Sept. 19, 1889] 



NATURE 



499 



many new economic journals. I give in the appended notes an 

 example of this c irrective process applied to a theory of great 

 worth and authority, and concerning the most vital interests, 

 such as the relations of employer and employed, and the 

 Socialist attack on capital (?). In directing this weapon of 

 criticism against Prof. Walker, I act upon the Miltohic rule for 

 selecting an adversary — 



" Best with the best, more glory will be won, 

 Or less be lost." 



In the preceding remairks I have had in view, as presumably 

 most favourable to computation, the case of bargains in which 

 there is competition on both sides. It is now to be added that 

 the mathematical method is nearly as applicable to a regime 

 of monopoly. Here Cournot, rather than Jevons, is our guide. 

 Cournot's masterly analysis of the dealings between a monopolist 

 seller and a number of buyers competing against each other 

 has been copied out of mathematics into the vulgar tongue by 

 many well-known writers, and need not here be repeated (/t). 



It- is in this department, perhaps, that we can best answer 

 Cairnes's challenge to Jevons to pioduce any proposition dis- 

 covered by the mathematical method which is not discoverable 

 by ordinary reasoning. Not, indeed, that the economist is 

 bound to answer that challenge ; any more than, in order to 

 prove the advantages of international trade, he is concerned to 

 deny that claret may be produced in Scotland. 



The following proposition is a particular case of a more 

 general theorem given by Cournot. Let there be a railway 

 and a line of steamers, each forming part of a certain through 

 journey, and separately useless ; the fares will be lower when 

 both means of transport belong to a single company than where 

 there is less monopoly, the two services being in the hands of 

 two companies, each seeking its own gain independently of the 

 other. 



The rationale of this somewhat paradoxical proposition is not 

 easily discerned without the aid of symbols. Cournot, in a 

 popular redaction (" Revue Sommaire ") of the theories which he 

 first conceived in a mathematical form, suggests, as a generally 

 intelligible explanation, that it is better to be at the mercy of a 

 single master than of several petty tyrants. But this seems to 

 be a commonplace of the sort which, in the absence of rigid 

 reasoning, has so often deceived the amateur economist. Might 

 it not be applied to the case of monopoly in general ? 



It would be hard to say how much this remarkable proposition 

 may add to the arguments in favour of the Government monopo- 

 lizing railways. Nor would I undertake to estimate the practical 

 significance of Cournot's numerous mathematical theorems on the 

 taxation of monopolists. We might perhaps compare the func- 

 tion of the sovereign science with respect to the theory of monopo- 

 lies to the duty of Government as to their management — to 

 exercise a general supervision without attempting to control 

 details. 



We have in the last few paragraphs been supposing monopoly 

 on one side of the market, on the other side a public competing 

 with each other. Let us now consider the bargain between two 

 monopolists, whether individuals, or rather corporate trading- 

 bodies, combinations in the most general sense of the term. The 

 mathematical analysis of this case brings very clearly into view 

 the important property, which is not very prominent in writings 

 of the pre-Jevonian era, that the bargain between two self- 

 interested co-contractors is not determinate in the same sense as 

 in a regime of perfect competition. 



No doubt, if we take a very simple case — such as that 

 imagined by De Quincey, of the bargain between the owner of 

 a musical -box and a colonist already on his way to a distant 

 region where n > luxuries can be purchased — it is easy to see that 

 the bargain may settle down at any point between certain limits. 

 15ut where both the amount of commodity 10 be sold and money 

 to be paid are variable, as in the momentous case of a bargain 

 between a combination of employers on the one hand and eni- 

 floyes on the other, it is a less familiar truth that the terms of 

 the contract are in general to some extent indeterminate. For 

 instance, the bargain may be either all in the interest of the one 

 party, say long hours and small pay, or, on the other hand, high 

 wages with much leisure. 



The significance of this proposition has been missed by many 

 of those who have treated the subject without the aid of the appro- 

 priate apparatus. Some fail to see that there is any peculiarity 

 in the bargain between isolated units. Another discerns the 

 indetcrminateness of the bargain only in the special case in 



which the article exchanged is a large indivisible object, like a 

 house. Another limits the difficulty to the case of a single 

 negotiation as distinguished from a contract which, as in the 

 actual labour market, may be modified from time to time. 

 Another tells us that in such a bargain the most anxious party 

 gains least. 



All these phrases seem to obscure the cardinal distinction that 

 perfect competition tends to a determinate settlement, whereas 

 in a regime of combination a principle of adjustment is still to 

 seek. What is that principle ? 



At a former meeting of the British Association, on the 

 occasion of a discussion on sliding scales, I stated the difficulty 

 which there might be, in the absence of competition, in defining 

 fair wages and reasonable terms, and I asked the eminent Pro- 

 fessor who introduced the subject in what direction one should 

 look for a solution of this difficulty. His reply imported, as I 

 understood, that no other general rule can be given but this : to 

 obtain a full knowledge of, and bring a candid judgment to bear 

 on, all the circumstances relevant to each case. To which I 

 would add that one circumstance relevant to this whole class of 

 cases is just the fact that there is in the abstract such a marked 

 difference between combination and competition. 



Possibly the dry light of abstract science may enable us to see 

 a little further into this difficulty. Analysis strongly suggests that 

 the right solution is what may be called the utilitarian arrange- 

 ment, that which is productive of the greatest sum total of 

 advantage for all concerned. The utilitarian determination is 

 clearly discerned to be by no means necessarily coincident with 

 the settlement towards which competition tends. For instance, 

 the vrai prix, in Condillac's sense, as determined by the play of 

 supply and demand in the labour market, might be such that 

 the entrepreneur class should take the lion's share, leaving the 

 labourer a bare and painful subsistence ; but there is no ground 

 to believe that this is the best possible arrangement. From an 

 abstract point of view it is by no means evident that a free 

 labour market "is the only way to equity, that any interference 

 with it must involve injustice " (Danson). Nor need it appear " a 

 great fundamental principle — as inevitable in its action as gravi- 

 tation — that a fair day's wages for a fair day's labour is deter- 

 mined by the proportion which the supply in the market bears to 

 the demand" (Rupert Kettle on "Arbitration"). It may be 

 true indeed, in a practical sense, that perfect competition is 

 "not less harmonious and beneficent in its operation than 

 gravity" (Walker, " Political Economy ") ; but theoretically it is 

 tenable that there is an adjustment of contracts more beneficent 

 than that which the mechanical play of competition tends to 

 establish (/). 



To introduce these philosophical conceptions of utilitarianism 

 will doubtless seem irrelevant to those who are immersed in the 

 details of business. But the practical man should be reminded 

 that in other spheres of action, politics and morals, the principle 

 of utility, however badly received at first, has exercised a great 

 influence — though doubtless not so great as was anticipated by 

 some theorists, and requiring to be largely tempered with common- 

 sense. 



Such, I think, are the principal points at which mathematical 

 reasoning is capable of being applied to political economy. In 

 estimating the use of this method it is natural to take as our 

 standard the helpfulness of mathematics in other departments of 

 science. 



As compared with mathematical physics, the mathematical 

 theory of political economy shows many deficiencies. First, there 

 is the want of numerical data, which has been already noticed. It 

 is true that there is a faint hope of obtaining what Jevons too con- 

 fidently expected — statistical data for the relations between supply 

 and price. It is true also that in the higher mathematics con- 

 clusions which are quantitative without being numerical are more 

 frequent than is usually supposed. Some political econopiy is 

 as exact as some mathematical physics. The fields cultivated by 

 Section A and Section F may overlap, but it must be admitted 

 that the best part of our domain corresponds to what is the 

 worst part of theirs. If you inquire as to the products of our 

 inferior soils, we must confess, if we do not wish to conceal the 

 nakedness of the land, that over a large portion of our territory 

 no crop is produced. We are employed only in rooting out the 

 tares which an enemy has planted. Much of our reasoning is 

 directed to the refutation of fallacies, and a great part of our 

 science only raises us lo the zero point of nescience from the 

 negative position of error. " Sapientiq prima stultitid 

 cartnsse." In this introductory portion of political economy 



