hoped, indeed, that through the practice of conciliation, in the course of generations, the dispositions of which the gratification constitutes self-interest may become more social, so that, for instance, an advantage founded on the extreme privation of others would not appear desirable to the capitalist employer of the future. But such "moralisation" of the saving classes, though it may be expected, need not be postulated for the working of conciliation. Intellectual sympathy alone might effect much. The arts by which the sympathetic imagination may be cultivated form a supremely important topic, but one which hardly falls under the theory of Distribution. 1 Note referring to p. 24. [On the remuneration for risk some additional light is derivable from Mr. Keynes' great treatise on Probability; where he shows that mathematical expectation-the product of advantage and the probability of obtaining it is not the measure of expediency (ch. xxvi. p. 311 et seq.; discussed by the present writer in Mind, 1922, vol. xxxi. p. 276 et seq.). The motives of the entrepreneur may be illustrated by the position of Paul in the classical problem which Mr. Keynes thus restates: "Peter engages to pay Paul one shilling if a head appears at the first toss of a coin, two shillings if it does not appear until the second, and in general 27-1 shillings if no head appears until the rth toss. What is the value of Paul's expectation? If the number of tosses is limited to a finite number n, the mathematical expectation is in. But, if n is large, no sensible person would give anything like that sum for the chance. Now Paul may be taken as typical of the entrepreneur. Peter in this case may fix what Paul must pay for a trial-corresponding, say, to the outlay on factors of production required for a unit of product. But Paul will have a say as to the amount which he stands to win by that outlay. Say the payment is in shillings or pounds, n not now indefinitely large; Paul 66 1 For example, co-operation, as many economists have pointed out, would have among its good effects that of enabling workmen to realise the position of employers. Again, the training of future business men in economics at the universities, as Professor Marshall has lately urged, would tend to develop the sympathetic use of the imagination. “It has been found,” he says, “ by experience in England and in America that the young man who has studied both sides of labour questions in the frank and impartial atmosphere of a great university is often able to throw himself into the point of view of the working-men and to act as interpreter between them and persons of his own class with larger experience than his own." See his address on "Economic Teaching at the Universities," published in the review of the Charity Organisation Society, January, 1903, noticed in the ECONOMIC JOURNAL, Vol. XIII. p. 155, and his Plea for the creation of a curriculum in economics (addressed to the Cambridge Senate), noticed in the ECONOMIC JOURNAL, Vol. XII. p. 289. Compare the expressions in the Report of the Anthracite Coal Commission, U.S.A. (1903), on the importance of a more conciliatory disposition in the operators and their employees." will demand a higher prize than the bare actuarial 2-1; unless he is a fatuous gambler (cp. Marshall, Principles, Bk. V. ch. vii. § 4, and p. 613, note, 5th edition; and Pigou on uncertainty-bearing). At what terms above the actuarial limit Paul will touch the point of indifference, what is his demand-schedule in respect of such transactions, depends upon his mentality, his "dispositions," in the phrase of Walras relative to supply and demand in general. Thus the share of the entrepreneur in the product equally with the share of the workman depends on the play of demand and supply. It is no more predetermined than the wage-fund.] (C) THE LAWS OF INCREASING AND DIMINISHING RETURNS [THE following article, published in the ECONOMIC JOURNAL 1911, formed (the greater part of) an introduction to a series of articles entitled Contributions to the Theory of Railway Rates; which was discontinued after 1913. This discussion of Increasing and Diminishing Returns which initiated the series is almost as applicable to a regime of Competition as to one of Monopoly. But its original use as an introduction to an essay on a certain kind of monopoly is occasionally discernible. There are here distinguished two definitions of increasing (and of diminishing) returns, which are respectively appropriate according as the magnitude of which increase (or diminution), is predicated is marginal or total. It is proposed to remove an ambiguity, the existence of which in so familiar a subject might have been deemed impossible, but that a similar confusion occurs in the matter of "sacrifice" incurred through taxation as pointed out below II. 115, and perhaps even (as there suggested) in a still higher sphere. The definition based on marginal production is here distinguished as primary, preferred as more directly related to theory of maxima. The use of the secondary definition is shown to present difficulties in the important case of plural factors of production. The conceptions having been made clear, some of the propositions of which they form the terms are restated. The advantages of Production-on-a-large-scale and of Division-of-labour are classified. There follows an inquiry into the meaning and properties of Joint Cost, and other cognate conceptions. In the course of the inquiry there comes into view that case of which the title to Joint Production has been disputed between Professor Pigou and other high authorities (see Index s.v. Joint Production).] Increasing Returns and Joint Cost admittedly play a great part in economics; but what that part is has been questioned. 1. Law meaning concept.-A first difficulty is occasioned by a certain ambiguity in the use of the word " law" in such phrases as the "law of increasing [or diminishing] returns." The word 'law in this connection is used sometimes in the narrow sense of a quantitative relation; sometimes in the larger sense connecting that conception with some other attribute. Thus the law of diminishing returns " may stand either for the conception of decrease in the rate at which production increases, or for a proposition connecting that conception with the increase in the number of producers under certain circumstances. Accordingly Mr. Flux well distinguishes the "definition or statement of the law" from the "assertion of its applicability." 1 So Mr. Maurice Clark, in his philosophical study on local freight discriminations, appears to treat the "law of joint cost" as equivalent to the term 'joint cost.'" 2 66 This sort of ambiguity is not unknown in other sciences. Thus the "law of error" is sometimes used to denote the relation between frequency and deviation which is expressed by a certain well-known curve (or function), and sometimes for the proposition that the said quantitative relation tends to be realised approximately in certain circumstances of general occurrence. Even in physical science such a phrase as "the law of the inverse square is not improperly, I think, sometimes used to denote simply a certain relation between the magnitude of a force and the distance at which it operates, a conception which may be predicated of different forces-now the attraction of gravitation, and now the repulsion of electricity. We may begin by interpreting the laws in question in the narrower sense. Let it not be objected that this is a matter of verbal definition. For, as Sidgwick reminds us, some of the most important inquiries have taken the form of a search for definitions. More reassuring to some may be the reflection that even in modern physical science half the battle often consists in obtaining what Whewell well described as clear and appropriate conceptions," ideas distinct and appropriate to the facts." 4 2. Provisional definition. The definition of the law as a term may be gathered from an authoritative statement of the law as a 1 Palgrave's Dictionary, Article on Law, p. 583. 2 Pp. 28, 29, 30. Political Economy, Book I. ch. ii. § 1, suggesting the application of this Platonic method to economic investigations; cf. Book II. ch. iv. note (ed. 3). 4 History of the Inductive Sciences, Book I. ch. iii. § 2 et passim. Mill, while refusing to Colligation the title of Induction, does not deny its supreme importance.-Logic, Book II. § 4. 1 proposition. The essential attribute is presented in the following passage which want of space compels me to separate from the explanation and limitations in the context-from Dr. Marshall's statement of the law of diminishing return with respect to agriculture:-" Our law states that sooner or later . . . a point will be reached after which all further doses will obtain a less proportionate return than the preceding doses." So with respect to manufactures, Dr. Marshall says:-" If a manufacturer has, say, three planing machines, . . . after they are once well employed, every successive application of effort to them brings him a diminishing return." 2 So Mr. Flux discriminates between Increasing or Diminishing Return by the change in "marginal expenses per unit."3 We are countenanced, I think, by good authority in adopting the following provisional definition of the terms. When on the application of two successive equal doses of productive power, the increment of product due to the first dose is less than the additional increment due to the second, the law of increasing returns is said to act; and conversely it is a case of diminishing returns when the increment due to the first dose is greater than the increment due to the second. The attribute which I regard as essential may be illustrated by a numerical example. In the accompanying table the first two columns are borrowed from an example given by Professor Carver.4 4 See Prof. Carver's Distribution of Wealth, ch. ii. p. 58, and compare his article in the ECONOMIC JOURNAL, Vol. XVIII. A part of Prof. Carver's third column, not shown in my Table I., is reproduced (with some additional matter) in my Table II. I have also taken the liberty of substituting in his first column for his figure 1 the figure 2. |