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That's not how GDP is calculated. It's roughly the total value added along each step of the production/sales chain. If every person were equally productive and were paid exactly the value they added, and there were no taxes or government spending, then GDP per capita would indeed be the same as the national wage, though of course this situation is idealized to a ridiculous degree.

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If everyone was paid exactly the value they added GDP per worker would be the average wage, with no caveats required.

Equal productivity would just mean the average and median wages would be the same.

Government spending, funded by taxes, contributes to the GDP like any other spending.

> Government spending, funded by taxes, contributes to the GDP like any other spending.

That's exactly the problem. You're thinking of Gross Value Added (GVA), which strictly talks about value added through normal economic activity. Once you start "removing" productivity through taxation and "adding" productivity back through spending/subsidies you have a new variable- the presence of that variable is the difference between GVA and GDP. That variable doesn't necessarily net out to 0 either, or even close, if the government runs a surplus or deficit as the United States does.

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