If the Fed wants to increase the supply of money with open-market operations, it would purchase government bonds from the public in the open market. It is just like creating money from thin air. The purchase increases the number of dollars in the hands of the public, thus raising the money supply of the economy.
It is given that the capital of the bank is $200 and it then take deposits worth $800. The reserve ratio is 12.5%. The rest of the deposits are used to make loans. First, calculate the amount of reserves the bank hold and the amount of money the bank lends as loans.
Calculation of reserves is as follow:
Thus, the amount of money that must be kept as reserves are $100.
The loan given by the bank is equal to $700 ($800-$100)
The Balance sheet of bank-H is as follows:
The leverage ratio is the ratio of the Banks's total assets to bank capital. Calculation of leverage ratio is shown below:
Thus, the leverage ratio is 5.
Suppose that 10% of the borrowers from bank-H default and these bank loans become worthless. It means $90 (10% of $900) is worthless now and all the loss is capital loss and must be deducted from capital of the owner.
It is seen from the balance sheets that before the default, the total assets of the bank are $1,000 and after the default the total asset of the bank is $910. The percentage change in total assets is shown below:
Thus, the bank's total assets decreased by 9%. (negative sign denotes decrease)
It is seen from the balance sheets that before the default, the capital of the owner is 200 and after the default the capital of the owner is $110. The percentage change in capitals is shown below:
Thus, the capital of the owner decreased by 45%. (negative sign denotes decrease)
The change is larger in bank capital as compared to change in bank's total assets because the bank mostly using other people's money as the deposits to make loans.
If the required reserve ratio is 10%, the money multiplier could be increase as
= 10, if banks hold no excess reserves and people do not keep some additional currency. The additional currency is the excess amount.
The maximum increase in the money supply from a $10 million open-market purchase is $100 million ($10 Million × 10). Money supply will be acceptable.
The smallest possible increase is $10 million if all of the money is held by banks as additional reserves. Increase in ratio will be kept as additional currency.