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Let’s look at an example at the micro level. Suppose the t-shirt company, Coolshirts, sells 10 t-shirts at a price of $9 each.
Then,
In other words, when we compute “real” measurements we are trying to get at actual quantities, in this case, 10 t-shirts.
With GDP, it is just a tiny bit more complicated. We start with the same formula as above:
For reasons that will be explained in more detail below, mathematically, a price index is a two-digit decimal number like 1.00 or 0.85 or 1.25. Because some people have trouble working with decimals, when the price index is published, it has traditionally been multiplied by 100 to get integer numbers like 100, 85, or 125. What this means is that when we “deflate” nominal figures to get real figures (by dividing the nominal by the price index). We also need to remember to divide the published price index by 100 to make the math work. So the formula becomes:
Now read the following Work It Out feature for more practice calculating real GDP.
It is possible to use the data in [link] to compute real GDP.
Step 1. Look at [link] , to see that, in 1960, nominal GDP was $543.3 billion and the price index (GDP deflator) was 19.0.
Step 2. To calculate the real GDP in 1960, use the formula:
We’ll do this in two parts to make it clear. First adjust the price index: 19 divided by 100 = 0.19. Then divide into nominal GDP: $543.3 billion / 0.19 = $2,859.5 billion.
Step 3. Use the same formula to calculate the real GDP in 1965.
Step 4. Continue using this formula to calculate all of the real GDP values from 1960 through 2010. The calculations and the results are shown in [link] .
| Year | Nominal GDP (billions of dollars) | GDP Deflator (2005 = 100) | Calculations | Real GDP (billions of 2005 dollars) |
|---|---|---|---|---|
| 1960 | 543.3 | 19.0 | 543.3 / (19.0/100) | 2859.5 |
| 1965 | 743.7 | 20.3 | 743.7 / (20.3/100) | 3663.5 |
| 1970 | 1075.9 | 24.8 | 1,075.9 / (24.8/100) | 4338.3 |
| 1975 | 1688.9 | 34.1 | 1,688.9 / (34.1/100) | 4952.8 |
| 1980 | 2862.5 | 48.3 | 2,862.5 / (48.3/100) | 5926.5 |
| 1985 | 4346.7 | 62.3 | 4,346.7 / (62.3/100) | 6977.0 |
| 1990 | 5979.6 | 72.7 | 5,979.6 / (72.7/100) | 8225.0 |
| 1995 | 7664.0 | 82.0 | 7,664 / (82.0/100) | 9346.3 |
| 2000 | 10289.7 | 89.0 | 10,289.7 / (89.0/100) | 11561.5 |
| 2005 | 13095.4 | 100.0 | 13,095.4 / (100.0/100) | 13095.4 |
| 2010 | 14958.3 | 110.0 | 14,958.3 / (110.0/100) | 13598.5 |
There are a couple things to notice here. Whenever you compute a real statistic, one year (or period) plays a special role. It is called the base year (or base period). The base year is the year whose prices are used to compute the real statistic. When we calculate real GDP, for example, we take the quantities of goods and services produced in each year (for example, 1960 or 1973) and multiply them by their prices in the base year (in this case, 2005), so we get a measure of GDP that uses prices that do not change from year to year. That is why real GDP is labeled “Constant Dollars” or “2005 Dollars,” which means that real GDP is constructed using prices that existed in 2005. The formula used is:
Rearranging the formula and using the data from 2005:
Comparing real GDP and nominal GDP for 2005, you see they are the same. This is no accident. It is because 2005 has been chosen as the “base year” in this example. Since the price index in the base year always has a value of 100 (by definition), nominal and real GDP are always the same in the base year.
Look at the data for 2010.
Use this data to make another observation: As long as inflation is positive, meaning prices increase on average from year to year, real GDP should be less than nominal GDP in any year after the base year. The reason for this should be clear: The value of nominal GDP is “inflated” by inflation. Similarly, as long as inflation is positive, real GDP should be greater than nominal GDP in any year before the base year.
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