Over time the CPI changes only as the prices associated with the items in the
fixed basket of goods change. In the example from Country B, the CPI increased
from 100 to 141 to 182 from time period 1 to time period 2 to time period 3.
The percent change in the price level from the base year to the comparison
year is calculated by subtracting 100 from the CPI. In this example, the
percent change in the price level from time period 1 to time period 2 is 141 -
100 = 41%. The percent change in the price level from time period 1 to time
period 3 is 182 - 100 = 82%. In this way, changes in the cost of living can be
calculated across time. These changes are described by the inflation rate.
That is, the rate of inflation from period 1 to period 2 was 41% and the rate of
inflation from period 1 to period 3 was 82%. Notice that the inflation rate can
only be calculated using this method when the same base year is used for all of
the CPI's involved.

While it is simple to calculate the inflation rate between the base year and a
comparison year, it is a bit more difficult to calculate the rate of inflation
between two comparison years. To make this calculation, first check that both
comparison years use the same base year. This is necessary to ensure that the
same fixed basket of goods and services is used. Next, to calculate the
percentage change in the level of the CPI, subtract the CPI for the later year
from the CPI for the earlier year and then divide by the CPI for the earlier
year.

In the example from Country B, the CPI for period 2 was 141 and the CPI for
period 3 was 182. Since the base year for these CPI calculations was period 1,
we must use the method of calculating inflation that takes into account the
presence of two comparison years. We need to subtract the CPI for the later
year from the CPI for the earlier year and then divide by the CPI for the
earlier year. That gives (182 - 141) / 141 = 0.29 or 29%. Thus, the rate of
inflation from period 2 to period 3 was 29%. Notice that this method works for
calculating the rate of inflation between a base year and a comparison year as
well. For instance, the CPI for period 1 was 100 and the CPI for period 2 was
141. Using the formula above gives (141 - 100) / 100 = 0.41 or 41%.

Calculating Inflation Using the GDP Deflator

The other major price index used to determine the price level is the GDP
deflator, a price index that shows how much of the change in the GDP from
a base year is reliant on changes in the price level. As covered in the
previous SparkNote, the GDP deflator is calculated by dividing the nominal
GDP by the real GDP (the details for calculating the nominal GDP and the
real GDP are presented in Part
1 of
this SparkNote).

For example, let's calculate, using the table above, the GDP deflator
for Country B in period 3 using period 1 as the base year. In order to find the
GDP deflator, we first must determine both nominal GDP and real GDP in period 3.
Nominal GDP in period 3 is (10 X $2) + (9 X $6) = $74 and real GDP in period 3
using period 1 as the base year is (10 X $1) + (9 X $6) = $64. The ratio of
nominal GDP to real GDP is ($74 / $64 ) - 1 = 16%. This means that the price
level rose 16% from period 1, the base year, to period 3, the comparison year.
Thus, the inflation rate from period 1 to period 3 was 16%. Notice that it is
important to use the earlier year that you want to compare as the base year in
the calculation of real GDP.

The inflation rate calculated from the CPI and GDP deflator are usually fairly
similar in value. In theory, there is a significant difference between the
abilities of each index to capture consumer's consumption choices when a change
in price occurs. The CPI uses a fixed basked of goods from some base year,
meaning that the quantities of goods and services consumed remains the same from
year to year in the eyes of the CPI, whereas the price of goods and services
changes. This type of index, where the basket of goods is fixed, is called a
Laspeyres index.