Suppose the \(\mathrm{FED}\) adds \(\$ 500,000\) to the reserves of the banking system. If the required reserve ratio is \(30 \%\), if banks maintain no excess reserves and if the public increases its holdings of currency by \(\$ 200,000\), what is the effect on the money supply?

Understanding the money multiplier is crucial for grasping how the banking system can influence the economy. It refers to the amount of money that banks can create with each unit of reserves. The formula used to calculate the money multiplier is: ewline ewline The money multiplier has an inverse relationship with the reserve ratio. This means that a lower reserve ratio leads to a higher money multiplier, allowing banks to lend out more money. In the exercise, a \(500,000 increase in bank reserves resulted in a potential increase in the money supply of \)1,666,500, using a money multiplier of 3.333, derived from the reserve ratio of 30%. However, this calculation assumes an ideal scenario with no currency drain and no excess reserves.

The reserve ratio is the fraction of deposits that banks are legally required to keep on hand as reserves. It can also be seen as a safety net to ensure banks have enough funds to meet the withdrawal demands of their customers. When the Federal Reserve (or FED) sets the reserve ratio, it is essentially controlling the lending capacity of banks.

The ratio is expressed as a percentage of the bank's total deposits. In our example, the reserve ratio is set at 30%, which means for every dollar deposited, banks must hold 30 cents in reserve and can lend out the remaining 70 cents. The reserve ratio not only influences the money multiplier but also affects the overall liquidity in the banking system.

The banking system plays a pivotal role in the money supply of an economy. It comprises a network of financial institutions that accept deposits, provide loans, and offer various other financial services. When the FED adds reserves to the banking system, it provides these institutions with more funds to lend.

Without excess reserves and assuming no other leakages, the banking system would multiply each dollar of reserves through lending, creating a cascading effect on money creation, as depicted in the exercise. However, in reality, banks might choose to hold excess reserves, or individuals may withdraw funds as cash, both of which limit the theoretical expansion of the money supply.

Currency holdings refer to the physical money that the public chooses to hold outside the banking system. This includes the banknotes and coins that individuals carry in their wallets or store at home. An increase in currency holdings means that more money is taken out of the banking system and is not available for lending.

This reduces the potential impact of the money multiplier. As shown in the exercise, when the public increases its currency holdings by $200,000, it effectively withholds this amount from the banking process, thus decreasing the total impact on the money supply. This 'leakage' is an important real-world consideration that impacts the theoretical expansion of the money supply.