Three different ways to calculate GDP

GDP is the Gross domestic product which is the total value of all things produced by an economy. There are three different ways to calculate GDP.

1. The expenditure approach

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.

2. The income approach

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. The production approach

The production side is where we calculate the total value of all goods produced in the economy. In essence, this is just calculating price times quantity of all goods in the economy. For example, consider an economy which produces 10 cars for $100 and 100 apples for $1 each. We could calculate GDP as follows:

GDP = 10*$100 + 100$1 = $1,100

Why are these all the same?

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

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