The consumer price index or CPI is a more direct measure than per capita
GDP of the standard of living in a country. It is based on the overall
cost of a fixed basket of goods and services bought by a typical consumer,
relative to price of the same basket in some base year. By including a
broad range of thousands of goods and services with the fixed basket, the CPI
can obtain an accurate estimate of the cost of living. It is important to
remember that the CPI is not a dollar value like GDP, but
instead an index
number or a percentage change from the base year.

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Constructing the CPI

Each month, the Bureau of Labor Statistics publishes an updated CPI. While
in practice this is a rather daunting task that requires the consideration of
thousands of items and prices, in theory computing the CPI is simple.

The CPI is computed through a four-step process.

- The fixed basket of goods and services is defined. This requires figuring
out where the typical consumer spends his or her money. The Bureau of Labor
Statistics surveys consumers to gather this information.
- The prices for every item in the fixed basket are found. Since the same
basket of goods and services is used across a number of time periods to
determine changes in the CPI, the price for every item in the fixed basket must
be found for every point in time.
- The cost of the fixed basket of goods and services must be calculated for
each time period. Like computing GDP, the cost of the fixed basket of goods and
services is found by multiplying the quantity of each item times its price.
- A base year is chosen and the index is computed. The price of the fixed
basket of goods and services for each comparison year is then divided by the
price of the fixed basket of goods in the base year. The result is multiplied
by 100 to give the relative level of the cost of living between the base year
and the comparison years.

Figure %: Goods and Services Consumed in Country B

For example, let's compute the CPI for Country B. In this simplified example,
consumers in Country B only purchase bananas and backrubs (lucky fools). The
first step is to fix the basket of goods. The typical consumer in Country B
purchases 5 bananas and 2 backrubs in a given period of time, so our fixed
basket is 5 bananas and 2 backrubs. The second step is to find the prices of
these items for each time period. This data is reported in the table, above.
The third step is to compute the basket's cost for each time period. In time
period 1 the fixed basket costs (5 X $1) + (2 X $6) = $17. In time period 2 the
fixed basket costs (5 X $2) + (2 X $7) = $24. In time period 3 the fixed basket
costs (5 X $3) + (2 X $8) = $31. The fourth step is to choose a base year and
to compute the CPI. Since any year can serve as the base year, let's choose
time period 1. The CPI for time period 1 is ($17 / $17) X 100 = 100. The CPI
for time period 2 is ($24 / $17) X 100 = 141. The CPI for time period 3 is ($31
/ $17) X 100 = 182. Since the price of the goods and services that comprise the
fixed basket increased from time period 1 to time period 3, the CPI also
increased. This shows that the cost of living increased across this time
period.

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Changes in the CPI over time

As we have just seen, the CPI changes over time as the prices associated with
the items in the fixed basket of goods change. In the example just explored,
the CPI of Country B increased from 100 to 141 to 182 from time period 1 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 the base period (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.

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Problems with the CPI

While the CPI is a convenient way to compute the cost of living and the relative
price level across time, because it is based on a fixed basket of goods, it does
not provide a completely accurate estimate of the cost of living. Three
problems with the CPI deserve mention: the substitution bias, the introduction
of new items, and quality changes. Let's examine each of these in detail.