MEASUREMENT OF VALUE - 
number of other commodities are treated in the same 
way, so that each stands at 100 for the base year 
and some other number, larger or smaller than 100 
according as its price has risen or fallen, for the period 
to be compared with the base-year. Then, as each 
of the commodities stands at 100 for the base-year, 
the average or “index-number ”’ for that year will 
be 100, while the index number for the other date will 
be the average of a number of figures each of which 
may be above or below 100. When this index- 
number is above 100, the excess will indicate a rise 
of that much per cent. in the general level of prices, 
and when it is below the deficit will indicate a fall 
of that much. Thus in what is known as Sauerbeck’s 
index number, in which the base or standard period 
is the years 1867- 77 averaged, the index number for 
1896 is 61 per cent. of the 1867-77 average; that 
for each of the years 1912 to 1914 is 85. Then there 
was an annual rise till 1920, for which the figure was 
25I. An abrupt fall to 155 follows for 1921, since 
when the figures have been 131, 129, 139, 136, 126 and 
122. (The figures for each year are the average of 
twelve end-of-month records, e.g. the 251 for 1920 is 
made up of figures rising from 245 in January to 266 
in April and falling to 207 in December.) There are 
many difficulties in the construction of an index 
number, the chief being that of finding commodities 
which do not vary much in kind or quality, and have 
prices about which dispute is impossible, but none 
of the difficulties are sufficient to prevent the method 
from making it possible to mrove any substantial 
change in the 7-acral le~.! +“ ~~ices and to measure 
approxima. magnitude. 
Gran*- .znges in the general level of prices 
{3 
v= 
ror 
t¢ discussion of the principles of index numbers, 
Bowlev, Elements of Statistics.