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The money supply multiplier is simply the multiplier that tells us how much the money supply will go up when a given amount of money is deposited in a bank.
When the money is deposited in a bank, some fraction of the money is then lent out. The borrower deposits the money in their own bank, which lends a fraction of it out in turn. This keeps happening over and over again.
The formula for this is simply 1/reserve requirement.
So, if the reserve requirement is .1 (10%), the money multiplier is 10. If this is the case, $1000 deposited in a bank will increase the money supply by $10,000.
The "multiplier effect" refers to the manner in which the supply of money circulating throughout the economy grows as financial institutions, mainly banks, lend out money they have attained through customer deposits. The money that banks lend out is that which is accumulated over time from customer deposits. Banks will routinely maintain a capital reserve--in effect, set aside a certain percentage of their total holdings--in the event of an emergency but also as a requirement dictated by the Federal Reserve Board of Governors and by the multinational Basel Accord, which stipulates that each participating country will require banks to maintain a reserve as a hedge against financial crises, such as occurred as recently as 2007–2008. That money, the majority of what each bank holds, is available for lending purposes, which, as noted, expands the aggregate money supply.
The formula by which the multiplier effect is calculated is dependent upon reserve requirements and so varies over time. That amount, the amount held in reserve, is divided into the total amount of deposits. As money is loaned out, that money is deposited, in turn, into other accounts and becomes available for additional lending. Hence, the original deposit creates a multiplier effect through the process of deposits and lending. Over time, the value of the initial deposit grows several times over as that initial seed money works its way through the economy. To reiterate, though, the multiplier effect is a product of the value of deposits divided by the reserve ratio.
The term multiplier in economic refers to change in an induced variable such as GDP per unit change in an external variable such as government spending.
Money supply multiplier is defined as the ratio of increase in money supply to the increase in bank reserves. Generally the the money supply multiplier is equal to the inverse of required reserve ratio. Thus for a required reserve ratio of 0.1 the money supply multiplier will be 10. Expressed as a formula Money supply multiplier can be represented as follows.
Money Supply Multiplier = (Change of money supply)/(Change of reserves)
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