If the simple money multiplier is 10, what is the reserve ratio?

If the simple money multiplier is 10, this means that each dollar of reserves held by the bank can support $10 of money in the economy. The simple money multiplier is the inverse of the reserve ratio. The reserve ratio (often denoted as R) is the fraction of deposits that a bank is legally required to keep on hand, either in its vaults or on deposit at the central bank.

To calculate the reserve ratio (R) when you know the simple money multiplier (m), you use the formula:

R = 1 / m

Given that the simple money multiplier (m) is 10, you can calculate the reserve ratio as follows:

R = 1 / 10 R = 0.10

Thus, the reserve ratio is 0.10, or 10%. This means that for every dollar of deposits, the bank must hold 10 cents in reserve.

Extra: The concept of the money multiplier is central to the field of fractional-reserve banking, which is the practice where banks accept deposits and make loans or investments, but are required to keep a fraction of their deposit liabilities in reserve as cash. This reserve requirement is set by the central bank and influences how much money a bank can create through lending.

Here’s how it works in simple terms: when someone deposits money in a bank, the bank isn’t required to keep all of that money on hand. Instead, it keeps a fraction of the deposit in reserve and can loan out the rest. When a bank gives out a loan, the money is redeposited into the banking system, becoming available to be loaned out again with the same reserve ratio, creating a cycle of money creation.

The money multiplier is an idealized number showing the maximum potential amount of money that can be created in the banking system for every dollar of reserves. It’s based on the assumption that banks lend out all of their excess reserves, that the borrowers spend all of the money they borrow, and that the people who receive that money in turn deposit it back into the banking system. In the real world, not all excess reserves are lent out, and not all money spends circulate back into the banking system as quickly or effectively as the theory assumes, so the actual multiplier tends to be smaller than the simple theoretical multiplier.