Fractional Reserve Banking Requirements

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    Hi Dr Herbener,
    Let’s say the reserve requirement is 10%.
    If I deposit 100$ in a bank, how much can that bank expand credit? Sometimes I read that it can then lend out 10$ (10% of 100$) and sometimes 1000$ (100$ =10% of 1000$).


    The formula is 1 – [reserve requirement]. So in this case it could increase credit by 90%. Rothbard discusses this, and explains why your second option is incorrect, in chapter XI of The Mystery of Banking, online here:


    For any particular bank, it depends on the stability of its reserve during the process of credit creation. For the banking system, the expansion is 1/RRR. In Ch. XI of Mystery of Banking, Rothbard demonstrates that even with competitive banks, which are restricted in their issue of fiduciary media by redemption of their money substitutes by non-clients, the existence of a central bank will result in credit expansion from fiduciary issue as the central bank expands the reserves of the banks.

    To use your example in Rothbard’s framework, suppose Customer X of Bank A deposits $100 cash in his checking account and the RRR=0.10, then the (minimum) the bank can expand its money substitutes by credit creation is $90. This assumes that Bank A makes a loan to a non-client, who will not accept a check drawn on Bank A but only cash. Then Bank A lends $90 in cash and is holding $10 against $100 deposit of Customer X. But the borrower either spends the cash or deposits it in his bank. If the cash is spend, the merchant then deposits it in his bank. Bank B, then, gets a cash reserve of $90 and credits Customer Y’s checking account with $90. Bank B can then lend $81 in cash and keep $9 reserve against the checking account of $90. And so on, until the entire banking system will have expanded checking accounts by $1,000 from the initial $100 increase in cash reserves.

    Any particular bank can expand further than the minimum if it makes loans to clients instead of non-clients. Clients are those people willing to accept the bank’s checking accounts as a medium of exchange. So the maximum that Bank A can expand with $100 additional reserve and a RRR=0.10 is $1,000. Since, in this case, it does not need to lend any of its cash reserve in the process of crediting credit. The borrowers are willing to accept checking accounts drawn on Bank A instead.

    Whatever might be the case for any particular bank, the banking system can expand by 1/RRR even in the case, as Rothbard demonstrated, where each bank can only expand by 1-RRR.


    I believe the description of banking put forth in Mystery of Banking and indeed most economics literature, that which leads to the existence of a “money multiplier” based on reserve ratio, is severely outdated.

    One should look into the topic of “Endogeneous Money” to get a more accurate picture of the banking system. ( Also “Understanding The Modern Monetary System” at

    In short, banks are never constrained by reserves. Banks are always capital constrained. Banks do not need reserves to make loans. Indeed, banks periodically seek reserves *after* the loans are made. So, it is irrelevant if you deposit $100 in the bank. If the bank finds a worthy borrower in demand of a loan then the bank will make the loan, and then seek the reserves afterward, purely for liquidity and regulatory reasons.

    The ONLY constraints are capital constraints, and on that topic I post here an excerpt from a discussion I had with someone with experience in the banking industry:

    “So, the TLDR; is that banks are technically constrained by their base “Capital” — that is they are only allowed to make a grand total amount of loans that is LESS than what the expected risk of default will be — so if a bank estimates that the “risk” of it’s portfolio or loans defaulting — going totally bad and left unpaid — is say 10%, then with base capital of say $100 million, that bank will not lend more than $1 billion in total (and indeed will stay far SHY of that total). “


    To be viable in a market economy, every business enterprise must be solvent and liquid. There are always two fundamental constraints on its activities as they affect its balance sheet. It must have sufficient capital as a buffer against a decline in the market value of its assets. It must also roughly match the time structure of its assets and liabilities. It must have sufficient short term assets to cover short term liabilities.

    If a bank issues liabilities against itself that are due to be paid on demand at par (i.e., its customers’ checking accounts) against the assets of the loans it creates for those customers, then it would be illiquid since its assets (the loans) have some time before maturity. The only asset that perfectly matches an on demand at par liability in its time dimension is cash. Other assets the bank holds that are available to it on demand at par match imperfectly. These are reserves. A bank can be ruined financially by creating loans out of thin air and writing them into customers’ checking accounts if doing so makes them illiquid because they failed to acquire reserves to hold against their on demand at par liabilities.

    Of course, a bank doesn’t need reserves in advance of creating credit out of thin air. But it needs to acquire and maintain reserves sufficient to make its balance sheet liquid just as it needs to acquire and maintain capital to make its balance sheet solvent.

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