5. One might think of this generalization as proceeding in market(.g, the arc IJ in Figure 2-5 n small changes in the ratio of delivered prices could alter irm to consider a new location in the long run. 15 Second distance from the market could be analyzed. Here again sing forces drawing the unit closer to the market or the ecisions as the scale of production increases or decreases I input mix, so that there will be changes in ideal weights 7. For this particular production process, a in the long run a switch from location j to rent if one recognizes that the optimal input ABCDEFG=Receipts from all markets combined e greater rate of output, larger amounts of xI tion closer to the source of x is. therefore 85802巴b英a8 some savings in fuel requirements per ton of ket, because the ideal weight of the input lire the use of more transferable inputs and In this ins It of the inputs. Orientation would then be shifted a location decisions are difficult to make. 16 o hand in hand, lessening the usefulness of is that one must look to changes in ideal t Receipts from orientation was that a unit disposes of all its Receipts from farthest market nis accords with reality in many, but by no s substantial in relation to the total demand vanity sold any one market and it may be profitable for or of "access to market" will entail nearness nay find that it can get its supplies of FIGURE 2-8: Aggregation of Demand Schedules e supply at any one source is not perfectly of Five Markets for the Product of a single Seller Figure 2-8 shows how we might, in principle, analyze the market-access advantages of a specific location in terms of possible sales to a number of different market points. In this illustration, there are five markets in all, assumed to be located at progressively greater distances from the seller. If the demand curve at each of those markets is identical in terms of quantities bought at any given delivered price(price of the goods delivered at the market ) then the demand curves as seen by the seller (that is, in terms of quantities bought at any given level of net receipts after transfer costs are deducted) will be progressively lower for the more distant markets. This is shown by the series of five steeply sloping lines in the left-hand part of the figure. If we now add up the sales that can be made in all markets combined, for each level of net receipts, we obtain the aggrega demand curve pictured by the broken line ABCDEFG. For example, at a net received price of oH (after covering transfer costs) it is possible to sell HL, H, HK, HL, and HM in the five markets respectively. His total sales will be He, which is the sum of HM plus MN(=HL) plus NP(=HK) plus PQ(H) plus QF(HD) This aggregate demand schedule and the costs of operating at the location in question will determine what profits can be made there by choosing the optimum price and output level, 17 At possible alternative locations, both market and cost conditions will presumably be different, giving rise to spatial differentials in profit possibilities Although the foregoing may describe fairly well what determines the likelihood of success at a given location, it is hardly a realistic description of the kind of analysis that underlies most location decisions. Following are descriptions of some cruder procedures for gauging access advantage of locations in the absence of comprehensive data. 2. 8 SOME OPERATIONAL SHORTCUTS For simplicity's sake, let us consider just the question of evaluating access to multiple markets. If, for example, a market-oriented producer seeks the best location from which to serve markets in fifty major cities in the United States, how might it proceed What it wants is some sort of "geographical center"of the set of fifty markets. Suppose that this center were to be defined a median point so located that half of the aggregate market lay to the north and half to the south of it, and likewise half to e east and half to the west 18 Then(if it were to be assumed that transport occurs only on a rectilinear grid of routes) the producer would have the location from which the total ton-miles of transport entailed in serving all markets would be a13 points within a locational triangle such as that presented in Figure 2-5. One might think of this generalization as proceeding in two steps. First, many points along an arc of fixed radius from the market (e.g., the arc IJ in Figure 2-5) can be considered, rather than simply concentrating on two such points. In this ease, even small changes in the ratio of delivered prices could alter the optimal input mix and the balance of ideal weights, forcing the firm to consider a new location in the long run.15 Second, the economic incentives drawing the location to points of varying distance from the market could be analyzed. Here again, consideration of ideal weights is in order, with the balance of opposing forces drawing the unit closer to the market or the material sources. The nature of the production process can also affect location decisions as the scale of production increases or decreases. Changes in the rate of output may well imply changes in the optimal input mix, so that there will be changes in ideal weights and probably in locational preferences. Such a situation is depicted in Figure 2-7. For this particular production process, a change in the rate of output from Q0 to Q1 would imply a new equilibrium location; in the long run, a switch from location J to location I is indicated as the rate of output is increased. The reason for this is apparent if one recognizes that the optimal input ratio changes from that represented by OR" to that represented by OR'; hence, at the greater rate of output, larger amounts of x1 are used relative to x2 per unit of production. As the ideal weights change, a location closer to the source of x1 is, therefore, encouraged. It is possible also that increases in the scale of operations may imply less than proportionate increases in the requirements for one or more of the transferred inputs. Thus large-scale steel making may yield some savings in fuel requirements per ton of output. Operations that have this characteristic would be drawn toward the market, because the ideal weight of the inputs decreases relative to that of the final product with increases in the scale of production. However, contrary forces may also be evidenced. Increases in scale may require the use of more transferable inputs and fewer local inputs per unit of output—for example, using more material and less labor. In this instance, the ideal weight of the final product may actually be reduced relative to the ideal weight of transferable inputs. Orientation would then be shifted away from the market. Thus valid generalizations concerning the effect of the scale of production on location decisions are difficult to make. 16 Indeed, at a practical level, changes in scale and changes in technology often go hand in hand, lessening the usefulness of analysis based on production processes currently employed. The essential point is that one must look to changes in ideal weights in order to assess changes in locational orientation. As relative prices or the scale of operations change over time, ideal weights may be affected. 2.7 SCALE ECONOMIES AND MULTIPLE MARKETS OR SOURCES Another simplifying assumption that we applied in our discussion of transfer orientation was that a unit disposes of all its output at one market and obtains all its supply of each input from one source. This accords with reality in many, but by no means all, cases. If a seller's economies of scale lead it to produce an output that is substantial in relation to the total demand for that output at a single market, it will face a less than perfectly elastic demand in any one market and it may be profitable for it to sell in such additional markets as are accessible. In that event, the location factor of "access to market" will entail nearness not just to one point, but to a number of points or a market area. Similarly, it may find that it can get its supplies of any particular transferable input more cheaply by tapping more than one source if the supply at any one source is not perfectly elastic. Figure 2-8 shows how we might, in principle, analyze the market-access advantages of a specific location in terms of possible sales to a number of different market points. In this illustration, there are five markets in all, assumed to be located at progressively greater distances from the seller. If the demand curve at each of those markets is identical in terms of quantities bought at any given delivered price (price of the goods delivered at the market), then the demand curves as seen by the seller (that is, in terms of quantities bought at any given level of net receipts after transfer costs are deducted) will be progressively lower for the more distant markets. This is shown by the series of five steeply sloping lines in the left-hand part of the figure. If we now add up the sales that can be made in all markets combined, for each level of net receipts, we obtain the aggregate demand curve pictured by the broken line ABCDEFG. For example, at a net received price of OH (after covering transfer costs) it is possible to sell HI, HJ, HK, HL, and HM in the five markets respectively. His total sales will be HF, which is the sum of HM plus MN (=HL) plus NP (=HK) plus PQ (=HJ) plus QF (=HI). This aggregate demand schedule and the costs of operating at the location in question will determine what profits can be made there by choosing the optimum price and output level,17 At possible alternative locations, both market and cost conditions will presumably be different, giving rise to spatial differentials in profit possibilities. Although the foregoing may describe fairly well what determines the likelihood of success at a given location, it is hardly a realistic description of the kind of analysis that underlies most location decisions. Following are descriptions of some cruder procedures for gauging access advantage of locations in the absence of comprehensive data. 2.8 SOME OPERATIONAL SHORTCUTS For simplicity's sake, let us consider just the question of evaluating access to multiple markets. If, for example, a market-oriented producer seeks the best location from which to serve markets in fifty major cities in the United States, how might it proceed? What it wants is some sort of "geographical center" of the set of fifty markets. Suppose that this center were to be defined as a median point so located that half of the aggregate market lay to the north and half to the south of it, and likewise half to the east and half to the west18 Then (if it were to be assumed that transport occurs only on a rectilinear grid of routes) the producer would have the location from which the total ton-miles of transport entailed in serving all markets would be a