498 



NA TURE 



[Sept. 19, 1889 



write out two hundred lines — the cost of ten marbles at twenty 

 lines per marble. 1 



To be sure, final utility may be conceived as operating by 

 itself without reference to cost of production, as we tacitly 

 assumed in our first paragraphs. Whereas the converse con- 

 ception of a traffic in discommodities ^ has less place in real 

 life. 



But it is not worth while weighing the two principles against 

 each other, in vacuo, so to speak, and abstracting the real cir- 

 cumstances by which each is differently modified. As these are 

 introduced, the balance will oscillate now in favour of one side, 

 now of the other ; perhaps leaving it ultimately uncertain 

 whether cost of production or final utility is the more helpful 

 in the explanation of economic phenomena. 



For instance, in our allegory let us introduce the supposition 

 that there is only one variety of cost — say, the common labour 

 of writing out verses. If, now, the authorities fix twenty lines as 

 the cost of a marble, and 200 as the cost of a top, it is predictable 

 that a top will be worth ten marbles. It is equally true indeed, 

 now as before, that the final utility of a top will be equal to 

 the final utility of ten marbles. But the latter proposition, 

 though equally true, is not equally useful. For it does not afford 

 the simple and exact method of prediction which is obtained by 

 the Ricardian view upon the supposition made. But then the 

 supposition that there is only one variety of sacrifice is not always 

 appropriate. And even if that were appropriate, it might not 

 be helpful when we introduce the condition that the cost of pro- 

 curing each article is not fixed definitely, but varies increasingly 

 or decreasingly with the amount procured. Thus, the cost of 

 the first marble given out might be twenty lines ; of the next 

 marble, twenty-one lines ; with an equally varying scale for 

 tops. Upon this supposition the two propositions that value 

 corresponds to final utility and also final disutility might be 

 eqvally true, but equally useless for the purpose of prediction. 



Again, it may be that a man is freer to vary the extent of his 

 expenditure than the duration of his work {g). The final dis- 

 utility experienced by the Secretary of this Association during its 

 meetings must be fearful. For it is not open to him to terminate 

 at pleasure his day's work, as if he were employed by the piece. 

 He would not, however, have accepted the office unless the 

 advantages, less by all the trouble, were at least as great as in 

 any other position open to him. Now this equation of the net 

 advantages in different occupations is — co-ordinately and (in a 

 mathematical sense) simultaneously with the equation of final 

 utility for different kinds of expenditure — a condition of normal 

 economic equilibrium {h). Yet again, the free play of this 

 tendency is impeded by the existence of " non-competing 

 groups." 



I cannot be expected here to enumerate all the conditions of 

 economic equilibrium. For a complete exposition of the com- 

 plexities at which I have thought it necessary to glance, I must 

 refer to the second book of Prof. Sidgwick's " Political Eco- 

 nomy." It will be evident to his readers ^ that what may be 

 called the general economic problem of several trading bodies 

 distributing and exchanging inter se under the influence of self- 

 interest and in a righne of competition is much more hopelessly 

 difficult than the as yet imperfectly solved dynamical problem of 

 several material bodies acting on each other in vacuo. When 



^ Suppose our allegorical schoolmaster should discontinue the system -of 

 rewards, and prefer to cultivate diligence by requinng each boy from time to 

 time to bring up a certain number of lines, written out — whether by himself 

 or another would not be scrutinized — or to be responsible for the cleaning of 

 a window, after the manner of Mr. Squeers's practical method. In the 

 traffic of discommodities which would be set up on this supposition, the 

 (negative) value of each article of exchange would be measured solely by its 

 disutility. However, it must be admitted, I think, that this latter hypothesis 

 is rather more absurd than the former abstraction — with reference to real life 

 at least ; for, as it happens, the traffic in impositions more nearly resembles 

 what is said to occur in actual schools. 



^ There occurs to me only one point at which the use of mathematical 

 illustrations more complicated than those which I have referred to in my 

 first two headings would conduce to the apprehension of Mr. Sidgwick's 

 theorems. I allude to his repeated statement that, not only in international 

 trade, as Mill pointed out, but also in trade in general, there may be several 

 rates of exchange at which the supply just takes off the demand. This 

 statement, taken without reservation, goes the length of destroying the 

 prestige which is now attached to competition. Prof Marshall, in an im- 

 portant passage, recommends arb trators and combinations to imitate the 

 method of a celebrated engineer, who, in order to make a breakwater, first 

 ascertained the slope at which a bank of stones would naturally be arranged 

 under the action of the waves, and then let down stones so as to form such a 

 slope (" Economics of Industry," p. 215). Now, if gravitation acted some- 

 times vertically and sometimes at an angle of 45°, if the forces of competition 

 tended to two distinct positions of equilibrium, the construction of the 

 economic breakwater would become- arbitrary. It is important, therefore, 

 to show the limits of Prof. Sidgwick's theory. See the appended note (7). 



Gossen, the predecessor of Jevons as an exponent of the law of 

 final utility, compares that principle to the law of gravitation, 

 and the character of our science to that of astronomy, he betrays 

 a too parental partiality. A truer, though still too flattering, 

 comparison would be afforded by some very immature and im- 

 perfect specimens of physics — say the theory of fluid motion 

 applied to the problems of house ventilation. 



There is a certain resemblance between the uniformity of 

 pressure to which the jostling particles of a gas tend and the 

 unity of price which is apt to result from the play of competition. 

 As the architect is guided by studying the laws according to 

 which air flows, so it will help the builder of economic theory 

 to have mastered the principle of movement towards equilibrium. 

 But even in the material constructions practice is apt to lag far 

 behind theory, as every reader in the British Museum knows. 

 Much less are we able to predict what currents will flow between 

 the different compartments of the industrial system. We know 

 so imperfectly the coefficient of fluid friction, and the other 

 conditions of the general problem : what compartments may be 

 regarded as completely isolated and hermetically sealed, which 

 partitions are porous and permeable. 



Moreover, there is one operation of competition, which it 

 does not seem easy or helpful to represent by physical analogies 

 — the transference from one occupation to another, the equation 

 of net advantages or total utilities in different employments ; 

 industrial as distinguished by Cairnes from commercial competi- 

 tion. The latter operation appears to me to admit much better 

 of mathematical expression than the former, which is not so 

 well represented by the equilibrium of a physical system.^ Ac- 

 cordingly, the equation of net advantages has been judiciously 

 omitted by Jevons in his formulation of the cost of production. 

 And the Helvetian Jevons, as we may call Prof. Walras, 

 appears to have altogether made abstraction of the cost of 

 production considered as importing sacrifice and effort. 



Prof. Walras, illustrating the operation of a simple market, 

 supposes each dealer, before going to market, to write down 

 his scale of requirements — how much he would be willing to 

 buy or to sell at each price. From these data it would be easy 

 to calculate beforehand the rate of exchange which would prevail 

 in the market formed by those individuals. But, when we 

 advance from the simplest type of market to the complexities 

 introduced by division of labour, it is seen to be no longer a 

 straightforward problem in algebra or geometry, given the 

 natures of all the parties, to find the terms to which they will 

 come. Here, even if we imagine ourselves in possession of 

 numerical data for the motives acting on each individual, we 

 could hardly conceive it possible to deduce a priori the position 

 of equilibrium towards which a system so complicated tends. 



Accordingly, it may be doubted whether the direct use of 

 mathematical formulae extends into the region of concrete 

 phenomena much below the height of abstraction to which 

 Jevons has confined himself. However, the formulation of 

 more complicated problems has still a negative use, as teaching 

 the Socratic lesson that no exact science is attainable. As 

 Dupuit, one of the greatest of Jevons's mathematical prede- 

 cessors, points out, " Quand on ne pent savoir une chose, c'est 

 deja beaucoup que de savoir qu'on ne salt rien " {Annalcs des 

 Fonts et Chaussks, 1844, p. 372). If, he says, the early theorists, 

 instead of formulating the balance of trade, had confined them- 

 selves to declaring the question above their powers, they would 

 probably have done a greater service than the successors who 

 refuted them. So Cournot, referring to his own mathematical 

 treatment of economics, "Aussi nos modestes pretensions 

 etaient-elles non d'accroitre de beaucoup la domaine de la 

 science proprement dite, mais plutot de montrer (ce qui a bien 

 aussi son utilite) tout ce que nous manque pour donner la 

 solution vraiment scientifique de questions que la polemique 

 quotidienne tranche hardiment" ("Revue Sommaire"). Similarly 

 Jevons says ("Theory of Political Economy," p. 157, second 

 edition), "One advantage of the theory of economics, carefully 

 studied, will be to make us very careful in our conclusions when 

 the matter is not of the simplest possible nature." 



In the vineyard of science, to perform the part of a pruning- 

 hook is an honourable function ; and a very necessary one in this 

 age of luxuriant speculation, when novel theories teem in so 



' Commercial competition might be likened to a system of lakes flowing 

 into each other; industrial competition to a system of vessels so communi- 

 cating by means of valves, that when the level of one exceeded that of 

 another to a certain extent, then per saltnm a considerable portion of the 

 contents of that one (a finite difference as compared with the differentials of 

 the open system) is discharged into the other. 



