Sometimes banks wish to hold reserves in excess of the legal minimum. Suppose that banks are initially fully loaned up and the required reserve ratio is 0.1. Then the Fed makes an open market purchase of $100,000 in government bonds, and each bank decides to hold excess reserves equal to 5 percent of its deposits.
a) Derive the demand deposit multiplier in this case. Is it larger or smaller than when banks hold no excess reserves?
b) What is the ultimate change in demand deposits in the entire banking system?
The maximum value for the money multiplier is equal to the reciprocal of the reserve (requirement) ratio, so that
M = 1 / r
where M = the money multiplier
r = the reserve ratio
Here the money multipliers ...
This explains the steps to calculate the demand deposit multiplier in a given case and the change in demand deposits across the entire banking system.