But I defined FRB different and how it actually happens in the real world today. Where deposits are immediately used as reserves for loaning money that does not exist.
I'm still not "getting it." Banks don't get to pick a reserve amount and then are able to loan out some multiple of that, they have to keep a % of deposits on-hand as a reserve. The alternative to fractional-reserve and full-reserve is no-reserve, where banks can freely loan out as much cash as they have -- it doesn't mean they get to create an infinite amount of cash to loan out.
Let's say the reserve ratio for banks in the US is a flat 9%. That means if a bank has $100b in deposits, they must keep $9b as cash or something which can be near-immediately turned into cash or regulators will shut them down. It doesn't mean that banks can use the $100b from deposits and claim it as a reserve which multiplies their amount to lend to $1.11t. I'm pretty darn sure that doesn't happen anywhere.
Of course if they were the only bank doing this. But they are not and when the loans get deposited at some other bank that other bank can again loan out a fraction and again and again and again and the end results is what I said it was.
That still doesn't make sense. The amount doesn't multiply.
If Joe Bob loans $100m to Bank A, then Bank A deposits in Bank B, then Bank B deposits in Bank C....
Bank A is only allowed to loan $91m to Bank B and must keep $9m on-hand to pay all of their depositors. Bank A now has $9m in cash, $91m as an asset in the form of a deposit, but they still have a $100m liability to Joe Bob, so they're done -- Bank A can't loan out any more of the $100m. They have $100m assets, $100m liabilities from the transaction.
Bank B now has a $91m deposit (cash). Bank B needs to keep $8.19m as a cash reserve and deposits $82.81m in Bank C. Bank B now has $8.19m as cash, and $82.81m as an asset in the form of a deposit with Bank C, but they still have a $91m liability to Bank B. Bank B is now done, they can't loan anymore money from the transaction which started with Joe Bob's deposit.
Bank C now has $82.81m, and let's say they loan it out to Producto Corp. at an interest rate high enough to profit off the deposit they got from Bank B. Bank C needs to keep $7.4529m in reserves to pay depositors, so they loan $75.3571m to Producto Corp.
Let's looks at the totals:
Assets created on paper: $373.81m ($24.6429m held as cash by the banks, $349.1671m in assets as the form of deposits)
Liabilities created on paper: $373.81m (assuming the times match up perfectly, when Bank C is repaid by Producto Corp., they pay Bank B $82.81m + interest, Bank B pays Bank A $91m + interest, and Bank A pays back Joe Bob $100m + interest)
Amount of money created when the transaction's over: 0 (they cancel each other out)
Yeah - I guess Bank A and Bank B could keep depositing money in each other, and then they could build up their assets (AND liabilities) by quadrillions but it doesn't make sense. It doesn't create any additional money to loan, just a bunch of pointless paperwork.
ETA: The exact same thing could be done with Bitcoin, except we're not subject to reserve ratios, so we could actually lend the whole amount out infinitely to each other. I loan Patrick 100BTC, he loans me 100BTC, and we keep doing it back and forth. We could have 1 trillion BTC worth of assets, but we'd also have $1t worth of liabilities. We could even not do the BTC exchange and just pass along "IOU BTC" notes to each other. Lending/depositing with each other doesn't create money, it just creates assets and liabilities on paper.
