How do the economical numbers add up for GDP?

I always wonder how economists calculate the productivity of a country. Say, in a simplified scenario, if county X has 10 companies and Com 1 produced $1M and sold to Com 2 and 3 for $0.5M each and 2 and 3 each sold for $1M to com 4 and 5 who sold $1M to com 6, 7, 8, and 9 each who each sold $2M to com 10 who sold the services and products to public for $16M. Does it mean the total GDP is $31M even though the final sales of end products is only $16M? Is there double counting in the former case?

Answer:
The answer is no, the GDP is not $31 million, and yes, it is indeed an instance of multiple counting.

The usual methods are to either count all spending on *final* goods and services (i.e. GDP = C (consumption expenditures by households) + Ig (investment by businesses) + G (government purchases of goods and services) + Xn (net exports)) or adding up the national income (rents + interest + profits + wages) and sticking on indirect business taxes, capital depreciation and net foreign factor income.

Of course, you *could* calculate the GDP from each production stage if you wanted to (though it would take a lot more time!). Instead of adding up the *total* value at each stage, as in your multiple counting example above, you only add up what's called the value added; that is, the market value of a firm's output less the value of the inputs the firm has bought from others.

In either case, the dollar sum we get is going to be equal to the value of the final good or service.

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How do the economical numbers add up for GDP?

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