The Economics of Welfare

Pigou, Arthur C.
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London: Macmillan and Co.
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4th edition.
33 of 73

Part II, Chapter XVIII


§ 1. THE discussion of the preceding chapter has necessarily been somewhat abstract. It has, however, practical applications of very great importance in connection with the problem of arranging the charges to be made for such things as water, gas, and electricity, when these commodities are supplied to different groups of consumers or for different purposes. Still greater interest attaches to it in connection with the rates chargeable by railway companies. Considerable controversy has taken place between those who hold that these rates should be based on "the cost of service principle." and those who would base them on the "value of service principle."*1 The "cost of service principle" is, in effect, the simple competition discussed in Chapter XI.: "the value of service principle" is discriminating monopoly of the third degree. In the light of what has been said, the issue between them can be clearly set out; and it will, in the present chapter, be examined. We have no concern with the circumstance, explained in Chapter XVI., that, in certain conditions, a railway with power to discriminate may find it profitable, as a temporary measure, to charge exceptionally low rates for transport between certain places or for certain selected commodities, with a view to building up a new demand; nor yet with the related circumstance that this policy, if the demand is really a new one, and not merely a substitute for another that has been supplanted, may be more advantageous to economic welfare, if not to the national dividend,*2 than anything which simple competition—unless it were modified by a system of State bounties—could evolve. These matters call for no further investigation here. Leaving them aside, I propose to exhibit the meaning, in concrete form, of the cost of service principle—or simple competition—and of the value of service principle—or discriminating monopoly of the third degree,—and to compare their respective consequences.


§ 2. It is generally agreed that, except in so far as the transport services sold to one set of purchasers are "supplied jointly" with those sold to another set, simple competition would tend to bring about a system of uniform rates per ton-mile for similar services.*3 For these services the level of the uniform rate would be such that the demand price and the supply price would coincide; and, when the service of railway transport was sold in conjunction with some other service, such as cartage or packing, an appropriate addition would be made to the charge. This general analysis can be briefly developed as follows.


First, the actual level of the uniform mileage rate, to which simple competition would lead on any particular railway, will depend on the circumstances and position of the railway. Ceteris paribus, a specially high rate would be appropriate if the route lay through districts where, as with mountain railways, the engineering costs of making a line are specially great, or where the traffic is very irregular from one time to another;*4 because, in these conditions, the supply prices of all quantities of transportation along the route are specially high. In like manner, ceteris paribus, a specially high rate would be appropriate if the route lay through sparsely populated regions where little traffic can be obtained, or through regions where the configuration of the country renders water transport a readily available substitute for land transport for certain classes of commodities between the terminals; because, in these conditions, the demand schedule is specially low, and the supply conforms to conditions of decreasing supply price; the expenses involved in building and working a railway adapted for a small amount of traffic being proportionately greater than those involved in the production of transport service on a large scale. It is, no doubt, in recognition of these considerations that the maxima, imposed in the British parliamentary freight classification, are made different for different lines, though the classification itself is, of course, the same for all of them.


Secondly, departures from the uniform mileage rate would occur under simple competition, in so far as buyers of a ton-mile of transportation require, along with this, other incidental services involving expense. The adjustments needed are exactly analogous to the adjustments made in the price of plain cotton cloth delivered c.i.f. to buyers who live at different distances from the seat of manufacture. Thus rates should be comparatively low for the transport of any class of goods, when the method of packing adopted is convenient to the railway. It is more costly, other things being equal, to carry small consignments than large. "Small consignments mean to a railway three distinct sources of serious additional expense: separate collection and delivery; separate handling, invoicing, accounting, etc., at the terminal stations; and bad loading in the railway wagons."*5 It is, therefore, proper that, in the British parliamentary classification, goods, which are placed in class A—the cheapest class—when loaded in lots of 4 tons, are raised to class B when despatched in loads of between 2 and 4 tons, and to class C when despatched in loads of less than 2 tons. On a like principle, it is proper that English railway companies should voluntarily make arrangements, under which certain goods are put into a class lower than the parliamentary classification requires, on condition that they are loaded in certain quantities or packed in certain ways. Further, when the method of packing is given, it is proper that rates per ton should vary with conditions that affect the cost of handling, such as bulk, fragility, liquidity, explosiveness, structure and so on; and also with the speed and regularity of the service required.*6 This point is clearly brought out in one of the decisions of the United States Railway Commissioners. They declared: "Relatively higher rates on strawberries appear to be justified by the exceptional character of the service connected with their transportation. This exceptional service is necessitated by the highly perishable character of the traffic, requiring refrigeration en route, rapid transit, specially provided trains, and prompt delivery at destination. There is also involved in this service extra trouble in handling at receiving and delivering points, the 'drilling' of cars in a train, reduction of length of trains to secure celerity of movement, partially loaded cars, the return of cars empty, and, perhaps, other similar incidentals."*7 Finally, it is proper that the rate for carrying from A to B goods that are to go forward to C on the same line should, in general, be less than the rate for so carrying goods destined for consumption at B. In so far as terminal charges are paid for in the rate, this is obvious, because, on the former class of goods, terminal charges at B are saved altogether. Even apart from terminals, however, the journey from A to B, as a part of a longer journey, is less costly than the same journey undertaken as an isolated whole. The reason is that, roughly speaking, the interval of idleness for engines and plant, following upon any journey, involves a cost properly attributable to that journey, and the length of the interval does not vary with the length of the journey which it follows. Thus, "long hauls get more mileage out of engines, waggons, train-staff, etc., than a number of short hauls, necessarily with waits between; engines and waggons are better loaded, and the line is more continuously utilised."*8 This consideration points to some form of tapering rate for the service of carriage, apart from terminal charges. The English (pre-war) classification of merchandise rates accepts this. It provides for one maximum ton-mile rate for the first 20 miles, a lower maximum for the next 30 miles, a still lower one for the next 50 miles, and the lowest of all for further distances. This scale does not include terminal charges, which are fixed independently of distance.*9


Thirdly, attention must be called to the fact that services, though physically similar, are not necessarily similar in respect of cost when they are rendered at different times or seasons of the year. This consideration is in practice chiefly important as regards the supply of electricity. In order that it may be possible to provide the current required at "the peak of the load," a large quantity of equipment must be erected additional to what would be required if there were no hours or seasons of exceptional demand. Let up suppose that during one-fifth of the time 2 million units per hour are wanted and during the rest of the time 1½ million units, and that, in consequence, the equipment costs 4/3 times what it would have done had 1½ million units been required always. Then the real cost of the peak-load current, so far as it depends on cost of equipment, can be calculated as follows: the equipment cost of producing the units needed in the aggregate of off-peak times is 4/5 times ¾ths (i.e. 3/5ths) of the total equipment cost, and the equipment cost of producing the units needed in peak times is 1/5 times ¾ths of the total equipment cost, plus the whole of ¼ of that cost, i.e. 2/5ths of the whole. That is, the cost of providing 2 million units at the peak is equal to 2/3rds that of providing 6 million units off the peak: or, in other words, the equipment cost (apart from prime cost) of peak-load service is twice as much per unit as the equipment cost of normal service. This shows that simple competition, or the cost of service principle, involves different charges for electricity supplied at different times. The same thing obviously holds good of telephone service and cable service—not to speak of hotel and lodging-house service in places that cater specially for seasonal visitors. In industries, the product of which can be stored in slack times, and where, therefore, the equipment can be adjusted to produce continuously the average output demanded, these differences should not exceed the cost and the loss of interest involved in storage. Railways, however, at least in the matter of passenger transport, are directly akin to electricity concerns, in that they provide a service which must be produced at the time that it is supplied. Consequently, the cost of service principle would seem to warrant higher fares for travel at busy seasons and at busy hours of the day than are charged at other times. Differential charges of this character are not, of course, exactly adjusted. Indeed, as a matter of fact, it so happens that, for other reasons, it is just for the most crowded parts of the day and week that the cheapest tickets (workmen's tickets and week-end tickets) are issued. In a concealed form, however, differential charges of this type do exist: for, when a man travelling as a straphanger in the London Tube at 5 o'clock in the evening pays the same absolute price as he does when travelling in comfort at 3 o'clock, he is paying that price for a different and much inferior service. There is just as real a differentiation as there would be if he travelled in equal comfort on both journeys and paid a considerably higher fare at the crowded time.


Lastly, the cost of service principle in some conditions leads logically to lower charges to people whose purchases are continuous than to those who buy intermittently. One reason for this is that a man taking continuous service cannot contribute to the peakiness of a peak load, whereas one taking intermittent service is likely, in some degree, to do this. Hence, if it is impracticable to charge differential rates directly as between peak and off-peak service, this may sometimes be attempted indirectly by differentiation between continuous and intermittent services. The device is an imperfect one, because a consumer, whose demand is intermittent but wholly off-peak, involves less cost than one whose demand is continuous. In practice this type of differentiation is found only in industries where special equipment has to be laid down to enable the service to be supplied to the various customers severally. Obviously, if this equipment is used rarely, a greater sum will have to be charged for each act of service than if it is used frequently. If desired, adjustment can be made by exacting a lump charge, or an annual rent, for the installation of the equipment and, thereafter, charging the same rate to everybody per unit of service obtained through it. This is, broadly, the plan in vogue with telephones. When, however, for any reason this plan is not followed, and the whole charge is levied through the price of the service, the cost of service principle necessarily leads to overt differentiation against customers whose individual load factor is small. But this consideration has no direct application to railway rates, since, apart from special sidings for which direct charges are made, railways do not provide equipment specialised to the service of particular customers.


§ 3. The results so far obtained are only valid in so far as transport services sold to different groups of purchasers are not jointly supplied. If they are jointly supplied, simple competition, or the cost of service principle, would no longer imply that, subject to the reservations of the preceding section, all ton-miles of transportation must be sold at the same price. It would not imply this any more than it implies that a pound of beef and a pound of hides must be sold at the same price. For, when two or more commodities or services are the joint result of a single process, in such wise that one of them cannot be provided without facilitating the provision of the other, simple competition evolves, not identical prices per pound (or other unit) of the various products, but prices so adjusted to demand that the whole output of all of them is carried off. Thus, if the transport of two commodities A and B, or the transport of commodity A for two purposes X and Y, were joint products, simple competition might well evolve for them different rates per ton-mile. It is, therefore, of great importance to determine how far the various services provided by railway companies are in fact joint products in the sense defined above.


§ 4. Many writers of authority maintain that joint costs play a dominant part in the industry of railway transportation. They believe that the transport of coal and the transport of copper along a railway from any point A to any point B are essentially and fundamentally joint products; and that the same thing is true of the transport from A to B of commodities to be consumed at B and the transport from A to B of commodities to be carried forward to C. This argument is developed by Professor Taussig as follows. First, he observes: "Whenever a very large fixed plant is used, not for a single purpose, but for varied purposes, the influence of joint cost asserts itself."*10 Further: "The labour which built the railway—or, to put the same thing in other words, the capital which is sunk in it—seems equally to aid in carrying on every item of traffic.... Not only the fixed capital of a railway, but a very large part, in fact much the largest part, of the operating expenses, represents outlay, not separate for each item of traffic, but common to the whole of it or to great groups of it."*11 The existence of a large mass of common supplementary costs is not, in Professor Taussig's view, by itself sufficient to bring joint supply into action. For that it is essential that the plant be used for varied purposes. Thus he writes: "Where a large plant is used for producing one homogeneous commodity—say steel rails or plain cotton cloth—the peculiar effects of joint cost cannot, of course, appear."*12 Further, he is willing to admit that the transport of tons of different things and the transport of the same thing for different purposes from A to B do constitute, in one sense, a single homogeneous commodity, on precisely the same footing as plain cotton cloth. The fact that some "carrying of tons" is sold to copper merchants and some to coal merchants does not imply that two different services are being provided, any more than the fact that some plain cotton cloth is sold to one purchaser and some is sold to another implies that two different commodities are being provided. He holds, however, that these different transports, though homogeneous in one sense, are not homogeneous "in the sense important for the purpose in hand—namely as regards the conditions of demand."*13 Thus his essential contention is that, when a commodity, in the production of which supplementary general costs play a large part, is supplied, not to different people in a single unified market, but in a number of separated markets, the provision to one market is supplied jointly with the provision to the other markets, in such wise that simple competition might be expected to evolve a system of divergent prices.


Now, whether or not the term joint products should be used of services related in the way that Professor Taussig is contemplating is, of course, a verbal question: but whether these services are joint products in such wise that simple competition might be expected to evolve a system of divergent prices is a real question. In my view, the conjuction of large common supplementary costs with separation between the markets to which their yield is supplied does not make railway services joint products in this—the only significant—sense. In order that they may be joint products, it is further necessary, not merely that additional investment in plant and so on may be used alternatively to facilitate the supply to either market, but that such additional investment cannot be used to facilitate the supply to one market without facilitating the supply to the other. The point may be illustrated as follows. When cotton goods are provided for two distinct and isolated markets, the costs of furnishing these different markets are, in great part, common: for they consist, to a large extent, of the supplementary expenses of the cotton industry, which cannot be allocated specifically to the goods destined for the different markets. A given addition to investment does not, however, necessarily add anything to the output available for each of the two markets. If, before it occurred, the first market received x units of cotton and the second y units, after it has occurred the extra cotton may be divided between them, or it may go wholly to the first, or wholly to the second. When, however, cotton fibre and cotton seed are provided for two distinct and isolated markets by one and the same process, a given addition to investment does necessarily add something to the output available for each of the two markets. In the latter case it is easily seen that simple competition will, in general, lead to divergent prices. In the former case, however, it will not do this. For, if there are a number of competing sellers supplying transportation, or anything else, to several markets with separate demand schedules, and if the price in one of these markets is higher than in another, it is necessarily to the interest of each individual seller to transfer his offer of service from the lower-priced market to the higher-priced market; and this process must tend ultimately to bring the prices in the different markets to a uniform level. This result, when conditions of simple competition prevail, obviously holds good independently of the question whether or not the commodity or service under discussion is one in the production of which supplementary costs are large relatively to prime costs. Hence Professor Taussig's argument cannot be accepted. Joint supply, in the sense in which we are here using the term, does not prevail in the industry of railway transport in that fundamental and general way that he supposes it to do.*14


§ 5. At the same time it should be clearly recognised that, in the services rendered by railway companies, joint supply does play some part. This is conspicuously true as between transportation from A to B and transportation in the reverse direction from B to A. The organisation of a railway, like that of a steamship company, requires that vehicles running from A to B shall subsequently return from B to A. The addition of a million pounds to the expenditure on moving vehicles necessarily increases both the number of movements of vehicles from A to B and the number of movements from B to A. This implies true jointness. It follows that a competitive system of railway or shipping rates would not, in general, make the vehicle charges the same for journeys from A to B and from B to A, but the direction, for which the demand was higher, would be charged a higher rate. This is, of course, the reason why outward freights from England are generally low, relatively to inward freights, for commodities of similar value. Our imports being largely food and raw materials, and our exports, apart from coal, mainly finished manufactures, the former naturally make a greater demand for shipping accommodation. If it were not for our coal exports, the disparity would be much greater than it is. There is a similar relation in the transport of goods—though not of passengers—between eastward and westward travel in the United States; because "those who supply the world with food and raw materials dispose of much more tonnage than they purchase."*15 This element of jointness is, however, of comparatively small importance. Contrary to the general opinion of writers on railway economics, the services provided by railway companies are, in the main, not jointly supplied. Hence, the conclusion emerges that, subject to the reservations set out in § 2, simple competition would, in general, evolve a system of equal ton-mileage rates for all commodities, whatever their character, and whether they are to be consumed at B or be sent on from B for some further part of a "long haul."


§ 6. The meaning in concrete form of "the value of service principle," or monopoly plus discrimination of the third degree, is more complicated. It was shown in the last chapter that a monopolist adopting this principle will divide the total market served by him into a number of minor markets, by discriminating between which he may make his aggregate advantage as large as possible. It was shown, further, that the kind of division best calculated to promote this end is one under which the separate markets are arranged, so far as practical considerations allow, in such a way that each higher-priced market contains as few demands as possible with a demand price lower than the highest demand price contained in the next market. When once the minor markets have been separated, the determination of the rates to be charged in them presents no analytical difficulty, and can be expressed in a simple mathematical formula.*16 It is not, indeed, true, as is sometimes supposed, that the relative rates charged to different markets will depend, if this plan is adopted, simply upon the comparative elasticities (in respect of some unspecified amount of output) of the demands of these markets, nor yet that they will depend simply upon the comparative demand prices (also in respect of some unspecified amount of output) ruling in these markets. The true determinant is the whole body of conditions represented in the complete demand schedules of the different markets.*17 Still, though the determinant is, in general, complex, when once the constitution of the different markets has been settled, it is precise. The real difficulty lies in the choice, limited, as it is, by practical conditions, which a railway company has to make between various possible systems of minor markets. The search for the most advantageous system—from the company's point of view—has evolved, in practice, elaborate schemes of classification both for passenger traffic and for goods traffic. To show the application of the value of service principle in practice, some description of these schemes is required.


In passenger traffic railway companies find the value of service principle most nearly satisfied by a classification based, in the main, on the relative wealth of different groups of persons, the presumption being that most of the demands for the transport of richer people yield demand prices higher than most of the demands for the transport of poorer people. Since it is impracticable to make a classification founded directly on differences of wealth, various indices or badges, generally associated with varying degrees of wealth, are employed. Thus, in the United States, certain railways make specially low rates for immigrants—lower than those required from native Americans,—even though the latter are willing to travel in immigrant cars.*18 In certain colonies there is a discriminating rate according to the colour of the traveller; black men, who are supposed, in general, to be less well-to-do, being charged lower fares than white men.*19 Again, in England, and still more markedly in Belgium,*20 railway companies charge specially low rates for workmen's tickets. This procedure is exactly analogous to that of those London shopkeepers who charge to customers with "good addresses" prices different from those charged to others, and of the Cambridge boatmen who used to charge a collective customer of five persons 5s. for the hire of a boat for an afternoon, while to a single person they would let the same boat for one shilling. A classification based on indices of wealth alone is, however, somewhat crude, since people of the same wealth will desire a given journey with very different intensities on different occasions. In recognition of this fact railway companies have constructed a variety of cross-groupings, based on such incidents as the degree of comfort or of speed with which, or the hour at which, journeys are undertaken, or the presumed purpose which these journeys serve. Thus the fares for first-class accommodation, or for conveyance by certain express trains, are made to exceed those for inferior accommodation or lower speed by more than the difference in the cost of providing these different sorts of service;*21 and specially low fares are sometimes charged for journeys made in the early morning.*22 In like manner, attempts are made to separate holiday journeys, of presumed low demand, from necessary business journeys, by the supply, on special terms, of tourist, week-end and excursion tickets.


In goods traffic railway companies find the value of service principle most nearly satisfied by a classification based, in the main, upon the relative value of the different commodities claiming transport, the presumption being that most of the demands for the transport of a more valuable group of goods yield demand prices higher than most of the demands for the transport of a less valuable group. The reason for this presumption is as follows. The demand price for the transport of any nth unit of any commodity from A to B is measured by the excess of the price of that commodity in B over its price in A, which would prevail if the said nth unit were not transported. But, on any law of distribution, the probable difference between the prices of any article in A and B respectively, which would arise if these two places were not connected by the assigned act of transport, is greater, the greater is the absolute price that would prevail in either of them; just as the probable difference in the heights of poplars in A and B is greater than the probable difference in the heights of cabbages. There is no reason to expect that the percentage difference will be greater for valuable than for cheap commodities, but there is reason to expect that the absolute difference will be greater. A study of the details of the classification adopted for British railways under the Railway Rates and Charges Act shows that, in the main, the value of the commodities concerned was taken as a basis. Broadly speaking, the lower the position of any class in the list, the cheaper are the goods that it contains.*23 In like manner, several of the decisions of the United States Railway Commissioners have been founded on the proposition that less expensive articles ought not to be put in a higher class than more expensive articles—chair materials than finished chairs, raisins than dried fruits, and so on.*24


Sometimes it is practically inconvenient for a company or a regulating authority to group goods directly in accordance with their value. When this is so, a like result can be obtained indirectly by grouping them according to indices whose differences are likely to correspond to differences of value. Thus, since the valuable qualities of any commodity are generally packed better than the cheap qualities, rates are sometimes made to vary with the elaboration of the packing employed. For example, in France, where good wines are generally packed "en barriques de 220 à 230 litres" and common wines "en demi-muids de 650 à 700 litres ou en wagons-réservoirs,"*25 wines in "barriques" are charged on a higher scale.


It must be added that, as with passenger service, so also with goods service, a classification based exclusively on the value of the commodities transported is necessarily somewhat crude. In consequence of this, cross-groupings based upon other incidents have also been employed. Thus, within each group of commodities of given value transported from A to B, a subdivision may be made between those which B can easily make for itself, or obtain elsewhere than from A, and those which it cannot so make or obtain; and a higher rate may be charged to the latter group. Again, within a homogeneous group made up of units of the same commodity, sub-groups are constructed. For example, vegetables imported from Germany to England during the weeks before the English crop is ready used to be charged more than vegetables imported from Germany to England after this crop had appeared; and the same thing is true of vegetables sent from the south to the north of France.*26 Sometimes, again, an attempt is made to charge different rates for the transport of the same thing according to the use to which it is to be put—bricks for building, paving bricks and fire bricks being put in different classes. It should be observed, however, that the United States Interstate Commerce Commission has declined to recognise the validity of a classification on this basis.*27 More important is the subdivision according to ultimate place of destination. Thus commodities sent from A to B, to be consumed at B, are placed in a different group, and charged, for that act of transport, a different rate, from commodities sent from A to B to be forwarded from B to C. The reason is that different parts of the world do not differ in nature in proportion as they differ in distance. There is not much ground for expecting a priori that the cost of producing a given commodity in B will differ from the cost in A to a greater extent if A is 500, than if it is 100, miles away. Consequently the demand for any rth mile's worth of carriage is probably less in long transports of goods than in short transports. This consideration applies with especial force to articles of food and raw material, which are physically adapted to growth over a wide range of temperature and climate. But it has some relation to all sorts of goods and is, no doubt, partly responsible for the systems of tapering rates for goods,—but not for passengers,—that prevail in England, France and Germany.*28 The case for discriminating rates is, however, much stronger, when A is connected with C by direct water transport, as well as by a railway from A to B plus either more railway or water from B to C. In these circumstances the demand price of many units of transportation from A to B, of any commodity to be consumed at B, is likely to be much higher than the demand price of any unit of transportation from A to B, of the same commodity to be carried on from B to C. Grouping in accordance with this fact is responsible for the occurrence of rates from Cheshire to London, for goods imported through Liverpool, much below the rates for corresponding goods originating in Cheshire. On the same principle, "special rates have been granted by the Prussian State Railways for the conveyance of grain traffic from Russia to oversea countries (Sweden, Norway, England, etc.), and the rate per ton per kilometre from the frontier to the German harbours, Königsberg, Danzig, etc., is lower than the charge for German grain between the same points.... It was pointed out that this specially low rate was granted with the object of securing the traffic to the Prussian railways, as it need not necessarily pass over the Prussian lines, but could go via Riga, Reval and Libau, and would have done so without this reduction in the rates."*29


§ 7. We are now in a position to compare the principle of cost of service and the principle of value of service from the point of view of the national dividend. It is well known that, in common opinion, the determination of railway rates by the value of service principle, or, in the alternative phrase, by what the traffic will bear, is unquestionably superior to its rival. The popular view, however, as I understand it, rests, in the main, upon two confusions. The first of these starts from the assumption that the transport of copper and the transport of coal, and the transport from A to B when further transport respectively is, and is not, required, are joint products. This assumption was shown to be unwarranted in § 4. It proceeds by means of the further assumption that to charge for joint products rates adapted to comparative marginal demands is to charge in accordance with the value of service principle. This assumption is no less unwarranted than the other. A moment's reflection shows that to charge for joint products in this way would be to follow the guidance of the cost of service principle, or—what is another name for the same thing—of simple competition. The second confusion is an ignoratio elenchi. Arguments are advanced to prove that the value of service principle, in the proper sense of discriminating monopoly, is superior to simple monopoly. Thus it is pointed out that, when the conditions are such that the rate most advantageous to himself which the monopolist can make, subject to the condition that equal rates shall be charged for the transport of copper and of coal, will cause him to stop transporting coal altogether while continuing to transport copper at a high rate, the national dividend could be increased by permission to discriminate between the two rates.*30 Such an argument, it is obvious, though valid in its own field, is wholly irrelevant to the question whether discriminating monopoly of the third degree is superior, not to simple monopoly, but to simple competition. When these confusions are swept away, the issue between the value of service principle and the cost of service principle in railway rates is seen to constitute a special case of the general issue, set out in the preceding chapter, between the said discriminating monopoly of the third degree and the said simple competition.


§ 8. The result of the discussion on that issue was that simple competition is, in general, the more advantageous. There emerged, however, one set of conditions, in which the advantage lies with its rival. These conditions are that, while no uniform price can be found which will cover the expenses of producing any quantity of output, a system of discriminating prices is practicable, which will make some output profitable. They have been illustrated by Principal Hadley, with special reference to discriminations between the charges for carriage from A to B that are made for goods going to B for consumption at B and for goods going to B for further transport to C. "Suppose," he writes, "it is a question whether a road can be built through a country district, lying between two large cities, which have the benefit of water communication, while the intervening district has not." To meet water competition, the charge for carriage from one extreme A to an intermediate point B must be low for goods to be carried forward to the other extreme C; so low that, if it were applied to all carriage from A to B, it would make the working of this part of the road unprofitable. But the demand for carriage from A to B, in respect of goods to be retained at B, is so small that this alone cannot support the road, no matter how low or how high the rates are made. "In other words, in order to live at all, the road must secure two different things—the high rates for its local traffic, and the large traffic of the through points, which can only be attracted by low rates. If they are to have the road, they must have discrimination."*31 An exactly analogous argument can be constructed in favour of discriminations in the tonmile rates that are charged on different commodities, when the conditions are such that, apart from discrimination, there would be no quantity of transportation units, the proceeds of whose sale would cover their expenses of production. On the same principle, it may be argued that in some circumstances a roundabout line should be permitted to charge abnormally low rates between its terminal points, with the effect of preventing the development of a direct line between these points; for conditions may be such that, apart from this arrangement, no roundabout line could be profitably built, and so centres which it might serve would suffer. I have no quarrel with the proposition that these conditions may occur in practice. Principal Hadley and his followers, however, not content with demonstrating that they are possible, implicitly add, without argument, that they are typical of the whole railway world, and suppose themselves, therefore, to have proved that the value of service principle ought to be followed in the determination of all railway rates. Such an unargued inference is, plainly, illegitimate. A careful inquiry is necessary concerning the range over which conditions of a sort to justify the value of service principle are likely to extend in practice.


§ 9. From an analytical point of view, the situation is simple. As explained in the preceding chapter, in order that monopoly plus discrimination of the first degree may create an output where simple competition fails to do so—I take the simplest case, in which the demand in one market is independent of the price in the other—certain relations, which were there described, between the general conditions of demand and of supply must exist. The conditions enabling monopoly plus discrimination of the third degree to lead to this result are less precise. Circumstances, in which discrimination of the first degree would only just succeed, will not, in general, enable discrimination of the third degree to succeed. We may conclude, roughly, however, that discrimination of the third degree will have a good chance of succeeding—a chance that is better, the more numerous are the markets between which discrimination is made, and the more satisfactory, from the monopolist's standpoint, is their constitution—when the conditions are such that discrimination of the first degree would succeed with a wide margin. Our problem is to determine how far this state of things is likely to occur in practice.


First: it has been shown that the likelihood of this is greatest in forms of investment in which the law of decreasing supply price acts strongly.*32 Among railways there is ground for believing that, at all events until considerable development has been reached, this condition is generally satisfied. The reason is that the fixed plant of a railway cannot, in practice, be so made as to be capable of effecting less than a certain considerable minimum of transportation. The aggregate costs of arranging for rail transport for one ounce per week are very nearly as great as those of arranging for the transport of many thousand tons. For the same heavy expenditure must be undertaken for surveying and legal charges, bridging valleys and torrents, tunnelling through rock, erecting stations and platforms, and so on. This implies that the law decreasing supply price acts strongly till a large investment has been made, and afterwards less strongly. So far, therefore, conditions in which discriminating monopoly would prove superior to simple competition are more likely to occur in railway service than in some other industries.


Secondly, it has been shown that the likelihood of discriminating monopoly yielding some output when simple competition yields none is greatest in forms of investment where the demand for the product is elastic.*33 In railway service, when once rates have been brought down to a moderate level, there is reason to believe that a small reduction of rates would call out a large increase of demand, not only from commodities that might otherwise have been transported by some other agency, but also from commodities that otherwise would not have been transported at all. In other words, there is reason to believe that the demand is, in general, elastic. Here, too, then, it may be said that railway service is more apt to yield conditions suitable for discriminating monopoly than some other industries.


Granted, however, both that the law of decreasing supply price acts strongly until considerable density of traffic has been attained, and that the demand for the service of railway transport is elastic, these conditions alone are by no means sufficient to ensure that discriminating monopoly would evolve some output, while simple competition would fail to do this. It is necessary, further, that the actual levels of demand price and supply price for a small quantity of service—more generally, the demand schedule and the supply schedule as a whole—shall be related in a particular way. Clearly, if the demand price for a small quantity is greater than the supply price, some output will be evolved under simple competition, and, therefore, the conditions we have in view do not arise. Clearly, again, if the demand price for a small quantity is very much less than the supply price, it is unlikely that any output will be evolved either under simple competition or under discriminating monopoly, and, therefore, again these conditions do not arise. In order that they may arise, a sort of intermediate position must, it would seem, be established. Thus, on the one hand, the district affected must not be too busy and thickly populated; on the other hand, it must not be too little busy and sparsely populated. There is a certain intermediate range of activity and population that is needed. This range, compared with the total range of possibility, is naturally not extensive. Hence the probability that the conditions necessary to make discriminating monopoly more advantageous to the national dividend than simple competition will be present in any railway selected at random at any time seems a priori to be very small. There are, indeed, many dicta of practical experts which suggest that they have in fact a wide range. But, as Edgeworth, who lays stress upon this point, recognises, "the testimony of high authorities would, no doubt, carry even greater weight if it should be repeated with a full recognition of the a priori improbability" to which it is opposed.*34


§ 10. It must be observed, however, that, as population and aggregate wealth in any country expand, the demand schedule for railway service, along any assigned route, gradually rises. Hence, though, at any moment selected at random, it is improbable that the conditions affecting any route, selected at random, are such that a railway rate system based on the value of service principle would be more advantageous to the dividend than one based on the "cost of service principle," it is not improbable that any route, selected at random, will pass through a period during which the conditions are of this kind. Such conditions tend to emerge when one point in the growth of wealth and population has been reached, and to disappear when another somewhat later point has been reached. If the cost of service principle ruled universally, and if no State bounties were given, certain lines would not be built till the arrival of the latter point—when there is hope of "building up" a demand by experience of supply, this point need not, of course, be such that the railway pays at the moment—despite the fact that they could have been built, with advantage to the community, on the arrival of the earlier point. The inference is that discrimination, or the value of service principle, should be adopted when any route is in the intermediate stage between these two stages, and that this principle should give place to simple competition, or the cost of service principle, as soon as population has grown and demand has risen sufficiently to lift it out of that stage.*35 The period proper to the value of service principle would seem, in most ordinary lines, to be a comparatively brief one.*36


§ 11. Even this limited application of the principle is only warranted on the assumption that there is no third way between the pure value of service principle and the pure cost of service principle. In fact, however, there is a third way. The cost of service principle may be maintained and the State may give a bounty. Plainly, with the help of a bounty exactly the same effect in speeding up the building of a railroad could be accomplished under the cost of service principle as would be accomplished under the value of service principle without a bounty. The community as a whole would be providing out of taxes the necessary profit for the railway, which, on the other plan, would come from the charges made to the people who buy the most highly charged freight service. Since the building of the railway is in the general interest, it would seem, on the whole, to be fairer that the taxpayers, and not a special class of traders—or rather, in the end, the consumers of these traders' products—should provide these funds. In view of the practical awkwardness of changing from a discriminating to a non-discriminating system of rates when the intermediate stage described in the preceding paragraph is passed, the plan of giving a bounty for a time and withdrawing it when it is no longer needed is also superior from the side of administrative convenience. If, on account of the indirect advantages of cheap railway transport in facilitating the division of labour between different parts of the country, making possible the development of large - scale localised industries, and, through the improved communication of markets, lessening local price fluctuations—all changes which, in one way or another, benefit production—it is held that the railway industry is one to which a general bounty should be accorded permanently, it is obvious that a second instrument for doing what bounties can do by themselves is not required and that no place is left for the value of service principle.


§ 12. Of the relative advantages of the cost of service principle, or prices proper to simple competition, and the value of service principle, or prices proper to discriminating monopoly, this is all that need be said. There is, however, yet another possible arrangement. Control might be exercised in such a way that a railway company should only secure competitive or normal profits on the whole, but these profits might be obtained by a combination of some charges below cost with others above cost, just as a doctor's profits are obtained by a combination of low prices to poor patients and high prices to rich patients. In one field of railway service there is a plain prima facie case for an arrangement of this kind. Great social advantage can be derived from the provision of cheap workmen's tickets: for in favourable circumstances this makes it possible for workpeople to live in the country, though working in towns, and thus to bring up their children in healthy surroundings.*37 Such provision can be ensured if railway companies (whose earnings are supposed to be kept down by regulation to a normal competitive level) are compelled to make it, and are allowed to recoup themselves by "monopolistic" charges upon other traffic. Plainly, however, exactly the same result can be achieved if the reimbursement required for the railway companies is provided out of the national revenue. There seems to be no good reason for throwing this burden upon persons who make use of the service of railways rather than upon the general body of taxpayers. For, though it may well be that railway service is a suitable object through which to impose a tax on these persons, we can hardly suppose that the extent to which they ought to be taxed through this object exactly corresponds to the amount of funds required for the bounty to poor purchasers of railway service. There is still less reason for allowing discriminated rates, determined, not in the purchasers' interest, but at the choice of the railway companies themselves. Hence this system of discriminated charges coupled with regulated profits cannot, on the whole, be justified. We are thus left with the cost of service principle, modified at need, sometimes by general bounties, sometimes by bounties on particular services deliberately sold for less than cost price.


§ 13. One last point remains. To apply this cost of service principle accurately involves, as was shown in § 2, a number of delicate adjustments. For the principle leads, not to a single price for everybody, but to prices that vary with the incidental costs attaching to each service and with the time at which it is furnished in relation to the peak of the load. To provide for these adjustments in practice is often a very difficult matter involving costly technique and account-keeping. It is, therefore, always a question how near to the ideal it is desirable to approach; at what point the advantage of getting closer is outweighed by the complications, inconveniences and expense involved in doing so. In the early days of the telephone service the desire for simplicity and ease in rate making led to a system in which flat rates were charged for the use of instruments, without any reference whatever to the number of calls made; and water rates are even yet often based, not on any measurement of the supply that is actually taken, but on an estimate of what is likely to be taken, derived from the rental of the houses served. For electricity, while ingenious meters have been devised, which not only record the supply taken, but also weight more heavily the part of it which is taken in the peak hours, nevertheless the high cost of any sort of meter still causes the service of small houses to be charged in many districts on a flat unmetered rate. In like manner, though for the transport of parcels it has been thought worth while to take account, in the charges made, of those differences in the cost of service which arise out of differences of weight, for the transport of letters this is not done: and for neither parcels nor letters are charges adjusted to the distance (within the British Empire) over which they have to be conveyed. On similar grounds of simplicity and cheapness, a railway administration, which had decided to base its rating system upon the cost of service principle, must, nevertheless, ignore, within considerable limits, differences in the weight of luggage which different passengers carry. This class of consideration shows that there is not necessarily any departure from the spirit of the cost of service principle when a railway administration elects to utilise a system of zone tariffs. A street railway system obviously must do this; for the mere fact that there is no coin smaller than a farthing makes it physically impossible to fix different fares for every different distance of journey. So long as the zones are narrow, zone tariffs on ordinary railways have an equally good defence. If, however, the zones are made broad, the cost of service principle is deliberately violated. A system under which the rates are the same for all places in broad zones involves substantial differentiation in favour of firms situated far from their markets, as against firms situated nearer to them. In effect, it confers upon them a kind of bounty at the expense of their rivals. It can, indeed, be shown that differentiation in favour of one source of supply as against another source may, in certain circumstances and if introduced in a certain manner, be advantageous to the national dividend. The sort of differentiation that results from the zone system is, however, random differentiation, not specially designed to favour a carefully chosen list of selected firms. It is, thus, on the average, like differentiation in favour of one set against another set of similar firms. This sort of differentiation causes the production (including transport) of some part of the commodity concerned to be carried out at greater real cost than is necessary; for the marginal real costs of producing anything in the distant source and bringing it to the market must necessarily be greater than the marginal real costs of producing it in the nearer source and bringing it to the market.*38 It is possible to maintain that the direct loss resulting from this may be balanced by the effect of the zone system in scattering the producing firms belonging to an industry, and so making combination, with the opportunity which this gives for anti-social monopolistic action, more difficult.*39 But this argument does not appear to have great force. It is not, in itself, desirable to check the formation of large productive units, since such units introduce economies. As will be argued presently, it would seem a better policy to attack the evil consequences of monopolistic action, which combination threatens, directly, rather than indirectly by attempts to discourage unification.*40

Notes for this chapter

It is interesting to note that the problem of how retail shops should distribute their charges for the act of retailing over the various commodities that they sell is very closely analogous to the problem of railway charges. Among retail shops, however, there is the additional complication that a retailer is sometimes able to obtain a general advertisement for his shop by selling particular well-known goods practically free of retailer's profit.
Cf. ante, Part II. Chapter III. § 4, footnote.
It is, indeed, sometimes maintained that this will only happen it "simple competition" is defined to include complete transferability of the things that are sold among customers, and it is pointed out that competition, apart from this condition, has proved compatible with discriminating charges for services sold to different sets of persons by shipping companies and by retailers; different sorts of cargoes are carried at different rates, and the absolute charge for retailing work is different in regard to different articles. (Cf. G. P. Watkins, "The Theory of Differential Rates," Quarterly Journal of Economics, 1916, pp. 693-5). Reflection, however, shows that, when competition really prevails, seller A must always endeavour to undersell seller B by offering to serve B's better-paying customers at a rate slightly less than B is charging, and that this process must eventually level all rates. The explanation of the discriminations cited above is, not the absence of complete transferability, but the fact that custom and tacit understandings introduce an element of monopolistic action.
Cf. Williams, Economics of Railway Transport, p. 212
Acworth, Elements of Railway Economics, p. 120.
Cf. Haines, Restrictive Railway Legislation, p. 148.
Quarterly Journal of Economics, November 1910, p. 47.
Acworth, Elements of Railway Economics, footnote, pp. 122-3.
Cf. Marriott, The Fixing of Rates and Fares, p. 21.
Principles of Economics, vol. i. p. 221. Cf. also vol. ii. p. 369.
Taussig, "Theory of Railway Rates," in Ripley's Railway Problems, pp. 128-9.
Principles of Economics, vol. i. p. 221.
Quarterly Journal of Economics, 1913, p. 381.
On the general subject of the relation of the concept of joint costs to railway service, cf. a discussion between Professor Taussig and the present writer in the Quarterly Journal of Economics for May and August 1913. Two further points should be added.

First, it is sometimes maintained that the concept of joint costs, in the sense assigned to it in the text, is applicable where only one sort of commodity is produced, provided that the units of process, by which the commodity is made, are large relatively to the units of commodity. When, for instance, the marginal unit of process produces 100 units of product, it may be argued that 100 units must yield a price sufficient to remunerate one unit of process, but that it is immaterial to the suppliers by what combination of individual prices the aggregate price of 100 units is made up. This suggestion, however, when stated in the above general form, ignores the fact that 100 units of product can be removed, not only by abstracting one unit from the fruit of each of a hundred units of process, but also by abolishing one unit of process, and that, under free competition, if any units of product were refused a price as high as 1/100th part of the supply price of a unit of process, this latter method of abstraction would naturally be employed. This shows that physically identical products, yielded by the same process at the same time, are not, in general, joint products in any sense, even though the marginal unit of the process of production is large. But this reply is not relevant, and the concept of joint supply cannot be ruled out, when the number of units of process that are actually being provided is the minimum number that it is practicable to provide so long as any are provided. In these circumstances there is nothing incompatible with the analysis of the text in regarding the resultant units of product as jointly supplied. The costs of constructing through any region the least expensive railway that it is possible to construct at all are joint costs of all the various items of service rendered by the railway. It is possible by following this line of analysis to reach the results obtained by the different line of analysis to be followed in § 8. In the special problem of the least expensive railway that it is possible to construct at all, the two lines are equally admissible. (Cf. Quarterly Journal of Economics, August 1913, p. 688.) Since, however, analysis by way of joint supply is only applicable in a single and peculiar type of problem, whereas analysis by way of discriminating monopoly, to be adopted in the text, is applicable to all problems, the latter method should be given preference.

Secondly, the concept of joint supply can, if desired, be applied to the same services rendered at different times by the same fixed plant. Thus the services of railways for night travelling and day travelling may be called joint, and different rates advocated on that ground. This consideration is especially important with electricity rates. It justifies differentiation of a form designed to carry off nearly equal supplies throughout the day or year. The same result can be obtained on a different route if we regard the services supplied at the two times as being the same service but subject to varying demands. The point of distinction, as against a railway carrying different things at the same time, is that the railway can be adjusted to carry any quantity of things, so that to carry A does not involve power to carry B; but a railway fitted to carry A in the day cannot be provided except in a form that gives power to carry A also at night. The distinction would, of course, lose most of its significance if the capital equipment were expected to maintain its full value over a defined period of use and not over a defined period of time; for then less night use now would make possible more day use later on. But in fact plant largely wears out through time independently of use; e.g. rails and ties deteriorate with weather (cf. Watkins, Electrical Rates, p. 203), and also tend to become obsolete.

Cf. Johnson, American Railway Transportation, p. 138. It should be noticed that, whereas there is little jointness as between first and third class passenger service on railways, there is probably a considerable element of such jointness as between first and third class service on ships; because the structure of a ship necessarily involves the provision at the same time of more and of less comfortable parts of the vessel.
Thus, let φ1(x1), (φ2)x2... represent the demand prices in n separate markets, and f(x) the supply price.

The prices proper to the separate markets under monopoly plus discrimination of the third degree are given by the values of φ1(x1), φ2(x2)... that satisfy n equations of the form:

These n equations are sufficient to determine the n unknowns.

Where the curves representing the demand schedules are straight lines, this complex determinant dissolves into a simple one, namely, the comparative demand prices of those units which are most keenly demanded in each of the several markets. Under these conditions, if conditions of constant supply price prevail, the monopoly price proper to each market can be shown to be equal to one half of the difference between the supply price and the demand price of the unit that is most keenly demanded there.
Quarterly Journal of Economics, November 1910, p. 38.
Cf. Colson, Cours d' économie politique, vol. vi. p. 230.
Cf. Rowntree, Land and Labour, p. 289.
M. Colson suggests that a plan, under which all trains should take third class passengers, the fast trains charging a supplement, would be superior to the present Continental plan, under which a passenger, who wishes to travel fast, has to pay the whole difference between third and second class fare.
Cf. Mahaim, Les Abonnements d'ouvriers, p. 12.
Cf. Marriott, The Fixing of Rates and Fares, p. 27 et seq., for these lists.
Cf. Quarterly Journal of Economics, November 1910, pp. 13, 15 and 29.
Colson, Cours d' économic politique, vol. vi. p. 227.
Cf. ibid, p. 227.
Ripley, Railroads, Rates and Regulation, p. 318.
Cf. Marriott, The Fixing of Rates and Fares, p. 43.
Report of the Railway Conference, 1909, p. 99.
Cf. ante, Part II. Chapter XVII. § 13.
Railroad Transportation, p. 115. It may conceivably be objected to the construction of a railway in these circumstances that it will injure the rival industry of water carriage to an extent that will offset the advantages to which it leads. This objection can, however, be shown to be inapplicable, so long as the railway as a whole pays its way. Cf. ante, Part II. Chapter IX. § 11.
Cf. ante, Part II. Chapter XVII. § 9, and Appendix III. § 26.
Economic Journal, 1913, p. 223.
Mr. Bickerdike (Economic Journal, March 1911, p. 148) and Mr. Clark (Bulletin of American Economic Association, September 1911, p. 479) argue, in effect, that the transition from the one system to the other should occur, not when rising demand lifts the railway in question out of the stage just described, but when, if ever, it rises so high as to impinge on that point of the supply curve at which a negative slope passes into a positive one. There is not, in my opinion, any adequate ground for this view.
It is possible to maintain, on lines similar to the above, that, after a railway has been built, and has reached the stage of profitable working on the cost of service principle, another stage will presently arrive, at which a return to the value of service principle would enable a second track to be laid down with advantage to the community, though, under a rate system based on the cost of service principle, such an extension would not as yet be profitable to the company. This argument justifies the establishment of a system of discriminating rates, to be applied to traffic carried on the new track only; and a modification of it justifies the establishment of such a system, to be applied exclusively to traffic carried in any additional train or truck which, apart from discrimination, it is just not worth while to run. In practice, however, it is impossible to apply the value of service principle in this limited way. If it is introduced for the traffic proper to the second track or the extra truck, it must, in real life, be introduced for all the traffic carried on the line. The argument set out above does not justify this.
In Belgium the system of cheap workmen's tickets, which has been carried to great perfection, seems to act in this way. (Cf. Rowntree, Land and Labour, p. 108.) Dr. Mahaim offers some confirmation of the view that it acts so in the fact that Belgium is a land of "large towns" rather than of "great cities," a much larger proportion of the population living in communes of from 5000 to 20,000 inhabitants in that country than in France or Germany (Les Abonnements d'ouvriers, p. 149). At the same time, Dr. Mahaim admits that the cheap tickets have also an adverse effect. "On commence par aller á la ville on á l'usine en revenant tous les soirs ou tous les samedis chez soi; puis on s'habitue peu á peu an nouvean milieu, et l'on finit par s'y implanter" (ibid. p. 143). In fact the cheap tickets "apprennent le chemin de l'èmigration."
Cf. Quarterly Journal of Economics, February 1911, pp. 292-3, 297-8 and 300: also Departmental Committee on Railway Rates, p. 10.
Cf. Quarterly Journal of Economics, May 1911, pp. 493-5.
Cf. post, Part II. Chapter XXI. § 2.

Part II, Chapter XIX

End of Notes

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