Credit Contraction Or Destruction – Formula for Deposit Creation
Credit Contraction is the opposite of credit creation and for the banking system, operates on identical principles when cash is lost or removed from the banking system.The banking system like individual banks must contract deposits when it is short of reserves but unlike individual banks, it must contract deposits by a multiple of the deficiency of reserves.
An individual bank can argument its reserves shortages by obtaining reserves from other banks, reducing loans and advancements or investments, liability management and borrowing from the central bank or by acquiring Euro-dollar, but such actions in the commercial banking system cannot relieve the system of its shortages, it will rather compound the situation because all or most banks are involved at the same time.
This is particularly so, when the central bank for purposes of restraining inflation decides not to provide commercial banks with additional reserves. A simple illustration will suffice, assume that the banking system is initially loaned up with every bank having a cash reserve of $10,000 total deposit of $50,000 and a loan profile and investments worth $40,000, suppose a depositor withdraws $1000 from bank A, the bank balance sheet will show thus;
Bank A
- Deposits =$49,000
- Cash = $9,000
- Loans and investments = $4,000
So against deposit liabilities of $49,000 and given a cash reserve requirement of 20%, bank A will need $9,800 as cash reserve the deficit of $800 will be made up by the depositing payments. After bank A has collected the amount from Bank B, the balance sheet of A and B will reflect thus,
Bank A
- Deposits =$49,000
- Total = $49,000
- Cash = $9,800
- Loans and investments = $39,200
- Total = $49,000
Bank B
- Deposits =$49,200
- Total = $49,200
- Cash = $9,200
- Loans and investments = $40,000
- Total = $49,000
To consider the Credit Contraction from the balance sheet of A, it will be clear that by depositing of some investments, it has been able to restore itself to a satisfactory position. But the balance sheet of B shows a reduction of $600 from its deposit and the same amount from its cash. This amount has been paid to bank A against its sale of investments of $600. Thus bank B is now deficient of cash to the extent of $640. To restore its position, it needs to sell some of the investments to someone who may be banking with C and who issues cheque against Bank C in payment. Upon receiving the payment from Bank C, the balance sheet of the banks will be
Bank B
- Deposits =$49,200
- Total = $49,200
- Cash = $9,800
- Loans and investments = $36,360
- Total = $49,200
Bank C
- Deposits =$49,360
- Total = $49,360
- Cash = $9,360
- Loans and investments = $40,000
- Total = $49,360
Bank C has a deficiency of cash, which it will make up by depositing its investments or by contracting load (Credit Contraction ) and the process goes on till all the effects are fully exhausted. Thu the original reduction of deposits by $1000 id followed by subsequent reduction of $800, $640, etc which is the reserve of the credit creation process.
Formula for Deposit Creation (Credit Contraction)
Having considered Credit Contraction, here is the formula for deposit creation. The result of the preceding analysis may be more readily obtained using the following formula;
D = R/r
Where r = reserve requirement (cash reserve ration)
R = volume of reserve in the commercial banking system initial deposit
D = amount of credit or demand deposit that will be created
For instance in our example R = $1000
R = 20% or 0.2 = D = 1000/0.2 = $5,000
As long as R and r remain unchanged, the maximum volume of deposits the banking system may maintain will be $5,000.
Alternatively we can find the Credit Contraction for the deposit multiplier using the following;
K = 1/r where
K = deposit multiplier
R = cash reserve ratio
Thus where cash reserve ratio is 20% or 0.2 the deposit multiplier becomes
K = 1/r = 1/0.2 = 5
If r =10%, the K = 1/0.1 = 10
Thus the higher the cash reserve ratio, the total deposit multiplier. The total deposit creation will be additional (DM) times the deposit multiplier K in essence Additional aggregate deposits D = AM & K.
Where the commercial banking system realize $10m as a result of government spending deposits will be expanded through loans and investments to the extent of $50m, if remains 20%, thus
= AM x K
= $10 x 5
=$50m
The process of Credit Contraction is complex and needs a wider understanding for an effective implementation.