Sept. 19, 18S9] 



NATURE 



497 



form. The advantage of what has been called the law of large 

 numbers may equally be enjoyed by a theory which deals with 

 markets and combinations. 



But, indeed, even the limited degree of arithmetical precision 

 which is proper to statistical generalizations need not be clained 

 by our mathematical method rightly understood. It is concerned 

 with quantity, indeed, but not necessarily with number. It is 

 not so much a political arithmetic as a sort of economical 

 algebra, in which the problem is not to find x and y in terms of 

 given quantities, but rather to discover loose quantitative rela- 

 tions of the form : x is greater or less than y, and increases or 

 decreases with the increase of z. 



Such is the character of what may be called perhaps the 

 leading proposition in this calculus — namely, the mathematical 

 theory of supply and demand. The use of a curve introduced 

 by Cournot to represent the amount of a commodity ofTTered, 

 or demanded, at any particular price, supplemented by Jevons's 

 theory of final utility {a), does not indeed determine what price 

 will rule in any market. But it assists us in conjecturing the 

 direction and general character of the effect which changes in 

 the condition or requirements of the parties will produce. For 

 example, in the case of international trade the various effects of 

 a tax or other impediment, which most students find it so diffi- 

 cult to trace in Mill's laborious chapters, are visible almost at a 

 glance by the aid of the mathematical instrument [b). It takes 

 Prof. Sidgwick a good many words to convey by way of a par- 

 ticular instance that it is possible for a nation by a judiciously 

 regulated tariff to benefit itself at the expense of the foreigner. 

 The truth in its generality is more clearly contemplated by the 

 aid of diagrams such as those employed by the eminent mathe- 

 matical economists Messrs. Auspitz and Lieben {c). 



There seems to be a natural affinity between the phenomena 

 of supply and demand and some of the fundamental concep- 

 tions of mathematics, such as the relation between function and 

 variable,^ between the ordinate of a curve and the corresponding 

 abscissa,^ and the first principle of the differential calculus ; 

 especially in its application to the determination of maxima and 

 minima. The principle of equilibrium is almost as dominant in 

 what Jevons called the mechanics of utility as in natural philo- 

 sophy itself. In so many instances does mathematical science 

 supply to political economy what Whevvell would have called 

 " appropriate and clear " conceptions. Their use might, per- 

 haps, be illustrated by comparing — however fancifully, and si 

 farva licet componere magnis — the advance in economics which 

 Jevons initiated or continued to the advance in mathematics 

 which the new and sublime method invented by Sir William 

 Hamilton appears to have effected. Algebra and geometry are 

 to ordinary language in political economy somewhat as qua- 

 ternions are to ordinary algebraic geometry in mathematical 

 physics, if we accept the view of the latter relation which has 

 been given by a very competent judge. Clerk Maxwell. " I am 

 convinced," he says, " that the introduction of the ideas as dis- 

 tinguished from the operations and methods of quaternions will 

 be of great use in the study of all parts of our subject, and 

 especially .... where we have to deal with a number of 

 physical quantities, the relations of which to each other can be 

 expressed far more simply by a few expressions of Hamilton's 

 than by the ordinary equations," ^ This is the spirit in which 

 the economist should employ mathematics — "the ideas as distin- 

 guished from the operations and methods." 



In considering the above-given, and indeed any concrete in- 

 stances, it is hardly possible to keep to what may be called the 

 simplest type of supply and demand, the ideal market in which 

 we contemplate only two groups of competitors and only two 

 articles of exchange ; say, gold for corn, or any other (juid pro 

 (]uo. In general, and especially when considering what rates of 

 exchange tend to rule in an average of transactions, it is proper 

 to take into account that the dealings in one market will affect 



• The treating as constant what is variable— e.g. supply, margin, wages 

 fund, is the source ot most of the fallacies in pohtical economy. 



^ For instance, the two meanings of increased demand— which Mr. Sidg- 

 wick has contrasted as the rwirand the extension of demand — are most easily 

 and with least liability to logomachy distinguished as the variation of an 

 ordinate (i) due to the displacement of the curve, the abscissa not varying, 

 or (2) corresponding to an increment of the abscissa, the curve being 

 undisturbed. 



3 Clerk Maxwell, " Electricity and Magnetism." Art. He says in the 

 context: "As the methods of Descartes are still the m^st familiar to stu- 

 dents of science, and as they are really the most useful for purposes of cal- 

 culation, we shall express all our results in the Cartesian form." Compare 

 Prof. Marshall's dictum with respect to the use of the vulgar tongue in 

 ■ Economic Reasonings," cited below, p. 9. 



those in another. If the etitrtpreficiir has less to pay for 

 machinery, cirdris paribus, he will be able to offer more on 

 the labour market. Thus we obtain the idea of a system of 

 markets mutually dependent. In a general view of this corre- 

 lation it is not necessary to distinguish whether the state of one 

 part is connected as cause or effect with the other parts of the 

 system. As Prof. Marshall ^ says:— "Just as the motion of 

 every body in the solar system affects and is affected by the 

 motion of every other, so it is with the elements of the problem 

 of political economy " (e). 



This conception of mutually dependent positions is one in 

 which minds disciplined in mathematical physics seem pecu- 

 liarly apt to acquiesce. In other quarters there may be observed 

 a restless anxiety to determine which of the variables in a system 

 of markets is to be regarded as determining or regulating the 

 others. In one of the principal economic journals there has 

 lately been a pretty stiff controversy on the question which of 

 the parties in the distribution of the national produce may be 

 regarded as " residual claimants upon the product of industry " 

 {Quarterly Journal of Economics, 1887, p. 287 ; 1888, p. 9) ; 

 whether it is the working class which occupies this preferential 

 position, or if the ' ' real keystone of the arch " is interest. Such 

 questions certainly admit of a meaning, and probably of an 

 answer. But they will probably appear of secondary importance 

 to those who accept, as the first approximation to a correct view 

 of the subject, the principle of mutual dependence— what may 

 be called the Copernican theory of distribution, in which one 

 variable is not more determined by another than the other is by 

 that one (/). 



Among the factors of this economic equilibrium I have not 

 as yet explicitly included cost of production. Rather, the sys- 

 tem of markets which so far I have had in view is that which 

 would arise if the articles of exchange were periodically rained 

 down like manna upon the several proprietors, and each indi- 

 vidual sought to maximize his advantage according to the law 

 of final utility. But now we must observe that self-interest does 

 not operate in this fashion. We must take account of efforts 

 and sacrifices. 



Here, again, the language of symbol and diagram is better 

 suited than the popular terminology to express the general idea 

 that all things are in flux, and that the fluxions are interde- 

 pendent. In Prof. Marshall's words, " As a rule, the cost of 

 production of a thing is not fixed ; the amount produced and its 

 normal value are to be regarded as determined simultaneously 

 under the action of economic laws. It, then, is incorrect to say, 

 as Ricardo did, that cost of production alone determines value ; 

 but it is no less incorrect to make utility alone, as others have 

 done, the basis of value" ("Economics of Industry," p. 148). 

 Among those who may have gone astray in the latter sense, 

 who, in their recoil from Scylla, are at least sailing dangerously 

 near Charybdis, may be placed the important Austrian school 

 who have rediscovered and restated the theory of final utility 

 without the aid of mathematical expression. To amplify a figure 

 suggested by one of them,- let us figure the hard conditions of 

 industrial life by the austerity of a schoolmaster, who, in order 

 to cultivate patience and fortitude in his scholars, should dis- 

 tribute among them certain rewards — it might be toys and sweets 

 — in return for certain amounts of fatigue and pain endured. 

 Thus, the cost of procuring a marble might be writing out 

 twenty lines ; the cost of a top, standing half an hour in the 

 stocks. Supposing exchange to be set up among the members 

 of the youthful population, free competition being assumed, there 

 would theoretically arise an equilibrium of trade in which the 

 value of each article would correspond to its final utility. That 

 is, if a top exchanged for ten marbles, it might be expected that 

 each boy would prize the last top about as highly as the last 

 decade of marbles which he thought fit to purchase. So far, 

 final utility may be regarded as the regulating principle. 



But it is equally true that the final r/iV-utilities of the exchanged 

 articles will be equal. If a top is worth ten marbles, we are 

 entitled to expect such an adjustment of trade that each and 

 every boy would as soon stand in the stocks half an hour as 



' In a remarkable review of Jevons's theory in the Academy of April t, 

 1872. 



'^ Cf. Prof. Bohm Bawerk : " Es kann ein Erzieher einem Knaben, urn 

 ihn gegen Weheleidigkeit_abzu!iarten, fiir die tapfere, freiwillige Erduldung 

 von bchmerzen ein sehnlich begehrtos Spielzeug in Aussicht stellen. So 

 untergeordnet das Vorkommeu solcher Falle aucn sein mag, so wichiig ist 

 es fur die Theorie festzustellen, dass Arbeit und Arbeitsplage doch nicht der 

 einzige Umstand ist, auf den sich . . , die Wertschatzung griinden kann." 

 — Konrad's Jahrbuch, 1886, p. 43. 



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