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Hayek said:We may start as before by examining the procedure of a single bank. At this bank a certain amount of cash is newly deposited: a sum, let us say, equal to 5 percent of its previous total deposits. If the policy of the bank was to keep a reserve of 10 percent against deposits, that ratio has now been increased, by the new deposit, to 14.3 percent, and the bank is therefore in a position, in accordance with its policy, to grant new credit. If we assume further that it re-lends 90 percent of the newly deposited money and that the whole of this is immediately utilized by the borrower (in order, let us say, to increase his purchases of raw materials) then the ratio of cash to deposits has again sunk to 10 percent. In so far as the bank does not change its policy its individual lending capacity is exhausted, in these circumstances, before it has even re-lent the whole of the amount newly deposited.
The effect of the sums newly deposited at one bank on the lending capacity of the whole banking system is, however, not exhausted by this transaction. If the borrower does not use the credit in a way that leads quickly to the market for consumers' goods, such as wage payments, but devotes it instead to the purchase of raw materials or half-finished products, then it is to be assumed that payment will be made by check and that the seller will hand over the sum received to his own bank for encashment, the amount being credited to his own account. The next consequence must be that the clearing-house position of this bank improves by exactly the amount transferred, and it therefore obtains an equivalent amount of cash from the bank that originally granted the credit.
For the second bank, therefore, the sum originating in the granting of credit and paid into its accounts (representing, as we remember, 90 percent of the original deposit) is just as much an original deposit, based on cash payments, as it was to the bank we originally considered. It will, therefore, be regarded as a basis for additional lending and used in just the same way as any other new deposit. If the second bank also keeps 10 percent of its deposits as cash reserves, it too will be in a position to lend 90 percent of the new deposit, and the same process will be continued as long as the amounts are merely transferred from bank to bank and are not taken out in cash. As every bank re-lends 90 percent of the amount paid into it and thus causes an equivalent increase in deposits for some other bank, the original deposit will give rise to credit representing 0.9+0.92+0.93+0.94… times the original amount. As the sum of this converging infinite series is 9, the banks will be enabled, in an extreme case, to create, against an amount of cash flowing in from an outside source, credit equal to nine times that amount. This becomes clear when we consider that the process can only stop when the last part of this cash is required for the 10 percent reserve of the deposits.
For simplicity's sake we have made use of an assumption that is undoubtedly incorrect, but which affects our conclusion only in so far as it reduces the actual amount of new credit the banks can create with a reserve ratio of 10 percent. Its omission leaves our fundamental conclusion intact: i.e., that they can grant credit to an amount several times greater than the sum originally deposited. In fact some part of the credit at least, if not on the first then on subsequent occasions, will always be withdrawn in cash and not deposited with other banks. For example, if 70 percent is always re-deposited instead of the full 90 percent, this amount being re-lent by every bank and the remainder being used in cash transactions, then the increase in deposits will give rise to additional credit equal to only 0.7+0.72+0.73… times (i.e., two and one-third times) the original. So long as any part of the credit granted is not withdrawn in cash but re-deposited with the banks, the latter will be able to create additional credit, of a larger or smaller amount, as a consequence of every increase in their cash holdings.[88] The lifetime of this pyramid of credit is limited to that of the first credit granted, save in the case (which can be assumed as long as there are no withdrawals from deposits) where it is immediately replaced by a fresh credit. If, however, deposits unexpectedly diminish at any part of the banking system, the process will be reversed, and the original diminution of deposits will occasion a contraction of credit correspondingly exceeding the amount withdrawn.[89]
In this connection we must note for further emphasis later the fact that the proportion in which the credit granted is transferred to other accounts — and not paid out in cash — must be regarded as subject to very wide fluctuations as between different individuals at a given moment, as well as between various periods of time for the economic system as a whole. We return later to the significance of this fact.
What has been said above should be sufficient to show that the possibility of creating credit over and above the sums deposited — which, under Continental banking conditions, is not open to any individual bank — is, however, open to the whole banking system of the country to a considerable extent. The fact that a single bank cannot do what is automatically done by the banking system as a whole also explains another circumstance, which might otherwise easily be cited as a proof of the impossibility of additional credit creation. If every bank could re-lend several times the amount deposited, there would be no reason against its offering a much higher rate of interest on deposits than it actually does, or, in particular, under the existing discount rates of the central banks, against its procuring cash in unlimited quantities by way of rediscount; for it would only have to charge its customers a small part of the rate of interest charged by the banks in order to make the business pay. This apparent contradiction between theory and practice is cleared up as soon as one realizes that an increase of deposits by a single bank only offers possibilities for credit creation to the banking system as a whole. But the importance of this circumstance transcends the mere clearing up of this difficulty.
From Monetary Theory and the Trade Cycle
If you've ever thought about why a crash can be so bad. Banks can be very inflationary even without a central bank if fractional reserve banking is sponsored.