Today bank reserves do not consist in gold or any other commodity, but of cash and the bank's own deposits at the Federal Reserve. Banks are legally required to hold reserves against their demand deposits. The fraction of total demand deposits that must be held as reserves is set by law, currently less than 10% on average. Let the legally required fraction of deposits kept as reserves be r. Then actual reserves above the requirement are excess reserves, and their fraction is \ — r.
To give a numerical example, assume that r is 10%, then (1 —r) is 90%. Assume that there is only one bank, a monopoly bank. An additional $100 cash deposit (or creation of new reserves of $100 by the Federal Reserve) results in an additional $100 demand deposit credited to the depositor. So far there is no creation of money, just a change from cash to demand deposit in the books of the depositor. But now the bank has $90 in excess reserves. It can lend out up to $900, creating demand deposits up to that amount in the name of the borrowers. Total additional demand deposits are now $1,000, consisting of the $900 new loans and the $100 demand deposit exchanged for the original cash deposit. Additional reserves are $100 (the original cash deposit). The 10% reserve requirement is met, $900 in new money has been created. The monopoly bank can expand its demand deposits by a factor of 1/r = l/.l = 10 times new reserves, because, being the only bank, it knows that all checks written against these new deposits will be redeposited with it.
If there are many different banks then each bank must assume that checks written on its new demand deposits will be deposited to another bank, and that it will quickly lose that amount of reserves in its account at the Federal Reserve, since that check will be cleared by transferring reserves from its account to the other bank's account at the Federal Reserve. Remember, the bank's deposits with the Federal Reserve count as reserves. Therefore, in the many-bank case, a single bank receiving an additional $100 cash deposit can only safely lend out its excess reserves, namely $90. But as that $90 is spent it is redeposited by the recipient in another bank. The second bank must keep 10% in reserve, so it has excess reserves of .9 ($90) = $81. The $81 is loaned, spent, and deposited in a third bank, which then can lend .9 ($81) = $72.90, etc. The result of this process of lending, spending, and redepositing is that the whole banking system, consisting of many different banks, ends up multiplying the new reserves by the same factor of 1/r as the monopoly bank does. So the banking system, whether a monopoly bank or many banks, has a reserves-to-deposit multiplier of 1/r. Of course, if we have a 100% reserve requirement, that would mean that r = 1, and consequently the deposit multiplier would be 1/r = 1/1 = 1, which would mean that banks could not create monev.
The banking system's (or monopoly bank's) gross profit from the original $100
cash deposit is the difference between the interest received on loans of $900
(newly created money) and interest paid on the original $100 cash deposit.
Even if the deposit rate of interest were equal to the loan rate of interest
there would be considerable margin for profit. Of course, the loan rate is
considerably higher than the deposit rate, increasing the margin substantially.
—For the Common Good: Redirecting the Economy toward Community, the Environment, and a Sustainable Future; Herman E. Daly & John B. Cobb, Jr. pp. 416-418.