I do not get how the money multiplier is supposed to work. If the reserve ratio is 10%, when a bank has $1000 it loans out 900, this creates a total of $1900. I do not get how new money is created when it was merely transferred from one entity to another.
You’re right in that no one is printing more money, but think of the practical implication of this idea.
First, imagine that banks must keep 100% of deposits on reserve. If I deposit 10 dollars, they cannot make any loans with this money. Using the formula, the money multiplier is 1-- 10 dollars gives 10 dollars.
If, on the other hand, the bank must keep 10% of deposits, then my deposit can be loaned out (up to 9 dollars). If I put 10 in the bank, and the bank loans 9 to someone else, there is effectively more money in the system (because the bank still owes me 10). Now, if that second person buys something for 9 dollars from a merchant and the merchant deposits 9 dollars in his bank, the bank can loan out 8.10 dollars from the merchant’s 9. This cycle could continue, but lets stop here to see the effect. After 10 dollars was deposited, an additional 9 + 8.10 = 17.10 was loaned out-- there was, in a practical sense, an increase in the amount of money available. This could happen to effectively have 10/0.10 = 100 dollars in the economy (if the cycle goes until completion).
This is the idea behind the money multiplier. Obviously, this doesn’t always happen until no further money can be lent out, but the theory tells us what could happen given a certain deposit and required reserve ratio.