What is the formula for the money multiplier?

The reserve requirement ratio is the minimum fraction of deposits that banks are required to hold as reserves and not loan out. Banks are obliged to hold a certain percentage of the deposits they receive as cash reserves, either in their vaults or as deposits with a central bank, like the Federal Reserve. This ratio is set by the central bank and varies from country to country. Let us denote the reserve requirement ratio as \(R\).

The money multiplier is the measure of the potential increase in money supply due to banks' lending activities. When banks receive deposits, they keep a part of it as reserves (as per the reserve requirement ratio) and loan out the rest. When the loan amount is spent, it becomes someone else's deposit. This cycle of depositing, reserving, and lending continues, creating a multiplier effect on the initial deposit. The money multiplier helps to understand the overall increase in the money supply from an initial deposit.

To calculate the money multiplier, we need to determine the amount of money that is created in every round of the deposit and lending process. The potential money supply H created from an initial deposit A, with a reserve requirement ratio R, can be expressed as the sum of the geometric series: \[H = A\times (1 + (1-R) + (1-R)^2 + (1-R)^3 + \cdots)\] By applying the formula for the sum of an infinite geometric series, where a common ratio is between -1 and 1, we can simplify the above expression: \[Money- Multiplier = \frac{1}{R}\] The formula for the money multiplier is the reciprocal of the reserve requirement ratio. To summarize, the money multiplier concept explains the potential increase in the money supply due to banks' lending activities, and the formula for the money multiplier is the reciprocal of the reserve requirement ratio, which can be calculated as \(\frac{1}{R}\), where R is the reserve requirement ratio.