Example of Fractional Reserve Banking with 20% Required Reserves

Example of Fractional Reserve Banking with 20% Required Reserves

Suppose the Fed conducts an open market purchase of a $1000 Treasury bill from the First National Bank. What would be the total effect on the money supply from this $1000 increase in the reserves if the required reserve ratio is 20%?

If banks do not hold any additional excess reserves, banks will make loans for the maximum amount of any new deposits. When the Fed purchases the $1000 government security from the First National Bank, the bank’s balance sheet changes as follows:

Table 36.
FIRST NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves
Deposits
Excess Reserves + $1000

Loans
Net Worth
Government Securities - $1000

Property & other assets

Since the bank has not acquired any additional deposits, its required reserves do not change. The sale of the Treasury bill has reduced the bank’s holdings of government securities by $1000. In exchange for the government bond, the Fed has credited $1000 to the First National Bank’s account at the Fed.

Since it is assumed banks do not want to hold any additional excess reserves, the First National Bank will loan out the $1000 to earn additional interest income. Suppose the First National Bank loans the $1000 to Adam Aardvark. It does this by increasing the balance in Adam’s checking account at First National Bank. The money supply has just increased by $1000. (Remember the M1 definition of the money supply is currency in circulation plus the balances in checking accounts plus travelers’ checks outstanding.)

Table 37.
FIRST NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves
Deposits
Excess Reserves - $1000

Loans + $1000
Net Worth
Government Securities

Property & other assets


Notice that the net affect of the open market operation is that the First National Bank has decreased its holdings of government securities by $1000 and increased its loans by $1000.

When people borrow money, they usually spend it right away. Suppose Adam buys a $1000 painting from Bernice Bear. Bernice now has $1000 she did not have before. Suppose she deposits this in her bank, Second National Bank. This bank will be required to keep 20% of this deposit as reserves, and will loan out $800.

Table 38.
SECOND NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $200
Deposits + $1000
Excess Reserves

Loans + $800
Net Worth
Government Securities

Property & other assets


Suppose Second National Bank loans $800 to Charlie Cheetah. Charlie uses the money to buy a stereo from Diego Dolphin. Diego now has $800 that he did not have before this transaction. Suppose Diego deposits the $800 in his bank, Third National Bank. This bank will be required to keep 20% of this deposit as reserves and will loan out the rest. This means the Third National Bank will increase its required reserves by $160 and will increase its loans by $640.

Table 39.
THIRD NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $160
Deposits + $800
Excess Reserves

Loans + $640
Net Worth
Government Securities

Property & other assets




Suppose Third National Bank loans $640 to Esmeralda Elephant. Esmeralda uses the money to buy a wide screen television from Francesca Ferret. Francesca now has $640 that she did not have before. Suppose Francesca deposits the $640 in her bank, Fourth National Bank. This bank will be required to keep 20% of this deposit as reserves and will loan out the rest. This means the Fourth National Bank will increase its required reserves by $128 and will increase its loans by $512.

Table 40.
FOURTH NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $128
Deposits + $640
Excess Reserves

Loans + $512
Net Worth
Government Securities

Property & other assets


Suppose Fourth National Bank loans $512 to Gary Gorilla. Gary uses the money to buy a sculpture from Helen Hyena. Helen now has $512 that she did not have before. Suppose Helen deposits the $512 in her bank, Fifth National Bank. This bank will be required to keep 20% of this deposit as reserves and will loan out the rest. This means the Fifth National Bank will increase its required reserves by $102.40 and will increase its loans by $409.60.

Table 41.
FIFTH NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $81.92
Deposits + $409.60
Excess Reserves

Loans + $327.68
Net Worth
Government Securities

Property & other assets


Suppose Fifth National Bank loans $327.68 to Ian Impala. Ian uses the money to buy a hand-made rug from Julius Jaguar. Julius now has $327.68 that he did not have before. Suppose Julius deposits the $327.68 in his bank, Sixth National Bank. This bank will be required to keep 20% of this deposit as reserves and will loan out the rest. This means the Sixth National Bank will increase its required reserves by $65.54 and will increase its loans by $262.14.


Table 42.
SIXTH NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $65.54
Deposits + $327.68
Excess Reserves

Loans + $262.14
Net Worth
Government Securities

Property & other assets


The open market purchase of a $1000 government security from the First National Bank has caused an increase in the money supply that is much larger than $1000. So for, the money supply has increased by $4095.10. Bernice Bear still has the additional $1000 in her account at the Second National Bank, Diego Dolphin still has the additional $900 in his account at Third National Bank, Francesca Ferret still has the additional $810 in her account at the Fourth National Bank, Helen Hyena still has the additional $729 in her account at the Fifth National Bank, and Julius Jaguar still has the additional $656.10 in his account at the Sixth National Bank. The additions to people’s checking accounts are $1000 + $800 + $640 + $512 + $409.60 + $327.68 = $3,689.28. This process could continue, however. Eventually the total increase in the money supply would be $5,000. The amount of money the banking system generates with each dollar of reserves is the money multiplier. The money multiplier is the inverse of the reserve ratio. In this example, the reserve ratio is .20. Thus the money multiplier is 1/.20 = 5. Thus, each dollar of reserves generates $5 of money. Since the open market operation increased reserves by $1000, the total effect on the money supply is 5 times $1000 = $5,000.

Notice that with a higher required reserve ratio, the increase in the money supply is smaller.
· A $1000 increase in banking system reserves caused a $10,000 increase in the money supply when the required reserve ratio was 10%.
· A $1000 increase in banking system reserves caused a $5,000 increase in the money supply when the required reserve ratio was 20%.