Thus some kinds of canning and preserving involve important weight and bulk loss as well as reduction of perishability. A further reason for the usual output orientation of modern by-product coke ovens is that the bulkiest output, gas, is in demand at the steel works where the coking is done. Coke produced by the earlier"beehive"process was generally made at coal mines, since weight loss more than offset fragility gain. (The gas went to waste.) Processing activities of course usually result in a product more valuable than the required amount of transferred inputs; and for a number of good reasons, transfer rates tend to be higher on more valuable commodities. Risk of damage or pilferage is greater there ic a greater interect cost an the working ranital tied nn in the enmmnditv in transit; and (as will be expl ained in the n nity to discriminate against high-value boring market orientation. 9 even when physical weight is zero or irrele energy, communications, and services g this information with the cost of an addit ransferable input or output is invol ved e categorizations of transfer-oriented activ S determination of locational preference that the unit we are considering is S the set of market locations and all that rema transferred input to that market more chea ts. The profitability of location at each FIGURE 2-2: Pairing of Sources and Markets he unit should locate source for a location at any the input more cheaply than for more than one market any of the market locations nging the ss and Ms. If the ich to locate. and then there nd of transferable input(for atterns and sand for molds) equired, say, x tons of one plex. In Figure 2-3, which may be at any one of those we can see immediately that formed by joining the input e points involved, as in Figure 2-3. If nan three sides the constraint will st ill e processing location, each attracting it towa ee pulls balance, so that a shift in any direc itive about which force will prevail. In t is, at least equal to the sum of all the other cases in which no single ideal weight gure: that is, the configuration of the M ion is such that the activity would be -or the market m. ll but with the same FIGURE 2-4: A Locational Triangle Conducive to iangle would be optimal, and we could Minimum Transfer Cost Location at the obtuse Corner We find, then, that it is not as easy as it first appeared to characterize by a simple rule the orientation of any given type of economic activity. If the activity uses more than one kind of transferable input(and/or if it produces more than one kind of transferable output ), we may well find that an optimum location can sometimes be at a market, sometimes at an input source. nd sometimes at an intermediate point. The steel industry is a good example of this. Some steel centers have been located at or near iron ore mines, others near coal deposits, others at major market concentrations, and still others at points not possessing ore or coal deposits or major markets but offering a strategic transfer location between sources and markets. Intermediate and varying orientations are most likely to be found in activities for which there are several transferable inputs and outputs of
11 Thus some kinds of canning and preserving involve important weight and bulk loss as well as reduction of perishability. A further reason for the usual output orientation of modern by-product coke ovens is that the bulkiest output, gas, is in demand at the steelworks where the coking is done. Coke produced by the earlier "beehive" process was generally made at coal mines, since weight loss more than offset fragility gain. (The gas went to waste.) Processing activities of course usually result in a product more valuable than the required amount of transferred inputs; and for a number of good reasons, transfer rates tend to be higher on more valuable commodities. Risk of damage or pilferage is greater; there is a greater interest cost on the working capital tied up in the commodity in transit; and (as will be explained in the next chapter) transfer agencies commonly have both the incentive and the opportunity to discriminate against high-value goods in setting their tariffs. Value gain in processing is thus an activity characteristic favoring market orientation. 9 An important observation of ideal weights is that they are real and measurable even when physical weight is zero or irrelevant. We can directly evaluate the ideal weights of inputs or outputs such as electric energy, communications, and services by determining the costs of transferring them an additional mile and then comparing this information with the cost of an additional mile of transfer on the appropriate corresponding quantity of whatever other transferable input or output is involved in the process. As mentioned earlier, the comparison of ideal weights permits at least tentative categorizations of transfer-oriented activities as input-oriented or output-oriented and points the way toward more specific determination of locational preference for specific units and activities. Suppose for example that we have determined that the unit we are considering is output-oriented. Then the choice of possible locations is immediately narrowed down to the set of market locations, and all that remains is to select the most profitable of these. For each market location, there will be one best input source, which can supply the transferred input to that market more cheaply than can any other source. Figure 2-2 pictures this pairing of sources and markets. The profitability of location at each market can thus be calculated, and a comparison of these profitabilities indicates where the unit should locate. The situation shown in Figure 2-2 has some other features to be noted. First, the best input source for a location at any given market is not necessarily the nearest. A more remote low-cost source may be able to deliver the input more cheaply than the higher-cost source that is closer at hand. Second, any one input source may be the best source for more than one market location (but not conversely). Third, there may be some input sources that would not be used by any of the market locations. Finally, Figure 2-2 could be used to picture the ease of an input-oriented unit, by simply interchanging the Ss and Ms. If the unit is input-oriented to a single kind of input, all that is needed is to choose the best source at which to locate, and then there will be a best market to serve from that location. Next, let us complicate matters a little by considering an activity that uses more than one kind of transferable input (for example, a foundry that uses fuel and metals plus various less important inputs such as wood for patterns and sand for molds). Initially we shall assume that the various inputs are required in fixed proportion. We now have three or more ideal weights to compare. For each ton of output, there will be required, say, x tons of one transferable input plus y tons of another. The question of orientation is now somewhat more complex. In Figure 2-3, which pictures one market and one source for each of two kinds of input, the most profitable location may be at any one of those three points or at some intermediate point. Retaining our assumption of a uniform transfer surface, we can see immediately that the choice of intermediate locations is restricted to those inside or on the boundaries of the triangle formed by joining the input sources and market points. This constraint upon possible locations will always apply when there are just three points involved, as in Figure 2-3. If there are more market or source points, so that we have a locational polygon of more than three sides, the constraint will still apply if the polygon is "convex" (that is, if none of its corners points inward). Looking at Figure 2-3, we can envisage three ideal weights as forces influencing the processing location, each attracting it toward one of the corners of the triangle. The most profitable location is where the three pulls balance, so that a shift in any direction would increase total transfer costs.10 In the case of three or more factors of transfer orientation, we can no longer be positive about which force will prevail. In fact, we can really be sure only if one of the ideal weights involved is predominant: that is, at least equal to the sum of all the other weights. It does not follow, however, that an intermediate location will be optimal in all cases in which no single ideal weight predominates. The outcome in such a case depends on the shape of the locational figure: that is, the configuration of the various source and market points in space. For example, in Figure 2-4 the configuration is such that the activity would be input-oriented to source S2 even if the relative weights were 3 for S1, 2 for S2 and 4 for the market M. 11 But with the same weights and a figure shaped like that in Figure 2-3, an intermediate location within the triangle would be optimal, and we could not describe the activity as being either input-oriented or output-oriented. We find, then, that it is not as easy as it first appeared to characterize by a simple rule the orientation of any given type of economic activity. If the activity uses more than one kind of transferable input (and/or if it produces more than one kind of transferable output), we may well find that an optimum location can sometimes be at a market, sometimes at an input source, and sometimes at an intermediate point. The steel industry is a good example of this. Some steel centers have been located at or near iron ore mines, others near coal deposits, others at major market concentrations, and still others at points not possessing ore or coal deposits or major markets but offering a strategic transfer location between sources and markets. Intermediate and varying orientations are most likely to be found in activities for which there are several transferable inputs and outputs of
plifying assumption of a uniform transfer surface, it the physical weights of transferred inputs and ot be altered. In practice, this is often not true. For sed as metallic inputs, but it is possible to step up the use larger proportions of scrap at locations where it fact, there is at least some leeway for responding to The same principle also applies more broadly to sferable as well as transferable inputs and outputs be replaced by labor-saving equipment where it is stitutions of this sort, consider the locational triangle consider the decision of a locational unit with two erable output with a market located at M. To focus as given by limiting our consideration to locations I FIGURE 2-5: A Locational Triangle: Analysis of e same production technology is applicable at either the Location Decision with Variable Factor Proportions l the market, which we shall consider later The delivered price of a transferable input is its price at the source plus transfer charges. In the present example, there are two such inputs, xI and x2. Their delivered prices are respectively (1) where pi and p2 are the prices of each input at is source, and ri and r2 represent transfer rates per unit distance for these puts. The distance from each source to a particular location such as I or J is given by di and dz It is significant that the relative prices of the two inputs will not be the same at I as at J. Location I is closer than J to the source of XI, but farther away from the source of x2. So in terms of delivered prices, xI is relatively cheaper at I and X2 is relatively cheaper at J. The total outlay (tO) of the locational unit on transferable inputs is TO-p1XI p2X2 This equation may be reexpressed o inputs that could be bought are determined by outlay line. 13 the possible combinations of inputs xI and X2that sents the iso-outlay lines associated with locations with location I is represented by AA, and that olved in transporting input I to I rather than to J ce ratio determines the slope of the iso-outlay line an that of BB. Also, it is important to recognize put ratio(x1/xe). Movement out along such a ra Increasing lich transferable inputs are used, any ray could however, that if the firm chose to use the inpi utlay by producing at location I and accepting the plied by OR, location I would be efficient in this greater than that implied by OR is used, the unit be efficient and the unit would locate at j. The icably bound As decisions are made concerning ame time consider its locational alternatives. The line denoted by Qo in that figure is referred to as stitute between inputs in the production process. It B ation represented by the coordinates of a point ation that will minimize the total cost of inputs. In FIGURE 2-6: lso-Outlay Lines, Input Choice, and Location nted by OR"and this, in turn, implies location at We might characterize the outcome of the decision process in this example as a locational orientation towards the input x2 The word"orientation"is used in a somewhat less restrictive way here than in previous examples. Here, it is only meant to suggest that the outcome of the production-location decision is that the unit was drawn toward a location closer to x2 as a result of the nature of its production process and the structure of transfer rates While the problem analyzed above concerns a decision between two locations, it can be extended to include all possible
12 roughly similar ideal weight. In the next chapter, when we drop the simplifying assumption of a uniform transfer surface, it will be possible to gain some additional perspective on rules of thumb about transfer orientation. 2.6 LOCATION AND THE THEORY OF PRODUCTION So far we have been assuming that for a particular economic activity the physical weights of transferred inputs and outputs were in fixed proportion; that is, the production recipe could not be altered. In practice, this is often not true. For example, in the steel industry, steel scrap and blast furnace iron are both used as metallic inputs, but it is possible to step up the proportion of scrap at times when scrap is cheap and to design furnaces to use larger proportions of scrap at locations where it is expected to be relatively cheap. In almost any manufacturing process, in fact, there is at least some leeway for responding to differences in relative cost of inputs and relative demand for outputs. The same principle also applies more broadly to nonmanufacturing activities, and it includes substitution among nontransferable as well as transferable inputs and outputs. Thus labor is likely to be more lavishly used where it is cheap, and to be replaced by labor-saving equipment where it is expensive. In order to explore some of the implications associated with input substitutions of this sort, consider the locational triangle presented in Figure 2-5.12 As in earlier examples, we shall once again consider the decision of a locational unit with two transferable inputs (x1 located at S1 and x2 located at S2) and one transferable output with a market located at M. To focus attention on the effects of input substitution, we shall take delivery costs as given by limiting our consideration to locations I and J, which are equidistant from the market, and we shall assume that the same production technology is applicable at either location. The arc IJ includes additional locations at that same distance from the market, which we shall consider later. The delivered price of a transferable input is its price at the source plus transfer charges. In the present example, there are two such inputs, x1 and x2. Their delivered prices are respectively p'1=p1 + r1d1 and (1) p'2=p2 + r2d2 where p1 and p2 are the prices of each input at is source, and r1 and r2 represent transfer rates per unit distance for these inputs. The distance from each source to a particular location such as I or J is given by d1 and d2. It is significant that the relative prices of the two inputs will not be the same at I as at J. Location I is closer than J to the source of x1, but farther away from the source of x2. So in terms of delivered prices, x1 is relatively cheaper at I and x2 is relatively cheaper at J. The total outlay (TO) of the locational unit on transferable inputs is TO=p'1x1 + p'2x2 (2) This equation may be reexpressed as x1=(TO / p'1) – (p'2 / p'1)x2 (3) For any given total outlay (TO), the possible combinations of the two inputs that could be bought are determined by equation (2), and these combinations can be plotted by equation (3) as an iso-outlay line.13 Locations I and J have different sets of delivered prices, and therefore the possible combinations of inputs x1 and x2that any given outlay TO can buy will vary according to location. Figure 2-6 presents the iso-outlay lines associated with locations I and J for a given total outlay and prices. The iso-outlay line associated with location I is represented by AA', and that associated with location J is represented by BB'. The shorter distance involved in transporting input 1 to I rather than to J implies that the price ratio (p'2/p'1) will be greater at location I. Since this price ratio determines the slope of the iso-outlay line (see equation (3) and footnote 13), we find that the slope of AA' is greater than that of BB'. Also, it is important to recognize that the slope of any ray from the origin, such as OR, defines a particular input ratio (x1/x2). Movement out along such a ray implies that more of each input is being used and that the rate of output must be increasing. Because we have relaxed the assumption restricting the ratio in which transferable inputs are used, any ray could potentially identify the input proportion used by the locational unit. Notice, however, that if the firm chose to use the input ratio identified with OR', it could produce more output for any given total outlay by producing at location I and accepting the iso-outlay line AA'. In fact, for any input ratio (x1/x2) greater than that implied by OR, location I would be efficient in this sense. By implication, if the production decision is such that an input ratio greater than that implied by OR is used, the unit would locate at I. Similarly, for any input ratio less than OR, BB' would be efficient and the unit would locate at J. The effective iso-outlay line is, therefore, represented by ACB’. The location decision and the production decision are therefore inextricably bound. As decisions are made concerning optimal input combination for a given level of output, the firm must at the same time consider its locational alternatives. The simultaneity of this process can be illustrated by reference to Figure 2-6. The line denoted by Q0 in that figure is referred to as an isoquant, or equal product curve, and characterizes the unit's ability to substitute between inputs in the production process. It indicates that the rate of output Q0 can be produced by every input combination represented by the coordinates of a point on that line. So for any specified output, there is a location and an input combination that will minimize the total cost of inputs. In our example, Q0 can be produced most efficiently at the input ratio represented by OR" and this, in turn, implies location at J.14 We might characterize the outcome of the decision process in this example as a locational orientation towards the input x2. The word "orientation'' is used in a somewhat less restrictive way here than in previous examples. Here, it is only meant to suggest that the outcome of the production-location decision is that the unit was drawn toward a location closer to x2 as a result of the nature of its production process and the structure of transfer rates. While the problem analyzed above concerns a decision between two locations, it can be extended to include all possible
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 a
13 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
minimum. This is an application of the principle of median location Naturally, a number of objections might be made to this procedure. One of the most obvious is that it is illogical to assume that our producer's sales pattern is independent of its location. It would be more reasonable to assume that the producer would have a smaller share of the total sales in markets more remote from its location, reflecting higher transport charges and other aspects of competitive disadvantage around this difficulty would be to decide that the producer is really primarily interested in marke possibilities only within, say, a radius of 400 miles, or only within the range of overnight truck delivery. It could then demarcate such areas around various points and select as its location the center of the area having the largest market volume A somewhat more sophisticated procedure would be to apply a systematic distance discount in the evaluation of markets by calculating what is called an index of market access potential for each of a number of possible locations. Thus to compute the potential index Pi for any specific production location(i), the producer would divide the sales volume of each market ()by the distance Dij from(i) to ()and then add up all the resulting quotients. Such potential measures have been widely used, with the distance (or transport costs, if ascertainable) commonly raised to some power such as the square. If the square of the distance is used, the potential formula becomes P (where M is market size and D is distance); and any given market has the same effect on the index as a market four times as big but twice as far away. In any ease, when the potential index P has been calculated for various possible locations, the location having the largest P can then be rated best with respect to access to the particular set of markets involved This measure of"potential, " in which each source of attraction has its value"discounted for distance, "is also generically known as a gravity formula or model-particularly when the attractive value is deflated by the square of distance over which the attraction operates. The reference to gravity reflects analogy to Newton' s law of gravitation(bodies attract one another in proportion to their masses and inversely in proportion to the square of the distance between them). William J. Reilly in 1929 proclaimed the Law of Retail gravitation on the basis of an observed rough conformity to this principle in the case of retail trading areas(a subject to be examined in more detail in Chapter 8), and John Q. Stewart and a host of others subsequently discovered gravity-type relationships in a wide variety of economic and social distributions. Gravity and potential measures have in fact been applied to almost every important measurable type of human interaction involving distance, and numerous variants of the basic formula have been devised. some of which we shall have occasion to examine later 19 All the shortcut methods described here have been widely used. Though they have been explained here in terms of the measurement of access to markets, or output access of potential locations, they are equally applicable to assessment of the input access potential of locations, when a unit is drawing on more than one source of the same transferable input. The measures can apply also to cases involving the transfer of services rather than goods-for example, measuring the job-access potential of various residence locations where a choice of job opportunities is desirable, or measuring the labor-supply access potential of altemative locations for an employer But at best, when a unit can serve many markets and/or draw from many input sources, the appraisal of alternative locations in terms of access is a complex matter. There is likely to be little opportunity to use the simple devices discussed earlier in this chapter, such as the balancing off of relative input and output weights, except perhaps as a means of initially narrowing down the range of locational alternatives. In such cases, the maps of cost and revenue prospects will show complex contours rather than simple ones as in the examples discussed earlier; and the evaluation of prospects at different locations will have to approach more nearly an explicit calculation of the expected costs, revenues, and profits at various possible levels of output at each of a large set of locations ine For most types of locational decision units, an exhaustive point-by-point approach in which theory and analysis abdicate in favor of pure empiricism would be so expensive as to outweigh any gain from finally determining the ideal spot. So there will al ways be a vigorous demand for usable shortcuts, ways of narrowing down the range of location choice, and better analytical techniques. The challenge to regional economists is to provide techniques better than hunch or inertia and cheaper than exhaustive canvassing of locations 2.9 SUMMARY This chapter deals with location at the level of the"location unit"as exemplified by a household, business establishment school, or police station. Location in terms of larger aggregates such as multiestablishment firms or public agencies, industries cities, and regions is taken up in later chapters. A single decision unit(for instance, a firm) can embrace one or more location Prospective income is a major determinant of location preference, but even in the ease of business corporations in which he profit motive is paramount there are other significant considerations, including security, amenity, and the manifold politica and social aims of public and institutional policy. Uncertainties, risks, and the costs of decision making and moving contribute to locational inertia and often to concentration The basis for locational preferences can be expressed generally in terms of a limited set of location factors involving both affecting a specific decision or type of location unit Location factors themselves have characteristic spatial patterns of advantage. Some factors, such as rent, may be relevant chiefly in comparing locations on a microspatial (small area)basis; other factors may emerge as important for macrospatial mparisons, involving locations far apart. Some location factors are primarily related to concentration: They may be most favorable in, say, large cities or dusters of activity or, alternatively, in small towns or rural locations. Other location factors involve transfer of input or output, so that locational advantage varies systematically according to distance. Other location
14 minimum. This is an application of the principle of median location. Naturally, a number of objections might be made to this procedure. One of the most obvious is that it is illogical to assume that our producer's sales pattern is independent of its location. It would be more reasonable to assume that the producer would have a smaller share of the total sales in markets more remote from its location, reflecting higher transport charges and other aspects of competitive disadvantage. One way to get around this difficulty would be to decide that the producer is really primarily interested in market possibilities only within, say, a radius of 400 miles, or only within the range of overnight truck delivery. It could then demarcate such areas around various points and select as its location the center of the area having the largest market volume. A somewhat more sophisticated procedure would be to apply a systematic distance discount in the evaluation of markets by calculating what is called an index of market access potential for each of a number of possible locations. Thus to compute the potential index Pi for any specific production location (i), the producer would divide the sales volume of each market (j) by the distance Dij from (i) to (j) and then add up all the resulting quotients. Such potential measures have been widely used, with the distance (or transport costs, if ascertainable) commonly raised to some power such as the square. If the square of the distance is used, the potential formula becomes = j Pi M j Dij ( / ) 2 (where M is market size and D is distance); and any given market has the same effect on the index as a market four times as big but twice as far away. In any ease, when the potential index P has been calculated for various possible locations, the location having the largest P can then be rated best with respect to access to the particular set of markets involved. This measure of "potential," in which each source of attraction has its value "discounted for distance," is also generically known as a gravity formula or model—particularly when the attractive value is deflated by the square of distance over which the attraction operates. The reference to gravity reflects analogy to Newton's law of gravitation (bodies attract one another in proportion to their masses and inversely in proportion to the square of the distance between them). William J. Reilly in 1929 proclaimed the Law of Retail Gravitation on the basis of an observed rough conformity to this principle in the case of retail trading areas (a subject to be examined in more detail in Chapter 8), and John Q. Stewart and a host of others subsequently discovered gravity-type relationships in a wide variety of economic and social distributions. Gravity and potential measures have in fact been applied to almost every important measurable type of human interaction involving distance, and numerous variants of the basic formula have been devised, some of which we shall have occasion to examine later.19 All the shortcut methods described here have been widely used. Though they have been explained here in terms of the measurement of access to markets, or output access of potential locations, they are equally applicable to assessment of the input access potential of locations, when a unit is drawing on more than one source of the same transferable input. The measures can apply also to cases involving the transfer of services rather than goods—for example, measuring the job-access potential of various residence locations where a choice of job opportunities is desirable, or measuring the labor-supply access potential of alternative locations for an employer. But at best, when a unit can serve many markets and/or draw from many input sources, the appraisal of alternative locations in terms of access is a complex matter. There is likely to be little opportunity to use the simple devices discussed earlier in this chapter, such as the balancing off of relative input and output weights, except perhaps as a means of initially narrowing down the range of locational alternatives. In such cases, the maps of cost and revenue prospects will show complex contours rather than simple ones as in the examples discussed earlier; and the evaluation of prospects at different locations will have to approach more nearly an explicit calculation of the expected costs, revenues, and profits at various possible levels of output at each of a large set of locations. For most types of locational decision units, an exhaustive point-by-point approach in which theory and analysis abdicate in favor of pure empiricism would be so expensive as to outweigh any gain from finally determining the ideal spot. So there will always be a vigorous demand for usable shortcuts, ways of narrowing down the range of location choice, and better analytical techniques. The challenge to regional economists is to provide techniques better than hunch or inertia and cheaper than exhaustive canvassing of locations. 2.9 SUMMARY This chapter deals with location at the level of the "location unit" as exemplified by a household, business establishment, school, or police station. Location in terms of larger aggregates such as multiestablishment firms or public agencies, industries, cities, and regions is taken up in later chapters. A single decision unit (for instance, a firm) can embrace one or more location units. Prospective income is a major determinant of location preference, but even in the ease of business corporations in which the profit motive is paramount there are other significant considerations, including security, amenity, and the manifold political and social aims of public and institutional policy. Uncertainties, risks, and the costs of decision making and moving contribute to locational inertia and often to concentration. The basis for locational preferences can be expressed generally in terms of a limited set of location factors involving both supply of locally produced and transferable inputs, and demand for transferable outputs satisfied both locally and at a distance; the inputs and outputs include intangibles. Various techniques exist for assessing the relative strength of location factors affecting a specific decision or type of location unit. Location factors themselves have characteristic spatial patterns of advantage. Some factors, such as rent, may be relevant chiefly in comparing locations on a microspatial (small area) basis; other factors may emerge as important for macrospatial comparisons, involving locations far apart. Some location factors are primarily related to concentration: They may be most favorable in, say, large cities or dusters of activity or, alternatively, in small towns or rural locations. Other location factors involve transfer of input or output, so that locational advantage varies systematically according to distance. Other location
factors, such as climate, depend wholly or mainly on natural geographic differentials, and still others, such as labor supply or taxes, have patterns whose origins and features may be quite complex and resistant to generalization Only the transfer-determined(distance-related) location factors are explored in detail in this chapter. When a location unit's locational preference depends primarily on transfer costs of input and/or output, the unit is called transfer-oriented; and, more specifically, it may also be input-oriented or output-oriented according to whether access to input sources or to markets for its output is the more important influence. If transfer costs per ton-mile are assumed to be uniform for all goods regardless of direction or distance(the assumption of a uniform transfer surface), and if the unit has only one input source and one market for its output orientation and location choice will depend simply on whether the transferred input used in a given period weighs more or less than the corresponding transferred output If there is a total of three or more input sources plus markets, the orientation is definite only if one of the weights is predominant(exceeding all the others combined). Otherwise, the orientation will depend partly on the spatial configuration of the input source and markets Differences among ton-mile transfer rates for different goods can be allowed for in the determination of optimum location replacing the relative physical weights of inputs and outputs with"ideal weights. Output orientation is encouraged not only by weight gain in the production process but also by gains in bulk, perishability, fragility, hazard, or value. Input orientation is encouraged by losses in these attributes While most of the analysis in this chapter has assumed that the production recipe requires that inputs are used in fixe proportion, we have recognized the implications that follow when flexibility of input use is allowed. In this instance, locators will adapt their input mix to the relative prices of the substitutable inputs at various locations. This increases the number of locations worth considering and means that the production-technique decision and the location decision are interdependent Further, as the scale of operation changes, the nature of the production process helps to determine whether larger-scale operations encourage orientation toward sources of transferable inputs or toward the market In real life, access advantages of location must often be assessed in terms of access to a whole set of markets and/or a whole set of input sources, and explicit comparative cal culations of probable sales, receipts, and costs at each location may be prohibitively difficult. A number of practical shortcut procedures have been developed for evaluating access factors of location under such conditions; they include a gravity formula, in which the attraction of a market or an input source is systematical ly discounted according to its distance from the location whose advantages are being assessed The analysis presented in this chapter is based on a model that concentrates attention on transfer factors, neglecting in the process some other potentially important considerations. For example, the effects of processing costs on location decisions are recognized explicitly only to the extent that those costs are affected by substitution possibilities in the production process Further, while the importance of multiple markets has been noted, many other issues concerning demand in space have been set aside for the time being. In the following chapter, we consider in additional detail the effects that transfer cost considerations may have on location choices. In Chapter 4 our attention will turn to issues concerning demand and spatial pricing decisions and then, in Chapter 5 to economies of concentration as they may affect processing costs TECHNICAL TERMS INTRODUCED IN THIS CHAPTER Weight-losing and weight-gaining activities Location decision unit Locational polygon Location factor Varignon frame Local (or nontransferable)inputs and outputs Predominant weight Transferable inputs and outputs Market or supply area Macrogeographic Median location principl Delivered price Access potential Gravity formula Reillys Law of Retail Gravitation Uniform transfer surface SELECTED READINGS Edgar M. Hoover, The Location of Economic Activity(New York: McGraw-Hill, 1948) Gerald J. Karaska and David F. Bramhall(eds ) Locational Analysis for Manufacturing( Cambridge, MA: MIT Press 1969) Steven M. Miller and Oscar W. Jensen, "Location and the Theory of Production: A Review, Summary, and Critique of Recent Contributions, "Regional Science and Urban Economics 8, 2(May 1978), 117-128 Leon N. Moses, "Location and the Theory of Production, " Quarterly Journal of Economics, 72, 2 (May 1958), 259-272 Jean H. Paelinek and Peter Nijkamp, Operational Theory and Method in Regional Economics(Lexington, MA: Lexington Books, D. C. Heath, 1976), Chapters 2-3 Harry w. Richardson, Regional Economics (Urbana: University of Illinois Press, 1978), Chapter 3
15 factors, such as climate, depend wholly or mainly on natural geographic differentials; and still others, such as labor supply or taxes, have patterns whose origins and features may be quite complex and resistant to generalization. Only the transfer-determined (distance-related) location factors are explored in detail in this chapter. When a location unit's locational preference depends primarily on transfer costs of input and/or output, the unit is called transfer-oriented; and, more specifically, it may also be input-oriented or output-oriented according to whether access to input sources or to markets for its output is the more important influence. If transfer costs per ton-mile are assumed to be uniform for all goods regardless of direction or distance (the assumption of a uniform transfer surface), and if the unit has only one input source and one market for its output, orientation and location choice will depend simply on whether the transferred input used in a given period weighs more or less than the corresponding transferred output. If there is a total of three or more input sources plus markets, the orientation is definite only if one of the weights is predominant (exceeding all the others combined). Otherwise, the orientation will depend partly on the spatial configuration of the input source and markets. Differences among ton-mile transfer rates for different goods can be allowed for in the determination of optimum location by replacing the relative physical weights of inputs and outputs with "ideal weights." Output orientation is encouraged not only by weight gain in the production process but also by gains in bulk, perishability, fragility, hazard, or value. Input orientation is encouraged by losses in these attributes. While most of the analysis in this chapter has assumed that the production recipe requires that inputs are used in fixed proportion, we have recognized the implications that follow when flexibility of input use is allowed. In this instance, locators will adapt their input mix to the relative prices of the substitutable inputs at various locations. This increases the number of locations worth considering and means that the production-technique decision and the location decision are interdependent. Further, as the scale of operation changes, the nature of the production process helps to determine whether larger-scale operations encourage orientation toward sources of transferable inputs or toward the market. In real life, access advantages of location must often be assessed in terms of access to a whole set of markets and/or a whole set of input sources, and explicit comparative calculations of probable sales, receipts, and costs at each location may be prohibitively difficult. A number of practical shortcut procedures have been developed for evaluating access factors of location under such conditions; they include a gravity formula, in which the attraction of a market or an input source is systematically discounted according to its distance from the location whose advantages are being assessed. The analysis presented in this chapter is based on a model that concentrates attention on transfer factors, neglecting in the process some other potentially important considerations. For example, the effects of processing costs on location decisions are recognized explicitly only to the extent that those costs are affected by substitution possibilities in the production process. Further, while the importance of multiple markets has been noted, many other issues concerning demand in space have been set aside for the time being. In the following chapter, we consider in additional detail the effects that transfer cost considerations may have on location choices. In Chapter 4 our attention will turn to issues concerning demand and spatial pricing decisions and then, in Chapter 5, to economies of concentration as they may affect processing costs. TECHNICAL TERMS INTRODUCED IN THIS CHAPTER Location unit Weight-losing and weight-gaining activities Location decision unit Locational polygon Location factor Varignon Frame Local (or nontransferable) inputs and outputs Predominant weight Transferable inputs and outputs Market or supply area Macrogeographic Median location principle Microgeographic Distance discount Delivered price Access potential Ubiquity Gravity formula Orientation Reilly's Law of Retail Gravitation Uniform transfer surface SELECTED READINGS Edgar M. Hoover, The Location of Economic Activity (New York: McGraw-Hill, 1948). Gerald J. Karaska and David F. Bramhall (eds.), Locational Analysis for Manufacturing (Cambridge, MA: MIT Press, 1969). Steven M. Miller and Oscar W. Jensen, "Location and the Theory of Production: A Review, Summary, and Critique of Recent Contributions," Regional Science and Urban Economics 8, 2 (May 1978), 117-128. Leon N. Moses, "Location and the Theory of Production," Quarterly Journal of Economics, 72, 2 (May 1958), 259-272. Jean H. Paelinek and Peter Nijkamp, Operational Theory and Method in Regional Economics (Lexington, MA: Lexington Books, D. C. Heath, 1976), Chapters 2-3. Harry W. Richardson, Regional Economics (Urbana: University of Illinois Press, 1978), Chapter 3