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.