Tabl. 8. The expansion of the money supply by a system of commercial banks

Bank	Reserves and Loans, $	Required Reserves, $	Excess Reserves, $	Created Money (the amount of money to lend), $
Bank A	100,00	20,00	80,00	80,00
Bank В	80,00	16,00	64,00	64,00
Bank С	64,00	12,80	51,20	51,20
Bank D	51,20	10,24	40,96	40,96
Other banks	204,80	40,96	163,84	163,84
The total amount of the money created				400,00

The money multiplier (m) shows the maximum amount of money, which can be created by one dollar of excess reserves, the required reserve ratio given. The money multiplier is inversely proportional to the required reserve ratio, or

m = 1 / R, where

m - a money multiplier

R - a required reserve ratio

So we can see that the larger the required reserve ratio is the smaller the money multiplier is; the less money can be created and the less the money supply is.

Now suppose the commercial banking system has $1 million in cash and for strictly commercial purposes would normally maintain cash reserves equal to 5% of sight deposits. Since sight deposits will be 20 times cash reserves, the banking system will create $20 million of sight deposits against its $1 million cash reserves:

cash reserves $1 mln  5%

sight deposits x - 100%

x = $1 mln x 100% : 5% = $20 mln.

Suppose the Bank now imposes a reserve requirement that banks must hold cash reserves of at least 10% of sight deposits. Now banks can create only $10 million sight deposits against their cash reserves of $1 million. Thus a reserve requirement acts like a tax on banks by forcing them to hold a higher fraction of their total assets as bank reserves and a lower fraction as loans earning high interest rates.

Thus, when the central bank imposes a reserve requirement in excess of the reserve ratio that prudent banks would nnywav have maintained, the effect is to reduce the creation of bank deposits, reduce the value of the money multiplier, and reduce the money supply. Similarly, when a particular reserve requirement is already in force, any increase in the reserve requirement will reduce the money supply.

The Discount Rate. Учетная ставка

The second instrument of monetary control available to the central bank is the discount rate.

The discount rate is the interest rate that the Bank charges when the commercial banks want to borrow money.

Suppose banks tMnk the minimum safe ratio of cash to deposits is 10%. Say their cash reserves are 12% of deposits. How far dare they let their cash reserves fall towards the minimum level of 10%?

Banks have to balance the interest rate they will get on extra lending with the dangers and costs involved if there is a sudden flood of withdrawals, which push their cash reserves below the critical 10% figure. This is where the discount rate comes in. Suppose market interest rates are 8% and the central bank makes it known it is prepared to lend to commercial banks at 8%. Commercial banks may as well lend up to the hilt and drive their cash reserves down to the minimum 10% of deposits. The banks are lending at 8% and, if the worst comes to the worst and they are short of cash, they can always borrow from the Bank at 8%. Banks cannot lose by lending as much as possible.

Suppose however that the Bank announces that, although market interest rates are 8%, it will lend to commercial banks only at the penalty rate of 10%. Now a bank with cash reserves of 12% may conclude that it is not worth making the extra loans at 8% interest that would drive its cash reserves down to the minimum of 10% of deposits. There is too high a risk that sudden withdrawals will then force the bank to borrow from the Bank at 10% interest. It will have lost money by making these extra loans. It makes more sense to hold some excess cash reserves against the possibility of a sudden withdrawal.

Thus, by setting the discount rate at a penalty level in excess of the general level of interest rates, the Bank can induce commercial banks voluntarily to hold additional cash reserves. Since banks have to hold more cash as reserves, the money multiplier is reduced, less money can be created and the money supply is lower.