Most newly-printed money is directly traded for old money. Money that makes its way to a bank (and most does – the shop you paid with cash brings that cash to the bank at the end of the day) is routinely checked for wear, and bills that are too damaged get sent to the central bank for replacement.
So in one sense, knowing the stock of paper money out in the world is a simple accounting exercise. It is the number of new bills the bank has distributed, minus the number of bills that have been returned. This calculation isn’t exactly correct, however, because some bills get completely lost or destroyed before returning to the bank. Over a long period of time, a bank that maintained a constant money supply in its accounting would produce a shrinking money supply in the real world. However, this is a round off error to a round off error to a round off error for a couple of reasons:
* It’s unusual for bills to be truly lost or destroyed. Many leave circulation, but that’s because someone is hoarding them.
* Lots of other things affect the ideal supply of paper money, such as the size of the population and amount/types of commerce. Banks are constantly adjusting for these factors, so the goal isn’t to maintain a constant money supply anyway.
* The supply of paper money is only a tiny fraction of all the “money” that a central bank is responsible for. Much of it is just numbers in computer systems. Actual monetary policy is done by influencing the supply of that money – a completely different topic. People will still talk about the central bank “printing money,” but this is just a metaphor/expression.
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