Suppose a bank acquires an additional \(\$ 1\) of deposits and no required reserve ratio exists. By how much could this one dollar deposit theoretically expand the money supply?

The money multiplier is a measure of the amount of money that banks can generate for each dollar of reserves (the amount of money banks hold in their accounts). In a fractional reserve banking system, banks are required to keep a certain percentage of their deposits as reserves and lend out the rest. When a bank receives a deposit, they can lend out all or a part of it. The portion they are allowed to lend out is determined by the reserve ratio. If there is no reserve ratio, we need to assume that banks can lend out the entire amount of the deposit.

The money multiplier (M) can be determined through the following formula: \[M = \frac{1}{RR}\] Where: - M is the money multiplier - RR is the reserve ratio

As there is no required reserve ratio, we can assume that banks can lend out the entire amount of the deposit. Thus, RR = 0. Using this value, we calculate the money multiplier: \[M = \frac{1}{0}\] However, dividing by zero is undefined in mathematics. Theoretically, if banks can lend out the entire amount of the deposit and there is no reserve requirement, the money multiplier would become infinitely large. This means that the $1 deposit could, in theory, expand the money supply by an infinite amount. In reality, banks would not lend out the entire amount of the deposit due to various factors such as risk management, liquidity needs, and regulatory restrictions. Therefore, the true money multiplier would not be infinite, but the theoretical expansion of the money supply would be much larger than with a required reserve ratio in place.