ON SLIDING SCALES AND ECONOMIC THEOET. 527 



assumption seems to me to be fundamental that ' doses ' of capital and 

 labour — to use tbe elder Mill's suggestive expression — can be applied to 

 the cultivation of land in infinitely small quantities, and that the returns 

 to those doses, when a certain point of cultivation has been reached in a 

 certain stage of civilisation, diminish also cceteris paribus by infinitely 

 small degrees. 



Or take again — though I do not lay much stress on this — one variety 

 of what I may perhaps call the application of the 'graphic method ' to econo- 

 mics. It seems to me — though I speak, I confess, with some hesitation — to 

 be impossible to represent, as some economists have done with conspicuous 

 success, economic theorems by geometrical curves unless we assume the 

 possibility of division into infinitely small quantities. 



This possibility, in fact, is the underlying basis of any theory of com- 

 petition, and in the final analysis of any such theory it cannot fail to 

 appear. The theory may indeed be only hypothetically true ; although for 

 my part I must confess that I am inclined to believe that it is a more 

 accurate and serviceable representation of fact than is sometimes main- 

 tained. The conditions, again, of the hypothesis must always be remem- 

 bered ; and it may be the case in some instances that the quantities into 

 which the commodity or service is capable of division may only be in- 

 finitely small in comparison with the great mass of the commodity or 

 service under consideration. But this possibility does not prevent the 

 theory from being hypothetically true ; nor, on the other hand, does it 

 obviate its failure to apply in its entirety to cases where this capacity of 

 infinite divisibility is lacking. 



One of these cases occurs whenever a combination of sellers meet a 

 combination of buyers. The commodity or service offered by either 

 party in exchange for that supplied by the other is ex hypnthesi whole and 

 indivisible. There may indeed possibly be — as we shall endeavour to 

 illustrate later — a maximum as well as a minimum limit beyond which it 

 may respectively be the interest of neither party to go. But no theory 

 of competitive economics — based as it is on the possibility of infinite sub- 

 division — will enable you to determine the precise point between these two 

 limits at which it is for the joint interest of the two parties to stop ; for 

 the commodities or services they are exchanging are, by the very terms of 

 the existence of the combinations, incapable of that infinite subdivision. 

 On the one side you have, roughly speaking, in the case of a sliding 

 scale a combined mass of labour offered for sale ; on the other, you have a 

 combined mass of remuneration, be it expressed in terms of nominal or 

 real wages or earnings — and by the very conditions of the combinations, 

 neither of these two masses is capable of infinite divisibility. If a com- 

 bination of buyers alone, or a combination of sellers alone existed, this 

 capability might indeed be impaired, but it would not be paralysed. The 

 one commodity or service off'ered in exchange would retain it, and the 

 other would lose it. And hence it is, I suppose, that Professor Sidgwick 

 has discussed ^ as a part of economic theory the action of monopoly or 

 combination. But the combination he considers is, as he himself ex- 

 presses it, only one-sided ; and the combinations in connection with a 

 sliding scale, which we are now discussing, are found on both sides. And 

 yet the existence of these combinations seems, we must remember, to be 

 a necessary condition of successful conciliation, or arbitration, or sliding 



• Principles of Political Economy, Book II ch x. 



