July II, 1889] 



NATURE 



243 



which indicates the amount which any individual is willing 

 to purchase at the price represented by the tangent of the 

 angle R' OQ. The advantage which the individual derives 

 from that purchase is represented by the length of the 

 line R r' — that is, supposing money to be a uniform 

 measure of value, which would cease to be true when the 

 transaction is on a very large scale : for instance, the 

 payment of so much as Q R would so cripple a person's 

 resources as to render money a more important object to 

 him, to alter his Wertschiitzung des Geldes. Still, even in 

 this general case, O N is regarded as a " curve of constant 

 satisfaction," which we may describe as much the same 

 as the " line of indifference " of the English publication 

 to which we have referred. By a parity of construction 

 we have the cost curve to represent the amount of money 

 in return for which one would just be willing to produce a 

 certain quantity of an article; and the offer or supply 

 curve indicating the amount which the producer will offer 

 at a certain price. 



The curves which we have described represent primarily 

 the effective dispositions of individuals. By superposition 

 of such individualistic curves, we obtain corresponding 

 collective curves. The intersection of the collective de- 

 mand curve and the collective offer curve gives the price. 

 On this point our authors' analysis throws some new light. 

 They point out that most of the curves with which we 

 have to deal are of the nature of an envelope, made up of 

 a number of distinct loci. Consider the cost curve of the 

 individual, for instance. His dispositions may be re- 

 presented by two discrete curves, according as we con- 

 sider different scales of production; say, hand- work and 

 manufacture by machinery, corresponding to the neigh- 

 bourhood of Q and q' respectively, in the accompanying 

 figure. The outer portions of these lines, marked black 











Q' 



in our figure, form the genuine cost curve ; from which a 

 similarly composite offer curve may be derived. This 

 sort of discontinuity has not been unnoticed by other 

 writers, in the case of production. But we believe that 

 Messrs. Auspitz and Lieben are the first writers who have 

 maintained that the locus on the side of consumption is 

 similarly composite ; that the demand curve is made up 

 of several bits, corresponding to different styles of hfe 

 (^Lebensiveise). 



It follows from these conceptions that the demand 

 and supply curve, whose intersection determines price, 

 must be of a simple shape, not re-entrant and crumple- 

 horned, as they have sometimes been represented. 

 Whence we may deduce that — theoretically, and on the 

 supposition of enlightened self-interest— the price which 



tends to prevail in an ideal market is not only determinate, 

 but unique. There cannot be, as it were, several solutions 

 of the equations of exchange. The interest of this con- 

 clusion will be apparent when it is remembered that the 

 contrary statement is advanced as important by Mill, with 

 respect to international trade, and by Prof. Sidgwick, 

 with respect to trade in general. 



The curves employed by Messrs. Auspitz and Lieben 

 assist us in conceiving a subject on which many mis- 

 apprehensions exist— the gain of foreign trade. It takes 

 Mill and Prof Sidgwick a good many words to prove 

 that it is possible for a country, by a judicious import or 

 export tax, to benefit itself at the expense of the foreigner. 

 The truth is seen much more easily, and in a higher 

 degree of generality, by a glance at the appropriate 

 mathematical diagrams. 



The method also adapts itself to the dealings of a 

 monopolist. The influence of a single large dealer in 

 competition with several small ones is represented by a 

 construction of peculiar beauty and originality. If it is 

 true that we are drifting towards a regime of trusts, com- 

 binations, and monster establishments, surely any ray of 

 new light on this somewhat unexplored field ought to be 

 welcomed. It may be difficult, perhaps, to estimate the 

 positive practical value of this use of the mathematical 

 method. We might compare, perhaps, the function of 

 the sovereign science in respect to the theory of mono- 

 polies, with the duties of government in respect to their 

 management — to exercise a general supervision without 

 attempting to control details. 



Messrs. Auspitz and Lieben have also treated the case 

 of monopoly in which an individual or combination deals 

 with another economic unit. They of course see the 

 point, which is often missed by the litterateur, that, without 

 perfect competition, the determination of price is, within 

 certain limits, indeterminate. On the question, what basis 

 of arbitration — in the absence of the mechanical principle 

 of competition — should prevail, we venture to regard their 

 answer as much more profound than that which has been 

 given by the most eminent English Professors. An agree- 

 ment to the terms which afford the greatest sum total of 

 utility will tend to come to pass. The utilitarian position 

 thus indicated would coincide with the settlement towards 

 which perfect competition tends, upon a certain con- 

 dition which our authors have introduced. The condi- 

 tion may be described as proper to perfect competition ; 

 namely, that every portion of an article should be ex- 

 changed at the same rate. We are not satisfied that our 

 authors are justified in predicating this condition of a 

 bargain, such as that between an employer and a com- 

 bination of workmen. Nor do we accept the implied 

 optimistic conclusion that, in the abstract at least, the 

 play of competition in the labour market tends to the 

 arrangement which is the best possible for all concerned. 



But we are sensible that on points so abstruse it is 

 hardly possible to make our own meaning, or that of our 

 authors, clear, without a more copious use of symbols and 

 verbal explanation than would be here admissible. We 

 regret, also, that, while indicating sqme salient features 

 of the work before us, we have not been able to bring 

 out the beauty and completeness of the whole. Perhaps 

 no other piece of reasoning which has issuetl from the 

 mathematical school of economics is so perfectly fitted 



