The actual magnitude of the money multiplier is determined by both legal and behavioral factors. For M1 it is about 3, and for M2 it is about 8. Since the money multiplier is defined as
the change in the money supply can be calculated as
D Money supply = Money multiplier x D Money base
Consequently, if the Fed bought $5 million of government bonds, M1 would increase ultimately by $15 million, and M2 would increase ultimately by $40 million.
Why is the M2 money multiplier larger? As loans are made and account balances rise, people have a tendency to keep most of those balances in term deposits to earn a higher rate of interest. Banks encourage this practice by offering higher interest rates on term deposits, because required reserves on term deposits are zero; banks can make more loans, and thus more profit, if extra deposits are in term deposits rather than demand deposits. As a result, M2, which includes term deposits, increases much more than M1, making the M2 multiplier larger.
increase in the money base is formalized by the concept of the money multiplier: the ultimate increase in the money supply per dollar increase in the money base. In this example, the money multiplier is 20. In formal terms it is written as
The calculation of 20 for the money multiplier is misleading, however. As deposits increase, you and others may wish to hold some fraction of these increased deposits in cash, draining reserves from the banking system. This response lowers the amount of extra loans the banking system can make, decreasing the magnitude of the money multiplier.
Other complications are possible. There are different legal reserve requirements for different types of deposits 10 percent for checking accounts, for example, and 0 percent for time deposits so that the value of the money multiplier may depend on the mix of accounts into which the money-supply increase goes. Another possible complication is that banks may wish to hold reserves in excess of those they are legally required to hold as a safety precaution against having to pay a penalty should their reserves inadvertently fall below their legal requirement. In general, the magnitude of the money multiplier is determined by the interaction of various legal requirements and behavioral reactions on the part of the public and commercial banks.
