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.
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.
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.
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.
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.