5o8 



NATURE 



[Sept. 19, 1889 



or combinations respectively. Then the locus of bargains 

 which it is not the interest of both parties to disturb is the con- 

 tract-cwve,pq (" Math. Psych.," /^<:. cit.). At what point, then, 

 on this curve will the transaction settle down ? If we assume 

 that the conditions of a market are retained, the required point 

 is at the intersection of the supply- and demand-curves, which is 

 on the contract-curve. That is the solution of Messrs. Auspitz 

 and Lieben ("Theorie," p. 381). It corresponds to the prin- 

 ciple laid down by Prof Marshall for the action of arbitrators 

 (referred to above in note). But Prof Menger, who has a 

 numerical scheme equivalent to a rudimentary contract-curve 

 (" Grundsiitze," pp. 176-78), and Prof. Bohm-Bawerk, referring 

 to the " Spielrau7n" afforded by the indeterminates of bargain, 

 recommend to "split the difference." Instead of "equal," 

 " equitable " division has been proposed by the present writer — 

 namely, that adjustment which produces the maximum of utility 

 to all concerned ; not subject to the conditions of a market, but 

 irrespectively thereof [equations (j8) and (7), without equation 

 (a) in note (e) above], the utilitarian arrangement, which also is 

 represented by a point in the contract-curve, say u in Fig. 9. 

 Such might seem to be the ideally most desirable arrangement ; 

 but very likely the practically best, the irpaKrov ays06v, is in the 

 neighbourhood indicated by Prof. Marshall and Messrs. Auspitz 

 and Lieben, 



(;«) The Austrian School.— Prof. Menger and his fol- 

 lowers have expressed the leading propositions of the economic 

 calculus — the law of diminishing utility, the law of demand 

 and supply, and so forth — by means of pirticular numerical 

 examples, supplemented with copious verbal explanation. Their 

 success is such as to confirm the opinion that the mathematical 

 method is neither quite indispensable nor wholly useless, nee 

 nihil nee omnia, like most scientific appliances. Conceding 

 that in the main they impart a saving knowledge of the 

 true theory of value, it may still be maintained that they 

 occasionally emphasize the accidents of a particular example 

 as if they formed the essence of the general rule ; that their 

 explanations are excessively lengthy ; and yet their meaning 

 sometimes is obscure. For instance, Prof Bohm-Bawerk 

 may seem to attach undue importance to his conception of 

 the Grenzpaar. He illustrates the play of demand and supply 

 by supposing a market in which on the one hand there are 

 a number of dealers each with a horse to sell, and on the other 

 hand a number of would-be buyers {Konrad's yahrbucJi, 

 1886; "Kapital," p. 211; cp. Mr. James Bonar's excellent 

 article in the Quarterly Jotirtial of Economics, 1888). The 

 latter are arranged in the order of their strength : first, the one 

 who is prepared to give most for a horse, the hitrhest price 

 which the second can afford is less, and so on. Parallel to this 



Fig. 10. 



arrangement is that of the would-be sellers : first, he who can 

 sell cheapest, and so on. Upon this hypothesis it might happen 

 that the fifth would-be buyer is willing to give a little more than 

 the lowest figure which the fifih would-be seller will take ; while 

 the sixth on the side of the buyers is not willing to give quite as 

 much as the sixth horse-dealer stands out for. In this case five 

 horses only will be sold ; and the couple who are the last between 

 whom a bargain is possible — buyer No. 5 and seller No. 5 — 

 enjoy a mighty distinction as the Grenzpaar ; an honour which 

 is to some extent shared with No. 6, the first couple between 

 whom a bargain is impossible. 



Now this attention 10 a particular couple is not always appro- 

 priate. How if the weakest actual buyer should prove to be, 

 not buyer No. 5 but buyer No. i, as to a second \iQX%e.'i Prof. 

 Bohm-Bawerk, indeed, has thought of this case, and called 

 attention to it in a note to his later redaction (" Kapital," p. 

 2x8). So far — although the whole simplicity of the scheme is 

 destroyed when wr permit second and third horses to the 

 different buyers andsellers — theconception of a "limiting couple" 

 may still be retained. It will be found, however, that this idea 

 is not appropriate to the general case of a divisible commodity, 

 which a single individual on one side of the market may buy 



from or sell to a large number on the other side. That general 

 case is much more clearly represented by a diagram like Fig. 10, 

 where the inner thin-lined curves represent the dispositions of 

 the individual dealer, the outer thick curves the collective supply 

 and demand (cp. Auspitz and Lieben, "Theorie der Preise "). 

 No doubt Prof. Bohm-Bawerk's conception is appropriate to a 

 particular case, that in which the kleiitste markiibliche Men- 

 geneinheit, in the phrase of Messrs. Auspitz and Lieben {ibid., 

 p. 123), is considerable. But it is better, with those eminent 

 theorists, to begin with the general or, at least, the simple case. 



As an instance of the excessive circumlocution in which the 

 purely literary method is liable to be entangled, we may notice 

 the doctrine of objective and subjective value, which occupies 

 many pages in the works which we have cited. I have been un- 

 able to find more in the distinction than what is visible on a 

 glance at the appropriate diagram. The individual's subjective 

 estimate of worth is expressed by his particular demand- or 

 supply-curve, Oe^, Oe^, &c., Og^, Og.^, &c., in Fig. 10. The 

 proper combination of those individual curves gives the collective 

 demand- and supply-curves, of which the intersection represents 

 the "objective" value. 



Moreover, verbal circumlocutions are so little adapted to ex- 



