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I saw this formula in following context:

I want to create Banker State. It's supposed to rely on profit from loans instead of taxes. I would like to keep taxes as low as possible.

Reply: what you're trying to do wouldn't work unless you were running massive trade surpluses (a la Saudi Arabia). The government debt represents nongovernment sector equity. (G-T)= -(S-I) -(X-M) The government fiscal deficit represents the nongovernment sector's net financial savings. Government trying to build positive debt means forcing the nongovernment sector to go into debt simply just to pay its tax bill. It doesn't work, it would create vertical unemployment & the automatic fiscal stabilizers would push the government fiscal's position (which is reaction to nongovernment sector spending behavior) into deficit.

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Since you already answered yourself I am just filling the textbook recommendation:

You could find more on this in Blanchard et al. Macroeconomics: an European Perspective. You will find this there (assuming based on the question you are looking something at undergraduate level).

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It's from sectorial balances. https://en.wikipedia.org/wiki/Sectoral_balances

https://shadowproof.com/2012/03/07/s-i-g-t-x-m/

Although it's quite strange that I can't find it in my macroeconomics textbook.

P.S. It's also worth noting that positive (G-T) represents government deficit, NOT government proficit. Although the formula can be changed to use (T-G) instead.

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