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Value  =  Price × Quantity      or Nominal GDP  =  GDP Deflator × Real GDP

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.

Coolshirt's nominal revenue from sales  =  Price × Quantity  =  $9 × 10  =  $90


Coolshirt's real income  =  Nominal revenue Price  =  $90 $9  =  10

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:

Real GDP  =  Nominal GDP Price Index

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:

Real GDP  =  Nominal GDP Price Index / 100

Now read the following Work It Out feature for more practice calculating real GDP.

Computing 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:

Real GDP  =  Nominal GDP Price Index / 100  =  $543.3 billion 19 / 100  =  $2,859.5 billion

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.

Real GDP  =  Nominal GDP Price Index / 100  =  $743.7 billion 20.3 / 100  =  $3,663.5 billion

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] .

(Source: Bureau of Economic Analysis, www.bea.gov)
Converting nominal to real gdp
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:

GDP deflator  =  Nominal GDP Real GDP  × 100

Rearranging the formula and using the data from 2005:

Real GDP  =  Nominal GDP Price Index / 100  =  $13,095.4 billion 100 / 100  =  $13,095.4 billion

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.

Real GDP  =  Nominal GDP Price Index / 100  =  $14,958.3 billion 110 / 100  =  $13,598.5 billion

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.

Questions & Answers

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opposite of inflation when the level of price of all goods and services decreased, and be careful about the level of price not the only price of one good or service
Inflation is an increase in the general prices of goods and services in an economy. Deflation, conversely, is the general decline in prices for goods and services, indicated by an inflation rate that falls below zero percent.
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Source:  OpenStax, Macroeconomics. OpenStax CNX. Jun 16, 2014 Download for free at http://legacy.cnx.org/content/col11626/1.10
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