676 REPOET— 1889. 



Professor Walras, illustrating the operation of a simple market, supposes each 

 dealer, before going to market, to writedown his scale of requirements — how much 

 he would be willing to buy or to sell at each price. From these data it would be 

 easy to calculate beforehand the rate of exchange which would prevail in the 

 market formed by those individuals. But, when we advance from the simplest 

 type of market to the complexities introduced by division of labour, it is seen to be 

 no longer a straightforward problem in algebra or geometry, given the natures of 

 all the parties, to find the terms to which they will come. Here, even if we imagine 

 ourselves in possession of numerical data for the motives acting on each individual, 

 we could hardly conceive it possible to deduce a priori the position of equilibrium 

 towards which a system so complicated tends. 



Accordingly it may be doubted whether the direct use of mathematical formulae 

 extends into the region of concrete phenomena much below the height of abstraction 

 to which Jevons has confined himself. However, the formulation of more complicated 

 problems has still a negative use, as teaching the Socratic lesson that no exact 

 science is attainable. As Dupuit, one of the greatest of Jevons's mathematical 

 predecessors, points out, ' Quand on ne pent savoir ime chose, e'est d6ja beaucoup 

 que de savoir qu'on ne sait rien.' ' If, he says, the early theorists, instead^ of 

 formulating the balance of trade, had confined themselves to declaring the question 

 above their powers, they would probably have done a greater service than the suc- 

 cessors who refuted them. So Cournot, referring to his own mathematical treat- 

 ment of economics, ' Aussl nos modestes pretensions 6taient-elles non d'accroitre de 

 beaucoup le domaine de la science proprement dite, mais plutot de montrer (cequi a 

 bien aussi son utility) tout ce que nous manque pour donner la solution vraiment 

 scientifique de questions que la polemique quotidienne tranche hardiment.' - Simi- 

 larly Jevons says,^ ' One advantage of the theory of economics, carefully studied, 

 will be to make us very careful in our conclusions when the matter is not of the 

 simplest possible nature.' 



In the vineyard of science to perform the part of a pruning-hook is an honour- 

 able function ; and a very necessary one in this age of luxuriant speculation, when 

 novel theories teem in so many new Economic journals. I give in the appended 

 notes an example of this corrective 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 Professor Walker, I act upon the Miltonic rule for selecting an 

 adversary : 



' Best with the best, more glory will be won. 

 Or less be lost.' 



In the preceding remarks 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 com- 

 peting against each other has been copied out of mathematics into the vulgar 

 tongue by many well-known writers, and need not here be repeated (Jt). 



It is in this department perhaps that we can best answer Cairnes's challenge to 

 Jevons to produce any proposition discovered 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 

 if 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, 



' Annales des Fonts et Chavssees, 1844, p. 372. 



'' Revue Sommaire. 



2 Theory of Political Economy, p. 157, second edition. 



