How is reserve money 'multiplied' by the banking system? I'ma an econ newbie so please forgive my lack of understanding.
I am confused as to how the money multiplier effect works. I get that the money multiplier effect doesn't actually hold true as banks don't loan out all their funds but I don't understand the mechanics behind how the multiplication takes place.
Initially I had thought that when, for example, a bank receives $10,000 from a Fed asset purchase, it is able to use the 10,000 USD to meet its (let's say 10%) reserve requirement, and can thus make 100,000 dollars in new loans. However I've just read an article by the Federal Reserve Bank of Chicago that suggests that this is not how money multiplication occurs, and instead that it occurs indirectly through many transactions (best demonstrated graphically, below). This confuses me, why doesn't the initial 10,000 dollars count as reserve money? Surely the  first bank could use it to loan out 100,000 dollars, creating an asset in the form of a loan and 'creating' a liability in the form of the borrower's deposit - isn't this how money is created?   Thank you in advance.
This overlaps an existing question: Can money multiplier happen within a single bank? The mechanics is described in there, and I think it addresses some of your questions.
My guess as to what is happening in the explanation you found is that there is an added behavioural assumption: banks only make loans up to the size of their excess reserve position. This means that if there is an injection of reserves, there can only be a loan of the same size as the injection, then a sequence of smaller loans. You then end up with diagram result. The reality is that this is not how banks operate, and they could just make a single loan and use up the excess reserves in one shot. (Obviously, could be done in smaller steps.)
The “sequence of small loans” story was probably in an old Economics 101 textbook, and it has been repeated many times. I have not seen a formal version of this model, so I have no idea why the non-existent constraint on loan size is imposed in the money multiplier model explanation.