deprived of their occupation, the investigation of the conditions which determine value. There would survive only the empirical school, flourishing in a chaos congenial to their mentality. 2. Professor Marshall exemplifies another use of mathematical reasoning when by means of his curves he demonstrates that it might be advisable to tax one kind of commodity and employ the proceeds in bountying another kind.1 The abstract reasoning serves as a corrective to what has been called the "metaphysical incubus" of dogmatic laisser faire. In the case of monopoly indeed this incubus has not been serious: "it has never been supposed that the monopolist in seeking his own advantage is naturally guided in that course which is most conducive to the well-being of society regarded as a whole." Nevertheless, in so far as something similar to the old doctrine of economic harmony seems to be reappearing among the apologists for railway administration, a certain interest may attach to propositions unexpectedly favourable to the intervention of Government in businesses subject to monopoly. Such is the proposition above proved, that when the supply of two or more correlated commodities such as the carriage of passengers by rail first class or third class-is in the hands of a single monopolist, a tax on one of the articles-e. g. a percentage of first-class fares-may prove advantageous to the consumers as a whole. Thus in the instance given the advantage would accrue not only to those who before the tax travelled third class, and continue to do so afterwards, but the travelling public in general, including firstclass passengers. The fares for all the classes might be reduced. 3. To obtain rules directly applicable to practice there would be required a knowledge of concrete details beyond what the present writer can command. Still, some suggestions bearing on the control of monopolies by governmental interposition may be derived from the preceding analysis. A first step in this direction was made by Cournot when he proved that a tax of an ordinary kind on a monopolised product has the effect of increasing the price. This is contrary to the judgment of some distinguished writers who hold that, the monopolist having already done his worst against the customer, the burden of the latter cannot be increased by a tax. There is, however, a limiting case in which the popular opinion is correct; namely, where a monopolist buyer deals with sellers of an article which is absolutely limited in quantity (land, for instance), or can only be increased with great difficulty. A building syndicate 1 Principles, Book V. ch. xii. pp. 555–7. Ibid. ch. xiii. (third ed.) buying up land from uncombined owners may afford an example. Cases specially favourable for the application of mathematical analysis occur where we have to deal with correlated (connected) supply and demand. Suppose, first, the supply only connected, as when a railway company, the greater part of whose expenditure (interest on capital, cost of repairs, etc.) cannot be attributed exclusively to one branch of the business, serves two classes of customers whose interests are quite separate, say traders requiring their goods to be carried and passengers other than commercial travellers. Here we must distinguish two classes: (a) complementary products, in the case of which the production of one article becomes less difficult and expensive by the increased production of the other article ("joint " products as defined by Mill are included in this class); (b) rival products, in the case of which the production of one article becomes more costly according as the production of the other is increased. The first case usually occurs where the law of increasing returns rules; for instance, if the general expenses of a railway do not increase in proportion to the traffic, the increase of one kind of traffic tends to make the increase of the other kind more remunerative (see above a more exact definition). Contrariwise, when the land or the capital at the disposal of the company is fully occupied, it is possible that the increase of one service may render another less profitable than it would otherwise have been. The proprietors of a railway with only one or two tracks may find that the increase of the goods traffic causes the passenger traffic to be attended with greater expense; the fuel of the company and the labour of its employees being wasted while the passenger trains have to wait in side tracks to avoid collisions. It is very possible that both tendencies may be present, not coincidently, but with reference to a different extent of variation in the products under consideration. Thus a certain increase in the goods traffic by crowding the present line as above described might act in rivalry to the passenger traffic; but with reference to a large increase in the goods traffic, such as to make it profitable to have an additional track and so obtain the economies of production on a large scale, the goods traffic may be considered as complementary to the passenger traffic.* I do not pretend to discern to which of the two categories each concrete case belongs; I only wish to distinguish their properties in the abstract. Among methods of governmental control, one of the most *See Index, sub voce Joint Production. important is that which consists in fixing a maximum tariff; provided that the maximum is not suspended on high, but is such as really to restrain the action of the monopolist; in which case its operation is nearly similar to that of a fixed tax. Suppose now that the price of one product is fixed, but not so that of another; or, what is more probable, that there is an effective maximum for one article and an inoperative maximum for another. The effect on the price of the second article will differ according as the products are complementary or rival. If they are complementary, the lowering of the price of the first is followed by the lowering of the price of the second; the benefit in respect of one commodity is a benefit also in respect of the other commodity. If the products are rival, there is a benefit to one class of consumers and a loss to another; provided, of course, that the loss to the monopolist is not so great as to induce him to give up the business. The same rule applies to the effects of a law which requires that the price of an article in one market should not exceed its price in another by more than a certain percentage.1 What is a benefit in respect of one commodity will be also a benefit in respect of the other, if the products are complementary; but a loss in the case of rival production. A corresponding rule applies to a tax of the kind called specific," that is, of so much per unit of commodity. The loss to one class of consumers will be a loss to the other class in case of complementary products; but a gain in the case of rival products. The case of connected demand does not admit of equally definite rules. It is probable, but not certain, that the rules enounced for rival and complementary production hold good respectively for complementary and rival demand. Thus a maximum which lowers the rate for the terminal services of a railway tends probably to raise the rates for carriage since the demands for the two services are complementary. But a maximum which lowers the fare for third-class passengers tends probably to lower the fares for the first class, since the demands for the two kinds of tickets are rival. The probability increases when the tendency of demand is in the same direction as that of production, and diminishes in the contrary case. These propositions respecting the influence of demand may 1 Generalising the conceptions of the American “ Short-haul Clause," as it is commonly understood. be applied to a law against differential charges and to a specific tax. A tax proportional to the profits of the monopolist falls entirely upon him, as Cournot and Professor Marshall have proved. It should be added that a "progressive" tax on monopoly profit acts similarly.1 The effect of limiting the profit of the monopolist to a fixed amount is generally indeterminate. It may be advantageous or detrimental to some or all or none of the various groups of his customers. The fixing a (bonâ fide) maximum rate of profit on the capital expended acts to the advantage of the consumer. I am not blind to the practical difficulties which stand in the way of a tax on the net profits of a monopolist, and of other measures that are here discussed. It cannot be too often repeated that the rules derived from mathematical reasoning are essentially abstract and require in practice to be largely diluted with common sense. 1 Since this article was printed I have found that Knut Wicksell had preceded me in pointing this out. (F) PROFESSOR SELIGMAN ON THE THEORY OF MONOPOLY [THIS article, which appeared in the ECONOMIC JOURNAL, 1897, under the title "Professor Seligman on the Mathematical Method in Political Economy," might, in accordance with that title, equally well have been placed in the mathematical section of this Collection. The subject-matter is the theory of monopoly ; the form is largely mathematical. The mathematical method is tested by an encounter with the classical method wielded by a powerful hand. The victory, if indeed it has been won, is of a somewhat Pyrrhic character. For it does not much redound to the credit of the mathematical method that the points in which it has an advantage are just those which have been neglected by an economist of conspicuous wisdom, one whose judgments on Income Taxes, Public Loans and other momentous interests are generally approved and followed. It is strongly suggested that matters which such an author did not take pains to state precisely cannot be of great importance. They might be compared to the points of detail on which the critical shoemaker corrected the masterpiece of the Grecian painter. Even without those little corrections the piece would no doubt have been a first-rate work of art. So the Art of Political Economy is not much affected by judgments on the question whether the taxation of a monopolised article is likely to be more or less burdensome to the consumer according as the production obeys the law of increasing or decreasing returns, or according as the demand is more or less elastic. Still, if such questions are posed, it is better not to answer them carelessly. The criticisms on the original version having been directed against the second edition of Professor Seligman's Shifting and Incidence, published 1899, some of them have now been withdrawn or modified in deference to emendations in the third edition, published 1910.] I. (1) Following the order in which Professor Seligman has discussed the several issues, I notice first his objection to my |