694 KEPORT — 1889. 



a genuine supply curve. For at any point on that part of the locus it is evidently the 

 interest of the individual to increase his production, price being constant. Stable 

 equilibrium, therefore, can exist only on the ascending, the unbroken branches. The 

 thick curve lines in the figure indicate the locus of greatest possiUe, as distinguished 

 from maximnm, utility. Suppose that at and above the price, corresponding to the 

 point q, it is the interest of the producer to adopt the larger scale of production. "Up 

 to that price his industrial dispositions will be represented by the inner curve ; on 

 reaching that point he will jump from q to q' and ascend along the outer curve. The 

 locus of greatest possible utiUty may be called the genuine or effective supply-curve, 

 A similarly shaped supply-curve may exist for other producers. Suppose now all 

 these individual effective supply-curves compounded, and we have the effective supply- 

 curve for the community, SS', which continually trends outwards. This character is 

 not annulled by the existence of steps in the tract MN, corresponding to the prices at 

 which the leap of each individual occurs. A fm-tiori the Demand-curve continually 

 trends outwards like that in Fig. 1 (cp. Auspitz and Lieben). It should seem, there- 

 fore, that theoretically on the supposition of enlightened self-interest there is only one 

 rate of exchange at which Supply is just equal to Demand. No doubt there is some- 

 thing to be said on the other side. Suppose the jump from q to q', or from q' to q, 

 involves expense and a breach of habit, which the ' economic man ' will not neglect. 

 A little attention will show that in this case the tract MN' of the Collective-curve 

 might break up in two separate branches. Moving from M upwards we should not 

 be on the same locus as from N downwards. 



(Ji) One-sided Monopoly.— In Fig. 8 let the curve SS' represent the demand of 

 the public for a monopolised article, the abscissa denoting price, the ordinate quantity. 

 Then, as Cournot shows, if there are no expenses of production the rectangle Oyrar 

 should be a maxivmmi (' Kecherches,' Ai-t. 25) ; or rather the greatest 2)ossi'ble. The 

 solution is not likely to be indeterminate, except in the particular case where the 

 Demand-curve is an equilateral hyperbola. Indeterminateness is similarly exceptional 

 when there are expenses of production (cp. Sidgwick ' Pol. Econ.,' Book ii. ch. 2, § 4). 



(Z) Two-sided Monopoly. — In Fig. 9 let 0^^ and Oq represent the curves of con- 

 stant satisfaction, or indifference curves (above note {d) ; ' Theorie der Praise,' 

 Appendix II. ; ' Mathematical Psychics,' p. 21) drawn through O for two indivi- 

 duals or combinations respectively. Then the locus of bargains which it is not the 

 interest of both parties to disturb is the contract-curve, jjq ('Math. Psych.' loc. 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 

 principle laid down by Professor Marshall for the action of arbitrators (referred to 

 above in note 1 , p. 675). But Professor Menger, who has a numerical scheme equivalent to 

 a rudimentary contract-curve ('Grundsatze,' pp. 176-8), and Prof essor Bohm-Bawerk, 

 referring to the 'Spielraum' afforded by the indeterminateness 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 (/8) and (7), without equation (a) in note (e) above), the utilitarian arrange- 

 ment, 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 practi- 

 cally best, the irpaKThv ayaeSv, is in the neighbourhood indicated by Professor Marshall 

 and Messrs. Auspitz and Lieben. 



(m) The Austeian School. — Professor Menger and his followers 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 particular numerical 

 examples, supplemented with copious verbal explanation. Their success is such as to 

 confirm tlie 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 emphasise the accidents of a particular example 

 as if they formed the essence of the general rule ; that their explanations are exces- 

 sively lengthy ; and yet their meaning sometimes is obscure. For instance. Professor 

 Bohm-Bawerk may seem to attach undue importance to his conception of the Grenz- 

 paar. 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 seU, and on the other 



