The monetary multiplier is a measurement of the effect that a loan of funds from a federal government has on the banking system. Each bank must keep a certain amount of those loaned funds in reserve but may then loan the rest out to other customers. Those funds then in turn end up in other banks until they are finally completely spent. Thus the monetary multiplier shows how a federal loan is actually worth many times its initial weight on the banking system.
One way that a struggling economy can be stimulated is through an infusion of funds from the federal government. These funds are usually generated by the federal government buying bonds from banks and their customers, which essentially creates new money for the economy. Although some of that money must stay in reserve by law, the rest circulates throughout the economy and actually becomes worth much more than its initial face value. How much exactly those funds are worth depends on the monetary multiplier.
Perhaps the easiest way to calculate the monetary multiplier is to take the legally required reserve ratio and divide it into one. For example, if the government required banks to keep 10 percent of loaned funds in reserve, then the multiplier would be one divided by 0.10, which comes to 10. This means that a loan of $10,000 US Dollars (USD) to banks from the federal government will be multiplied by 10 and would be actually be worth $100,000 USD to the economy.
To understand this process, it's important to understand that a bank that must keep 10 percent in reserve still has 90 percent of those federal funds available to loan out to other customers. When a customer takes a portion of that money from the bank, he may deposit it into another bank. This second bank then has 90 percent of those funds available to loan out to other customers. In other words, the 10 percent that must be reserved is shared between all of the banks.
Another useful function of the monetary multiplier is that it allows banks to calculate how much money may be loaned out to customers. Many banks determine their own reserve ratio that is higher than the minimum stipulated by federal law. Using this ratio, the bank can calculate its own multiplier. This amount is multiplied by the amount of excess reserves that a bank has to come up with the maximum amount that the bank may loan.