Suppose the ratio of deposits that banks hold in the form of reserves is 7 percent. Suppose further that people want to hold 8 percent of their deposits in the form of cash. Then, if the fed wants the money supply to be $6,228 billion, what is the necessary level of high powered money?
Assume an economy in which the reserve ratio is 15 percent, people hold 10% of their deposits in the form of cash, and there are no other leakages. (a) Compute the value of the money multiplier. (b) If the current level of high-powered money is $1,500 billion, what is the money supply in this economy? (c) How much does the money supply change if the fed buys $30 billion of U.S. government treasury bills from a government bond dealer? How about if banks borrowings of reserves from the fed decline by $6 billion? (d) if the fed set a target money supply of $6,424 billion what would it have to do to achieve that target?
The first thing you need for this is to define the leakage adjusted money multiplier.
Assume the required reserve ratio is r, the banks' propensity to hold excess reserve, as a fraction of total reserves is e and borrowers' tendency to hold cash, as a fraction of cash is c. Then,
the leakage-adjusted money multiplier = 1/(r+e+c)
In this case banks do not have a tendency to hold excess cash, and hence e = 0. The required reserve ratio in the first case is 7%, and the borrowers' tendency to hold ...
The leakage adjusted money multiplier is explained with calculations in 372 words.