Calculating Real GDP

Calculating Real GDP Formula

Before we get to calculating real Gross Domestic Product (GDP) with a formula, we have to define some terms that we will be frequently using. GDP is used to measure the total value of all final goods and services produced in a nation in a year. This sounds like a straightforward number, right? It is if we are not comparing it to a previous year's GDP. Nominal GDP is a nation's output calculated using the prices of goods and services at the time of production. However, prices change every year due to inflation, which is an increase in the general price level of an economy.

When we want to compare past prices and GDP to current ones we need to take inflation into account by adjusting the nominal value to reflect these price changes. This adjusted value is referred to as real GDP.

If prices have increased due to inflation we can assume that to calculate real GDP we must deflate GDP. The amount by which we deflate GDP is called the GDP deflator. It can also be referred to as the GDP price deflator or the implicit price deflator. It measures the change in price from the current year to the year with which we want to compare GDP. It takes into account goods purchased by consumers, businesses, the government, and foreigners.

So, what is the formula for calculating real GDP? For the formula for real GDP, we need to know the nominal GDP and the GDP deflator.

\[ Real \ GDP= \frac { Nominal \ GDP } { GDP \ Deflator} \times 100\]

Calculating Real GDP: GDP Deflator

To calculate the GDP deflator, we need to know the nominal GDP and the real GDP. For the base year, nominal and real GDP are both equal and the GDP deflator is equal to 100. The base year is the year that other years are compared to when constructing an index like the GDP deflator. When the GDP deflator is more than 100 it indicates that prices rose. If it were less than 100 it would indicate that prices have fallen. The formula for the GDP deflator is:

\[ GDP \ Deflator= \frac {Nominal \ GDP} {Real \ GDP} \times 100\]

Calculating Real GDP from Nominal GDP

When calculating real GDP from nominal GDP, we need to know the GDP deflator so that we know how much the price level has changed from one year to the next because this makes the difference between real and nominal GDP. Differentiating between real GDP and nominal GDP is important for understanding how the economy is performing in current times versus the past. Nominal GDP is useful when looking at current values and prices since it is in "today's money." Real GDP, however, makes a comparison with past output more meaningful since it equalizes the value of the currency.

Then, by dividing nominal GDP by the deflator we can calculate real GDP because we have accounted for inflation.

We will use this formula:

\[ Real \ GDP= \frac { Nominal \ GDP } { GDP \ Deflator} \times 100 \]

Let's look at an example to help it make sense. We will solve for the real GDP of year 2.

The GDP deflator is the price level of final goods and services compared to the base year and nominal GDP is the value of final goods and services. Let's plug in these values.

\(Real \ GDP=\frac {$2,900} {115} \times 100\)

\( Real \ GDP=25.22 \times 100\)

\( Real \ GDP=$2,522\)

Real GDP was higher in year 2 than in year 1, but inflation ate away $378 worth of GDP from year 1 to year 2!

Though real GDP did increase from $2,500 to $2,522, the economy did not grow as much as the nominal GDP would have had us think since the average price level rose as well. This calculation can be applied to any year before or after the base year, not just directly after it. In the base year, real GDP and nominal GDP have to be equal.

Calculating Real GDP with Price Index

Calculating the real GDP with the price index is similar to calculating it with the GDP deflator. Both are indexes that measure inflation and reflect the current state of a country's economy. The difference between them is that the price index includes foreign goods that consumers bought while the GDP deflator only includes domestic goods, not imported ones.

The price index is calculated by dividing the price of a market basket in the selected year by the price of the market basket in the base year and multiplying it by 100.

\[Price \ Index \ in \ given \ year =\frac {Price \ of \ Market \ Basket \ in \ given \ year} {Price \ of \ Market \ Basket \ in \ Base \ Year} \times 100\]

In the base year, the price index is 100 and the nominal and real GDP are equal. Price indexes for the United States are published by the U.S. Bureau of Labor Statistics. To calculate real GDP using the price index, we use the following formula:

\[Real \ GDP= \frac {Nominal \ GDP} {\frac {Price \ Index} {100}}\]

Let's look at an example where year 1 is the base year:

\(Real \ GDP=\frac{$670} {\frac{117} {100}}\)

\(Real \ GDP=\frac{$670} {1.17}\)

\(Real \ GDP=$573\)

The real GDP is $573, which is less than the nominal GDP of $670, indicating that inflation is occurring.

Calculating Real GDP Using Base Year

Calculating real GDP using a base year helps economists make more accurate calculations on changing levels of actual output and prices. The base year provides a reference with which other years are compared when constructing an index. With this real GDP calculation, a market basket is required. A market basket is a collection of certain goods and services whose changes in price are a reflection of changes in the greater economy. To calculate the real GDP using a base year, we need the price and quantity of goods and services in the market basket.

This market basket only has apples, pears, and bananas. The price is the per unit price and the quantity is the total quantity consumed in the economy. The base year will be 2009.

Use Table 4 to calculate nominal GDP by using price and quantity. To calculate nominal GDP, multiply the price (P) and quantity (Q) of each good. Then, add the total amount earned from each good together to calculate the total nominal GDP. Do this for all three years. If that seemed confusing, have a look at the formula below:

\[Nominal \ GDP=(P_A \times Q_A)+(P_P\times Q_P)+(P_B\times Q_B) \]

\( Nominal \ GDP_1=($2_A \times 700_A)+($4_P\times 340_P)+($8_B\times 700_B) \)

\(Nominal \ GDP_1=$1,400+$1,360+$5,600\)

\(Nominal \ GDP_1=$8,360 \)

Now, repeat this step for the years 2010 and 2011.

\(Nominal \ GDP_2=($3_A\times840_A)+($6_P\times490_P)+($7_B\times880_B)\)

\(Nominal \ GDP_2=$2,520+$2,940+$6,160\)

\( Nominal \ GDP_2=$11,620\)

\(Nominal \ GDP_3=($4_A\times1,000_A)+($7_P\times520_P)+($8_B\times740_B)\)

\(Nominal \ GDP_3=$4,000+$3,640+$5,920\)

\(Nominal \ GDP_3=$13,560\)

Now that we have calculated nominal GDP for all three years, we can calculate real GDP with 2009 as the base year. When calculating real GDP, the price of the base year is used for all three years. This eliminates inflation and only takes the quantity consumed into account. The calculations for the base year do not change when calculating real GDP with this method.

\(Real \ GDP_2=($2_A\times840_A)+($4_P\times490_P)+($8_B\times880_B)\)

\(Real \ GDP_2=$1,680+$1,960+$7,040\)

\( Real \ GDP_2=$10,680\)

\(Real \ GDP_3=($2_A\times1,000_A)+($4_P\times520_P)+($8_B\times740_B)\)

\(Real\ GDP_3=$2,000+$2,080+$5,920\)

\(Real \ GDP_3=$10,000\)

Table 5 shows the side-by-side comparison of nominal GDP vs real GDP after using the base year's price to calculate real GDP. Real GDP was lower than nominal GDP, indicating that, overall, the goods in this market basket experienced inflation. Although it cannot be said that other goods in this economy experienced the same level of inflation, it is expected to be a relatively close estimate. This is because the goods that go into a market basket are specifically selected because economic experts believe that the market basket provides an accurate picture of the current population's economic habits.

Calculating Real GDP Per Capita

Calculating real GDP per capita means that real GDP is divided by the population of a country. This figure shows the living standard of the average person in a country. It is used to compare the living standard of different countries and in the same country over time. The formula for calculating real GDP per capita is:

\[Real \ GDP \ per \ Capita=\frac {Real \ GDP} {Population}\]

If real GDP is equal to $10,000 and the population of a country is 64 people, real GDP per capita would be calculated like this:

\(Real \ GDP \ per \ Capita=\frac {$10,000} {64}\)

\(Real \ GDP \ per \ Capita=$156.25\)

If the real GDP per capita increases from one year to the next it indicates that the overall standard of living has increased. Real GDP per capita is also useful when comparing 2 countries with very different population sizes since it compares how much real GDP there is per person rather than as a whole nation.