Computing Real Values Using Price Indexes

Suppose your uncle started college in 1998 and had a job busing dishes that paid $5 per hour. In 2008 you had the same job; it paid $6 per hour. Which job paid more?

At first glance, the answer is straightforward: $6 is a higher wage than $5. But $1 had greater purchasing power in 1998 than in 2008 because prices were lower in 1998 than in 2008. To obtain a valid comparison of the two wages, we must use dollars of equivalent purchasing power. A value expressed in units of constant purchasing power is a real value. A value expressed in dollars of the current period is called a nominal value. The $5 wage in 1998 and the $6 wage in 2008 are nominal wages.

To convert nominal values to real values, we divide by a price index. The real value for a given period is the nominal value for that period divided by the price index for that period. This procedure gives us a value in dollars that have the purchasing power of the base period for the price index used. Using the CPI, for example, yields values expressed in dollars of 1982–1984 purchasing power, the base period for the CPI. The real value of a nominal amount X at time t, X_t, is found using the price index for time t:

Real value of X_t = X_t / Price index at time t

Let us compute the real value of the $6 wage for busing dishes in 2008 versus the $5 wage paid to your uncle in 1998. The CPI in 1998 was 163.0; in 2008 it was 216.5. Real wages for the two years were thus,

Real wage in 1998 = $5 / 1.630 = $3.07

Real wage in 2008 = $6 / 2.165 = $2.77

Given the nominal wages in our example, you earned about 10% less in real terms in 2008 than your uncle did in 1998.

Price indexes are useful. They allow us to see how the general level of prices has changed. They allow us to estimate the rate of change in prices, which we report as the rate of inflation or deflation. And they give us a tool for converting nominal values to real values so we can make better comparisons of economic performance across time.

Self Check: Price Indexes and Real Data

Answer the question(s) below to see how well you understand the topics covered in the previous section. This short quiz does not count toward your grade in the class, and you can retake it an unlimited number of times.

You’ll have more success on the Self Check if you’ve completed the two Readings in this section.

Use this quiz to check your understanding and decide whether to (1) study the previous section further or (2) move on to the next section.