Private Real Estate Investment: Data Analysis and Decision Making_2

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Private Real Estate Investment: Data Analysis and Decision Making_2 4 Private Real Estate Investment Wheat Farmer Pea Farmer 100 100 80 80 60 60 Rent Rent 40 40 20 20 0 2 4 6 8 10 01234567 Distance Distance FIGURE 1-1 Wheat and pea farmers’ bid rent curve. distance from the center are all revenues exhausted? Locating outside of that distance would produce negative revenue, an economic consequence that prevents a user from locating there. Notice that, given the inputs, the wheat farmer can afford to locate farther away. Stated differently, the pea farmer MUST locate closer in. Wheat farmer Pea farmer R ¼ pa À w À tam ¼ 0 R ¼ 10à 10 À 50 À :5à 10m ¼ 0 R ¼ 15à 10 À 75 À 1à 10m ¼ 0 m ¼ 10 ¼ Maximum distance m ¼ 7:5 ¼ Maximum distance By assuming an arbitrary value for m and solving for t, we can determine the slope of each party’s bid rent curve. Notice that the pea farmer’s slope is greater. What does this mean to the way both parties will bid for land closer to the center of the city? Wheat farmer Pea farmer R ¼ 10à 10 À 50 À tà 10à 10 ¼ 0 R ¼ 10à 10 À 50 À tà 10à 7:5 ¼ 0 t ¼ :5 ¼ Slope of bid rent curve t ¼ 1 ¼ Slope of bid rent curve Placing them both on the same plot is useful at this stage, noting that the point where the curves cross is the point on the land where the bids are equal. Prior to that point, the pea farmer is willing to pay the most for the land; beyond that point, the wheat farmer bids more than the pea farmer. Setting the two rent equations equal to each other, inserting the fixed inputs, and solving for m tells us the location on the land of the crossover point. Figure 1-2 shows the point on the land where both parties bid an equal rent and the amount of that rent. 5 Why Location Matters bids are equal Rent wheat pea 25 5 Distance FIGURE 1-2 Rent at the point where bids are equal. 10à 10 À 50 À :5à 10m ¼ 15à 10 À 75 À 1à 10m m¼5 R ¼ 10à 10 À 50 À :5à 10à 5 R ¼ 25 A little experimentation with different values for the fixed inputs leaves one with the insight that (in our stylized example) nothing matters but transportation cost. Mathematically, this can be verified by taking the first derivative of R with respect to m, with the quantity produced standardized to 1. dR ¼ Àt dm From this, we again see that in our simple model rent is a negative function of transportation cost. EXAMPLE #2—SEVERAL COMPETING USERS IN DIFFERENT INDUSTRIES Building on this, let us model an entire city with multiple users, each having a different transportation cost. We assume that user classes locate in concentric rings radiating out from the center of the city. The innermost is the central business core of commercial users (com), followed by an interior light industrial ring (indI), then residential (res), a second industrial ring of heavy manufacturers (indII), and finally, agricultural users (agr). Note that transportation costs per unit decrease in the outward direction with each user, resulting in a flatter slope for each curve as we progress outward. The combination of all users on a single graph leads to what is known as the bid 6 Private Real Estate Investment Rent All Users 140 Commercial Industrial I Residential 104 Industrial II 90 Agricultural 30 10 Distance 10 20 30 40 50 FIGURE 1-3 Bid rent curves for a city with different land uses. TABLE 1-1 Cross points and rent where land use changes Distance Rent com 0 140 com-indI 3. 104 indI-res 5. 90 res-indII 25. 30 indII-agr 35. 10 rent surface or rent gradient. Note in Figure 1-3 that the largest land mass is taken by residential. Why might that be so? Following our ...