Answer:
If the required reserve ratio is 15 percent, the largest possible increase in the money supply that could result is $200 million, and the smallest possible increase is $30 million.
Step-by-step explanation:
In order to determine the largest possible increase in the money supply we have to determine the money multiplier. The money multiplier measures the banks' capacity to "create" money by lending it.
Money multiplier = 1 / reserve ratio = 1 / 15% = 6.667
maximum increase in money supply = inflow of funds x money multiplier = $30 million x 6.667 = $200 million.
The banking system creates money by first receiving deposits, e.g. you deposit $1,000 in your savings account, and then lending money to another client. The bank will lend $850 (-15% required reserve) to John that will purchase a bike. The seller of the bike receives the money form John and deposits the $850 in his own bank. Then this second bank will lend $722.50 to Sarah. Sarah will use the money to purchase a new computer and a printer from Tom. Tom then deposits the money in his bank, and then his bank lends $614 to Sally, and the wheel goes on and on.
Assuming that the banks decide to not lend any portion of the $30 million to their clients and instead uses them to increase their reserves, the smallest possible increase in the money supply would be the $30 million.
This money creating process is possible because we use a fractional banking system, which means that the banks are only required to keep a fraction of total deposits as reserves.