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GDP = C + I + G + (X-M)

If GDP is supposed to count only final goods and services, why include I? Eg if build public roads, can count as G; if build factory, can count when factory produces goods and those goods are sold.

Put differently, counting I seems to double count. Eg if one counts spending on factory as I today, when the factory produces and sells goods tomorrow and in subsequent periods, the counting is done again (eg I, followed by C).

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Investing is about "new" things that did not exist. Any acquisition of a previously existing asset, such as a house, is considered as Savings rather than Investment. Moreover, Investment is not consumed at the present time and are expected to provide flows for longer periods of time.

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