Calculation of real GDP: formula and per capita (2023)

"GDP has increased by 15%!" "Nominal GDP has fallen by X during the recession!" "REAL GDP that!" "The assessed GDP!" "The price index!"

Does it sound familiar? We hear similar phrases from the media, political analysts and economists all the time. We are often expected to simply know what "GDP" is without knowing more about what it entails. Gross Domestic Product (GDP) and its various forms is much more than an annual figure. If you've been looking for clarity about GDP and its various calculations, you've come to the right place. In this explanation, we will learn how to calculate real GDP, nominal GDP, base years, per capita and price indices. Let's do this!

Calculating the real GDP formula

Before we get to the actual calculationGross domestic product (GDP)With a formula, we need to define some terms that we will use frequently. GDP is used to measure the total value of everyoneFinaleGoods and services produced in a country in a year. That sounds like a simple number, right? It is if we don't compare it to last year's GDP.nominal gross domestic productis a nation's output, calculated using the prices of goods and services at the time of production. However, prices change every year due toInflation, i.e. an increase in the general price level of an economy.

If we want to compare past prices and GDP with current ones, we have to useInflationby adjusting the nominal value to take these price changes into account. This adjusted value is referred to asGDP real.

Gross domestic product (GDP)It measures the total market value of all final goods and services produced in an economy in a given year.

nominal gross domestic productis a nation's GDP calculated using the prices of goods and services at the time of production.

GDP realis a nation's GDP after adjusting for changes in the price level.

losBIP-Deflatormeasures the price change from the current year to the year we want to compare GDP to.

If prices have increased due toInflationwe can assume that we need to calculate real GDPventGDP. The amount by which we deflate GDP is calledBIP-Deflator.It can also be called the GDP price deflator or the implied price deflator. It measures the price change from the current year to the year with which we want to compare GDP. It considers goods purchased by consumers, businesses, the government, and foreigners.

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

\[ Real \ PIB= \frac { Nominal \ PIB } { PIB \ Deflactor} \times 100\]

What is GDP?

GDP is the sum of:

  • Household spending on goods and services or personal consumption expenditure (C)
  • Cash expenditures for investments or private gross investments (I)
  • Government Expenditure (G)
  • Net Exports or Exports minus Imports (\( X_n \))

With this we get the formula:

\[ PIB=C+I_g+G+X_n \]

To learn more about what goes into GDP and more about the difference between nominal GDP and real GDP, read our explanations.

-Measurement of domestic production and national income

- PIB nominal vs PIB real

Real GDP calculation: GDP deflator

To calculate the GDP deflator we need to know the nominal GDP and the real GDP. For himbase year, nominal and real GDP are equal and the GDP deflator is equal to 100. The base year is the year to which other years are compared when constructing an index as a GDP deflator. If the GDP deflator is greater than 100, this indicates that prices have increased. If it were less than 100, it would indicate that prices have fallen. The formula for the GDP deflator is:

\[ PIB \ Deflactor= \frac {PIB \ Nominal} {PIB \ Real} \times 100\]

Let's say nominal GDP was $200 and real GDP was $175. What would the GDP deflator be?

\( PIB \ Deflactor= \frac {$200} {$175} \times 100\)

\( PIB \ Deflactor= 1.143 \times 100\)

\( PIB \ Deflactor= 114.3\)

The GDP deflator would be 114.3. This means that prices have risen compared to the base year. This means that the economy did not produce as much as it first appeared because part of the increase in nominal GDP was due to higher prices.

Calculation of real GDPof nominal GDP

When calculating real GDP from nominal GDP, we need to know the GDP deflator in order to know how much the price level has changed from one year to the next, as this accounts for the difference between real and nominal GDP. The distinction between real GDP and nominal GDP is important in understanding how the economy is performing today compared to the past. Nominal GDP is useful when looking at current values ​​and prices as it is in "today's money". However, real GDP makes a comparison with past production more meaningful as it is equal to the value of the currency.

So if we divide nominal GDP by the deflator, we can calculate real GDP because we took it into accountInflation.

We will use this formula:

\[ Real \ PIB= \frac { Nominal \ PIB } { PIB \ Deflactor} \times 100 \]

Let's look at an example to make it more meaningful. We will solve for year 2 real GDP.

YearBIP-Deflatornominal gross domestic productGDP real
year 11002.500 $2.500 $
year 21152.900 $X

Table 1 - Calculation of real GDP using GDP deflator and nominal GDP.

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 enter these values.

\(Real\PIB=\frac {$2.900} {115}\times 100\)

\( Real \ PIB=25,22 \times 100\)

\(Real\PIB=$2.522\)

Real GDP was higher in year 2 than in year 1, butInflationIt eliminated $378 of GDP from year 1 to year 2!

Although real GDP rose to $2,522 from $2,500, the economy did not grow as much as nominal GDP suggested as average price levels also rose. This calculation can be applied to any year before or after the base year, not just immediately after it. In the base year, real GDP and nominal GDP must be equal.

YearBIP-Deflatornominal gross domestic productGDP real
year 197$560$X
year 2100$586$586
year 3112$630$563
year 4121$692$572
year 5125$740$X

Table 2 - Calculation of real GDP using GDP deflator and nominal GDP.First we calculatereal GDP for the year 5.\(PIB\ real= \frac {$740} {125} \times 100\)\(Real \PIB= 5,92 \times 100\)\(Real\PIB=$592\)Now calculate real GDP for year 1.\(Real \PIB= \frac {$560} {97} \times 100\)\(Real\PIB= 5,77\mal 100\)\(Real\PIB=$577\)

As you can see in the example above, real GDP does not have to increase just because nominal GDP and the GDP deflator did. It depends on how much the GDP deflator has gone up and how much inflation the economy has experienced.

Calculation of real GDPwith price index

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

The price index is calculated by dividing the price by ashopping basketin the selected year by the price of the basic basket in the base year and multiplied by 100.

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

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

\[BIP \ Real= \frac {BIP \ Nominal} {\frac {Preis \ Index} {100}}\]

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

Yearprice indexnominal gross domestic productGDP real
year 1100$500$500
year 2117$670X

Table 3 - Calculation of real GDP using a price index

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

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

\(Real\PIB=$573\)

Real GDP is $573, which is less than nominal GDP of $670 suggestingInflationIt happens.

Calculation of real GDPusing the base year

Calculating real GDP using a base year helps economists make more accurate estimates about changing output levels and real prices. The base year provides a reference against which other years are compared when compiling an index. Using this real GDP calculation ashopping basketIt is necessary. Ashopping basketIt is a collection of specific goods and services whose price changes reflect changes in the overall economy. To calculate real GDP using a base year, we need the price and quantity of goods and services in theshopping basket.

Ashopping basketesa collection of specific goods and services whose price changes are designed to reflect changes across the economy. It is also known asshopping cart.

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

Yearprice of apples\(_A\)Number of Apples\(_A\)Price of pears\(_P\)Number of pears\(_P\)Banana price\(_B\) (per pack)Number of Bananas\(_B\)
2009$2700$4340$8700
2010$3840$6490$7880
2011$41.000$7520$8740

Table 4 - Calculation of real GDP using a base year.

Use Table 4 to calculate nominal GDP using price and quantity. To calculate nominal GDP, multiply the price (P) and quantity (Q) of each good. Then add the total amount received from each good to calculate nominal total GDP. Do this for every three years. If this seemed confusing to you, take a look at the following formula:

\[Nominales BIP=(P_A\times Q_A)+(P_P\times Q_P)+(P_B\times Q_B)\]

\( Nominal \ PIB_1=($2_A \times 700_A)+($4_P\times 340_P)+($8_B\times 700_B) \)

\(Nominal \PIB_1=$1.400+$1.360+$5.600\)

\(Nominal\PIB_1=$8.360\)

Now repeat this step for the years 2010 and 2011.

\(Nominal\PIB_2=($3_A\times840_A)+($6_P\times490_P)+($7_B\times880_B)\)

\(Nominal \PIB_2=$2.520+$2.940+$6.160\)

\(Nominal\PIB_2=$11.620\)

\(Nominal\PIB_3=($4_A\times1.000_A)+($7_P\times520_P)+($8_B\times740_B)\)

\(Nominal \PIB_3=$4.000+$3.640+$5.920\)

\(Nominal \PIB_3=$13.560\)

After we have calculated the nominal GDP for the three years, we can calculate the real GDP using 2009 as the base year. When calculating real GDP, the price of the base year is used for all three years. This removesInflationand only considers the amount consumed. The base year calculations do not change when real GDP is calculated using this method.

\(Real\PIB_2=($2_A\times840_A)+($4_P\times490_P)+($8_B\times880_B)\)

\(Real \ PIB_2=$1.680+$1.960+$7.040\)

\(Real\PIB_2=$10.680\)

\(Real\PIB_3=($2_A\times1.000_A)+($4_P\times520_P)+($8_B\times740_B)\)

\(Real\PIB_3=$2.000+$2.080+$5.920\)

\(Real \PIB_3=$10.000\)

Yearnominal gross domestic productGDP real
20098.360 $8.360 $
201011.620 $10.680 $
201113.560 $10.000 $

Table 5 - Comparison of nominal and real GDP after calculating real GDP using a base year

Table 5 shows the direct comparison of nominal GDP to real GDP after using the base year price to calculate real GDP. Real GDP was lower than nominal GDP, indicating that it generally includes goodsshopping basketExperiencedInflation. While it cannot be said that other commodities in this economy have experienced the same level of inflation, it is expected to be a relatively accurate estimate. This is because the goods that go into a shopping basket are specifically selected because economists believe that the shopping basket gives an accurate picture of the economic habits of the current population.

Calculation of real GDPper person

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

\[Real\BIP\per\Capita=\frac{Real\BIP}{population}\]

If real GDP is $10,000 and a country's population is 64 people, real GDP per capita would be calculated as follows:

\(Real\BIP\per\Capita=\frac {$10.000} {64}\)

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

If real GDP per capita increases year on year, this indicates that the general standard of living has improved. Real GDP per capita is also useful when comparing two countries with very different population sizes as it compares how much real GDP is per person rather than in an entire nation.

Calculation of real GDP: key points

  • The formula for calculating real GDP is: \[Real\BIP=\frac{Nominal\BIP}{BIP\Deflator}\times 100\]
  • Nominal GDP is useful when looking at current values ​​and prices as it is in "today's money". However, real GDP makes a comparison with past production more meaningful as it is equal to the value of the currency.
  • Calculating real GDP using a base year provides a benchmark against which other years are compared when compiling an index.
  • If real GDP is less than nominal GDP, that tells usInflationhappened and the economy hasn't grown as much as it seems.
  • Real GDP per capita helps with the comparisonthe standard of living of the average person in all countries.
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