You also sometimes see, as in that image, that someone has divided that number up by the amount of taxpayers, to get a smaller, but somehow more intimidating number, often claimed to be your share. That's way too much money for you to personally pay back, no matter how much you pull your pockets out, and so the implication of this is that the debt is too big and we should do something about it. If not for us, then for our children and grandchildren, who shouldn't have to pay for our extravagant lifestyles.
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This sounds like it makes a lot of sense. We should be responsible and pay our own way. That's how we generally manage our personal finances; people can get in a lot of trouble with personal debt, and constantly racking up more of it is a pretty well-trod path toward ruin. But the analogy breaks down when we look at government debt, because of one slightly weird fact: governments don't have to pay off their debts.
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"Is that true? Can someone check if this guy's right?"
The reason you or I have to pay off our debts is because we one day hope to stop working and retire. Our income will go to zero, and we'll have to live off our savings, which will be kind of tough if that's a negative number. But because a government will never retire, and will (probably) always have a stable and growing income, there's no reason it ever needs to pay off its debt. It can pay off the interest on it essentially forever. For example, the U.S. government still "owes" most of the debt it accumulated during World War II.
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