Essentially all of the bailout money was paid back to the Federal government, which was then free to spend it on other things. The problem was that banks were *insolvent* in the short term, and unable to perform their usual function (of lending money and hence increasing the practical number of dollars in the world). Bailing the banks out was a moral hazard to be sure, but it also prevented an economic collapse similar to the one that occurred in 1929.
It’s important to remember that government debt is the *basis of our currency*, so the government borrowing money is the main way that we make more currency. Government overspending has the same function for our economy that gold mining once did (in the 19th century). It creates more money, which lubricates literally everything we do that requires buying, selling, or renting stuff.
Money creation (“mining”) is so important that the government can and will, if necessary, borrow money specifically to blow shit up out in the desert (i.e. to waste the money they borrow). That is exactly as productive, from the global perspective, as gold mining was 120 years ago (i.e. not at all, except for creating more money). The government debt is then used by banks to create even more money — which then circulates, allowing people to buy and sell stuff. That process is a little weird for an ELI5, but it works.
The huge benefit of anchoring the dollar to government debt, rather than to precious metal, is that the amount of government debt can be tuned to match the number of dollars in the world to the amount of buying and selling that needs to go on to keep everyone fed.
That is important because large economies work in non-intuitive ways, and keeping enough money moving around is just as important to an economy as keeping enough oil moving around is to an automobile engine (and for similar reasons). If there isn’t enough oil in your car, the engine won’t run long and will seize. The same thing happens to entire economies when there isn’t enough currency to go around.
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