# Money multiplier

The money multiplier (also called the credit multiplier or the deposit multiplier) is a measure of the extent to which the creation of money in the banking system causes the growth in the money supply to exceed growth in the monetary base.

The multiplier is the multiple by which the expansion in the money supply is greater than the increase in the monetary base: if the multiplier is 10, then a £1 increase in the monetary base will cause a £10 increase in the money supply.

Most discussions of the multiplier do not discuss what measure of the money supply is being increased. As it is usually restricted to deposits in banks, this implies that we are talking about M1 (most commonly) or M2. Multipliers can also be calculated for broad money measures such as M3 and M4.

## The deposit expansion multiplier

The easiest way to understand how the multiplier works is to consider what happens under simplifying assumptions:

• Banks keep a fixed fraction of deposits to meet the reserve requirement.
• Customers of the banks pay each other by cheque (or transfer etc.) but not by withdrawing cash to make payments.
• When customers do not receive these payments they do not withdraw any of the money from the bank.

Now consider a the following sequence of events

1. An initial deposit is made of £100
2. The bank is able to lend £90 of this. The borrower draws cheques against the £90 balance now in their account that the payees deposit in accounts in the same of other banks. Now customer balances have increased by the original £100 plus the £90 from the new cheque deposits: a total of £190
3. The bank can now lend 90% of the £90, a further £81.
4. Total deposits are now increased by another £81 to £ to £271
5. This process repeats and the total increase in bank deposits is 10 times the amount initially deposited: i.e. £1,000

As you might infer from the above, the multiplier is the reciprocal of the reserve requirement. If the reserve requirement was (a very high) 20% the multiplier would be 1 ÷ 0.2 = 5

## The complex multiplier

The above illustrates the principal, but what happens if we lift the simplifying assumptions? Customers will keep some money as cash rather than in the bank, and banks will keep central bank balances and cash for transactions in addition to the reserve requirement. This gives us a similar formula for the complex multiplier:

(1 + c)/(r + e + c)

Where:
c is the proportion of their money customers keep as cash,
r is the reserve requirement, and,
e is the reserves banks keep in addition to the reserve requirement.

There are plenty of other corrections that can be made, and more complex models than a simple static multiple. This being economics there is also plenty of argument about the significance of the money multiplier, its determinants, and even whether it exists in all modern economies.