Roger W Schmenner, Making Business Location Decisions(Englewood Cliffs, NJ: Prentice-Hall 1982) Michael J. Webber, Impact of Uncertainty on Location( Cambridge, MA: MIT Press, 1972) Alfred Weber, Uber den Standort der Industrien(Tubingen: J. C. B. Mohr, 1909): C. J. Friedrich(tr ) Alfred Weber's Theory of the Location of Industries( Chicago: University of Chicago Press, 1929) ENDNOTES Arecurrent problem in industry is that of determining optimal locations for centers of economic activity. The problems of locating a machine or department in a factory, a warehouse to serve retailers or consumers, a supervisor's desk in an office, or an additional plant in a multiplant firm are conceptually similar. Each facility is a center of activity into which inputs are gathered and from which outputs are sent to subsequent destinations. For each new facility one seeks, at least as a starting point if not the final location, the spot where the sum of the costs of transporting goods between existing source and destination points(such as the sources of raw materials, centers of market demand, other machines and departments, etc )and the new Economic Facilities, " Management Science, 13, 6(February 1967), B-240. This article and the references appended review some techniques for solving locational problems, with special applicability to problems of layout at the intrafirm, intraplant, and even more micro levels 2. Some factors that may influence the decision to expand on site, establish a branch plant, or relocate are discussed by Roger W. Schmenner, Making Business Location Decisions(Englewood Cliffs, N.J. Prentice-Hall, 1982), Chapter 1, and idem Choosing New Industrial Capacity: Onsite Expansion, Branching, and Relocation, " Quarterly Journal of Economics, 95, 1 ( August1980),103-119 3. See Harry W. Richardson, Regional Economics(Urbana: University of Illinois Press, 1978), pp. 65-70, for a discussion of alternatives to profit maximization in location decisions 4. For convenience, we shall be using the very broad term"transfer"to cover both the transportation of goods and the transmission of such intangibles as energy, information, ideas, sound, light or color. Modes of transfer service and some characteristics of the cost and price of such service are discussed in Chapter 3 5. Blast furnaces use coke rather than coal, but as a rule the coke is made in ovens adjacent to the furnaces. Thus for purposes of location analysis, a set of coke ovens and the blast furnaces they serve may be considered as a single unit. See also the note to table 2-1 6. E. M. Hoover and Raymond Vernon, Anatomy of a Metropolis( Cambridge, Mass. Harvard University Press, 1959), pp 55-60 and Appendix F, pp. 277-287. Campbell computed the state and local tax bills for a sample of 25 selected firms placed hypothetically at 64 alternative locations in the New York metropolitan region 7. Location and Space-Economy(Cambridge, Mass. MIT Press, 1956), p. 140 8. Orientation is a word with an interesting origin It seems that until a few centuries ago, maps were customarily presented with east at the top, rather than north as is now the convention. In reading a map, the first thing to do was to get it right side up; in other words, to place east(oriens, or rising sun)at the top. In location theory, then, orientation means specifying in which direction the activity is primarily attracted: to cheap labor supplies, toward markets, toward sources of materials, and so on. Transferred-output (market)orientation and transferred -input(material) orientation are handily lumped together under the heading"transfer orientation 9. It is difficult to conceive of a rational production process involving value loss. But an interesting case of manipulation of output value to save on delivery costs appears at a smelter in Queensl and visited by one of the authors. The smelter, located on top of its mines, produces copper, zinc, lead, and silver, all in semirefined form, for transport to refineries. The silver is not cast into pigs; instead it is mixed with lead in lead-silver pigs so as to make it less worth stealing in transit 10. In fact, a simple analog computer can be built to determine optimum location under the simplified conditions we have assumed. Imagine Figure 2-3 laid out to scale on a table top, with holes bored and small pulleys inserted at the corners of the triangle. Three strings run over the three pulleys and are joined together within the triangle. Underneath the table, each string has attached to it a weight proportional to the ideal weight of the corresponding transferred input or output. The knot joining the three strings will then come to rest at the equilibrium point of the three forces, which is the maximum profit location. This device is known as the Varignon Frame, after its inventor, and is far more frequently described than constructed or actually sed Its main service to location economics, in fact, is pedagogical: It helps in visualizing the economic interplay of location factors through a familiar analog. Alternatively and more precisely(though precision is scarcely relevant for this problem), the solution can be computed mathematically, as explained in H. w. Kuhn and R F Kuenne, "An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economies, "Journal of Regional Science, 4, 2(1962), 21-23 A geometric method of solution for the ease of a triangular figure was presented as early as 1909 by George Pick in the mathematical appendix to Alfred Weber, Uber den Standort der Industrien(Tubingen: J. C B. Mohr, 1909); C J. Friedrich(tr ), Alfred Weber's Theory of the Location of Industries(Chicago: University of Chicago Press, 1929).A Varignon Frame is pictured in Figure 45 on p. 229 of the English edition Il. In terms of the three-way tug-of-war analogy, a weaker puller can defeat two stronger ones if the latter two are pulling almost directly against one another, as SI and M are in this figure. For the specific numerical case at hand, it can be cal culated that a force of 2 can prevail against opposing forces of 3 and 4 if the latter two are pulling in directions more than 151.7 legree divergent. (The reader who has been exposed to elementary physics will recognize here a basic laboratory exercise involving the parallelogram of forces. )The geometric analysis and proofs for the case of the locational triangle will be found in e sources mentioned in footnote 10 12. There has been substantial interest in the theoretical implications of input substitution for the location decision. A 16
16 Roger W. Schmenner, Making Business Location Decisions (Englewood Cliffs, NJ: Prentice-Hall 1982). Michael J. Webber, Impact of Uncertainty on Location (Cambridge, MA: MIT Press, 1972). Alfred Weber, Über den Standort der Industrien (Tübingen: J. C. B. Mohr, 1909); C. J. Friedrich (tr.), Alfred Weber's Theory of the Location of Industries (Chicago: University of Chicago Press, 1929). ENDNOTES 1. "A recurrent problem in industry is that of determining optimal locations for centers of economic activity. The problems of locating a machine or department in a factory, a warehouse to serve retailers or consumers, a supervisor's desk in an office, or an additional plant in a multiplant firm are conceptually similar. Each facility is a center of activity into which inputs are gathered and from which outputs are sent to subsequent destinations. For each new facility one seeks, at least as a starting point if not the final location, the spot where the sum of the costs of transporting goods between existing source and destination points (such as the sources of raw materials, centers of market demand, other machines and departments, etc.) and the new location is a minimum." Roger C. Vergin and Jack D. Rogers, "An Algorithm and Computational Procedure for Locating Economic Facilities," Management Science, 13, 6 (February 1967), B-240. This article and the references appended review some techniques for solving locational problems, with special applicability to problems of layout at the intrafirm, intraplant, and even more micro levels. 2. Some factors that may influence the decision to expand on site, establish a branch plant, or relocate are discussed by Roger W. Schmenner, Making Business Location Decisions (Englewood Cliffs, N.J.: Prentice-Hall, 1982), Chapter 1, and idem, "Choosing New Industrial Capacity: Onsite Expansion, Branching, and Relocation," Quarterly Journal of Economics, 95, 1 (August 1980), 103-119. 3. See Harry W. Richardson, Regional Economics (Urbana: University of Illinois Press, 1978), pp. 65-70, for a discussion of alternatives to profit maximization in location decisions. 4. For convenience, we shall be using the very broad term "transfer" to cover both the transportation of goods and the transmission of such intangibles as energy, information, ideas, sound, light, or color. Modes of transfer service and some characteristics of the cost and price of such service are discussed in Chapter 3. 5. Blast furnaces use coke rather than coal, but as a rule the coke is made in ovens adjacent to the furnaces. Thus for purposes of location analysis, a set of coke ovens and the blast furnaces they serve may be considered as a single unit. See also the note to Table 2-1. 6. E. M. Hoover and Raymond Vernon, Anatomy of a Metropolis (Cambridge, Mass.: Harvard University Press, 1959), pp. 55-60 and Appendix F, pp. 277-287. Campbell computed the state and local tax bills for a sample of 25 selected firms placed hypothetically at 64 alternative locations in the New York metropolitan region. 7. Location and Space-Economy (Cambridge, Mass.: MIT Press, 1956), p. 140. 8. Orientation is a word with an interesting origin. It seems that until a few centuries ago, maps were customarily presented with east at the top, rather than north as is now the convention. In reading a map, the first thing to do was to get it right side up; in other words, to place east (oriens, or rising sun) at the top. In location theory, then, orientation means specifying in which direction the activity is primarily attracted: to cheap labor supplies, toward markets, toward sources of materials, and so on. Transferred-output (market) orientation and transferred-input (material) orientation are handily lumped together under the heading "transfer orientation." 9. It is difficult to conceive of a rational production process involving value loss. But an interesting case of manipulation of output value to save on delivery costs appears at a smelter in Queensland visited by one of the authors. The smelter, located on top of its mines, produces copper, zinc, lead, and silver, all in semirefined form, for transport to refineries. The silver is not cast into pigs; instead it is mixed with lead in lead-silver pigs so as to make it less worth stealing in transit. 10. In fact, a simple analog computer can be built to determine optimum location under the simplified conditions we have assumed. Imagine Figure 2-3 laid out to scale on a table top, with holes bored and small pulleys inserted at the corners of the triangle. Three strings run over the three pulleys and are joined together within the triangle. Underneath the table, each string has attached to it a weight proportional to the ideal weight of the corresponding transferred input or output. The knot joining the three strings will then come to rest at the equilibrium point of the three forces, which is the maximum profit location. This device is known as the Varignon Frame, after its inventor, and is far more frequently described than constructed or actually used. Its main service to location economics, in fact, is pedagogical: It helps in visualizing the economic interplay of location factors through a familiar analog. Alternatively and more precisely (though precision is scarcely relevant for this problem), the solution can be computed mathematically, as explained in H. W. Kuhn and R. F. Kuenne, "An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economies," Journal of Regional Science, 4, 2 (1962), 21-23. A geometric method of solution for the ease of a triangular figure was presented as early as 1909 by George Pick in the mathematical appendix to Alfred Weber, Über den Standort der Industrien (Tübingen: J. C. B. Mohr, 1909); C. J. Friedrich (tr.), Alfred Weber's Theory of the Location of Industries (Chicago: University of Chicago Press, 1929). A Varignon Frame is pictured in Figure 45 on p. 229 of the English edition. 11. In terms of the three-way tug-of-war analogy, a weaker puller can defeat two stronger ones if the latter two are pulling almost directly against one another, as S1 and M are in this figure. For the specific numerical case at hand, it can be calculated that a force of 2 can prevail against opposing forces of 3 and 4 if the latter two are pulling in directions more than 151.7 degrees divergent. (The reader who has been exposed to elementary physics will recognize here a basic laboratory exercise involving the parallelogram of forces.) The geometric analysis and proofs for the case of the locational triangle will be found in the sources mentioned in footnote 10. 12. There has been substantial interest in the theoretical implications of input substitution for the location decision. A
seminal work in this area is that of Leon N. Moses, "Location and the Theory of Production,"Quarterly Journal of Economics 72, 2(May 1958), 259-272 More recently, important contributions have been made by Amir Khalili, Vijay K. Mathur, and Diran Bodenhorn, "Location and the Theory of Production: A Generalization, "Journal of Economic Theory 9, 4(December 1974), 467-475; and Stephen 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. The last of these also includes excellent references to other work in this area 13. Notice that the iso-outlay line is linear. It has the form xI=a+ Bx2, where the slope(B)is-(p2/pl), and the vertical intercept(a )is (TO/pl) 14. It is possible that the equal product curve denoted by Q0 in Figure 2-6 could be tangent to the iso-outlay line on both line segments, AC and CB. In this instance, either location would minimize costs 15. If all points along the arc are considered, the effective iso-outlay line(ACB in Figure 2-6) becomes a smooth curve that is convex to the origin. See Moses, "Location and the Theory of Production 16. The modern literature on this subject ignores possible interactions between transferable and local inputs as the scale of roduction increases(see the references in footnote 12). Interactions of this sort are common and have been of some historical importance in location decisions. Thus while a number of conclusions can be drawn concerning locational orientation and the nature of the production process when the separability of transferable and local inputs is assumed, the usefulness of these results is severely limited 17. The concepts of demand in space and spatial pricing are discussed in Chapter 4. 18. For a uniform transfer surface, this can be done by preparing a map showing the sales volume of each market noted at its proper location. Align a ruler north and south and push it across the map from one edge, keeping track of the total sales volume of markets passed as the ruler advances. Stopping when that total equals half of the aggregate sales volume for all markets, draw a vertical line. Repeating the process with the ruler held horizontally and moved gradually from top or bottom, get a horizontal line in similar fashion. The intersection of the two lines is the required minimum transport cost point 19. For a comprehensive survey of the literature on the theory and application of gravity models, see Gunnar Olsson Distance and Human Interaction: A Review and Bibliography(Philadelphia: Regional Science Research Institute, 1965),as well as Chang-I Hua and Frank Porell, "A Review of the Development of the Gravity Model, "International Regional Science Review 4, 2( Winter 1979),97-126 3 Transfer Costs 3.1 INTRODUCTION The discussion of individual locations in the previous chapter placed many restrictions on the nature of transport costs for the sake of exposing some fundamental characteristics of location decisions. While we recognized that in the real world different kinds of inputs and outputs are transferred at different costs and that weight is often an inappropriate measure of input and output quantity, we assumed that transfer costs along a route were proportional to distance. Further, we ignored the fact that transfer generally has to follow an established route between established terminal service points rather than going as the crow flies. We also failed to distinguish between money costs, time costs, and still other kinds of costs entailed in transfer and ignored the great differences in cost and service capabilities of different techniques or modes of transfer, as well as the distinction between costs to the transfer firm or agency and costs to the user of transfer service In this chapter we hasten to remedy these omissions in order to get a more realistic understanding of how transfer costs affect the location of activities 3.2 SOME ECONOMIC CHARACTERISTICS OF TRANSFER OPERATIONS It is much easier to develop an understanding of the complex variations of transfer services, costs, and rates if we first te some basic economic characteristics of transfer activities in general TABLE 3-1: Illustrations of Combinations of Transfer Modes and Objectives of the costs are fixed-that is, they reflect way and terminals. Partly for this reason, p可yf Prinmary Purpose of the Transfer osts per unit of service tend to be lower ovement of People tHings [ Information likewise, costs are generally lower when aircraft). There are additional savings in Personal Messengers. travel per se aRnIeS manual) work one specific location unit to another)is between locations, and others principally transit or other ting, and billing ices generally serve many pairs of points Transport of monopolistic control rather than in perfect p disproportionate shares of the transfer other graphic-to"charge what the traffic will bea special purpos disappear completely. Somewhere in the Electrie power cable or wire by wire or cable special advantages for a certain range of Radio or other Radie or according to purpose. The purposes of The"hierarchical"ordering in Table 3-1 (as shown by the fact that the cells below the diagonal are blank)is interesting. It 17
17 seminal work in this area is that of Leon N. Moses, "Location and the Theory of Production," Quarterly Journal of Economics, 72, 2 (May 1958), 259-272. More recently, important contributions have been made by Amir Khalili, Vijay K. Mathur, and Diran Bodenhorn, "Location and the Theory of Production: A Generalization," Journal of Economic Theory 9, 4 (December 1974), 467-475; and Stephen 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. The last of these also includes excellent references to other work in this area. 13. Notice that the iso-outlay line is linear. It has the form x1=a + ßx2, where the slope (ß) is - (p'2/p'1), and the vertical intercept (a ) is (TO/p'1). 14. It is possible that the equal product curve denoted by Q0 in Figure 2-6 could be tangent to the iso-outlay line on both line segments, AC and CB'. In this instance, either location would minimize costs. 15. If all points along the arc are considered, the effective iso-outlay line (ACB' in Figure 2-6) becomes a smooth curve that is convex to the origin. See Moses, "Location and the Theory of Production." 16. The modern literature on this subject ignores possible interactions between transferable and local inputs as the scale of production increases (see the references in footnote 12). Interactions of this sort are common and have been of some historical importance in location decisions. Thus while a number of conclusions can be drawn concerning locational orientation and the nature of the production process when the separability of transferable and local inputs is assumed, the usefulness of these results is severely limited. 17. The concepts of demand in space and spatial pricing are discussed in Chapter 4. 18. For a uniform transfer surface, this can be done by preparing a map showing the sales volume of each market noted at its proper location. Align a ruler north and south and push it across the map from one edge, keeping track of the total sales volume of markets passed as the ruler advances. Stopping when that total equals half of the aggregate sales volume for all markets, draw a vertical line. Repeating the process with the ruler held horizontally and moved gradually from top or bottom, get a horizontal line in similar fashion. The intersection of the two lines is the required minimum transport cost point. 19. For a comprehensive survey of the literature on the theory and application of gravity models, see Gunnar Olsson, Distance and Human Interaction: A Review and Bibliography (Philadelphia: Regional Science Research Institute, 1965), as well as Chang-I Hua and Frank Porell, "A Review of the Development of the Gravity Model," International Regional Science Review 4, 2 (Winter 1979), 97-126. 3 Transfer Costs 3.1 INTRODUCTION The discussion of individual locations in the previous chapter placed many restrictions on the nature of transport costs for the sake of exposing some fundamental characteristics of location decisions. While we recognized that in the real world different kinds of inputs and outputs are transferred at different costs and that weight is often an inappropriate measure of input and output quantity, we assumed that transfer costs along a route were proportional to distance. Further, we ignored the fact that transfer generally has to follow an established route between established terminal service points rather than going as the crow flies. We also failed to distinguish between money costs, time costs, and still other kinds of costs entailed in transfer and ignored the great differences in cost and service capabilities of different techniques or modes of transfer, as well as the distinction between costs to the transfer firm or agency and costs to the user of transfer service. In this chapter we hasten to remedy these omissions in order to get a more realistic understanding of how transfer costs affect the location of activities. 3.2 SOME ECONOMIC CHARACTERISTICS OF TRANSFER OPERATIONS It is much easier to develop an understanding of the complex variations of transfer services, costs, and rates if we first note some basic economic characteristics of transfer activities in general. In transfer operations (except for a few primitive types) substantial components of the costs are fixed—that is, they reflect overall and longrun commitments such as the provision and maintenance of right of way and terminals. Partly for this reason, transfer operations are characteristically subject to important economies of scale. Costs per unit of service tend to be lower (and service more convenient and faster) on routes with larger volumes of traffic. Likewise, costs are generally lower when larger quantities are moved in single-movement units (for example, ships, trains, or aircraft). There are additional savings in transfer cost when the single consignment (that is, what is moved at one time from one specific location unit to another) is larger. Some of these scale economies apply principally to costs of actual movement between locations, and others principally to costs of establishing and operating terminals and such operations as selling, accounting, and billing. Because of these characteristics, firms or public agencies providing transfer services generally serve many pairs of points and many different classes of customers, and operate with a substantial element of monopolistic control rather than in perfect competition. The rates for the various services rendered can be set so as to recoup disproportionate shares of the transfer operation’s fixed costs from rates on those services for which demand is least elastic—to "charge what the traffic will bear." Finally, human ingenuity has continually devised new technologies or modes of transfer to serve various special purposes. Although each new mode may partly supplant an older one, it is rare for any mode to disappear completely. Somewhere in the world there is still in use nearly every transfer mode ever devised. Each mode has special advantages for a certain range of services, and is thus partly competitive and partly complementary to other modes. As Table 3-1 shows, transfer operations can be classified according to means or according to purpose. The purposes of transfer are to move people, goods, energy, or information from one place to another—information being broadly defined to include queries, aesthetic and emotional effects, and in fact all messages via any of the senses. The "hierarchical" ordering in Table 3-1 (as shown by the fact that the cells below the diagonal are blank) is interesting. It
reflects the fact that the most primitive and versatile means of transfer is movement of people, which can accomplish any of the four purposes. Specialized modes of transfer for shipping goods other than on people's backs can at the same time serve to transfer energy and information. Still more specialized means of energy transmission can also transmit information; and final ly we have specialized modes for information transmission(communication )that cannot move people, goods, or energy 3. 3 CHARACTERISTIC FEATURES OF TRANSFER COSTS AND RATES 3.3. 1 Route Systems and Service Points Perhaps the most notable difference between reality and the uniform transfer surface assumed in the previous chapter is the channelizing of transfer services along definite routes, which only rarely represent the straight path of shortest distance between an origin and a destination point There are two distinct reasons for this channelization. One is the economies of traffic volume already referred to as a nearly universal characteristic of transfer. Even primitive societies where all transfer is pedestrian generally develop networks of established trails, which make it easier to move and harder to get lost. Each mode of transfer has its own set of route-volume economies. If these economies are substantial up to a large volume, the route network for that mode will tend to be coarse; if heavier traffic means only small savings, there can be a finer network of routes providing less circuitous connections between The second reason for route channelization is that some areas are naturally harder to traverse than others. Thus all modes of land transport have reason to favor level, well-drained land and temperate climate and to avoid unnecessary stream crossings in laying out routes. All routes crossing major mountain ranges funnel into a few selected passes or tunnels. Simil arly, ocean shipping routes have to detour around land masses and also have to pay some attention to ocean currents, winds, shoals iceberg zones, and of course, the availability of harbors. As a result, there is a more or less recognized network of regular shipping lanes. " Even air transport is restricted in choice of routes between any two terminals by the system of navigational aids and safety regulations comTE Any kind of communications system requiring either fixed-line facilities(such as cables)or relay stations is likewise Scale economies apply not only to route facilities such as trails, track, roads, pipelines, cable, and navigational aids, but also to"service points"where transfer by the mode in question can originate and terminate. Thus there are certain minimum costs of establishing a railroad station or even a siding; the same applies to piggyback terminals, ports for ships and aircraft, transformer stations on long-distance electric transmission lines, and telephone exchanges and switchboards. There is an economic constraint on the spacing of transit stops along a route, since more stops slow the service. People making shopping ips generally prefer to do all their errands with a minimum number of separate stops-except for those who view shopping as a recreation Consequently, the pattern of transfer services offered by any particular mode is al ways spotty, linking up a limited number of pairs of points by routes usually longer than the straight-line distance; and a transfer of a specific shipment, person, or item of information from initial origin to final destination frequently entails the use of more than one link or mode In addition to restricting the number of routes and service points, transfer scale economies in many instances have the om larger terminals. This works in several h volume. Thus a larger-diameter pipeline -lane highway can carry more than twice as e median divider is narrow Terminal plus line-haul costs. 15. 000-lb shipment efficiently if they handle large volumes of k cargoes such as grain, coal, and ores, and the operator of individual transfer services, uality of service. Your letters will probably tions are made more frequently. If you are arge transport terminal, not only because the oe points and a variety of special types of Terminal plus line-haul costs, 25,000-Ib n prior to actual movement, and also some dinarily does not depend on the distance to ↑ Terminal cost. Terminal cost 25, 000-lb shipment 15.000-lb, shipment the total costs of a shipment will generally rtional to distance. and the average transfer ength of haul in miles amental one and appears in every kind of rious missions, there is almost al ways some oot, we may first have to make sure that we FIGURE 3-1: Terminal and Line-Haul Costs of Motor Carriers vision, put the dog out and lock the door.If by Length of Haul and Size of Shipment, Central Region, 1979 o appear In Figure 3-1 the costs of movement per se(called the line-haul costs) appear to be nearly proportional to distance. That is, the slanting lines in the figure are not very curved for hauls of more than a hundred miles or so. This implies that the marginal
18 reflects the fact that the most primitive and versatile means of transfer is movement of people, which can accomplish any of the four purposes. Specialized modes of transfer for shipping goods other than on people’s backs can at the same time serve to transfer energy and information. Still more specialized means of energy transmission can also transmit information; and finally we have specialized modes for information transmission (communication) that cannot move people, goods, or energy. 3.3 CHARACTERISTIC FEATURES OF TRANSFER COSTS AND RATES 3.3.1 Route Systems and Service Points Perhaps the most notable difference between reality and the uniform transfer surface assumed in the previous chapter is the channelizing of transfer services along definite routes, which only rarely represent the straight path of shortest distance between an origin and a destination point. There are two distinct reasons for this channelization. One is the economies of traffic volume already referred to as a nearly universal characteristic of transfer. Even primitive societies where all transfer is pedestrian generally develop networks of established trails, which make it easier to move and harder to get lost. Each mode of transfer has its own set of route-volume economies. If these economies are substantial up to a large volume, the route network for that mode will tend to be coarse; if heavier traffic means only small savings, there can be a finer network of routes providing less circuitous connections between points. The second reason for route channelization is that some areas are naturally harder to traverse than others. Thus all modes of land transport have reason to favor level, well-drained land and temperate climate and to avoid unnecessary stream crossings in laying out routes. All routes crossing major mountain ranges funnel into a few selected passes or tunnels. Similarly, ocean shipping routes have to detour around land masses and also have to pay some attention to ocean currents, winds, shoals, iceberg zones, and of course, the availability of harbors. As a result, there is a more or less recognized network of regular "shipping lanes." Even air transport is restricted in choice of routes between any two terminals by the system of navigational aids and safety regulations. Any kind of communications system requiring either fixed-line facilities (such as cables) or relay stations is likewise constrained to a limited set of routes. Transfer is really "as the crow flies" only within the range of direct wave or beam transmission. Scale economies apply not only to route facilities such as trails, track, roads, pipelines, cable, and navigational aids, but also to "service points" where transfer by the mode in question can originate and terminate. Thus there are certain minimum costs of establishing a railroad station or even a siding; the same applies to piggyback terminals, ports for ships and aircr aft, transformer stations on long-distance electric transmission lines, and telephone exchanges and switchboards. There is an economic constraint on the spacing of transit stops along a route, since more stops slow the service. People making shopping trips generally prefer to do all their errands with a minimum number of separate stops—except for those who view shopping as a recreation. Consequently, the pattern of transfer services offered by any particular mode is always spotty, linking up a limited number of pairs of points by routes usually longer than the straight-line distance; and a transfer of a specific shipment, person, or item of information from initial origin to final destination frequently entails the use of more than one link or mode. In addition to restricting the number of routes and service points, transfer scale economies in many instances have the effect of making costs and rates lower on more heavily used routes and to and from larger terminals. This works in several ways. In some cases, it is primarily a question of direct cost reduction associated with volume. Thus a larger-diameter pipeline requires less material and less pumping energy per unit volume carried, and a four-lane highway can carry more than twice as much traffic as a two-lane highway, with less than twice as wide a right of way if the median divider is narrow. Similarly, terminals and other transfer service points can often operate more efficiently if they handle large volumes of traffic. Examples are the huge specialized facilities for loading and unloading bulk cargoes such as grain, coal, and ores, and the more specialized equipment found at large communications terminals. But apart from and in addition to such volume-of-traffic savings in cost to the operator of individual transfer services, there are likely to be important advantages for the users of the services in terms of quality of service. Your letters will probably be delivered sooner if you put them in a heavily used mailbox from which collections are made more frequently. If you are shipping goods to a variety of destinations, it may pay to choose a location near a large transport terminal, not only because the departures are more frequent but also because there are direct connections to more points and a variety of special types of service. 3.3.2 Long-Haul Economies Virtually every kind of transfer entails some operation at the point of origin prior to actual movement, and also some further operation at the destination point. The cost of these "terminal" processes ordinarily does not depend on the distance to be traveled, whereas the costs of actual movement ordinarily do. Because of these terminal costs, the relationship between route distance and the total costs of a shipment will generally behave as shown in Figure 3-1. Transfer costs are characteristically less than proportional to distance, and the average transfer cost per mile decreases as the length of haul increases. This principle is a fundamental one and appears in every kind of transfer mode, even the simplest. When we leave our homes or work places on various missions, there is almost always some act of preparation that imposes a terminal cost in terms of time. Even if we go on foot, we may first have to make sure that we are acceptably clad against the strictures of convention or weather, turn off the television, put the dog out, and lock the door. If we drive, the car has to be activated. If we use public transit, we have to wait for it to appear. In Figure 3-1 the costs of movement per se (called the line-haul costs) appear to be nearly proportional to distance. That is, the slanting lines in the figure are not very curved for hauls of more than a hundred miles or so. This implies that the marginal
cost of transfer(the cost for each added unit of distance)is constant. We can think of a few circumstances in which movement costs per se might rise faster than in direct proportion to distance, such as the case of a perishable commodity where it becomes creasingly difficult and expensive to prevent deterioration as time passes, or the case of journeys where after a certain point rther travel becomes disproportionately more irksome. But these are rare exceptions. In general, we can expect movement costs to be either less than proportional or roughly proportional to distance When might they rise at a slower than linear rate? This can be expected in the case of transport of goods or people, since it takes some time to accelerate to cruising speed and to decelerate to a stop. An example is the case of transit vehicles with their frequent stops. A one-mile journey between subway stations takes considerably less time and energy than two half-mile journeys. Somewhat more complicated instances are those of intercity trucks, buses, or ships, which have to thread their way slowly through congested areas in the first and last parts of their journeys, and that of the airplane, which has to climb to ruising altitude and down again as well as to follow the prescribed takeoff and landing patterns. In all these cases, the overall an important determinant of the costs of rendering the service, since such items as the wages of vehicle operators, interest ut peed of a trip increases with distance even if cruising speed is constant. Speed is not merely an aspect of quality of service he capital invested in vehicles, insurance, and part of the vehicle depreciation are proportionate to time rather than distance For long hauls, such line-haul economies are of course relatively less significant. The difference in overall speed between an 800-mile and a 900-mile rail or truck haul is probably not great. 1 And in the case of telecommunication or electric powe transmission, which do not entail moving any tangible objects over the route and in which transfer time is negligible, it is not obvious that average line costs per mile should systematically fall with greater distances. Line losses on transmission lines are proportional to distance, and booster or relay stations on cable or microwave communication routes are needed at more or less uniform distance intervals. For radio wave communication, however, the required transmitter power rises as the square of the 3.3. 3 Transfer Costs and Rates As was noted earlier, many kinds of transfer service are performed by parties other than the user, and the usual presence of substantial fixed costs and limited competition gives a transfer agency a good deal of leeway in shaping tariffs so as to crease profits. Some classes of traffic may accordingly be charged barely enough to cover the out-of-pocket costs they occasion, while others will be charged far more than their pro rata share of the transfer agency's fixed costs. The general principle governing profit-maximizing price discrimination is to discriminate in favor of customers with more elastic demands Moreover, the rates charged by transfer agencies are themselves only part of the total time and money costs entailed in bridging distance At longer distances sales promotion and customer servicing are more costly or less effective, and larger at the advantages of location at or near larger Costs(mode A) oncentrations of terminal acti vity, there is more ifferent modes. The bargaining power of transfer agency is more elastic--consequently, they may ood service. over and above the cost and service 5 Costs(mode c) and long-haul rates, matters cannot be quite so Costs(mode B) tion to distance would then have a flatter slope r charge is a larger part of the total price of the sequently, the elasticity of demand for transfe will discriminate in favor of such hauls. (See Rates poly over a very wide range of lengths of haul. ders of the same mode of service. even more to istics and is more efficient than other modes for we would not have the variety of modes that Length of haul erways and pipelines are generally the cheapest ial advantages of flexibility and convenience in -ing a wide range of lengths of haul for some FIGURE 3-2: Transfer Cost Gradients for Three the lowest-cost mode for long hauls. the cost Competing Modes and Resulting Gradient of Transfer Rates used to represent truck, rail, and water transport In a situation similar to that in Figure 3-2, the operators of each mode will find that the demand for their service is particularly elastic in those distance ranges where some alternative mode can effectively compete for the traffic; consequently here is likely to be competitive rate cutting on those classes of traffic. The final rate pattern might look something like the black line in Figure 3-2 For each distance range, the lowest-cost mode determines the general level of rates, and the progression of rates is rounded off in the most competitive distance ranges where two or more different modes share the traffic We would expect this outcome regardless of whether the rates in question are for the transport of goods, energy, or people
19 cost of transfer (the cost for each added unit of distance) is constant. We can think of a few circumstances in which movement costs per se might rise faster than in direct proportion to distance, such as the case of a perishable commodity where it becomes increasingly difficult and expensive to prevent deterioration as time passes, or the case of journeys where after a certain point further travel becomes disproportionately more irksome. But these are rare exceptions. In general, we can expect movement costs to be either less than proportional or roughly proportional to distance. When might they rise at a slower than linear rate? This can be expected in the case of transport of goods or people, since it takes some time to accelerate to cruising speed and to decelerate to a stop. An example is the case of transit vehicles with their frequent stops. A one-mile journey between subway stations takes considerably less time and energy than two half-mile journeys. Somewhat more complicated instances are those of intercity trucks, buses, or ships, which have to thread their way slowly through congested areas in the first and last parts of their journeys, and that of the airplane, which has to climb to cruising altitude and down again as well as to follow the prescribed takeoff and landing patterns. In all these cases, the overall speed of a trip increases with distance even if cruising speed is constant. Speed is not merely an aspect of quality of service but an important determinant of the costs of rendering the service, since such items as the wages of vehicle operators, interest on the capital invested in vehicles, insurance, and part of the vehicle depreciation are proportionate to time rather than distance. For long hauls, such line-haul economies are of course relatively less significant. The difference in overall speed between an 800-mile and a 900-mile rail or truck haul is probably not great.1 And in the case of telecommunication or electric power transmission, which do not entail moving any tangible objects over the route and in which transfer time is negligible, it is not obvious that average line costs per mile should systematically fall with greater distances. Line losses on transmission lines are proportional to distance, and booster or relay stations on cable or microwave communication routes are needed at more or less uniform distance intervals. For radio wave communication, however, the required transmitter power rises as the square of the range. 3.3.3 Transfer Costs and Rates As was noted earlier, many kinds of transfer service are performed by parties other than the user, and the usual presence of substantial fixed costs and limited competition gives a transfer agency a good deal of leeway in shaping tariffs so as to increase profits. Some classes of traffic may accordingly be charged barely enough to cover the out-of-pocket costs they occasion, while others will be charged far more than their pro rata share of the transfer agency’s fixed costs. The general principle governing profit-maximizing price discrimination is to discriminate in favor of customers with more elastic demands and against those with less elastic demands. Moreover, the rates charged by transfer agencies are themselves only part of the total time and money costs entailed in bridging distance. At longer distances, sales promotion and customer servicing are more costly or less effective, and larger inventories need to be held against fluctuations in demand or supply. Traffic Volume. Taking these considerations into account, we can see that the advantages of location at or near larger transfer terminals can be even greater than was suggested earlier. At such concentrations of terminal activity, there is more likelihood of sharp competition among rival transfer agencies of the same or different modes. The bargaining power of transfer users is greater and their demand for the services of any one particular transfer agency is more elastic—consequently, they may get particularly favorable treatment in the establishment of rates or especially good service, over and above the cost and service advantages inherent in the scale economies of the terminal operations themselves. Relation of Rates to Length of Haul. In the relation between short-haul and long-haul rates, matters cannot be quite so simply stated. First, a transfer agency with a monopoly would generally be impelled to set rates discriminating against short-haul traffic. With reference to Figure 3-1, the line showing rates in relation to distance would then have a flatter slope than the line showing the relation of costs to distance. The rationale for such discrimination is that for longer hauls the transfer charge is a larger part of the total price of the goods at their destination than it is for a shorter haul of the same goods. Consequently, the elasticity of demand for transf er service is likely to be greater for longer hauls, and the rational monopolist will discriminate in favor of such hauls. (See Appendix 3-1 for a simple mathematical statement of this point). In practice, however, a single transfer agency is unlikely to hold a monopoly over a very wide range of lengths of haul. The greater the distance, the more likely it is that there will be alternative providers of the same mode of service. Even more to the point is the probability of effective intermodal competition. Each technique or mode of transfer has its own cost and service characteristics and is more efficient than other modes for some classes of service and less efficient for other classes (were this not so, we would not have the variety of modes that exists). Thus jet aircraft excel in providing fast long-distance transport; waterways and pipelines are generally the cheapest ways of moving bulk materials in large quantities; the motor vehicle has special advantages of flexibility and convenience in local and short-distance movement; and so on. Clearly, if we are considering a wide range of lengths of haul for some commodity, the lowest-cost mode for short hauls need not be the same as the lowest-cost mode for long hauls. The cost gradients might be expected to intersect as in Figure 3-2, which has often been used to represent truck, rail, and water transport costs but would also be applicable to a variety of other intermodal comparisons. In a situation similar to that in Figure 3-2, the operators of each mode will find that the demand for their service is particularly elastic in those distance ranges where some alternative mode can effectively compete for the traffic; consequently, there is likely to be competitive rate cutting on those classes of traffic. The final rate pattern might look something like the black line in Figure 3-2. For each distance range, the lowest-cost mode determines the general level of rates, and the progression of rates is rounded off in the most competitive distance ranges where two or more different modes share the traffic. We would expect this outcome regardless of whether the rates in question are for the transport of goods, energy, or people
cation, since the essence of the situation is that different modes have comparative advantages for different is to make the gradient of transfer rates with respect to distance much own earlier in Figure 3-1. In other words, the tendency to a falling ated. We shall see later the locational implications of comparative rates differ from comparative transter on among two or more a cost advantage as to where there is rules were the legacy among ow see how such Some uch differences reflected in €XtrabulkaddS€ to transport see syster governing or dangerous commodity expensive. service at sl ed to be charged more for a lo game, or for crossing the None gency. since in e But olicy rather than costs. In par relative to costs for thin The ra that a seller's profits are vith relatively elastic den Wher ny given distance, transport cos such as coal o gravel is ship freight rate to the ill charge a higher margin ov est of the carrier but cation and use ent in transfer y reflect the mentioned. This per pound of a n according to value formation, a "higher-value consig trattic will bear on a to those judg of different speeds or other qualities elasticities of demand as well as the relative costs. Lower lor such a way as to retlect the estimated relative lephone rates on nights and weekends are an example Differentiation of Rates According to Direction Most modes of transportation use vehicles that must be returned to the
20 or for communication, since the essence of the situation is that different modes have comparative advantages for different distances. The effect, as graphically shown in Figure 3-2, is to make the gradient of transfer rates with respect to distance much more curved than the single-mode transfer cost gradients shown earlier in Figure 3-1. In other words, the tendency to a falling marginal cost of transfer (to the user) with increased distance is accentuated. We shall see later the locational implications of this and the other characteristics of transfer cost and rate gradients being noted here. Competitive and Noncompetitive Routes. Still another way in which comparative rates differ from comparative transfer costs is with respect to different routes. Between some pairs of points there is effective competition among two or more alternative transfer agencies or modes, while between other pairs of points one agency or mode has such a cost advantage as to constitute, for practical purposes, a monopoly. The margin between rates and out-of-pocket costs will be small where there is effective competition and large where there is more monopoly power. The effects of this kind of discrimination on transfer rate structures are discussed in considerable detail in every textbook on the economics of transportation, usually in reference to the structure of railroad and truck freight rates as affected by competition among the rail, highway, and waterway modes and among alternative railroad routes. Recent efforts toward regulatory reform have substantially lessened restrictions on rate-setting practices. Previously, complex pricing rules were often established in the interest of some rather elusive objectives of maintaining competition and preserving equities of particular areas and transport agencies, which placed limits on rate-setting behavior of the sort just described. While the legacy of these regulations is still in evidence, much more flexibility in rate setting is now permitted. Discrimination Among Services and Commodities. The locational significance of transfer rate differentials among different goods or services was taken into account in our discussion of ideal weights in Chapter 2. Let us now see how such differentials arise. Some transfer services are by their nature costlier to provide than others, and we should expect to see such differences reflected in rates. A ton of pingpong balls or automobile bodies is much bulkier than a ton of steel plates. Since extra bulk adds to transport cost in every mode of transport except possibly the use of pack animals or human carriers, we are not surprised to see systematically higher freight rates per ton on bulky goods. This is one basis for the official commodity classifications governing regulated tariffs. Similarly, we should expect to pay more for shipping a perishable, fragile, or dangerous commodity (such as meat, glassware, or sulfuric acid). Extra-fast service and the carrying of small shipments are more expensive. In passenger transport it costs more to provide extra space and comfort. In addition, the marginal costs of added service at slack times are far less than at times of peak capacity use of the facilities, so that we are not surprised to be charged more for a long-distance phone call during business hours, for using a parking lot on the afternoon of a football game, or for crossing the Atlantic in summer. None of the foregoing differentials in rates necessarily involves any discrimination on the part of the transfer agency, since in every case there is an underlying difference in costs that is passed on to the user. But there are still further systematic transfer rate differentials that reflect discriminatory rate-making policy rather than costs. In particular, we find that rates are high relative to costs for the transfer of things of high value, and low relative to costs for things of low value. The rationale is essentially the same as that already adduced in the case of long versus short hauls; namely, that a seller’s profits are enhanced by discriminating against buyers with relatively inelastic demands and in favor of buyers with relatively elastic demands. When a commodity such as cigarettes or scientific instruments, with a high value per pound, is shipped any given distance, transport costs will be a smaller part of the delivered price than will be the case when a low-value commodity such as coal or gravel is shipped the same distance. Consequently, the demand for transport of cigarettes will be much less sensitive to the freight rate than will the demand for transport of coal, and any rational profit-seeking transport agency will charge a higher margin over out-of-pocket costs on cigarettes than on coal. Such discrimination, by the way, is not merely in the interest of the carrier but under some conditions may serve the public interest as well, through promoting a more efficient allocation and use of resources. It may enable a greater amount of transfer service to be provided with any given amount of investment in transfer facilities. Consequently, we find that freight tariff classifications and special commodity rates rather systematically reflect the relative prices per ton of the various commodities, in addition to such other factors as have already been mentioned. This means that finished goods as a rule pay much higher freight rates than do their component intermediate goods or raw materials, since production processes normally involve getting rid of waste components and adding value. For the transfer of people and for communication, the measure of unit value corresponding to the price per pound of a transported commodity is not so easy to assign or visualize. The basic rule of transfer rate discrimination according to value still applies; but it is generally obscured by the fact that in the transport of people and information, a "higher-value" consignment is given a qualitatively different transfer service. When it is a question of passenger travel, people will set their own valuations simply in terms of how much they are willing to pay for a trip rather than forgo it. Transfer agencies do not attempt to charge what the traffic will bear on a person-by-person and trip-by-trip basis but often provide special services (higher speed, greater comfort, and the like) to those willing to pay more. Similarly in the case of communications, it is generally impossible for the seller of the service to judge how valuable a particular transmission is to the communicator and charge accordingly; but a choice of different speeds or other qualities of service can be set up, and the rates for these can be adjusted in such a way as to reflect the estimated relative elasticities of demand as well as the relative costs. Lower long-distance telephone rates on nights and weekends are an example. Differentiation of Rates According to Direction. Most modes of transportation use vehicles that must be returned to the