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Let me introduce my question with an example. There is a company producing cars. $20$ cars are produced, with a value market of $20000u$. $\textrm{GDP} = 20\cdot20000u = 400000u$. Assume that the company doesn't purchase any intermediate good, so all the income, $400000u$ goes for the company, and you can compute (income approach) $\textrm{GDP} = \textrm{S} + \textrm{B}$, where $\textrm{S}$ stands for salaries and $\textrm{B}$ for benefit. But we are somehow assuming that the company will get $400000u$ for selling the cars. What would happen if they only sell 15 cars? They will only get $15\cdot20000u = 300000u$, so $\textrm{S} + \textrm{B} \neq \textrm{GDP}$. I have read that this is written down as if the company buys the $5$ remaining cars, but there is no money transfer here, so they can't distribute the $100000u$ worth of cars between $\textrm{S}$ and $\textrm{B}$. Why would the income approach for GDP hold in general?

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Using the income approach, GDP is the sum of compensation of employees, gross operating surplus, gross mixed income, and taxes less subsidies on production and imports. Gross operating surplus includes not only corporate profits but also increases in inventory valuation.

In the above example, using the income approach, the 15 sold cars will reflect under corporate profits and the value of the 5 unsold cars will reflect in an increased inventory valuation. Using the expenditure approach, the 15 sold cars will reflect under consumption expenditures and the 5 unsold cars will reflect changes in inventory valuation under investment. In practice, you cannot determine the value of a car until it is sold, so most accounting standards will conservatively use the cost to produce the car for inventory valuation. Since the cost of production in the example is unrealistically zero, the change in inventory valuation would also be zero in both approaches. Note that even if a less conservative accounting standard was used, both approaches would lead to the same result as it would affect the valuation of the 5 unsold cars in the same way.

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