b - d ] Structure Rent: c Agricultural lot Rent Ra= ra q Distance: d Border: bW.C.W2 MIT Center for Real Estate Components of Land Rent: [ Housing rent-structure rent] /q Land rent r(d) Location Rent: k [ b - d ]/q Agricultural Rent: ra Distance: d Border: bMIT Center for Real Estate 6). City Comparisons: a). More population N implies higher R(d) b). Denser cities have higher land rent? c). Transportation improvements: reductions in k. d). Transportation access: increases V. (Bombay, SF). e). Other geographies [islands, coastlines]MIT Center for Real Estate Bombay: World Bank Project. What are the benefits of constructing a new bridge? Edge of DevelopmentFarm LandCBD218OceanBombay BridgeFigure by MIT OpenCourseWare.MIT Center for Real Estate 7). Population growth at rate 2g implies boundary [b] growth rate of g [see previous equation] bt = b0egt nt = n0e2gt 8). Hence Ricardian Rent for existing structures located at (d) in time t: Rt(d) = (raq + c) + k(bt–d) [d<bt]MIT Center for Real Estate Expansion of Housing Rent as the city grows in population and the border moves from b0 to bt. Center b0 bt distance (d) House Rent R (d)Location rent Structure rent Agricultural rentMIT Center for Real Estate 9). Price of existing structures at (d) in time 0 is PDV of future Rent. With discount rate i: P0(d)= raq/i + c/i + k[b0 – d]/i + kb0g/[i-g]i term1= value of land used perpetually in agriculture term2= value of constructing structure term3= value of current Ricardian Rent term4= value of future growth in Ricardian Rent [note that d<b0, and i>g, if g=0 reduces to ?]MIT Center for Real Estate 10). Spatial multipliers or capitalization rates. With much effort the price/rent multiplier today for existing structures is: P0(d)/R0(d) = 1/i + kb0g /i[i – g] R0(d) As we examine farther locations where rent is lower this term implies a greater price multiple or lower cap rate. Why? With no growth [g=0] the multiple is the inverse of the discount rate – at all locations More?MIT Center for Real Estate 11). Like land rent, land price is a residual from structure price, for existing structures. pt(d) = [Pt(d) –c/i]/q What about the price of land beyond the current border (b0). In t years from now the border will have expanded to b0egt . Inverting, land at distance d> b0 will be developed in T = log(d/b0)/g years from now.MIT Center for Real Estate 12). Hence for d>b0 the value of land has two components: the discounted value of agricultural rent until developed, plus its value once developed – discounted to now. p0(d) = PDV0→T (ra) + e-iT pT(d) = ra/i + e-iT kbTg/[i – g]iq For locations d=b0egT which will be developed at T years hence. Notice that as g hits zero the last term vanishes. Where are land prices most volatile as g fluctuates?MIT Center for Real Estate The components of Land Prices Land Price p0 (d) developed vacant Current Location Value Future Increase in Location Value Agricultural value Center b0 DistanceMIT Center for Real Estate Numerical Example • Parameters: N=2million, q=.25 acre (.0004 square miles), k=$200 per mile per year, c=$7000, i=.07, ra=$1000 per year, V=.6 • Solution: b = 20 miles (approximate) R(0) = $11,250, R(b) = $7250 r (0) = $17,000 (acre), r(b) = $1000 If g=.02, then: P(b) = $127,000, P(0)=$184,000 p(b) = $105,000, p(0) = $334,000MIT Center for Real Estate The Four variables of the simple model do quite well in explaining the large difference in average house prices between US metro areas. 1990 Construction Cost Index 1990 Value 1980 HHs* 1990 HHs % Difference Boston CMSA 248.8 176,400 1,219,603 1,547,004 26.8 Cincinnati CMSA 203.9 71,400 586,818 652,920 11.3 Dallas/Ft. Worth CMSA 187.9 78,700 1,076,297 1,449,872 34.7 Denver CMSA 198.4 89,300 609,360 737,806 21.1 Detroit CMSA 227.4 69,400 1,601,967 1,723,478 7.6 Houston CMSA 192.8 63,800 1,096,353 1,331,845 21.5 Kansas City MSA 209.7 66,500 493,485 602,347 22.1 Los Angeles CMSA 239.8 211,700 4,141,097 4,900,720 18.3 Miami CMSA 191.1 88,700 1,027,347 1,220,797 18.8 Minneapolis MSA 213.7 88,700 762,376 935,516 22.7 New Orleans MSA 188.2 70,000 418,406 455,178 8.8 Philadelphia CMSA 230.5 102,300 1,925,787 2,154,104 11.9 Phoenix MSA