is not strictly linear, but appears linear on a piecewise basis. The aggregation of various uses, each with a different transportation cost (and, therefore, a different slope), creates this shape. From this we may speculate that different individual users within any one sector each may also have slightly different transportation costs, and the aggregate of the linear bid rent curves of these different users produces a curve for any specific use that is also not a straight line (Figure 1-7). Under these conditions one might reasonably assume that the functional form of the bid rent curve for all individual users would be R ¼ e Àax , where x is distance from the center of the city, the exponent a is a decay rate that may be observed in the market as one moves away from the center, and e is the base of the natural logarithm. EMPIRICAL VERIFICATION Suppose we collect data on actual rent paid by users alon g a line in a certain direction moving away from the center of the city (or any high rent point), TABLE 1-2 Land Mass in Square Miles Allocated to Different Uses com area 28.27 indI area 50.27 res area 1884.96 indII area 1884.96 agr area 2513.27 52535 Distanc e 140 104 90 30 10 Rent FIGURE 1-6 Bid rent surface for the entire city. 8 Private Real Estate Investment such as reflected in Table 1-3. The first element in each pair is the distance from the center, the second is the rent paid at that point, and the third is the natural log of the rent, a useful conversion for further analysis. A plot of the distance and rent data in Figure 1-8 shows a nearly linear decay in rent as distance increases. We are interested in the relationship between distance and rent. A common method for investigating the relationship between two variables is linear regression analysis. For this, we use the natural log of rent as the dependent variable. Figure 1-9 shows a plot of the data in Table 1-3. Not surprisingly, it appears linear because taking the natural log of a curved function has the effect of ‘‘linearizing’’ the function. We then fit the regression model (Equation 1-3): Log R½¼Log ke Àxd ÂÃ ¼ Log k½Àxd ð1-3Þ where k is the regression constant, x is the slope, and d is distance from the center. The intercept and slope terms are shown in the regression equation: Log R½¼6:71003 À0:0155191x (A complete regression analysis appears among the electronic files for this chapter.) Exponentiating 2 both sides of the regression equation produces the conclusion that one may estimate rent based on a fixed intercept multiplied 1234567 Distance 0.2 0.4 0.6 0.8 1 Rent R= e − ax FIGURE 1-7 A well-behaved, smooth bid rent curve. 2 There is some doubt that ‘‘exponentiating’’ is a word. The Oxford English Dictionary does not carry ‘‘exponent’’ as a verb. However, we need a word for the cumbersome statement ‘‘using each side of the entire equation, each, as an exponent for the base of the natural log ’’ For this we press ‘‘to exponentiate’’ into service. Why Location Matters 9 TABLE 1-3 Rent Data Distance Rent LN (rent) 0 821 6.71052 1 808 6.69456 2 795 6.67834 3 783 6.66313 4 771 6.64769 5 759 6.632 6 748 6.6174 7 736 6.60123 8 725 6.58617 9 714 6.57088 10 703 6.55536 11 692 6.53959 12 681 6.52356 13 671 6.50877 14 660 6.49224 15 650 6.47697 16 640 6.46147 17 630 6.44572 18 621 6.43133 19 611 6.4151 20 602 6.40026 21 592 6.38351 5101520 Distanc e 650 700 750 800 Rent FIGURE 1-8 Plot of rent vs. distance. 10 Private Real Estate Investment times the base of the natural logarithm taken to an exponent that is composed of the product of the decay rate (as a negative number) and the distance. R ¼ 820:597e À0:0155191x Hence, if one is at the center, where distance is zero (x ¼ 0), the rent is the intercept. R ¼ 820:597 when x ¼ 0 On the other hand, if one is ten miles from the center (x ¼ 10), the rent is R ¼ 702:638 when x ¼ 10 Recall Figure 1-7 and its pronounced convexity to the origin. This noticeable convexity is because the decay rate (.5) was fairly large. Figure 1-10 reflects the decay rate derived from our regression. As the decay rate is quite small and the range of distance is short, the curve appears linear. The same curve is more pronounced over a longer distance (Figure 1-11). So we see that while the curve is a function of the decay rate, for small decay rates its curvature is only apparent over longer distances. 0 5 10 15 20 Distance 6.4 6.45 6.5 6.55 6.6 6.65 6.7 Log [Rent ] FIGURE 1-9 Plot of natural log of rent vs. distance. Why Location Matters 11 AN ECONOMIC TOPOGRAPHICAL MAP The world is not flat and neither are its land economics. The story becomes more realistic when one considers the theory in three dimensions. After all, there are an infinite number of directions away from any particular high rent location. One would expect the decay rate to vary in different directions. A stylized version of this uses the trigonometry employed in topography. 3 1234567 Distance 760 780 800 820 Rent R=820.597e −ax FIGURE 1-10 Bid rent curve suggested by regression analysis. 50 100 150 200 Distance 200 400 600 800 Rent R=820.597 e −ax Distance 0–200 FIGURE 1-11 Regression bid rent curve over a longer distance. 3 A more complete elaboration of this process with interactive features may be found at www.mathestate.com. 12 Private Real Estate Investment The so-called ‘‘path of progress’’ is the direction in which the decline in rent is the slowest, thus the decay rate is the slowest because higher rent is persistent in that direction. In that direction the decline is relatively flat. The opposite case is that of the steepest decay rate. As rents decline fastest, the decay rate is larger in the direction people are not locating. The three-dimensional parametric plots in Figure 1-12 show the economic topography where a ¼ .1 (Figure 1-12a) or a ¼ .02 (Figure 1-12b) to simulate the way rent changes as one travels around the land. RELAXING THE ASSUMPTIONS All models are only approximations of reality. Unfortunately, we attempt better approximations at the expense of generality. Nonetheless, the exercise of testing the model unde r more realistic assumptions is useful. One way to move closer to what we actually observe is to relax some of the assumptions. The first might be the idea that the urban business environ- ment is monocentric. In Figure 1-13a we see the potential for two high rent areas in a given market. This representation suggests that the secondary point of high activity might be somewhat flat at the top, representing an econo- mic oasis of activity where rents are generally high in a small area. This is the relaxation of the assumption that the greatest activity takes place at the absolute center. Rotating Figure 1-13a to see the rear of it in Figure 1-13b reveals an area of depressed rent. Clearly, there are as many portrayals of this condition as there are different cities on earth. Figure 1-13 could also depict the relaxation of the no transaction costs assumption. Zoning, a constraint on freedom of choice in how one uses one’s land, is essentially a transaction cost. If government imposes zoning that prohibits land use in a certain area, the consequence can be higher rent for that use in the area where that use is permitted. Another explanation for a plot like Figure 1-13 might be non-uniform transportation costs in one direction caused by natural barriers such as a river or mountain that must be crossed. One might also see an impact on the rent gradient as transportation costs differ in directions served by mass transit. Whether these graphical depictions represent reality is an interesting debate. One can challenge the notion that the market is symmetrical around a point, calling into question whether the most intense activity takes place on a single spot. Clearly, over time ‘‘clusters’’ of similar businesses gather in certain areas. Particular areas become ‘‘attractors’’ for certain kinds of industries. The list of exceptions to the basic theory is long. The primary value of the sort of analysis undertaken in this chapter is to provide a logical framework for location decisions and guide the thoughtful land consumer to a rational Why Location Matters 13 choice of location. As one delves more de eply into the exceptions to the general principal, one gets closer to what we observ e in practice at the expense of a loss of generality. Regardless, with each special case we see repeated the importance distance plays in the decision. Apparent exceptions often just change the place from which we are distant, not the actual –20 0 20 North–South ( a ) –20 0 20 East–West 0 0.25 0.5 0.75 1 Ren t −50 −25 0 25 50 North–South(b) − 50 −25 0 25 50 East–West 0 0.25 0.5 0.75 1 Ren t FIGURE 1-12 Economic topography maps with different values for a. 14 Private Real Estate Investment –25 0 25 North–South (a) –25 0 25 East–West 0.25 0.5 0.75 Rent 0 25 −25 0 25 0.25 0.5 0.75 Rent −25 North–South (b) East–West FIGURE 1-13 Market with two high rent districts. Why Location Matters 15 importance of distance. Thus, the connection between location and distance remains key. This book wi ll discus s the careful use of data often. In the case of market rents, one must be mindful of the fact that no dataset supplants a careful market survey in the local area of a target acquisition. However, as real estate markets become more efficient and data is more robust, the sort of models developed here will assist buyers in ‘‘getting up to speed’’ in an unfamiliar market. Having been instructed by the CEO of an REIT or real estate fund to visit a new city and investigate real estate opportunities there, an acquisition team may first consult data before landing in a market where local players dominate transactions. A WINDOW TO THE FUTURE Table 1-3 shows rent data collected along a line stretching away from a high rent location. Real estate data always has some location attribute. In the past that attribute was its street address. Later, a zip code was added. Recently, longitude and latitude points have been included. Each of these steps moves us closer to a time when the theoretical graphs shown in this chapter can be displayed as actual data points and the economic topographical map will represent a real world situation. Data represents reality, and there will be times when reality conflicts with theory. In Figure 1-14a we see a void where a lake, a public park, or a block of government buildings might be. In Figure 1-14b we see a number of missing data points throughout, each of which represents a location where rent is not reported. One of these could be owner occupied housing, another a church or a school, but some will be where rent is being paid and no inquiry has been made. In time as data collection is more streamlined and coverage is more complete, the grid will become finer and the picture more complete. There are a number of excellent data gatherers and providers; some are independent firms, and some are in-house for major real estate companies. It is to these industry support groups we direct a final appeal. As real estate data becomes more plentiful, observations of rent across the land will become more compact, filling in the grids necessary to describe the actual shape of the bid rent surface. For highly developed countries with efficient markets in financial assets, one would expect that real estate data gatherers and providers will deliver not only the raw information, but analytics based on that information. For countries with nascent market economies where data collection is just beginning, one hopes that those interested in market development will use the models above as templates to guide their database design at the early stages. 16 Private Real Estate Investment REFERENCES 1. Alonzo, W. Location and Land Use. Cambridge, MA: Harvard University Press. 2. Geltner, D. M., & Miller, N. G. Commercial Real Estate Analysis and Investments. Upper Saddle River, NJ: Prentice Hall. 3. Kline, M., Mathematics for the Non-Mathematician. New York: Dover Publications, Inc. 4. von Thunen, J. H. (1966). The Isolated State. New York: Pergamon Press. 5. www.mathestate.com. (a) (b) FIGURE 1-14 Viewing the location decision through data. Why Location Matters 17 [...]... how land may be used The unanswered question is: Shall the choice be made by the landowner or the community in which the land is located? Tariffs and trade agreements govern how commerce crosses international boundaries Laws prohibiting collusive and coercive activities govern domestic trade at a national level Our interest lies in local government For the private real estate investor, local land use... investor, local land use regulation is a significant aspect of the decision making process In urban settings it is no overstatement to say that real estate investment success is, in large part, dependent on an understanding of the regulatory environment in which the local real estate market exists Whether zoning or rent control, real estate investors ignore local politics at their peril Several general... the competing interests represented in the private economic market Land Use Regulation 37 and the market for public services and lifestyle This chapter presents just one example of many It is estimated that 80% of the decisions made by the typical Southern California City Council are land use decisions In effect, this makes local politicians the largest real estate agent in the city How well they do... operating as a governmental jurisdiction  Build and test a model that chooses the proper level of regulation that optimizes community satisfaction  Explore the consequences of over-regulation and its affect on other municipal services 19 20 Private Real Estate Investment  Review a case study using actual data in a real setting to illustrate how land users may deal with local government in the face... maximizes the function because the Log is monotonic and concave for all positive log bases 4 This ignores the interplay between taxes and the level of sales which is not our story 28 Private Real Estate Investment equation ab g À ag ¼0 þ A À A0 A ð2-8Þ Transferring the second term on the left of Equation (2-8) to the right-hand side produces Equation (2-9) and sets marginal cost equal to marginal benefit... from the optimal and resultant loss in utility may persuade the one vote an investor needs from the local council If the vote is close and swing vote is rational, this argument may only need to ring true with that one member Utility, U, changes with the change in allowed advertising, A, the efficiency of advertising, g, and community disutility for advertising (as expressed 32 Private Real Estate Investment... down There are hundreds, if not thousands, of examples from the residential field to draw from Rather than take one of those and its somewhat straightforward Land Use Regulation 23 analysis, the setting for the analysis here comes from the commercial area This presents additional challenges that deserve attention and at the same time illustrates how a somewhat esoteric land use conflict can be modeled THE... CHAPTER 2 Land Use Regulation We now understand better than before how small groups can wield power in excess of their relative voting strength and thus change the structure of property rights to their advantage, perhaps at the expense of the majority of voters Thrainn Eggertsson in Economic Behavior and Institutions, p 62 INTRODUCTION Chapter 1 dealt with how market participants make land use decisions... of 43.0556 Inserting that answer and the appropriate values from Table 2-1 into Equation (2-4) produces utility of 358,071 Locating 358,071 on the plot in Figure 2-4 shows that indeed utility peaks at that value Notice the importance of domain and range values with changes 30 Private Real Estate Investment TABLE 2-1 Numeric Values for Variables in Functions for Utility and Optimal Advertising a b g A0... thinking about land use regulation and (2) a rational model to describe a conflict between property owners and a regulatory agency The chapter will propose a theoretical model that permits one to optimize the conditions of regulation in a general sense Following that, an actual municipal decision is illustrated with a case study based on real data The theory of rent determination advanced in Chapter 1 was developed . 6.60 123 8 725 6.58617 9 714 6.57088 10 703 6.55536 11 6 92 6.53959 12 681 6. 523 56 13 671 6.50877 14 660 6.4 922 4 15 650 6.47697 16 640 6.46147 17 630 6.445 72 18 621 6.43133 19 611 6.4151 20 6 02 6.40 026 21 . actual 20 0 20 North–South ( a ) 20 0 20 East–West 0 0 .25 0.5 0.75 1 Ren t −50 25 0 25 50 North–South(b) − 50 25 0 25 50 East–West 0 0 .25 0.5 0.75 1 Ren t FIGURE 1- 12 Economic topography maps with different values for a. 14 Private Real Estate Investment 25 0 25 North–South (a) 25 0 25 East–West 0 .25 0.5 0.75 Rent 0 25 . thousands, of examples from the residential field to draw from. Rather than take one of those and its somewhat straightforward 22 Private Real Estate Investment analysis, the setting for the analysis