688 REPOET — 1889. 



forward those which occur to me as the best — if, indeed, there is any absolutely best 

 in the matter of expression. For some purposes it would have been proper to take 

 account of the various qualities of land (as I have elsewhere done — ' Brit. Assoc. 

 Eep.' 188G). For other purposes it would be well to put labour hired by the entre- 

 preneur as an independent variable. When this or any other variable is omitted we 

 are to understand that there is implied the best possible arrangements with respect 

 to the variables which are not expressed. The nature of this implication is shown in 

 the following note. 



(9) So far we have been taking for granted that the entrepreneur does his best, 

 without reference to the motives acting upon him, the pleasures procurable by the sale 

 of his product. Formally it would be proper to take account that the utility-function 

 ■i/y. involves the effort, say e,., explicitly, as fatigue diminishes advantage, and 

 implicitly, as exertion increases production. Corresponding to the new variable we 

 have a new equation, the complete differential of i|/,. with reference to e,., say 



CzjJ^ + { -'\ -^— = o. It is a nice question how far effort should be regarded as an 



V der) \dfr) der 



independent variable ; how far the essential principle of piece-work prevails in modern 



industry. 



(7i) Industrial Competition.- — The condition that net advantages should be 

 equal in industries between which there is mobility may thus be contemplated. Let 

 us put the advantage of an individual, say No. r, engaged in the occupation s as a 

 function of his net income, the price of the articles on which his expenditure is 

 made, and the disutility of effort. Say <;),., (f,.s (ir„ ir, .... e„),Pi,p„ . . . . — e„) ; 

 where </)„ is a utility-fimction, not necessarily the same for the same individual in 

 different occupations, since his indulgences may vary with the nature of his employ- 

 ment ; fre— a symbol not identical with the/ of the last but one note — is the indi- 

 vidual's net earnings in the business s, involving prices ir, tt^, &c., of all manner of 

 agents of production, involving also as stated in note g the effort e^s ; p^, jh &c., are 

 prices of articles of consumption as a function of which the individual's advantage 

 may be obtained by means of the equations (o) and (;3) in note (e) — eliminating the 

 quantities consumed. The last variable in the function ip„, the explicit Crs, has a 

 negative sign prefixed, to indicate that the direct effect of increased fatigue is 

 diminished advantage. 



The equation of Net Advantages imports that the advantage, <!>„, of the occupation 

 which the individual chooses is not less than 0„, the advantage of any other occupa- 

 tion open to him. It is important to observe that for all occupations the complete 



differential with regard to e is zero ; in symbols i^A j +\ ;r ) =^- ■^'^* *^is equa- 

 tion conveys no presumption that the final disutility in different occupations is the 



same that ( -5^ ) = ( -*- ). The equation of final disutility holds only where efforts 



\dersJ \dertJ 

 and sacrifices are capable of being applied in ' doses ' to any number of occupations. 

 The latter is the only case, I think, contemplated by Jevons in his analysis of Cost of 

 Production (' Theory,' ch. v.). The inquiry, what is meant in general by saying that 

 the cost of production of two articles is equal, must start from right conceptions about 

 Final and Total Utility. But this is not the place to follow up the difficult investi- 

 gation. I do not attempt here to discuss any matter fully, but only to illustrate the 

 suitability of the subtle language of mathematics to economical discussions. 



(i) Peofessor Walker's Theory of Business Profits.— Professor Walker's 

 theory as stated in the ' Quarterly Journal of Economics' for April, 1887, involves 

 the proposition that the remuneration of the lowest, the least gifted employers, is on 

 a level with that of the labouring class. Concerned as we are here with methods 

 rather than results, it is allowable to posit this premiss without expressing an opinion 

 as to its accuracy. It is fortunate not to have to take sides on an issue concerning 

 which the highest authorities are divided, and statistical demonstration is hardly 

 possible. 



But, though the expositor of method is not called to dispute the truth of this 

 proposition, he has something to say against the evidence which has been adduced 

 in proof of it. He must enter a protest against the form of the following argu- 

 ment : — 



' Let our hypothesis be clearly understood. We assume, first, that there is ia a given 



