5o6 



NATURE 



\Sept. 19, 1889 



the departments of employer and workman ; whether the mobi- 

 lity is one-sided, like that of fluid allowed by a valve to escape 

 from one vessel to another, but not back again — see the end of 

 the passage cited on p. 505 from the Quarterly Journal of 

 Economics— or whether the permeation is perfect.) If O^^ i^ 

 small, if the part played in production by the marginal employers 

 is insignificant, it is probable that the annihilation of the higher 

 grades will result in the destruction of the greater part not only 

 of profits, but also of wages. 



Accordingly it appears, in general, inexact to say that the 

 "surplus which is left in the hands of the higher grades of em- 

 ployers ... is oi iheu ov/n crt&iion" (Quarterly journal 0/ 

 Economics, April 1887, p. 274) ; if we define their own creation 

 as the difference between the actual produce and that which 

 would have existed if their superior faculties had not been exer- 

 cised. In that sense (and what other sense is there ?) the surplus 

 of the higher grades is likely to be much less than their own 

 creation (especially in the case where the marginal employers 

 are relatively few). We seem to have proved too much. But 

 may we not deduce the quod est demonstrandum, that actual 

 profits are deserved, from the larger proposition that the entre- 

 preneurs' "own creation " is by a certain amount greater than 



Fig. 7. 



their profits? No; for that larger proposition is blocked by 

 the antinomy that the workmen (or the higher grades of them 

 may by parity claim the greater part of the produce as their 

 "own creation" — what would not have existed but for the 

 exertion of their faculties. 



In short, we know no more than we knew at first — viz. that 

 the distribuend is produced jointly by the owners of brain and 

 muscle, that the terms of the distribution are determined by 

 supply and demand, and that in this, as in every other market, 

 each more favoured nature enjoys a rent, or differential advan- 

 tage [the nature of which is well illustrated by Messrs. Auspitz 

 and Lieben's construction indicated in our note (f)J. That the 

 surplus earning of the superior entrepreneur is his own creation 

 is true of the individual, but not of the class ; in division, but 

 not in composition. 



However, Prof. Walker may have tacitly made some specific 

 assumptions as to the quantities involved {e.g. the proportion of 

 produce with which the marginal entrepreneurs are concerned) ; 

 or I may have misinterpreted his statements. Even so, the 

 liability to such misconstruction is a defect in the purely literary 

 method. 



It would be easy in the case of less eminent writers to exemplify 



the part which the mathematical organon may play in lopping; 

 the excrescences of verbal dialectics. But I must content my- 

 self with briefly adverting to one of Prof. Walker's critics, Mr. 

 Sidney Webb. His able paper on the " Rate of Interest and the 

 Laws of Distribution " appears to me to contain several points 

 deserving of attention ; with respect to which mathematical con- 

 ceptions may assist the reader in distinguishing the original from 

 the familiar, and the true from the misleading. 



(i) Mr, Webb restates the theory formulated by Jevons, that 

 capital is ideally distributed according to the law of "equal 

 returns to the last increments" (" Rate of Interest and Laws of 

 Distribution," by S. Webb, pp. 10, ii, 21 of paper reprinted 

 from Quarterly Journal of Economics, January 1888). 



In symbols [see above, note (/), p. 504] let the net earning of 

 any individual be /rlr,.)- iCr ; where /r is a function differing for 

 different individuals according to their faculties and opportunities, 

 Cr is the amount of borrowed capital employe i by the individual ;. 

 I is the rate of interest ; land and labour are not expressed. In 

 equilibrium, 



dMcr)_^^ , ^ df>ic^) ^ dficA ^ _ _ _ 

 dc,. dcs dct 



(2) Again, Mr. Webb discerns that the "law of 

 diminishing returns " is applicable to capital as well 

 as to land [ibid., pp. 9, 20, &c. ). This is probably 

 a new truth to the literary economist, who will 

 have some difficulty in reconciling it with the lam 

 of increasing returns received into the text-books. 

 To the mathematician it is evident that, in order to 

 maximize the net earnings f{c) - ic, not only must 

 the first differential of this expression vanish, but 



also the second differential, — -, must be negative^ 



dc-' 



which is the law of diminishing returns It is 

 quite consistent with the supposition that for certain 

 values of the variable, not admissible as a solution 



of the problem, ^ should be positive, agreeably to 



dc 



the law of increasing returns. 



Diagrammatically, let us represent the conditions 

 under which capital is applird by a certain indi- 

 vidual, according as the scale of production is large 

 or small, by the curves pq and p'q' in Fig. 7 ; where 

 the abscissa denotes quantity of capital, and the 

 ordinate the increment of (gross) produce due to 

 an increment of capital. There cannot be equili- 

 brium, unless the increment denoted by the ordinate 

 is just balanced by the sacrifice thereby incurred — 

 in the case which I have supposed, the payment 

 of interest. There cannot, then, on this supposi- 

 tion, be stable equilibrium, unless the curve i.s 

 ascending. The descending (dotted) branches 

 correspond to the law of increasing returns. (The 

 explanation of other features in the figure is given 

 in the next note.) 



(3) Mr. Webb dwells much on "the special industrial advan- 

 tages not due to superiority of site or skill" which are enjoyed 

 by some individuals. The use of an expression for the product 

 like our/r may serve at least to keep in mind the existence of 

 such specialities. It also brings into view a difficulty which has 

 not been sufficiently noticed by those who use rettt in its 

 metaphorical or secondary sense. 



Suppose the extra produce is a function involving several 

 variables (or parameters) like land, ability, opportunity. Say, 

 y; = F(\, a, 01 . . . ), where F is a form common to the com- 

 munity, and A, o, CO denote the quality of land, ability, and 

 opportunity peculiar to the individual. If the extra produce is 

 F(A., a, w) - F(o, 0, o) ; is F(A., 0, o) - F(o, o, o) the " economic 

 rent" of land ; F(o a o) -- F(o, o, o) the rent of ability ; F(o w) 

 -F(o o) the extra produce due to opportunity ? (Md., pp. 16, 

 17). If so, the three parts do not make up the whole. 



(4) Anyway, to call the third extra produce interest^ is very 

 unhappy. Its affinities are evidently with rent (cf. Sidgwick, 

 " Pol. Econ.," book ii. ch. vii. § 4). 



(5) I should not have complained about the use of a term, but 

 that it is connected with Mr. Webb's main contention against 

 Prof. Walker, to which I am unable to attach significance: 



