Explain why a single commercial bank can safely lend only an amount equal to its excess reserves, but the commercial banking system as a whole can lend by a multiple of its excess reserves. What is the monetary multiplier, and how does it relate to the reserve ratio?

An individual bank can only lend an amount equal to its pre-loan excess reserves.There’s a possibility that the lending bank has to clear the checks for the entire amount loaned. In such a case, the bank will lose the whole amount it lent. If the bank loans beyond its excess reserves, it might be short of credit.Therefore, the bank can loan only an amount equal to its excess reserves for safety purposes.

On the other hand, the commercial banking system can lend money by multiple of its excess reserves because the reserves are not lost from the whole system. The reserves transfer from one bank to the other in the system. Also, the money multiplier comes into effect when some amount is loaned, creating additional money in the economy.

The monetary multiplier is the rate by which the money supply in the economy increases by an extension of loans. It defines the relationship between excess reserves and the new checkable deposit money created by all the banks collectively.

It has negative relation with the required reserve ratio. The smaller the required reserve ratio, the larger the lending capacity of the banking system; thus, higher will be the monetary multiplier.

The following formula shows the relationship between the money multiplier and the required reserve ratio:

$m=\frac{1}{r}$

Where m is the monetary multiplier and r is the required reserve ratio.