Question

if 20,000 fell from the sky while the required ratio is 20% what is the minimum and maximum change to the money supply?

Answer 1

The money multiplier in this case would be , where RR is the reserve ratio, ie or . The maximum change to the money supply would be , for delta-ER would be the change in excess reserves, which in this case, is 20,000. Hence, the maximum change would be or . But, this includes the 20,000 which fell from the sky, and the actual change would be 100,000 minus 20,000, ie 80,000. Hence, for 20,000 increase in currency, the maximum change in the money supply would be 80,000.

The reason being that when 20,000 falls from sky, and people deposit it to the bank, and the banks loans all the ER keeping the 20% reserve, the money supply does increases to 5 times or 100,000. But, this value consumes the currency deposited to the bank (the 20,000 which fell from sky). Hence, the actual increase in money supply is the difference between the change in money supply and the currency deposited to the bank (which is the currency in the bank, not in the market).

The minimum change would be for the multiplier being 1, ie , which would be the case in which the banks keeps all the money and doesn't loan to anybody. It is feasible since the RR is the minimum amount of money as ER that the banks may keep, and the banks may set it 100%. In that case, the total change would be or or . Again, this also causes the currency of 20,000 out of the market to the bank, as before. Hence, the actual change in money supply in this case would be the 20,000 minus 20,000 or 0.

Hence, the maximum change is 80,000 and the minimum change is 0.

Note : The money supply is currency in circulation along with the bank deposits. In maximum case, the bank deposits increase, but the currency in circulation is out, which is also true in the later case.