Dr. Barry Haworth
University of Louisville
Department of Economics
Economics 202

### Understanding the Consumer Price Index

The consumer price index is obtained by dividing the expenditure on a set of consumer goods in one year (the current year) by the expenditure on that same set of goods in the base year. For example, let’s assume that consumer expenditure on a specific set of goods in the base year (1996) was \$20,500 and, in 2004, consumer expenditure on that same set of goods was \$25,000. We put these numbers together as \$25,000/\$20,500, which is 1.22. It is common to then multiply this result by 100, giving us a CPI of 122. Other CPI values are calculated in exactly the same manner, always dividing a given year’s expenditure by that of the base year. Note that we’ll always be dividing the current year expenditure for any given year (or period) by the same number. This implies that if we calculate the CPI for the base year we divide base year expenditure by base year expenditure, making the base year CPI always equal to 100.

1. Interpreting our result
Because the true rate of inflation cannot be observed, we can use the CPI (and similar price indexes) to help us approximate the true inflation rate. Our (fictitious) CPI value for 2004 is 122, and in 1996 is 100. Calculating the percentage change in the CPI between these two years gives us our approximation of the inflation rate. Here, we see that consumer prices between the base year and current year have increased by 22%. The most basic interpretation of this price level change is to say that what cost \$100 in 1996, now costs \$122 in 2004.

2. Problems with interpretation

a. Changes in product quality - Suppose that gasoline producers decide to upgrade the quality of the gas they sell in 2005 by adding certain chemicals that help keep residue from building up in the carburetor. Because changes in product quality can lead to at least small increases in price, we can expect the price of gas to increase. Even if there are no changes in the price of any other good in the economy, the higher gas prices in 2005 will lead to an increase in the 2005 CPI. Does this imply that inflation is worse?

At first glance, this CPI value does seem to be telling us that the average price of consumer goods and services is greater. However, we need to consider what’s happened here. As stated above, when calculating the CPI, we compare the prices of a specific set of goods in one year to the prices of that same set of goods in the base year. In this example, the price of gas in 2005 is not for the exact same good that we consider from 1996. In other words, changes in quality tend to cause the CPI to overstate the true rate of inflation - which means that statisticians must “adjust” the CPI appropriately.

b. Introduction of new goods - When calculating the CPI, we need to decide upon a specific set of goods that will make up our consumer basket. Let’s assume that we base our consumer basket on what the typical consumer bought in 1996. Assume further that, in 1996, home entertainment expenditures included VCRs, but not DVD players. What happens when DVD players start replacing VCRs? Ordinarily, we’d expect to see the price of VCRs fall. This implies that the CPI in 2005 will decrease (ceteris paribus). The problem with interpreting this as saying that inflation has changed is similar to what was described above. In this case, the consumer basket for the typical consumer in 1996 is not the same as the basket for the typical consumer in 2005. This causes the CPI to misrepresent the true inflation rate, and also necessitates some statistical adjustment.

c. Product substitution during inflationary times - When the consumer basket is determined, we measure expenditure on some fairly general categories. For example, amongst everything else that goes into the CPI, the CPI considers expenditure on food categories like red meat, poultry, vegetables, etc. The CPI does not, however, consider who sells the product or (necessarily) whether the product is a high or low quality item. Assume that the typical consumer buys all organic food in 1996. If prices rise by 22% between 1996 and 2004, and your income doesn't, then you may start to get concerned about how much you spend at the supermarket. Up until now, let’s assume you behaved just like the typical consumer. Your progressive loss of purchasing power though leads you to buy less expensive, non-organic food. If the typical consumer continues to buy organic food, and organic food prices rise, then the CPI will rise (ceteris paribus).

Does this higher CPI mean that inflation has cut into your purchasing power? Not really, because your purchases are not the same as the typical consumer. That is, the change in the CPI reflects what happens to the typical consumer, but not necessarily to those who don’t behave like the typical consumer. A reported increase in inflation doesn’t mean that all consumers spend more, just the typical consumer.

3. Converting Nominal Income into Real Income
It is common knowledge that the cost of living (or inflation) makes the income earned in 1899 very different from the income earned in 1999, and comparisons between income earned in a city like New York and a city like Louisville somewhat difficult. In these situations, we turn to the CPI for assistance. It is possible to use the CPI to deflate nominal income into real income. That is, remove the impact of inflation on income and convert that income into something we can compare over time or across locations.

Suppose someone earns \$48,000 in 1996 and 2004. We know that this person’s purchasing power is less, but by how much? By comparing the income earned in each year by the CPI in that year, we have our answer. The first step is to find out how the CPI has changed between the current year and base year. To do this, divide the CPI for that year by 100. We then divide the current year’s income by whatever we got in this first step.

The 1996 CPI is 100. If we divide that CPI by 100, then we have 1. Dividing the 1996 income by 1, we have a real income of \$48,000. That is, \$48,000 in income buys \$48,000 worth of goods and services.

The 2004 CPI is 122. If we divide that CPI by 100, we have 1.22. Dividing the \$48,000 earned in 2004 by 1.22, we have a real income of \$39,344. Our \$48,000 income in 2004 only buys \$39,344 worth of goods and services. In 8 years, inflation has caused the purchasing power of that \$48,000 to decrease by about \$8,600.