applying the formula to enunciate the effect of a change in e, I treated B as constant,1 forgetting that it involved e. The following is, I now think, a more correct statement. In any given case it is impossible to say whether the increase of elasticity conduces to the increase or the decrease of the efficacy of a tax to raise price; unless we are given not only c' (which may be supposed), but also e', involving the curvature of the demand curve, which is not, I think, usually given,2 even as to sign, much less with the quantitative precision which would often be necessary for the present purpose. But the expression for 4, though perfectly indeterminate for Δτ' any particular case, may afford, I think, a certain presumption for the long run. Suppose the sign of c' to be given, e.g.+, the law of decreasing returns prevailing. Then in the long run of cases— while e' is now positive, now negative in sign, now large, now small in absolute quantity-for a majority of those cases an increase of e would be attended with an increase in the denominator Δρ of the above-written expression for or rather what it becomes Δτ' when both numerator and denominator are divided by e, and, therefore, a decrease of the ratio under consideration. Conversely, when the law of increasing returns prevails, c' being negative, an increase of elasticity is likely to be attended with an increase in the efficacy of taxation to raise price. To the extent of the former clause I have to retract my original statement. But I am still able to affirm universally, without reference to the law of cost, the contradictory of Professor Seligman's theory that "the greater the elasticity of demand the more favourable-other things being equal-will be the position of the consumer"; if the situation of the consumer is tested, as it ought to be, not so much by the rise of price as by the loss of consumers' surplus. Employing the proper criterion of the consumers' welfare, we may affirm, " the greater the elasticity of demand the more unfavourable-other things being equal-will be the situation of the consumer.' "3 1 ECONOMIC JOURNAL, Vol. VII., p. 228, note 4 continued from p. 227. 2 As to this unknown element, see E, I., p. 135, and (, II. 394. The loss of consumers' surplus consequent on raising the price from p to p+ Ap is approximately (cp. E, pp. 117, 132) xAp; where x is the product, which, by Cournot's equation (3) of ch. v. = e(p-c). Therefore the loss of consumers' surplus (p-c)AT This expression for the loss of consumers' surplus is always positive, both the For the purpose of obtaining propositions in Probabilities, as the preceding may be described, I submit that symbols seem to have an advantage even over diagrams-not to speak of numerical illustrations. Thus it may be objected to our diagrammatic proof 1 of proposition (2) that some a priori knowledge derived from analysis is required to guarantee the legitimacy of our supposition that the law of cost only is varied, other things being preserved constant. A diagrammatic proof of proposition (3) would be even more precarious. (3) One more of Professor Seligman's general reflections : 66 It may even be doubted whether the mathematical method has independently discovered any important principle susceptible of practical application that could not have been also expressed in everyday language.” Those who have followed the preceding discussion may be disposed to admit that, if the mathematical method does not itself discover important practical principles, it may at least be usefully employed to test the principles which a distinguished practical economist regards as important. If it is worth his while to employ some pages of economic analysis and numerical examples in endeavouring to prove those principles, it is worth our while to employ some lines of symbol in endeavouring to disprove them.* The negations are often also affirmations, but not very confident ones. It is as if an opponent should prophesy that the last week of April or May would be the coldest part of the month. The reply is that what we know about the matter points in a contrary direction : there is a constant cause making for greater heat-namely, the position of the earth relatively to the sun-in the latter part of each month; though doubtless that tendency may be counteracted by unpredictable vicissitudes of weather. What if the more abstract part of political economy, like the more sublime part of astronomy-that which contemplates the mechanism 2 numerator (= AT≈ ÷ e) and the denominator (for the reason given in note 1 to p. 168) being positive. The loss is in the long run greater the greater e is, since one term of the denominator becomes less as e becomes greater; while the other term of the denominator which involves e may be treated as inoperative (if not diminishing), on an average, in the long run of all possible values (positive and negative) of e', in our ignorance of e'. Thus the loss of consumers' surplus is likely to be greater the greater the elasticity. 1 Above, p. 155. * There are here omitted some sentences referring to the second edition of Shifting and Incidence, but less pertinent to the third edition. of the heavenly bodies external to our system-were not at present susceptible of direct practical application, the mathematical theory of economics might still confer a benefit analogous to that which the mathematical theory of astronomy conferred when it discredited the pernicious pretensions of the astrologers. There are those who think that even of the received economic analysis the most important function is negative. Thus Mr. Leslie Stephen : "Political economy, as I venture to think, has been especially valuable in what I have called its negative aspect. It has been more efficient in dispersing sophistries than in constructing permanent theories. Economic writers have exploded many absurd systems. They have so far cleared the way for an application of sounder methods. But the complexity of the problem is so great. . . ." 1 The sort of sophistry which has been eradicated from the general field of economics by the received organon finds a still virgin soil in the nooks and corners of which the cultivation requires the implements of mathematics. The trenchancy of this criticism is not inconsistent with the diffidence which is proper to an inexact science, and the respect which is due to a high authority. For on the one hand, the region of hypothetically abstract theory, to which this polemic is confined, forms the one territory of economics in which issues may be fought out without compromise, there being a right diametrically opposed to the wrong. And on the other hand, it is no discredit to the ablest combatant, when he is unprovided with the proper weapons, to succumb. 1 Life of Fawcett, p. 149. (G) RAILWAY RATES [THIS article, which was published in the ECONOMIC JOURNAL, 1912, as the second section of the series announced as "Contributions to the Theory of Railway Rates," deals with some leading problems in Railway Economics. The function of discrimination is investigated on the lines of Dupuit. There comes up for reconsideration the vexed question of the relation between through fares lowered by competition and fares to intermediate localities which are subject to monopoly. The discrepancy in this matter between expert practice and abstract theory is explained by the circumstance that the theory may be too abstract, not taking into account the monopolist's concern for interests in the distant future. The monopoly also may be not pure, but mixed with competition or altruistic motives. A return to the subject is promised; but this is one of the promises which were swallowed up by the War]. The classical economists rather anathematised than analysed monopoly. It was reserved for Cournot to cultivate this neglected branch of economics; gathering the first-fruits of the mathematical method. Cournot and his mathematical successors have fully discussed what may be called the leading case: that of a monopolist dealing with a whole class of mutually competitive customers at one and the same price. Some acquaintance with the laws governing this comparatively simple case is here presumed. My contributions are directed to a subject less generally studied,2 the case in which the monopolist discriminates between different classes of customers. I build upon the foundations laid by Dupuit.2 1 For instance, Adam Smith's dictum, "The price of monopoly is upon every occasion the highest which can be got" (Wealth of Nations, Book I. chap. vii.), J. S. Mill's dictum, "Monopoly value does not depend on any peculiar principle, but is a mere variety of the ordinary case of demand and supply" (Political Economy, Book III. chap. ii. § 5), seem wanting in precision. 2 See his epoch-making papers, De la mesure de l'utilité des travaux publics and De l'influence des péages sur l'utilité in the Annales des Ponts et Chaussées, 1844 and 1849, which will be found among the periodical publications in the library of the British Museum. Some extracts from Dupuit's papers are given in my article in the ECONOMIC JOURNAL, September, 1910. The corner-stone of this building is formed by a conception which Dupuit introduced under the designation "rente des acheteurs" the money-measure of the benefit accruing to purchasers from obtaining articles which they purchase at a certain price, while they would have been willing to give more for those articles rather than go without them altogether. The sum of money designated by the term in question may, I think, be an object of science as well as the sum designated by the more familiar term price. The monetary equivalent of total utility may be as objective as the monetary equivalent of final utility. It should be observed, too, that often the Rente des Acheteurs with which we are here concerned does not consist only of Consumers' Surplus in the phrase adopted by the second founder of the theory, but also of a certain Producers' Surplus which consists of money, and does not require, like Consumers' Surplus for the most part, to be evaluated by an unusual or hypothetical transaction. Thus, if a railway lowers the rate for carriage of coal to a residential and manufacturing town (dependent on that railway for its supply of coal), not only will there be a gain of Consumers' Surplus to those who use coal for domestic purposes, but also the manufacturers becoming able to extend their use of coal in various directions will presumably secure a greater surplus of money profit. I propose to subsume the two kinds of advantage which may accrue to the purchasers of monopolised services under the title "Customers' Benefit." 66 The theory which I attempt to construct is based mainly on the first principle of pure economics, the prevalence of selfinterest. In the words of Professor Cohn, comparing the different motives by which railway managers are actuated, "by far the weightiest are assuredly the egoistic motives." 1 In the words of another high authority,2 the constant effort of every railway company [is] to secure the volume of traffic and to maintain the fares that will jointly yield maximum net profit." "The main purpose of the railway manager is to secure present or prospective profit for the stockholders." 3 But while reasoning from this premiss, I do not forget that a concrete railway company is far from being a perfect monopoly; and I will point 1 "Weitaus die wichtigsten sind allerdings die egoistischen." Englische Eisenbahnen, vol. ii. p. 398, and context adducing evidence that" das Eigennutz ” is the predominant motive. * Johnson and Huebner, Railway Traffic and Rates, p. 227. The words relate to passenger traffic, but may safely be generalised. Compare the context, p. 216. A qualification of this assumption, made by the distinguished writers, will be noticed in the sequel. Op. cit., p. 228. |