It's more accurate to say they loan out a multiple of deposits based on the inverse of the fraction (the "money multiplier"). If someone puts 1 million in the bank and the fractional reserve is 20 percent, they can now create loans of up to 4 million. Such that the reserve is 20 percent of their total assets of 5 million (= 4 million loans + 1 million cash).

Again no, neither of these are accurate. Modern banks do not operate on a fractional reserve basis at all. This is a falsehood peddled by well out of date undergrad econ textbooks

https://www.bankofengland.co.uk/quarterly-bulletin/2014/q1/m...

I'm describing what fractional reserve means. Technically that fraction has been set to zero very recently so it is trivial though still not false. This was discussed a lot elsewhere on this board.

If that you say is true then banks could lend infinite money to their friends and never collect it.

Well, except the friend part the money supply has never shrunk so far.

No, fractional reserve means that they can lend out $800K of the $1M deposited, even though the $1M is still counted as the depositor's money and also $800K is a available to lend.

https://en.m.wikipedia.org/wiki/Fractional-reserve_banking

Can you describe the mechanism by which deposits held by a bank are lent to borrowers under the fractional reserve system described in that Wikipedia article?

"Fractional-reserve banking is the system of banking operating in almost all countries worldwide,[1][2] under which banks that take deposits from the public are required to hold a proportion of their deposit liabilities in liquid assets as a reserve, and are at liberty to lend the remainder to borrowers"

Yes now it says:

“to lend the remainder to borrowers”

Can you describe how money that a bank has in deposits is lent out to borrowers?

Ok you then make an agreement with another bank and that constraint is literally irrelevant.

But there's no multiplier as you describe it. It appears though. First deposit $1M. Then create that loan for 800k, and deposit it right back in the same bank. Now the bank has $1M versus 800k loans so the reserve is back above the 20 percent reserve requirement. We don't even need to work out the math, just keep repeating the process with smaller loans until we reach our limit at the reserve, which clearly must be (the very same) $1M in deposits, and the max of $4M loans, making for $5M total. Accounting rules to prevent this being done by a single bank alone just means it takes more banks trading loans to get the same effect. Rather than a wonky description of the rules, basic econ class still has the variations covered.

The way banks work is this:

There is the department that issues loans. Their job is to identify credit worthy borrowers and issue loans to them.

Then there is the department that handles compliance. Their job is to make sure the bank complies with the various regulations imposed by the government, such as Basel III and capital requirements and the like.

They are separate operations though. The people issuing loans don't call up the people complying with regulations and check whether or not there are enough reserves there to issue loans today, they just issue as many loans as they possibly can because that's how they make money.

Banks borrow from each other to satisfy their liqudity and other requirements, and the central bank is generally a lender of last resort, so banks can always satisfy their short term flow of funds requirements by borrowing money. The reason banks want to attract depositors is that it's CHEAPER than borrowing the money, and without any deposits they may not actually be profitable.

So the more deposits a bank can attract, the more profitable their lending operations are, but their lending operations are not constrained by their reserves per se.