Multiple Expansion

We have seen that a single bank in a banking system can lend rupee for rupee with its excess reserves. What is the lending ability of the commercial banking system or in other words, what is the ability of the entire banking system to create money?

When the banks receive an initial increase in their reserves, they utilize them as basis for lending purposes or for buying securities or both. The persons who receive them will receive in the form of demand deposits. Whatever may be the form in which the proceeds are initially received, the public is free to change the forms and propositions in which it will hold them. The public may prefer to hold all the proceeds in the form of demand deposits or it may take at least some to be held in the form of additional currency outside the banking system. The sizes of the money supply creation will be affected substantially by the public's choices as to the forms and propositions in which it will hold the proceeds from the banks' new loans and security purchases.

If all the proceeds continue to be held as demand deposits, all the initial increase of reserves remains in the banks to serve as a basis for additional demand deposits. Increase in money supply then depends on the size of the total reserve requirement (i.e. cash reserve ratio with the RBI and statutory liquid ratio).

On the other hand, money expansion will be restricted if some of the proceeds are taken in the form of currency and held as such outside the banking system.

Let us take a simple case assuming that the total reserve requirement is 20 percent against each rupee in demand deposits held by the commercial banks (i.e. we make no distinction between the cash reserve ratio and statutory liquidity ratio) and that all the reserves can be kept with the RBI.

Further, let us assume that if any bank becomes capable of increasing its loan, an amount equal to those reserves will be loaned to one borrower who will write a cheque for the entire amount of the loan and deposits it in another bank.

Let us suppose RBI has bought from Mr X Rs.1,000 worth of government securities. Mr X deposits the Rs.1,000 cheque in Bank A and the bank's reserves with the RBI increase by Rs.1,000 and demand deposits also rise by Rs.1,000 (a1). We shall record only changes in the various commercial banks. Thus, Bank A's Balance Sheet will appear as follows:

Balance Sheet of Bank A

As only 20% of new reserves are required to be deposited with the RBI as required reserves, the remaining Rs.800, excess reserves can be freed for lending. Remembering that a single commercial bank, such as Bank A, can lend only an amount equal to its excess reserves, we conclude that Bank A can lend a maximum of Rs.800. When a loan for this amount is negotiated, Bank A's loans will increase by Rs.800, and the borrower will get a Rs.800 demand deposit. Let us add these figures to Bank A's balance sheet (a₂).

But now we must invoke our third assumption: The borrower draws a cheque for Rs.800 - the entire amount of the loan - and gives it to someone who deposits it in Bank B. Bank A loses both demand deposits and reserves in the Reserve Bank equal to the amount of the loan (a₃). The net result of all the transactions is that Bank A's reserves in the Reserve Bank now stand at Rs.200 (= Rs.1000 - Rs.800), loans at Rs.800, and demand deposits at Rs.1000 (= Rs.1000 + Rs.800 - Rs.800) as shown below. Note that Bank A is just meeting the 20 percent total reserve requirement.

Balance Sheet: Commercial Bank A

Bank B acquires both the demand deposits and the reserves in the Reserve Bank which Bank A has lost. Bank B's balance sheet looks like this (b₁):

Balance Sheet: Commercial Bank B

When the cheque is drawn and cleared, Bank A loses Rs.800 worth of demand deposits and reserves in the Reserve Bank and Bank B gains Rs.800 in deposits and reserves. But 20 percent, or Rs.160, must be kept in the Reserve Bank as required reserves against the newly acquired Rs.800 demand deposits. This means that Bank B has Rs.640 (= Rs.800 - Rs.160) in excess reserves. It can therefore lend Rs.640 (b₂). When the borrower draws a cheque for the entire amount and deposits it in Bank C, both the demand deposits and reserves of Bank B fall by Rs.640 (b₃). As a result of these transactions, Bank B's reserves in the Reserve Bank will now stand at Rs.160 (= Rs.800 - Rs.640), loans at Rs.640 and demand deposits at Rs.800           (= Rs.800 + Rs.640 - Rs.640) as shown below. Note that after all this has occurred, Bank B is just meeting the 20 percent total reserve requirement.

Balance Sheet: Commercial Bank B

We are off and running again. Bank C has acquired the Rs.640 in demand deposits and reserves in the Reserve Bank lost by Bank B. Its balance sheet statement appears as follows (c₁):

Balance Sheet: Commercial Bank C

Exactly 20 percent, or Rs.128, of this new deposit will be required reserves, the remaining Rs.512 being excess reserves. Hence Bank C can safely lend a maximum of Rs.512. Suppose it does (c₂) and suppose the borrower draws a cheque for the entire amount and gives it to someone who deposits it in Bank D (c₃) the balance sheet would read as:

Balance Sheet: Commercial Bank C

Bank D - the bank receiving the Rs.512 in deposits and reserves in the Reserve Bank - now notes these changes on its balance sheet (d₁) as shown below.

It can now lend Rs.409.6 (d₂). The borrower draws a cheque for the full amount and deposits it in another bank (d₃).

Balance Sheet: Commercial Bank D

This procedure goes on. And the new money created will be equal to -

         1,000 + 800 + 640 + 512 + .................

Thus, on the basis of Rs.1000 in excess reserves, the commercial banking system is able to lend by a multiple of 5, when the total reserve requirement is 20 percent, even though a single bank can lend only an amount equal to its excess reserves. This is so because reserves lost by Bank A are acquired by Bank B and those lost by B are gained by C and so on. Hence, although reserves can be, and are, lost by individual banks in the banking system, there can be no loss of reserves for the banking system as a whole. Thus, though each individual bank can only lend an amount equal to its excess reserves, the banking system can lend by a multiple of its excess reserves.

Now, keeping the reserve requirement at 20 percent, let us assume that if the banks are capable of increasing its loan, an amount equal to the excess reserves will be loaned to one borrower, who may prefer to have some currency with him i.e. let us assume the public's preferred currency/deposit 'C' ratio to be 0.1.

Let us take the same case where the RBI has bought from Mr. X Rs.1,000 worth of government securities who deposits in Bank A and prefers to withdraw Rs.91 (maintaining currency/deposit ratio of 0.1). The remaining Rs.909 will be the increase in demand deposits of Bank A. Bank A's reserves with the RBI will increase, with the increase in demand deposits, by Rs.182 (i.e. 909 x 0.2) and the remaining Rs.727 will be loaned to Mr. Y. Mr. Y draws cash of Rs.66 and draws a cheque for the remaining amount of Rs.661 on  Bank A and deposits it in  Bank B. Bank B's demand deposits will rise by Rs.661 and loans Rs.529 to Mr. Z keeping Rs.132 as reserves with the RBI, Mr. Z withdraws Rs.48 in cash and puts a cheque for the remaining Rs.481 in Bank C and the procedure goes on .....

Total increase in demand deposits will be equal to 909 + Rs.661 + Rs.481 + .....

	=	909 [1 + 0.727 + (0.727)2 + .....]
	=	909 x		= 3,330
Total increase in currency will be -
	=	91 + 66 + 48 + ......
	=	91 [1 + 0.727 + (0.727)2 + ...] =
	=	Rs.333
Total increase in money supply
	=	Increase in demand deposits + Increase in currency
	=	3,330 + 333 = Rs.3,663