264 REPOET — 1887. 



professional payments) enters in as an independent item ; but the price 

 of industrial labour (ordinaiy wages) only as representative, and in the 

 absence, of the finished products. 



In constructing the formula for combining the quantities and prices 

 thus defined, we may first distinguish the abstract and ideally simple case 

 in which exactly the same quantity of each article is consumed at the two 

 epochs. In this case the method of procedure is that indicated by Professor 

 Sidgv/ick in his Political Economy (Book I. chap. ii. s. 3) : ' Summing 

 up the amounts of money paid for the things consumed • at the old and the 

 new prices respectively,' and [to find the value of the Unit at the later 

 epoch] dividing the latter sum by the former. 



A difiiculty arises when we introduce the concrete circumstance that 

 the quantities consumed at the two epochs are not the same. We might 

 distinguish two grades of this deflection from the abstract ideal : (I) 

 where the interval of time between two revisions being very small the 

 variations in the amounts consumed are slight, differentials, we might call 

 them ; and (II) integral or considerable changes which occur in the course 

 of a long interval of time. 



1. The method of procedure in the first case may thus be symbolised : 

 Let a, /3, y, &c., be the quantities of commodities consumed * at the initial 

 epoch, and a', j3', y', &c., at a subsequent epoch ; it is assumed that 



— ^ IT ^^ ^^^ *^°- = ^ nearly. And similaily for a second subsequent 



a" ft" 

 epoch — = -^ = 1 nearly. Upon these assumptions several methods of 



determining the Unit present themselves. Let us designate the prices at 

 the initial epoch by p^. p^ Py, &c., and at a subsequent epoch pj pj pj, &c. 

 Then, 



(1) "We may take the type which first presents itself upon Professor 

 Sidgwick's view of the problem, viz. — 



gjj'a + ftp' 13 + &c- 

 upa + ftpff + &c. 



This method is (in effect) adopted by Mv. Sauerbeck for years earlier 

 than 1866-77 (' Journ. Stat. Soc' 1866, pp. 595-613). 



The method is also exemplified by Mr. Giffen's retrospective estimate 

 of the change in the value of money between 1873 (and 1883), and earlier 

 years (Report on Prices of Exports and Imports, 1885, Table V.). 



(2) The next type, also given by Professor Sidgwick,^ is the con- 

 verse of the first, viz. — 



a'p'a + ft'p'e + &c. 

 a'p^ + ft'pff + &c. 



This method is exemplified by Mr. Giffen in his Table IV. (Reports 

 1881, 1885), by Mr. Mulhall, and by Mr. Sauerbeck (for years after period 

 1867-77), (' Journ. Stat. Soc' 1886, p. 595). 



' Agreeably to this definition the prices on which the Consumption Standard is 

 based should theoretically be the prices paid by consumers — retail prices. For 

 tJiis purpose wholesale prices are to be employed only in the absence of the proper 

 statistics, as an index of prices paid for the finished products — a very imperfect 

 index, as Dr. Scharling, in his excellent paper on retail prices, and other authorities, 

 have shown. 



- See the passage above referred to. 



