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This is not exactly how fractional reserve banking works. I think that there is a misconception that if, for example, there is a bank regulation that allows 10% fractional reserve banking, then if a bank has $1 million in deposits (of actual cash that people gave to the bank to put in their checking accounts) the bank can make $10 million in loans, with $9 million being "created out of thin hair". In fact, if a bank has $1 million in deposits it can make only $900k in loans. Indeed, suppose you are a bank and you have $1 mil in deposits, which you keep as reserve with the central bank. Now someone asks for a $900k loan. Now you have $1.9 mil in deposits ($1.9 mil liabilities), and you have $1 mil kept with the central bank in cash, and $900k owed from the guy with the loan (total $1.9 mil in assets, it checks out). Now the guy with the loan withdraws his $900k to pay for his house or whatever; the bank gives him the $900k from the cash account it has at the central bank. Now the bank has $1 mil in liabilities (the checking accounts of the depositors), $100k in cash with the central bank, and $900k owed from the guy with the loan. Everything still checks out, but now the cash on hand is just $10% of the assets. The bank has reached the fractional reserve limit, and it is not allowed to make any more loans. |
The geometric sum to infinity ends up being 1/reserve_ratio; so if that's 10% in this example, the theoretical money creation is 10x.