Thanks for arguing in good faith.

> No, you don't get it. Imagine if there was a single bank and no cash withdrawals. The bank can't run out of liquidity, ever. If you buy something from a company, the money lands in the bank account of the company, which is managed by the same bank. This means as long as there is no cross bank transfer, there is no limit to how much money can be created.

Yes, monopolies are bad. I completely agree with your analysis here. That's one reason why central banks can get away with so much.

> But here is where it gets weirder. Imagine if there are two banks now. Surely now the idea presented above breaks down the moment there is a cross bank transfer, right? Except it's not that simple. There is merely a limit to how much of the created money can leave the bank in one direction. If the cross bank transfers are balanced so that for every transfer from bank one to bank two, there is a transfer from bank two to bank one, then you are back in unlimited money territory.

Here's where it gets interesting.

Assume there are n banks. Let's also assume for the sake of simplicity that transfers behave a bit like Brownian motion. That means on average we don't expect any bias in transfers between banks, but we also expect some random variance.

Say, our banks settle their net transfers at the end of the day. With a bit of math, we see that the expected variance for any bank proportional to something like gross transfers of that bank, and thus the standard deviation is proportional to the square-root of gross transfers. (It also depends on n.)

Our commercial banks settle by exchanging reserves, eg central bank base money or perhaps they ship physical gold. We can assume that they want to avoid being short of reserves when it comes to settling, but it's not infinitely, and holding reserves costs money. So in practice they'll settle on some multiple of the standard deviation as their precautionary reserves. If the amount of total reserves in the banking system is fixed, that'll place a limit on how much banks will want to expand their total balance sheets.

See https://oll-resources.s3.us-east-2.amazonaws.com/oll3/store/... for more on this topic and a better analysis.

The above was about reserves and how demand for pre-cautionary reserves limits the size of the aggregate balance sheet of all banks.

Now the other question is: why do banks bother with deposits?

So, let's assume that our bank makes a loan to a customer: they create a deposit / loan pair out of thin air that adds up to zero. Now the customer spends that deposit. On average we can assume (n-1)/n parts of the deposit go to other banks and 1/n stays with the originating bank (by the assumption that our average bank has a market 1/n market share.) Those (n-1)/n parts get transferred to other banks, and thus they drain our reserves in the settlement at the end of the day.

If we can attract enough deposits, we can make up for that outflow and have a nice 0 in the net settlement.

The above is all assuming there's no regulation that requires a specific amount of reserves or capital etc, and it's all set by each bank purely by commercial necessity. You are right that there's no one fixed limit, but the limits are also not arbitrary.

Instead of attracting deposits a bank can also sell of the loan it just made. Or it can borrow and use that loan as collateral. But economically, that's all basically equivalent to a deposit in different guises.

About liquidity: in a functioning modern economy, as long as you are solvent you can always get liquidity. (But conversely that means that your counterparties will treat any liquidity problems they see with you as signs of underlying solvency problems.)

You might also like https://www.cato.org/blog/diamond-dybvig-panic-1907 (or https://archive.is/uRtmw) on bank runs.