ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 265 



(3) The third type is a mean between the first two, viz.-:- 



" ap^ +lipfi + &c. ^ a'p^ + 13' p^ + &c.' 



Professor Sidgwick has suggested and remarked upon this procedure 

 in a note. It has been noticed also by Drobisch. 



(4) The next type is also a mean : — 



i(a + aO X/, + 1 (f3 + /3')p',+ &C . 

 1 (a + a')p^ + ^{fi + l3')p^+ &c. 



suggested independently by Professor Marshall and the present writer. 



(5) The next type is one adopted by Mr. Palgrave : — 



ay. X^ + B'p'^ X^+&c. 



o!p'.+P'p'a+ &c. 



(6) The sixth type is that which Mr. Giffen has employed in his 

 Table III. Put ,a and ^p^ for the quantity and price of the first com- 

 modity in 1875 (or other year selected as representative). Then for the 

 increase in the value of money in the year whose symbols are a', p'^, as 

 compared with year a, p^, write : — 



,a,p^X^^^^^^^ + ,P^p^X^-^^:ZPl 



P^ P? 



fl-iP^ + fiiP^ + ^C- 



The expression for what we have called the Unit is found by adding 



unity to the above (substituting ^ for - ^°~^'' ). 



Pa P,. 



(7) Next we may place the formula of Drobisch, of which the prin- 

 ciple is to compare the price at different epochs of an objective unit, 

 such as a hundredweight, supposed to be made up of all sorts of articles 

 in the proportion in which they enter into national consumption. In our 

 notation the formula (for what is here called the unit) becomes 



^'P' . + (3'p'fi + &c . _^ a p^ + /3 p ^ + &c. 

 a' + /3' + &c. • ^+^"4- &c. 



(8) Last, but not least, either in respect of bulk or of theoretic 

 weight, occurs the formula of Dr. Julius Lehr (referred to above, p. 263), 

 of which the principle is to compare the price at different epochs of a 

 pleasure-unit, or unit of final utility. The formula may be thus con- 

 veyed in our notation :— The mean ' Genusseinheit,' or final utility, of the 



first commodity is " , ■ Of such units these came into consump. 

 ap^ + «i5\. ^ 



tion, a at the first epoch, and a' at the second. Now sum up all the 

 Gemisseinheiten for all the commodities which came into consumption at 

 the initial epoch, and divide the national expenditure (ap, + /3p^ -|- &c.) 

 by the sum of Gemisseinheitefi. Thus you have the average price at the 

 initial epoch of a Genusseinheit; say Pi . Similarly determine Pj for 

 the posterior epoch. Then Pg -i- Pi is the required unit.' 



' With regard to the formula proposed by Dr. Lehr, the present writer agrees with 

 the criticism expressed by Professor Lexis in a recent number of Conrad's Jahrhuch- 



