The Economics of Welfare

Pigou, Arthur C.
(1877-1959)
CEE
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First Pub. Date
1920
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London: Macmillan and Co.
Pub. Date
1932
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4th edition.
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Part II, Chapter XVII
DISCRIMINATING MONOPOLY

II.XVII.1

§ 1. UP to this point we have supposed that monopolisation, when it occurs, will be of the simple form which does not involve discrimination of prices as between different customers. We have now to observe that this variety of monopolization is not the only possible sort. Discriminating power will sometimes exist alongside of monopolistic power, and, when it does, the results are affected. It is, therefore, important to determine the circumstances in which, and the degree to which, monopolists are able to exercise, and find advantage in exercising, this power.

II.XVII.2

§ 2. The conditions are most favourable to discrimination, that is to say, discrimination will yield most advantage to the monopolist, when the demand price for any unit of a commodity is independent of the price of sale of every other unit. This implies that it is impossible for any one unit to take the place of any other unit, and this, in turn, implies two things. The first of these is that no unit of the commodity sold in one market can be transferred to another market. The second is that no unit of demand, proper to one market, can be transferred to another market. The former sort of transference needs no description, but the latter is somewhat subtle. It would occur if the promulgation of different rates for transporting coal originating in A and coal originating in B enabled the more favoured district to increase its production of coal, and, therefore, its demand for carriage, at the expense of the less favoured district. In order that the conditions most favourable to discrimination may prevail, this sort of transferability, as well as the other, must be excluded. Under the monopolistic arrangements practicable in real life the above kinds of transferability are absent or present in varying degrees. I propose to set out a series of examples under each of the heads just distinguished.

II.XVII.3

§ 3. Units of commodity are entirely non-transferable when the commodity in question consists of services applied directly by the sellers to the persons of their customers, such as the services of medical men, barristers, teachers, dentists, hotelkeepers and so forth. A medical man's offer to charge any one set of persons less than any other set cannot lead to the one set becoming middlemen for the services which the other set desire. Services applied directly by the seller to commodities handed to them for treatment, such as the service of transporting different articles, are also entirely non-transferable. A railway's offer to charge one price for a ton-mile of transport service to copper merchants and a lower price to coal merchants cannot lead to any middlemen device, because it is physically impossible to convert copper into coal for the purpose of transport and afterwards to reconvert it. A slightly, but only slightly, lower degree of non-transferability exists among services that are normally rendered in physical connection with the private dwellings of purchasers. Gas and water supplied to private houses are instances in point. Here transference is not entirely excluded, because it is possible, at sufficient cost of money and trouble, to detach the commodities from the distributing plant along which they are brought and to carry them elsewhere. Lesser degrees of non-transferability exist among commodities whose transference is obstructed merely by high costs of transportation or by tariff charges. The degree of non-transferability in these circumstances may, evidently, be large or small, according as the distance, or the rate of customs duty, that separates two markets between which discrimination is attempted is large or small. In like manner, various degrees of non-transferability can be brought about artificially by enforcing upon purchasers contracts that penalize re-sales. For example, in the Ruhr coal district, the (pre-war) agreement made by the syndicate with industrial purchasers provided "that re-sale to railways, gas works, brick works or lime-kilns, or any reshipment from the original point of destination, shall be penalized by an addition of 3 marks per ton to the selling price."*72 If no agreement of this kind, no cost of carriage, and no tariff exist, complete transferability will prevail.

II.XVII.4

§ 4. Units of demand are almost completely non-transferable from one market to another, when the commodity concerned is something ready for final consumption, and when the markets, between which discrimination is to be made, are distinguished according to the wealth of the purchasers. It is clear, for instance, that the willingness of doctors to charge less to poor people than to rich people does not lead to any rich people, for the sake of cheap doctoring, becoming poor. In like manner, the provision of the service of transport at different rates to coal merchants and to copper merchants does not lead to any copper merchants, for the sake of the cheap transportation, becoming coal merchants. No doubt, in both these examples some slight transference may be achieved through successful fraud, such as a pretence on the part of rich people that they belong to the poorer group, and the smuggling of copper in the guise of coal; but this kind of thing is of no practical importance. It is interesting to note that sellers often attempt artificially to create the above type of non-transferability by attaching to different grades of their product trade marks, special brands, special types of packing and so on—all incidents designed to prevent possible purchasers of the grades that are highly priced relatively to the cost of production from becoming, instead, purchasers of the grades that are sold at a lower rate of profit.*73 A smaller degree of non-transferability exists between the markets for hotel accommodation in the season and out of the season; for heavy discrimination might cause a considerable number of people to change the time of their holiday. A still smaller degree of non-transferability exists between the markets for railway transport from A to B, which are provided respectively by traders in A wishing to send a given commodity direct to B, and by traders in C wishing to send this commodity to B through A. For a large difference in the rates charged would cause production, that would normally occur at the less favoured, to take place instead at the more favoured, point. Perfect transferability exists when the markets are distinguished by some badge, the attachment of which involves no cost, as, for example, if railways charged one fare to passengers carrying pencils and another fare to passengers without pencils. The immediate effect of this discrimination would be to transfer all demands from the less to the more favoured market, and discrimination would yield no advantage to the monopolist.

II.XVII.5

§ 5. When a degree of non-transferability, of commodity units on the one hand or of demand units on the other hand, sufficient to make discrimination profitable, is present, the relation between the monopolistic seller and each buyer is, strictly, one of bilateral monopoly. The terms of the contract that will emerge between them is, therefore, theoretically indeterminate and subject to the play of that "bargaining" whose social effects were analysed at the end of Chapter IX. When a railway company is arranging terms with a few large shippers, the indeterminate element may have considerable importance. Usually, however, where discrimination is of practical interest, the opposed parties are, not a single large seller and a few large buyers, but a single large seller and a great number of relatively small buyers. The loss of an individual customer's purchase means so much less to the monopolistic seller than to any one of the many monopolistic purchasers that, apart from combination among purchasers, all of them will almost certainly accept the monopolistic seller's price. They will recognize that it is useless to stand out in the hope of bluffing a concession, and will buy what is offered, so long as the terms demanded from them leave to them any consumers' surplus. In what follows I assume that the customers act in this way. So assuming, we may distinguish three degrees of discriminating power, which a monopolist may conceivably wield. A first degree would involve the charge of a different price against all the different units of commodity, in such wise that the price exacted for each was equal to the demand price for it, and no consumers' surplus was left to the buyers. A second degree would obtain if a monopolist were able to make n separate prices, in such wise that all units with a demand price greater than x were sold at a price x, all with a demand price less than x and greater than y at a price y, and so on. A third degree would obtain if the monopolist were able to distinguish among his customers n different groups, separated from one another more or less by some practicable mark, and could charge a separate monopoly price to the members of each group. This degree, it will be noticed, differs fundamentally from either of the preceding degrees, in that it may involve the refusal to satisfy, in one market, demands represented by demand prices in excess of some of those which, in another market, are satisfied.

II.XVII.6

§ 6. These three degrees of discriminating power, though all theoretically possible, are not, from a practical point of view, of equal importance. On the contrary, in real life the third degree only is found. No doubt, we can imagine conditions in which discrimination even of the first degree could be achieved. If all consumers had exactly similar demand schedules,*74 it could be achieved by the simple device of refusing to sell in packets of less than the quantity which each consumer required per unit of time, and fixing the price per packet at such a rate as to make it worth the consumer's while, but only just worth his while, to purchase the packet. Thus, if every demander would give for a hundredth physical unit of commodity, when he already has ninety-nine units, the sum of one shilling, but would prefer to give 300 shillings for a hundred units rather than have no units at all, the monopolist may make his unit of sale one hundred physical units and charge for this unit of sale a price of 300 shillings. If there is no combination among the buyers, the number of units sold will then be the same as would have been sold at a price of one shilling per physical unit, and, in effect, the physical units satisfying demands of different keenness will have been sold at different prices. But this method of discrimination, whether in a complete or a partial form, is scarcely ever practicable, because the individual demand schedules, of which the market demand schedule is made up, are, as a rule, very far indeed from being similar. For this reason an analysis of the method is of academic interest only.*75 Apart from this method, discrimination of the first degree might still conceivably be established by detailed separate bargaining with every separate customer. But that method would involve enormous cost and trouble. Furthermore, since it implies separate bargains with individuals, it opens the way, not only to error, but also to the perversion of agents through bribery. These considerations are, in general, sufficient to make monopolists themselves unwilling to adopt the method; and, even if they were not thus unwilling, it would be hardly possible for the State, in view of the large opportunities for "unfair" competition which the method affords, to leave their hands free. "Whatever financial advantage there may be in charging against each act of transport a rate adapted to its individual circumstances, the arbitrary nature of a system of rates arranged on this plan implies so much uncertainty and lends itself to such serious abuses, that we are compelled to condemn it."*76 Thus a powerful influence is always at work persuading or compelling monopolists to act on general rules, with published tariffs, guarded, as effectively as may be, against the undermining influence of unpublished rebates. This means that they cannot, except in extraordinary circumstances, introduce either the first or the second degree of discrimination, and that the third degree is of chief practical importance.

II.XVII.7

§ 7. Monopoly plus discrimination of the third degree is not a determinate conception. It is theoretically possible to divide any market in an indefinitely large number of different ways, of which some would be more, and others less, advantageous to the monopolist. If the monopolist had an absolutely free hand in the matter, the division he would choose would be such that the lowest demand price in sub-market A exceeded the highest demand price in sub-market B, and so on throughout. If the aggregate demand of the markets collectively had an elasticity greater than unity throughout, the resulting system would be identical with that proper to the second degree of discrimination, for the lowest demand price in each group would also be the price calculated to yield maximum monopoly revenue from that group. If the aggregate demand had not an elasticity greater than unity throughout, the maximising price in some groups would be greater than the lowest demand price in those groups, and the system would, therefore, be different from the above. In any event the separation of markets, in such wise that the lowest demand price in the first exceeds the highest demand price in the second, and so on, would obviously be better, from the monopolist's point of view, than any other kind of separation. But in practice the monopolist's freedom of action is limited by the need, already referred to, of acting on general rules. This consideration makes it necessary that he shall choose, for his sub-markets, groups that are distinguishable from one another by some readily recognisable mark. Moreover, since a hostile public opinion might lead to legislative intervention, his choice must not be such as to outrage the popular sense of justice. Thus, he will not distinguish and bring together entirely new groups, but will make use of distinctions already given in nature. Nor is this all. For in some circumstances the condition of non-transferability holds good, not generally, but only as between certain markets, which are constituted independently of the monopolist's volition. Thus, the existence of an import tariff or of high transport charges on imports to all parts of his country's frontier—a condition easiest to realise when that country is an island—may make it possible for a seller to charge a lower price for his goods abroad than at home without the risk of inviting the return and resale of his exports. Clearly, therefore, a monopolist cannot hope to find a series of sub-markets that conforms to his ideal altogether, but he may find one in which only a comparatively small number of the demand prices embraced in the first sub-market are lower than the highest demand price of the second sub-market, and so on throughout all the sub-markets.

II.XVII.8

§ 8. I now pass to an analysis of consequences, and, as in the preceding chapter, I shall begin with monopolized industries to which entry can be restricted. The analysis, to be complete, would need to take account of the fact that, in real life, the demand of one purchaser for any rth unit of a commodity is sometimes, in part, dependent upon the price at which this commodity is being sold to other purchasers.*77 When markets are interdependent in this way, the issue is complicated, but the broad results, though rendered less certain, are not, it would appear, substantially altered. Consequently in the following pages I shall assume that the quantity demanded in each sub-market depends only on the price ruling in that sub-market. This procedure enables resort to be had to the same general method that has been pursued hitherto.

II.XVII.9

§ 9. As already explained, practical interest centres upon monopoly plus discrimination of the third degree. But, before studying this, we may, with advantage, glance at the simpler problem presented by the two higher forms of discrimination. It is easily seen that, in industries in which the rates of change in supply price from the standpoint of the industry are identical with the rates of change from the standpoint of the community, under monopoly plus discrimination of the first degree, it will always pay the monopolist to make the ideal amount of investment and to produce the ideal output. This implies that, under conditions of constant supply price, monopoly plus discrimination of the first degree will make the national dividend the same as simple competition would have made it. Under conditions of decreasing and of increasing supply price it will always improve on the result of simple competition. The extent to which it improves on it will be measured by the extent to which the output proper to simple competition differs from the ideal output. This is evidently greater, the more elastic is the demand for the commodity produced by the industry and the more markedly the conditions of the industry depart in either direction from those of constant supply price. Finally, it should be observed that, when conditions of decreasing supply price prevail, monopoly plus discrimination of the first degree may increase the size of the national dividend in a more special way. It may bring about a considerable amount of socially desirable investment in an industry, in which, under a regime of simple competition, it would not have been to anybody's interest to make any investment at all. It is shown in Appendix III. that this result is most likely to be realised (1) if, other things being equal, supply price decreases sharply, in such wise that a small increase of output involves a large fall in supply price per unit, and (2) if, other things being equal, the demand for the commodity or service is elastic till fairly low price levels have been reached.*78

II.XVII.10

§ 10. In industries where the rates of change of supply price from the standpoint of the industry and of the community are not identical, matters are slightly more complicated. As was shown in Chapter XI. §§ 6-8, we are entitled to presume that the rate of change from the standpoint of the community will, in general, be a smaller negative or a larger positive quantity than the rate from the other standpoint. It can be inferred that the output proper to discriminating monopoly of the first degree will be less than the ideal output. In industries of decreasing supply price from the standpoint of the industry, it will be greater than the output proper to simple competition, and, therefore, nearer than that output to the ideal output. In industries of increasing supply price from the standpoint of the industry, it will be less than the output proper to simple competition. But the output proper to simple competition may in this case be greater than the ideal output. It is, therefore, possible that the output proper to discriminating monopoly of the first degree may be further than the output proper to simple competition from the ideal output. Since, however, as was observed in Chapter XVI. § 2, monopolistic action is chiefly to be expected in industries of decreasing supply price, this possibility is of small importance.

II.XVII.11

§ 11. It is readily seen that the effects of monopoly plus discrimination of the second degree approximate towards those of monopoly plus discrimination of the first degree, as the number of different prices, which it is possible for the monopolist to charge, increases; just as the area of a polygon inscribed in a circle approximates to the area of the circle as the number of its sides increases. Let us call the output proper to discrimination of the first degree, that is to say, the ideal output, a. Then monopoly of the second degree would lead to an output less than a, but approaching more nearly towards it the larger is the number of the different price groups which the monopolist is able to distinguish; and the value of the marginal social net product of resources invested in our industry would, in like manner, approach more nearly towards equality with the value of the marginal social net products in general, the larger is this number.

II.XVII.12

§ 12. The study of monopoly plus discrimination of the third degree is more complicated than that of either of the two higher forms. In the discussion of these we have been able to make use of a simple relation between the aggregate output which comes about in various circumstances and the output which I have called the ideal output. According as actual output exceeds, falls short of, or is equal to the ideal output, we could conclude that the value of the marginal social net product of resources invested in our industry falls short of, exceeds, or is equal to the value of the marginal social net product of resources in general. But, under monopoly plus discrimination of the third degree, the relation between actual output and ideal output no longer suffices for a criterion. The reason is that, when a demand represented by a demand price p is satisfied, it is not necessary, as it has been necessary so far, that all the demands represented by demand prices greater than p shall have been satisfied.

II.XVII.13

On the contrary, the monopolist may, in one market, be satisfying all demands represented by demand prices higher than p, while, in another market, he is refusing to satisfy any demands whose demand prices fall short of (p+h). It follows that the resources invested in the industry fall into a number of different parts, in each of which the value of the marginal social net product is different. Consequently, we have no longer to ask how the value of the marginal social net product of resources invested in the industry is related to the value of the marginal social net product of resources in general, but how the various values of marginal social net products of resources invested to cater for each of the several markets of the industry are related to that standard. Our ideal output ceases to be a single output of the whole industry, and becomes a number of separate outputs sold in separate markets. A given output of the whole industry may be broken up in different ways among these markets, and the system of values of marginal social net products will be different according to the way in which it is, in fact, broken up. Hence a study of the effect which monopoly plus discrimination of the third degree produces upon output is only a first step to a study of the effect which it produces, as compared with that which simple monopoly and simple competition respectively produce, upon the relation between the values of marginal social net products in different parts of the industrial field. Nevertheless, it is well that such a study should be made. To facilitate it, let us suppose that the demands for the product of an industry can be broken up into two markets A and B, between which price discrimination is feasible; and let us ask, first, whether output under discriminating monopoly of the third degree will be absolutely greater or smaller than output under simple monopoly and simple competition respectively.

II.XVII.14

§ 13. To compare the output proper to discriminating monopoly of the third degree with that proper to simple monopoly, we may conveniently distinguish three principal cases. First, let the conditions be such that, under simple monopoly, some of the commodity, in which we are interested, would be consumed in both A and B. In these conditions there is no adequate ground for expecting either that output under discriminating monopoly of the third degree will exceed, or that it will fall short of, output under simple monopoly; if the curves of demand and supply are straight lines, the two outputs will be equal.*79 Secondly, let the conditions be such that, under simple monopoly, some of the commodity would have been consumed in A, but none in B. In these conditions it is impossible that the introduction of discriminating power should lead to diminished output. On the contrary, if there is any substantial demand in B, it must lead to increased output. The amount of the increase will be specially great if the demand in B is elastic, and if the commodity obeys the law of decreasing supply price (simpliciter). These conditions are often fulfilled among Kartels selling regularly at specially low rates in markets, foreign and other, where they are exposed to competition. An interesting practical inference is that, if a commodity, whose production obeys the law of decreasing supply price, is monopolised, it is to the interest of the consumers in the producing country that the Government should allow the monopolist to make sales abroad at lower prices than at home, rather than that, while still permitting monopoly, it should forbid this discrimination. This inference cannot be upset by reference to the more advanced industries that use the commodity as a raw material, because the sales abroad, being at market prices there,—prices which the monopolistic exports cannot in ordinary circumstances sensibly affect—do not enable foreign users to get it appreciably more cheaply than they could before. Finally, let the conditions be such that, under simple monopoly, none of the commodity would have been consumed in either A or B. In these conditions it is obviously impossible that the introduction of discriminating power should lead to diminished output. It is possible that it may lead to increased output. The condition for this is the same as the condition, mentioned in the next paragraph, that enables discriminating monopoly of the third degree to yield some output, though simple competition would yield none.

II.XVII.15

§ 14. We have now to compare the output proper to discriminating monopoly of the third degree with that proper to simple competition. Under conditions of constant and of increasing supply price it is obviously impossible for discriminating monopoly of any degree to make output greater than it would be under simple competition. Discriminating monopoly of the third degree must make it smaller than it would be under that system. When, however, conditions of decreasing supply price prevail, the question is more complex. It has been proved in an earlier section that, in that event, monopoly plus discrimination of the first degree must raise output above the quantity proper to simple competition. Furthermore, it is evident that discrimination of the third degree approximates towards discrimination of the first degree as the number of markets into which demands can be divided approximate towards the number of units for which any demand exists. Hence it follows that, under decreasing supply price, monopoly plus discrimination of the third degree may raise output above the competitive amount, and is more likely to do this the more numerous are the markets between which discrimination can be made. Sometimes, but not, of course, so frequently as with discrimination of the first degree, discriminating monopoly of the third degree will evolve some output where simple competition would have evolved none. In view, however, of the limitation, which practical considerations impose, alike upon the number of markets that can be formed, and upon the monopolist's freedom to make up the several markets in the way most advantageous to him, it appears, on the whole, exceedingly improbable that, in an industry selected at random, monopoly plus discrimination of the third degree will yield an output as large as would be yielded by simple competition.

II.XVII.16

§ 15. In the preceding paragraphs we have compared the absolute amount of output under discriminating monopoly of the third degree with the absolute amount under simple monopoly and simple competition respectively. The next step is to compare the measure of approximation towards the ideal output that is attained under these different systems. What has been said enables us to conclude broadly that, whatever law of supply price prevails, discriminating monopoly of the third degree is likely to yield an output nearer to the ideal output than simple monopoly yields; but that it is not likely to yield an output nearer to it than simple competition yields. When, however, the conditions are such that (1) there is an ideal output (other than a zero output), (2) simple competition yields no output, and (3) discriminating monopoly of the third degree yields some output, this output must be nearer to the ideal output than the zero output of simple competition.

II.XVII.17

§ 16. I now return to the considerations suggested in § 12. It was there pointed out that the measure of correspondence between the actual aggregate output of an industry and the ideal output is not, when discriminating monopoly of the third degree is in question, the decisive index that it is in other circumstances. Suppose, for example, that discriminating monopoly of this degree brings about an output closer to the ideal output than either simple monopoly or simple competition would bring about. We cannot infer from this that the value of the marginal social net product of resources employed in the industry is brought nearer to the value of marginal social net products in general. For there is no longer any such thing as the value of the marginal social net product of resources employed in the industry. There are different values of marginal social net product in different portions of the industry. The value of the marginal social net product of resources that serve the needs of low-priced markets is smaller than the value of the marginal social net product of those that serve high-priced markets. Hence, even when, in any industry, discriminating monopoly makes aggregate output more nearly conformable to ideal output than simple monopoly or simple competition would do, it does not follow that it will involve greater equality between the values of marginal social net products over industry as a whole. Nor need we stop at this negative result. It can be shown, further, that the establishment in any industry of a given output associated with discriminating prices is likely to conduce less towards equality among the values of marginal social net products as a whole than the establishment of the same output associated with uniform prices. For let the value of the marginal social net product of resources in general be P; and let the quantity of resources invested in our industry be such that, if the product is sold at the same price in all markets, the value of the marginal social net product of the resources employed to supply each of them will be equal to p. Then, if this same quantity of resources is invested in the industry, but the product is sold at a higher price in some markets than in others, the value of the marginal social net product of the resources utilized for the higher-priced markets will be greater than p, and that of the resources utilized for the lower-priced markets will be less than p. This implies that the mean square deviation (our measure of inequality) of these various values from P is likely to be greater than it would have been if all of them had stood at p. Hence the probability that discriminating monopoly of the third degree will be more favourable to equality among the values of marginal social net products than simple monopoly or simple competition is less than the probability that it will be more favourable than they are to the production of the ideal output. The probability that it will be more favourable than they are to the national dividend is, therefore, also less than that probability.

II.XVII.18

§ 17. So far we have supposed that discriminating monopoly is coupled with power to restrict the entry to the monopolised industry. When this condition is not satisfied, reasoning analogous to that employed at the close of the preceding chapter is applicable. Resources tend to be attracted into the industry till the point is reached at which the expectation of earnings there is equal to that ruling elsewhere. So long as monopoly prices are maintained, this means that a considerable part of the resources so attracted is standing idle and is yielding no net product whatever. It is evident, therefore, that the national dividend suffers more from discriminating monopoly without restriction of entry than it does from discriminating monopoly plus restriction of entry. But, as with simple monopoly, so also here, it may, nevertheless, be desirable that restriction should be forbidden, because, when it is absent, there is a better chance that the entrenchments of monopolistic power will ultimately be broken down.


Notes for this chapter


72.
Walker, Combination in the German Coal Industry, p. 274.
73.
It must be added, however, that, though trade marks are sometimes mere devices for creating monopoly power, there is, nevertheless, a valid reason for protecting them against infringement by legal enactments, because "an inducement is thereby given to make satisfactory articles and to continue making them." (Cf. Taussig, American Economic Review Supplement, vol. vi., 1916, p. 177.)
74.
A person's demand schedule for any commodity is the list of different quantities of that commodity that he would purchase at different price levels. Cf. Marshall, Principles of Economics, p. 96.
75.
For such an analysis, cf. my paper "Monopoly and Consumers' Surplus," Economic Journal, September 1904.
76.
Colson, Cours d' économie politique, vol. vi. p. 211. Special opportunities for injurious discrimination of this sort exist when a railway company is itself a large producer of some commodity, say coal, which it also transports for rival producers. To prevent the obvious abuses to which this state of things may lead, the "commodity clause" of the Hepburn Act passed in 1906 in the United States made it unlawful for any railway to engage in interstate transport of any commodity which had been mined or manufactured by itself. The law does not, however, prevent a railway from transporting a commodity produced by a company in which it holds a majority of the shares, and it can, therefore, be evaded without great difficulty. (Cf. Jones, The Anthracite Coal Combination, pp. 190 et seq.)
77.
Cf. ante, Part II. Ch. XI. § 13.
78.
Cf. Appendix III. §26.
79.
Cf. Appendix III. § 28.

Part II, Chapter XVIII

End of Notes


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