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 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 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 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 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 transfer 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 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 point of origin if the trip is to be repeated. Only by coincidence will the demand for transport in both directions balance. Ordinarily one direction or the other will have excess vehicle capacity that could accommodate more goods or people at an extremely low out-of-pocket cost. A rational rate-making policy will then quote lower back-haul rates in the underutilized direction.

That direction can sometimes change rather often—for example, in intraurban travel there is a morning inbound and an afternoon outbound rush hour, and in some instances lesser reversals around the noon hour and in the evening. On weekends there is a reverse pattern of recreational travel from and to the main urban area. In this particular case, highway and bridge tolls and transit fares do not embrace the back-haul pricing principle, but they easily could, and it might be persuasively argued that they should.

Differentiation of charges on passenger travel according to direction is likewise not applied to intercity or other interregional travel within a country. We might wonder why not, in view of the frequency of the practice in commodity transport. The essential difference between people and goods in this context is that people want to return home eventually and goods do not. Accordingly, "people flows" have a natural tendency to balance out over any substantial time interval. On certain international travel routes, however, the seasonal imbalance of travel demand is enough to induce airlines and shipping firms to vary their rates seasonally according to direction, and there have been at times special one-way bargain rates to entice permanent migrants to areas considered underpopulated.

Interestingly enough, there are a few kinds of goods transport that use no durable vehicles and for which there is consequently no question of back-haul rates. Some rivers are one-way routes for the transport of logs or for primitive goods-carrying rafts that are broken up at the down-stream end, and pipelines normally operate in similar one-way fashion. Telecommunications media and power transmission lines likewise have no back-haul problem. Nothing is moved, so nothing needs to be brought back.

Simplification of Rate Structures. The foregoing discussion gives some idea of the many "dimensions" in which transfer rates can logically be differentiated: according to mode, direction, specific origin and destination, quality of service, size of consignment, and nature of the commodity or service transferred. Clearly, there is some point at which detailed proliferation of individual rates produces a tariff schedule of impractical complexity, and various simplifications and groupings commend themselves.

The variety of rates charged for transport of different commodities, for example, is held within bounds by assigning most commodities to one of a limited number of classes and letting a single schedule of rates apply to that class as a whole. The determination of individual rates for each and every pair of points served by a transfer system is analogously simplified by grouping some of these points into zones or rate blocks. For example, rail freight rates for some commodities between Pittsburgh and other parts of the country are applied not just to Pittsburgh proper but to a much larger area embracing the major part of six contiguous counties. Rate setting behavior of this type is particularly prevalent when competitive pressures do not force a close correspondence between the transfer agency’s actual costs and the prices that are charged. An illustration of the application of the rate block principle to rates graded by route distance is shown in Figure 3-3, which gives us a still more realistic picture of rate patterns than we had in Figures 3-1 and 3-2.

3.3.4 Time Costs in Transfer

We have already indicated one way in which the time consumed in transfer is felt in costs: Both the labor and the capital used in the transfer operation are hired on a time basis, so the labor cost and the capital cost of a trip will be less if the trip is faster. It is the high speed of aircraft, particularly jets, that enables them to transport passengers and certain kinds of freight at costs per mile comparable to those of ground transport. The capital and labor costs per hour are spread over at least ten times as many miles.

Quite apart from this, speed means cheaper transfer for users because they bear "inventory costs" associated with the length of time that the trip takes.² In goods shipments, there is the cost of interest on the capital tied up in shipments in transit, insurance premiums, and the risks of delay—considerations obviously more weighty when interest rates are high. Moreover, many kinds of goods deteriorate so rapidly with the passage of time that it is well worth paying more for their fast delivery. There are the obvious physical perishables such as fresh meat, fish, fruit, or vegetables, and also a further class of perishables such as fashion clothing, magazines, and newspapers, which lose value as they become out of date. In the transmission of information, the very word "news" suggests quick perishability, and the more quickly perishable forms of information provide a rapidly rising demand for a variety of telecommunication services.

Finally, in the transfer of human beings, the time of the user of the service is even more highly valued than are the rather high costs of transporting this delicate type of freight. The basis for the high valuation placed on travel time is primarily that of opportunity cost. People begrudge the time spent in traveling because they could be using that time pleasantly or profitably in some other way.

The value each of us imputes to the time spent on travel can vary greatly according to circumstances, length and purpose of the trip, and the characteristics of the person. Recreational travel is supposed to be a pleasure in itself. For such obligatory journeys as commuting to work, it is sometimes suggested that the commuter’s hourly earnings rate while working should be applied to the travel time also. However, such a basis may well be too high.³ In order to suggest the magnitude of time costs of human travel, let us consider the case of an individual who values his travel time at $7.50 an hour. If he travels, say, at 30 miles an hour, his time costs are 25 cents a mile, comparable to the money costs of driving a standard car. Decisions by commuters concerning the use of alternative transfer modes can easily be influenced by costs of this size.

3.4 LOCATIONAL SIGNIFICANCE OF CHARACTERISTICS OF TRANSFER RATES

We have seen that the structure of transfer rates departs markedly in a number of ways from the straightforward proportionality to distance that was assumed in our simplified discussion of individual locations in Chapter 2. What does this mean in terms of modified conclusions or new insights?

3.4.1 Effects of Limited Route Systems and Service Points

In our initial discussion of transfer orientation, the economic advantages of proximity to markets and input sources were envisaged as conflicting forces, and the most profitable location appeared as the point on a two-dimensional surface where these forces just balanced.

Some route networks are so dense that transfer can be effected in an almost straight path between any two points. A relatively close approximation to a uniform transfer surface is a city street system; though even here the shortest possible route and the fastest possible route may both be substantially longer than crow-flight distance. But on a coarse route network, the locational pulls toward input sources and markets are exerted in a one-dimensional way, along the routes. Does this significantly affect orientations of specific units of activity?

The best way to visualize the effect is to consider a route system connecting three points, A, B, and C, which we might identify as the market and the sources for two transferable inputs for a unit of some type of economic activity. Figure 3-4 shows four different configurations that this route system might take.⁴

Let us now assign ideal weights to A, B, and C. It is easy to see that if any of these ideal weights is predominant (exceeds the sum of the other two), there is no contest: That point is the optimum location so far as transfer costs are concerned, regardless of route layout. But what if the ideal weights are more evenly balanced, with none predominant-say, 2, 3, and 4 for A, B, and C respectively? These are the weights shown in parentheses at the A, B, and C points on System 1 on the left side of Figure 3-4.

In System 1, we see that the optimum location now turns out to be B. For all possible locations between A and B, there would be a net gain in moving toward B, since in that direction we have a pull corresponding to the combined ideal weights of B and C, or 3 + 4 =7, whereas there is a counterpull toward A of only 2. The strengths and directions of these pulls are shown by the small circled numerals with arrows attached. If the ideal weights represent, say, cents per mile per unit of output, then there will be a net transfer cost saving of 5 cents per unit of output in moving 1 mile closer to B from any alternative location to the left of B. Similarly, we find that for any location between B and C, there is a net gain of 1 cent per unit of output (3 + 2 — 4) from shifting the location 1 mile nearer B. Once we are at B, there is no incentive to shift farther; the optimum location has been found.

This device of totaling the forces in each direction and thus finding the favorable direction of location shift along each route segment is a handy technique for analyzing network location in simple cases and is the conceptual basis of the linear programming approach for determining the optimum point.⁵

Let us now apply this procedure again to System 1 of Figure 3-4, changing the ideal weights from 2, 3, and 4 to 4, 2, and 3, as shown in the map at top right in the figure. Again we come out with the intermediate point B as the optimum location, despite the fact that it has the smallest ideal weight of the three! We begin to suspect that there is some special advantage in being in the middle; and this is, in fact, the "principle of median location," mentioned in Chapter 2. If we have three points arranged along a route as shown, and if none of their ideal weights is predominant, then the transfer orientation is always to the middle point.⁶

Applying the same procedure to System 2 of Figure 3-4 (and still assuming that none of the ideal weights is predominant), we find that the optimum point is the junction J. In System 3 it is A, J, or B, depending on the relative lengths of the route segments AB, BJ, and AJ and the ideal weights of A, B, and C. And in System 4 it could be A, B, or C. We note, then, that in every one of the four systems the optimum location is always at an intermediate point (one from which routes lead in at least two directions) and never at an end point.

This holds true regardless of the ideal weights so long as none is predominant, and regardless of the length of the dead-end route segments (AB and BC in System 1; AJ, BJ, and CJ in System 2; CJ in System 3). Finally, it is quite immaterial which of the points are markets and which are input sources. In these illustrations, such identification was deliberately avoided.

It is clear that when none of the ideal weights predominates, we cannot predict the orientation of a locational unit simply on the basis of its inputs and outputs; we can say, however, that it will locate not at dead ends but at points reachable from at least two directions—whether these be input sources, markets, or junctions.

3.4.2 General Locational Effect of Transfer Rates Rising Less than Proportionally with Distance

Ideal weight expresses extra cost imposed per unit of added distance— in other words, the marginal cost of transfer with respect to distance. Our initial image of the relation of transfer cost to distance (Figure 3-1) showed this marginal cost as almost uniform, corresponding to a constant ideal weight regardless of distance.

The more realistic transfer rate gradient in Figure 3-3, flattening off at longer distances, implies that ideal weights and the locational pulls of transfer cost factors are not constant but systematically weaker at long range and stronger at short range. If we seek a physical analogy, then, it should not be that of a weight on a string as in the Varignon Frame, nor that of a stretched spring, but that of a force more like gravitation or magnetism.

This feature of transfer rates tends to enhance the advantages of location at input sources and markets and to reduce the likelihood of location at intermediate points. Each input source and market point, in fact, becomes a local optimum location, in the sense that it is better than any location in the immediately adjacent area. The search for the most profitable location for a unit, then, is a little like the search for the highest altitude in a landscape studded with hillocks and minor and major peaks. In such a landscape, we could not rely on getting to the highest point by simply continuing to walk uphill but would have to make some direct comparisons of the heights of various peaks. Analogously, a program for determining the ideal location of a transfer-oriented activity unit generally cannot rely entirely on gradients of transfer cost or measurements of ideal weights but at some stage must incorporate direct comparison of specific source and market locations.

This principle is illustrated graphically in Figures 3-5 and 3-6. In Figure 3-5, we have the transfer charges per unit of output as they would be at various points along a route running through the input source and the market point. The two black lines show how the input transfer and output transfer charges per unit of output vary with location of the facility. The white line at the top of the figure shows total transfer charges on a unit of output plus the amount of input required to produce it.

It will be observed that there are local minima of total transfer charges at the input source and at the market. In this case, the total costs for a location at the market would be slightly lower than for a location at the source, but both are much lower than those at surrounding locations.

Figure 3-6 shows a two-dimensional pattern of profits with three transfer points involved: They could be, say, two input sources and a market. Here the profits per unit of output⁷ are shown by contour (iso-profit) lines connecting points of equal advantage. A local peak appears at each of the three points, with that at S₂ the highest.

3.4.3 Modal Interchange Locations

It has been suggested above that the long-haul discount characteristic of transfer costs and rates lessens the transfer advantages of locations that are neither sources nor markets for transferable inputs and outputs. Some kinds of intermediate points, however, are relatively attractive in terms of transfer costs.

Most transfers involve one or more changes of mode or other terminal type of operation en route rather than proceeding right through from initial origin to final destination. This situation becomes more frequent as the variety of available transport modes increases, each with its special advantages for longer or shorter hauls, larger or smaller shipments, high speed, low money cost, and so on.

Textbooks often tell us that points of transshipment or modal interchange, such as ports, are particularly strategic locations because location of a processing facility at such a point "eliminates transshipment costs."

Such a statement may be misleading. Let us take a simple hypothetical case involving a flour mill. Grain is collected at an inland point connected by rail to a port (transshipment point), from which ships go to a market for flour. We want to choose among three possible locations for the mill: (1) at the grain-collection point, (2) at the port, or (3) at the market. To focus directly on the question of the transshipment point’s possible advantage, we assume that the handling and transfer costs (per barrel of flour) are the same for flour as for grain, which makes the grain-collection point and the flour market equal in locational advantage. The question, then, is whether location at the transshipment point (port) is superior or inferior to the grain-source and flour-market locations for the mill.

Let us denote the elements of cost as follows, per barrel of flour:

The costs involved for each of the three mill locations are as itemized in Table 3-2.

We notice that for each of the three possible mill locations, the total cost is the same: M + B + W + 2(L + U). Although the transshipment point location is apparently just as good as either of the others, it does not show any special advantage. Indeed, we might surmise that more realistically it would be under some handicap. With either of the other two mill locations, it might be possible to achieve some savings by direct transference of the grain or flour from rail to ship (the U and L operations at the port) at less cost than is involved in the two separate port transfers (grain from rail to mill, and flour from mill to ship) that are involved if the mill is located at the port. This possible saving is suggested by the square brackets in Table 3-2.

If we modify the preceding case by assuming that flour is more costly to ship, unload, or load than is grain, then the most economical location is at the market; location at the grain-collection point would be less advantageous, and location at the port would be intermediate in terms of cost.

Clearly, then, we must explain the observed concentrations of activity at ports and other modal interchange locations on the basis of other factors. Some (the transport advantages of junction points with converging or diverging routes) have already been mentioned. A modal interchange point is likely to have such nodal characteristics, if only because different transfer modes have route networks of different degrees of fineness, so that where they come in contact, there is likely to be more than one route of the mode with the finer network.

The focusing of transfer routes upon points of modal interchange reflects scale economies in transfer and terminal operations, and sometimes also the lie of the land. Thus along a coastline, suitable natural harbors are limited in any event, and scale economies tend to restrict the development of major ports to an even smaller selection of points. The same applies to crossings of a mountain range or a large river.

A further characteristic advantage of modal interchange points is that they are likely to be better provided with specialized facilities for goods handling and storage than are most other points.

3.5 SOME RECENT DEVELOPMENTS CONCERNING THE STRUCTURE OF TRANSFER COSTS

3.5.1 Introduction

The preceding sections have focused on some important aspects of the structure of transport rates and characteristics of route systems. As has been demonstrated, they provide information that can be used in conjunction with the theoretical insights gained from Chapter 2 in order to appreciate more fully the role that transfer factors may play in location decisions. In some instances, changes that take place in the markets of important commodities in a national or international context or changes in basic technological relations can have direct effects on the spatial distribution of economic activity. These effects often, but certainly not always, manifest themselves as a result of changes in transfer costs.

In this section, attention is directed to two such changes, both much in evidence at this time. We attempt to use the location principles that have been developed in order to understand some of the spatial consequences of higher energy prices and technological changes concerning the processing and transmission of information. It should be emphasized that our treatment of issues related to these phenomena is speculative and illustrative. There is a very slim factual basis on which to gauge any of the effects that will be mentioned. However, it is hoped that this analysis will demonstrate how even elementary location theory can help us to speculate constructively.

3.5.2 Higher Energy Prices and the Pattern of Industrial Location

The rapid increase in energy prices during the decade of the seventies affected our economy in many ways. We are acutely aware of the impact of this phenomenon on the rate of economic growth as well as on the distribution of income. However, little attention has been paid to the effect of higher energy prices on the spatial distribution of economic activity. It is important to recognize these spatial effects as well as the mechanics by which they are transmitted.

The effect of higher energy prices since the 1970s on locational choice might be considered from several perspectives. It would be possible, for example, to examine the nature of commuting or shopping behavior when people are confronted with higher motor fuel prices. Alternatively, we might recognize that higher energy pries have affected production decisions as well as the transport costs on material and finished products. This being so, our previous analysis of transfer-oriented industries would imply that, for at least some locational units, the spatial consequences of higher energy prices will depend on the nature of responses in production and the kind of changes in the structure of transport costs that take place. Much of the preceding discussion in this text has pointed to the result that the orientation of industry toward particular inputs or toward the market can be influenced by these locational determinants. We are well equipped to understand many issues related to the effects of higher energy prices if we examine the systematically in this context.

It has been pointed out (see Figure 3-2) that intermodal competition among transfer agencies leads to a gradient of transfer rates with respect to distance that is much more curved than that of any single-mode cost gradient. For long hauls, customers will find that the decrease in transfer rates with increased distance is accentuated by competition of this sort. The locational significance of this characteristic of transfer rates is that it puts intermediate locations (places that are not markets or sources of transferable inputs) at some disadvantage.

One channel by which higher energy prices might affect location decisions is through their effect on the structure of intermodal transfer costs.⁸ As shown in Table 3-3, transfer modes differ in their intensity of energy use. Specifically, shorter-haul transport by motor carriers (trucks) is most energy intensive, whereas rail and barge transport, which generally involve longer distances, are much more energy efficient. The most direct consequence of this is that we might expect the tapering off of transport rates with distance to become yet more accentuated as a result of higher energy prices; short-haul (truck) rates will increase relative to long-haul (rail and barge) rates. By our earlier arguments, the attractiveness of end-point locations is enhanced as a result of this effect.

The differential impact of higher energy prices on alternative modes of transport can be expected to have more subtle effects, however. Modes differ not only in their competitiveness by length of haul, but also in the kinds of commodities that they can most effectively transport. For example, not only is trucking particularly suited for the transfer of commodities over short distances, but it is also best suited to commodities that have a high ratio of value to weight and to commodities that must be shipped in small lots.⁹ Both of these characteristics encourage the use of trucks to deliver finished and other highly processed goods to market. Conversely, because of the high fixed costs and relatively low line-haul costs associated with rail and barge modes, they not only have an advantage on longer hauls but also are particularly suited to the transfer of bulk commodities with low value-to-weight ratios, a category that often includes raw materials.

These considerations imply that the changes in relative freight rates (truck versus rail or barge) that are the result of higher energy prices may have some significant effect on material versus market orientation. The energy intensity of truck transport will be reflected in higher line-haul rates for this mode as compared to other modes. Additionally, because of the relatively inelastic demand for transport services associated with high value-to-weight commodities, more for the energy price increases can be expected to be passed on by agencies serving this class of goods. Smaller portions of energy price increases will be passed along by those modes that service low value-to-weight commodities because of the sensitivity of their demand to price increases. Therefore, in the tug-of-war governing location decisions for industries that are sensitive to transport costs, we should expect that the pull of the market will be enhanced relative to that of transferable inputs as transport rates on finished goods increase relative to those associated with materials.

We should recognize that this analysis concentrates on only one component of the "ideal weight" measures defining locational pulls. It has been argued that energy price increases will be reflected in transport rates. The other component of ideal weight is, of course, the physical weight of the transferable input or output. There are some evidence that the materials and energy are substitute inputs in the production process associated with U.S. manufacturing as a whole.¹⁰ This would imply that an increase in energy prices may increase the weight of materials transferred for output of a given weight. Such a change would tend to increase the ideal weight of materials and may serve to counteract any tendency toward market orientation due to changes in relative transport rates. The highly aggregative nature of empirical evidence concerning this matter precludes any definitive judgment, however.

Higher domestic energy prices not only affect transport and production costs, they also imply substantial shifts in the spatial distribution of income. Energy-producing regions have gained for at least two reasons. Greater local production at higher prices obviously has meant greater income to workers as well as to the owners of capital in these regions.¹¹ Further, while price controls on domestic petroleum and natural gas production are being phased out, the presence of these restrictions has meant at least a short-run advantage to energy consumers in energy-producing regions. They have faced relatively lower energy prices than they would in regions that must rely exclusively on higher-priced, imported energy. Therefore, recognition of the concept of "market access potential" developed in Chapter 2 would indicate that for some locational units higher energy prices mean that the median location of the market will shift in the direction of those regions with substantial existing or developing capacity in energy production.¹²

While we have been able to identify certain gross tendencies that may be manifest as a result of higher energy prices, this analysis is only suggestive of the kind of forces at work. Individuals who are concerned with the behavior of specific industries could obtain more detailed information on transport modes and on the character of production and markets that are relevant to their interests. They might then be in a position to know whether transport rate, production, or market considerations will be most influential.

3.5.3 Technological Change in Data Processing and Transmission

In contrast to the behavior of energy prices, the cost of moving and processing information has fallen dramatically in recent years, and the end is not in sight. Advances in electronics technology have abruptly enhanced the efficiency of computers and our ability to interact with them. At the same time, developments in communications technology have weakened the constraints of distance on some types of location decisions. Significant locational effects are emerging on both the microspatial and the macrospatial levels, foreshadowing still further shifts.

As we shall see in Chapter 7, the internal spatial arrangements of urban areas are shaped largely by considerations of access—it might even be said that access is what cities are all about. At this microspatial level, the journey to work and one’s ability to maintain close, flexible contact with customers, suppliers, co-workers, and friends are major determinants of both business and residence location. So if people or firms find that their work and other activities no longer demand close physical contact, locational incentives will change. For example, it is now becoming increasingly practicable to use computer hookups to communicate with other workers or with central data banks. As a result, the valuation of locations with respect to their nearness to long-established foci of urban economic activity is changing considerably. This "communications revolution" has potentially wide implications. Some people have speculated that the "cottage industry" of the near future will comprise people who work at home and maintain business contacts via integrated computation and communications systems. Early evidence of such a trend is already appearing.

For some activities, the very nature of outputs or inputs, or both, may change as a result of advances of the sort just mentioned. Banking is an obvious case in point. From one perspective, deposits received by a bank may be regarded as inputs; banks then take those inputs and use them to earn income by "selling" loans and other investments and services. Alternatively, one might view the receiving of deposits as a form of services provided by the bank and thus as one of the bank’s outputs.

Until recently, the deposit activity of a bank was essentially non-transferable, and many separate banking offices were needed to service adequately a large urban area full of depositors and borrowers. But the deposit services of a bank may soon become very transferable indeed. We see already more and more banking machines acting as robot tellers; banking by phone is developing, and banking via home computer is in the offing.

So depositors who now have to travel to a bank, or use the mails, will soon find that the bank’s services travel instantly to them. With the proliferation of electronic transactions and home computer terminals, we can foresee that the customer service area of a single banking office will no longer be confined to a neighborhood, and that presumably far fewer bank locations will be needed.

Locational relations among different activities likewise are subject to important alteration when the transferability of information is greatly enhanced, as is now happening. An example of this is firms that provide troubleshooting and repair service to users of complex equipment. The easy and quick availability of such services has been an important factor to many firms. While maintenance specialists can be dispatched some distance to attend to problems, speed is of the essence. Close proximity to the suppliers of the service has meant speedy attention, less down time, more regularity of production, and therefore lower operating costs. There is even a saving in capital costs as fewer machines are needed to ensure a given rate of production and as goods spend less time in the production process.

But in recent years some highly sophisticated "smart" machines that incorporate computer systems to monitor performance have also been endowed with a capacity for self-diagnosis. When a problem occurs, such a machine is capable of immediately signaling the probable nature and extent of the difficulty. This information can be relayed by wire to central service facilities that are equipped to interpret it and to recommend or provide maintenance or repair procedures entailing a minimum of delay. Thus the integrated character of industries can take on new forms. The repair facility now has greater flexibility of location as the transfer costs on its output are reduced and the firm operating the complex equipment faces lower transfer costs on an important service input. Both are able to respond more freely to other locational factors.

The communications revolution promises likewise to have significant effects on locational relationships among establishments of the same firm. In a study of branch plants in four states over the period 1967—1976, Rodney A. Erickson and Thomas R. Leinbach found that the size of branch plants is positively related to their distance from corporate headquarters. The farther away from headquarters, the larger the branch tends to be.¹³

This relationship reflects the handicap that distance has always imposed on a firm’s ability to centralize decision-making and at the same time to keep in touch with and direct the operations of scattered field offices or branches. Branches have had to become more autonomous and assume more decision-making functions as their distance from headquarters increases. It may be surmised that current and foreseeable advances in data processing and transmission will alter this relationship. Effective centralized coordination and control at long distances should become more feasible. Specialized operations of large firms may be oriented more closely to their specific markets without sacrificing adequate contact with headquarters.

3.6 Summary

This chapter explores (1) the ways in which transfer costs in the real world are not simply proportional to crow-flight distance as was assumed in Chapter 2, and (2) the locational significance of such departures from a uniform transfer surface.

Transfer operations almost always involve a large element of fixed costs. Consequently, there are important scale economies related to route traffic volume, terminal volume, and size of individual movement unit and consignment. There is also wide leeway for transfer agencies in apportioning their fixed costs over various classes of services so as to improve capacity utilization, meet competition, and increase profits.

Transfer services by any one mode are generally confined to a limited network of routes and service points, determined by variations in terrain and scale economies. Transfer costs by any one mode also generally rise less than proportionally with longer distance—mainly because of terminal cost, but also often because of lower line-haul cost per mile on longer hauls.

The pattern of rates charged by transfer agencies is even less like a uniform transfer surface than is the pattern of transfer costs. There is normally rate discrimination in favor of larger-volume services, longer hauls, routes and types of services where interagency or intermodal competition exists, and goods of low value relative to their weight or bulk. Further, where the demand for transfer between two points is not the same in both directions and returnable vehicles are used, cheaper back-haul rates in the direction of lower transfer demand are likely.

Other important characteristics of transport rates have been noted. Rate structures are generally simplified by setting uniform rates for categories of services and ranges of distance, shipment size, and so forth, rather than setting a separate rate for each service. Additionally, time costs are an important part of total transfer cost for high-valued or perishable shipments and especially for transfer of people and information.

Each of these departures from the uniform transfer surface has an effect on locational preferences. We have also recognized that both long-haul economies and the restriction of transfer to limited systems of routes and service points enhance the locational advantages of markets, input sources, and route junctions, including modal interchange points.

Together with the theoretical basis developed in Chapter 2, these considerations provide a framework for examining the locational implications of changes in our economy that alter the structure of transfer costs.

TECHNICAL TERMS INTRODUCED IN THIS CHAPTER

SELECTED READINGS

Benjamin Chinitz, Freight and the Metro polls, a report of the New York Metropolitan Region Study (Cambridge, Mass.: Harvard University Press, for the Regional Plan Association, 1960).

Benjamin Chinitz, "The Effect of Transportation Forms on Regional Economic Growth," Traffic Quarterly, 14 (1960), 129-142. Reprinted in Gerald J. Karaska and David F. Bramhall, Locational Analysis for Manufacturing (Cambridge, Mass.: MIT Press, 1969), pp. 83-96.

John R. Meyer, M. J. Peck, J. Stenason, and C. Zwick, The Economics of Competition in the Transportation Industries (Cambridge, Mass.: Harvard University Press, 1959).

Hebert Mohring, Transportation Economics (Cambridge, Mass.: Ballinger, 1976).

APPENDIX 3-1

Rate Discrimination by a Transfer Monopolist

Assume that a good is to be shipped to various markets from a single point of origin. At each market the quantity sold (and consequently the quantity shipped to that market) will be

q =a — b(p + r)

Where p is the price at the point of origin (the same for all markets) and r is the transfer charge.

The transfer agency’s cost of carrying the good to a market x miles away from the point of origin is (g + tx) per ton, where g is terminal cost and t is line-haul cost per mile.

On shipments to a market at a distance x, therefore, the transfer agency will make a net return of

Z =(a — bp — br)(r — g — tx)

Differentiating,

dZ / dr=a — bp — 2br + bg + btx

and the most profitable rate to charge (r*) is calculated as follows:

a — bp — 2br* + bg + btx=0

r*=(a — bp + b) / 2b + tx / 2

The ideal tariff will be a flat charge equal to

1/2 [(a / b) + g — p]

plus half the line-haul cost for each mile of haul.

ENDNOTES

1. In regard to trucking cost, "The ICC has consistently reported that line-haul costs decline with distance shipped. However, this is largely a spurious correlation, reflecting the fact that size of shipment and length of haul are correlated, and not attributable, as the ICC implies, to some operating characteristics that makes line-haul ton-mile costs substantially less on a two-hundred-mile than on a one-hundred-mile trip Total unit costs do decline with distance, however, because of the distribution of terminal expense over a large number of ton miles." John R. Meyer and others, The Economies of Competition in the Transportation Industries (Cambridge, Mass.: Harvard University Press, 1959), p. 93.

2. Illustrative of the indirect "inventory economies" of faster transport, United Air Lines in 1961 suggested that "UAL Air Freight can be profitable when the added cost of shipping by air freight is less than 9½% of the cost value of the goods involved." This conclusion is based on the estimate that air freight shipment can, on the average, reduce warehousing requirements by about 40% and inventory requirements by about 20%. For the average product shipped, warehousing charges run about 12% of cost value, and inventory charges about 25%; thus the total saving by air freight amounts to a little more than 9½% of the cost value of the goods. It is easy to see that the appeal of air freight is likely to be higher for goods wit high value per pound. Note also that the savings associated with air freight is sensitive to interest rates. When higher interest rates prevail, reductions in inventories and in delays associated with warehousing can mean considerable savings to customers who use this mode of transfer.

3. 0n the private and social evaluation of personal travel time, see Colin Clark, Population and Land Use (London: Macmillan, 1969; New York: St. Martin’s Press, 1969), pp. 377-379; Albert Rees and George P. Shultz, Workers and Wages in an Urban Labor Market (Chicago: University of Chicago Press, 1970); and Thomas Domencich and Daniel McFadden, Urban Travel Demand (New York: North-Holland, 1975). The consensus seems to be that people rate the disutility of travel to work at only about one-third to one-half of their earnings rate; but that there are some additional costs of longer commuting time which are borne by the employer (wage premiums, increased absenteeism and tardiness, and lowered productivity through fatigue) and which might be of similar order of magnitude to the costs borne by commuters themselves. Some studies have estimated the valuation of private costs to be substantially lower than one-third of the earnings rate. See William C. Wheaton, "Income and Urban Residence: An Analysis of Consumer Demand for Location." American Economic Review 67, 4 (September 1977), 620-631, for references to several of these studies.

4. The "forks" mentioned in Figure 3-4 are defined as three-branch (Y) junctions. Readers may wish to amuse themselves by constructing the four additional kinds of networks that are possible with no more than three ends and no more than three forks: no ends, two forks; one end, three forks; two ends, two forks; and three ends, three forks. The sum of the number of forks and ends is always even.

5. See Robert Dorfman, "Mathematical or ‘Linear’ Programming: A Nonmathematical Exposition," American Economic Review, 43, 5 (December 1953), 797-825.

6. This conclusion throws some additional light on the significance of the shape of the locational polygon where the route constraint is ignored (see Figures 2-3 and 2-4 in the previous chapter). In Figure 2-4, the locational triangle was compressed so that the obtuse corner was the optimum transfer location. As the triangle is squeezed, it obviously approaches closer and closer to the configuration of a single line, with the obtuse corner becoming the intermediate point on the line, like point B in System 1 of Figure 3-4.

7. We are assuming that all inputs and outputs other than those specifically mentioned are ubiquitous, so that processing costs would be the same at all locations. The activity is assumed to be wholly transfer-oriented.

8. Details on some of the issues raised in the remainder of this section may be fond in Frank Giarratani and Charles F. Socher, "The Pattern of Industrial Location and Rising Energy Prices," Atlantic Economic Journal 5, 1 (March 1977), 48-55. For a theoretical discussion of some related topics, see Noboru Sakashita, "The Location Theory of Firm Revisited: Impacts of Rising Energy Prices," Regional Science and Urban Economics, 10, 3 (August 1980), 423-428.

9. Commodities with a high value-to-weight ratio can more easily pass along to their customers the high ton-mile charges associated with truck transport.

10. Ernst R. Berndt and David O. Wood, "Technology, Prices, and the Derived Demand for Energy," Review of Economics and Statistics 57, 3 (August 1975), 259-268.

11. See William H. Miernyk, Frank Giarratani, and Charles Socher, Regional Impacts of Rising Energy Prices (Cambridge, Mass.: Ballinger, 1978), pp. 57-76.

12. Not all energy-producing regions can be expected to share equally in these advantages. For example, some coal-producing regions have been severely affected by restrictions placed on the use of coal with high sulfur content because of environmental concerns.

13. Rodney A. Erickson and Thomas R. Leinbach, "Characteristics of Branch Plants Attracted to Nonmetropolitan Areas," in Richard E. Lonsdale and H. L. Seyler (eds.), Nonmetropolitan Industrialization (Washington, D.C.: V. H. Winston, 1979), p. 68.