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According to the income approach GDP is equal to wages + rent + interest + profit, income from taxes isn't included.

The government provides people and organizations with public goods (like roads and the national defence). It can provide said public goods because it taxes its population. It seems for me that government receiving taxes can be viewed as transfer of money for public goods from population to the government. So it seems quite strange that incomes of government from taxation aren't included, despite its goods being an important part of the economy.

Or maybe we don't count government incomes from taxes because we adopt different perspective on it? Maybe we view it as a parasite that just sucks money out of the economy, without giving anything in return? If yes, then why do we ignore public goods that the government provides?

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Actually you could use taxes because GDP formula using income approach can be also expressed as value added at basic prices + taxes less subsidies. However, you can’t do it at the same time when using the approach in your question as you would be double counting.

Using:

$$GDP= w+i + r+ \pi + o$$

Where $w$ are wages $i$ interest income $r$ return on capital $\pi$ profits and $o$ something you forgot in your question adjustments for things like net foreign factor income, capital consumption and revenue from some gov enterprise (not tax revenue) etc.

You would be double counting if you would include taxes, because taxes are subtracted from these. If you earn 100e and government taxes 10e then economy does not suddenly have 110e. The 10e is just transfer.

If government invests the money in some productive way it will show up as an gov revenue from those productive activities.

The value of public goods like army is already reflected in the income approach as soldiers earn wages, military contractors profits etc. The same holds for any other public good. Let’s say you build a road there are wages to be paid, contractors get profit etc.

Also, when government engages in pure transfers - for example redistribution this can’t show up on national accounts as it does not create more output in the economy, it’s just juggling output around.

However, this is not because government is viewed as parasitical. If you are Ralwsian or Utilitarian transfers from rich to poor are moral imperative. But economics is not moral philosophy it’s a science and GDP is a measure of output that is grounded in real production and fact of the matter is that transfers don’t create any additional output by themselves.

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    $\begingroup$ @user161005 1/3 it would be because to my best understanding the formula using w i r \pi does not deduct taxes from these. Otherwise, the tax would have to be added in o but as I understand it it’s not. o might include some tax adjustments but these are for things like vat that’s rebated when business do transaction between each other. It also includes things like capital depreciation adjustments and some balance of payment adjustments and so on. It does not have to be negative always. It will always depend on the actual adjustments some of them are also positive. $\endgroup$ – 1muflon1 Dec 22 '19 at 13:17
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    $\begingroup$ @user161005 2/3 When I was talking about subtracting taxes I did not meant it in the context of formula - probably I should have chosen different wording because I can see how that might have confused you. I meant to say that the formula just looks at the pretax income (to my best knowledge). Yes gov. revenue from government run businesses appears in o. $\endgroup$ – 1muflon1 Dec 22 '19 at 13:23
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    $\begingroup$ 3/3 loans are real services. You get to expand your budget constraint in the present at the expense of your budget in the future which is socially very useful as it allows to smooth consumption. The people who provide loan provide real service and hence increase real output the same way as waiters at your table increase r output by serving. Sure sometimes taking bad loan today may mean you will be less productive in future (this holds for almost anything -think bad food). But GDP measures output at a point of time the interest rate for loan makes GDP higher now even if next y it can be lower $\endgroup$ – 1muflon1 Dec 22 '19 at 13:32
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    $\begingroup$ @user161005 depends on the expressions. Sales taxes net of subsidies could be both +- depending on whether subsidy lower (+) or higher (-) than taxes, net foreign factor income depends on difference between GDP and GNP, depreciation is added (since you are doing GDP which is “gross” product). We caught NFFI because that’s still income earned by the residents, (on intuitive level this is similar to including net exports in GDP using cost approach) . Depreciation has to be added because GDP is gross measure not net measure of output so it should not be lower for depreciation $\endgroup$ – 1muflon1 Dec 22 '19 at 15:06
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    $\begingroup$ @user161005 that was mistake I edited it out, I was thinking about depreciation and then started writing about NFFI - got myself confused and realized it only once I hit send $\endgroup$ – 1muflon1 Dec 22 '19 at 15:19

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