How to calculate nominal GDP, real GDP, nominal GDP growth and real GDP growth

Consider the following economy which produces two goods, wine and cheese in the two periods of time.

Year Price of cheese Quantity of Cheese Price of Wine Quantity of Wine
2010 $5 2 Blocks $10 4 bottles
2011 $12 3 Blocks $17 3 bottles

Nominal GDP

Nominal GDP is the total dollar value of all goods and services produced in an economy. There are only two goods, wine and cheese, in our assumed economy. The formula for nominal GDP is as such:

Nominal GDP = P_{cheese}*Q_{Cheese} + P_{cheese}*Q_{Cheese}

Where P_{wine} is the price of wine, Q_{wine} is the quantity of wine, P_{cheese} is the price of cheese and Q_{cheese} is the quantity of cheese.

We could calculate the nominal GDP for the year 2010 as follows:

Nominal GDP in 2010 = $5*2 + $10*4 = $50

We could also calculate nominal GDP for the year 2011 as follows:

Nominal GDP in 2011 = $12*3 + $17*3 = $87

Real GDP

In this previous example, we saw our nominal GDP increase from $50 to $87 despite the fact that we only have only one additional block of cheese but one less bottle of wine. Most of this increase in GDP was due to prices rising, not because we were producing more output.

When calculating real GDP, we calculate it holding prices constant. This means that we choose a “base year” for prices and calculate GDP using those prices instead of the prices corresponding to the same year (the base can be any year we choose, as long as it’s consistent). In our previous example, we could set 2010 as the base year. We could calculate GDP as follows:

Real GDP in 2010 = $5*2 + $10*4 = $50

And real GDP for 2011:

Real GDP in 2011 = $5*3 + $10 * 3 = $45

In this case, real GDP is smaller in 2011 than it was in 2010. This is in contrast with nominal GDP which was larger in 2011 than it was in 2010.
We could also have calculated real GDP using 2011 as the base year. The calculations for real GDP in each period would be as follows:

Real GDP in 2010 = $12*2 + $17*4 = $92

And real GDP for 2011:

Real GDP in 2011 = $12*3 + $17*3 = $87

Again real GDP is higher in 2010 than it is in 2011. However, the values for real GDP are also higher. This is because we used higher base year prices.

Given that real GDP is sensitive to the base year used, it is mostly useful to compare relative output between periods.

Nominal GDP growth

Nominal GDP growth is the measure of how much GDP grows from one period to the next. The definition for nominal GDP growth is as follows:

Nominal GDP growth = \frac{\text{Nominal GDP in 2011 - Nominal GDP in 2010}}{\text{Nominal GDP in 2010}} * 100

We can use our calculations from above to calculate the nominal GDP growth:

Nominal GDP growth = \frac{$87 - $50}{$50} * 100 = 74%

Real GDP growth

Real GDP growth is the measure of how much real GDP grows from one period to the next. The definition for real GDP growth is as follows:

Real GDP growth = \frac{\text{Real GDP in 2011 - Real GDP in 2010}}{\text{Real GDP in 2010}} * 100

The problem is that we have different measures for real GDP depending on what year that we choose as the base year. Let’s calculate the real GDP using both base years.

Real GDP growth with 2010 as base year = \frac{$45 - $50}{$50} * 100 = -10%
Real GDP growth with 2011 as base year = \frac{$87 - $92}{$92} * 100 = -5.43%

And here we have a problem. The measures of real gdp growth depends on the choice of base year that we have chosen. To overcome this problem, we can use chained volume series but that will be left for another post.