Care must be taken, however, when using index numbers. The index
number always tells you the percentage change compared with the base
year, but when comparing an index number across non-base years, the
percentage change in the index number is not given by the absolute
difference in the values of the index number. For example, if you want to
know how much steel output changed from 2014 to 2016, we know from
Table 2-3 that the index number for steel output increased from 125.0 to
132.5. But this is not an increase of 7.5 percent. The percentage increase in
steel output is computed as
percent.
More Complex Index Numbers
Perhaps the most famous index number used by economists is the index
of average prices—the Consumer Price Index (CPI). This is a price index
of the average price paid by consumers for the typical collection of goods
and services that they buy. The inclusion of the word “average,” however,
makes the CPI a more complex index number than the ones we have
constructed here.
With what you have just learned, you could construct separate index
numbers for the price of beef, the price of bus tickets, and the price of
Internet packages. But to get the Consumer Price Index, we need to take
the average of these separate price indexes (plus thousands of others for
the goods and services we have ignored here). But it cannot be a simple
average. Instead, it must be a weighted average, in which the weight
assigned to each price index reflects the relative importance of that good
(132.5−125.0)/125.0=7.5/125.0=0.06