# Three different ways to calculate GDP

Three methods of calculating GDP:

Gross Domestic Product (GDP) measures the total value of all goods and services produced within an economy. It is used as a macroeconomic measure of the total income of a country.

There are three different methods (Expenditure, Income and Production) which can be used to measure the GDP of a country. All of these methods in theory should sum to the same amount.

## 1. Expenditure method

The expenditure approach is where you add up all the various types of spending which occurs within an economy. There are 4 different types.

### Consumption (C)

Consumption is all the spending that households do on goods and services. For example, the amount of apples a household purchases; the amount of money spent on healthcare; the amount of money spent purchasing new cars and the money spent on pizza are all examples of consumption spending.

### Investment (I)

Investment is the spending that firms do machinery and equipment to operate their businesses. Examples of investment spending would be a mining company purchases a truck to transport coal; It companies purchasing new computers and the purchase of a new plane for an airline company.

### Government Spending (G)

Government spending is the spending that the government conducts within an economy. Examples of government spending include spending on defense; spending on health care; building of roads and education spending.

### Net Exports (NX)

Net exports is defined at the purchases of domestically produced goods by foreigners subtracted from the purchases of internationally produced goods by local residents. In essence, it is the value of what is sent overseas minus the value of stuff that comes here.

If an airline company operating in USA purchases a new plane from France, this would be considered an import for USA and an export for France. This would cause the net exports to decrease for USA whilst causing the net exports to increase for France.

An interesting case is where a foreign student from China comes and studies at a school in the USA. This is considered an export from USA to China since the USA is producing a service (education) which is essentially being "sent" to a Chinese student who is from the chinese economy. Thus, China is importing education from USA.

Therefore, if we add up these 4 components we get:

GDP = C + I + G +NX

This is also called the demand approach to calculating GDP since all these components are demands for goods and services. It is looking at the demand side of the economy.

For example, using the input-output tables for Australia you can calculate the GDP for Australia in the year 2018 with:

$C = 969,173$
$I = 418,703$
$G = 309,325$
$X = 308,306$
$M = 357,121$

Giving $GDP = 969,173 +418,703 + 309,325 + 308,306 - 357,121$

$GDP = 1,659,604$

where GDP is measured in millions of dollars.

## 2. Income method

The income approach is when you add together all factor payments to calculate GDP. Factor payments are all the payments that go to inputs to produce output. Typically, the main factor payments are: profits, returns to labor and returns to capital. The formula for the income approach is as follows:

GDP = π + wl + rk

where:

π = profits that firms make

wl = wage * total labour provided - this is the returns to labour.

rk = rental rate of capital * the amount of capital provided

## 3. Production method

The production method (or value added) is where we calculate the total value of all goods produced in the economy minus the value of intermediate goods.

Consider an economy which produces steel and cars. Suppose the economy produces 100 units of steel which it sells for $1 and it produces 10 cars, using 5 units of steel, which it sells for$100.

As the production of steel requires no intermediate inputs, the value added from the production of steel is $100. The production of cars produces$1000 worth of cars using $50 of steel. Therefore, the value added is$950.

The total value added/GDP of the economy is thus $1050. Alternatively, we could have added the total amount spent on the cars$1000 and total spend on steel $100 giving$1100 and then subtracted the $50 of intermediate inputs to also get$1050.

## How are all measures equivalent?

Consider the following example to illustrate how these all arrive at the same value. Suppose that the economy has 1 firm producing 1 type of good. The firms profit function would look like:

π = P*Q - wl - rk

where P*Q is the price times the quantity of output. Essentially profit equals the revenue earned from selling output minus how much they need to pay labor and capital. We can re-arrange this equation as such:

P*Q = π + wl + rk

As we can see, the left hand side just equals value of all goods produced in the economy. This is the value we would arrive at if we used the production approach. The right hand side equals all the income payments. In essence, all the revenue earned from producing a goods must be distributed as either profit or to the factors that produced it. And since all income is either saved, consumed or given to the tax in income payments, it is easy to see that:

π + wl + rk = C + I + G + NX

## Further reading & references

This post has outlined the three different methods in which GDP can be calculated in a very simple manner. For a better understanding on how GDP is calculated or for a reference, please consult the UN website here.

The following is a useful textbook which outlines how to calculate GDP using each method and has problems:
Tempini Macdonald, N. (1999). Macroeconomics and business. London: International Thomson Business Press.