Explain how to use the reserve requirement to expand the money supply.

Reserve requirement is the percentage of deposits that banks are required to hold as reserves at the central bank or as vault cash. This policy is set by the central bank in an economy, and it ensures that banks have enough funds to meet depositors' withdrawal requests and to maintain financial stability.

Money supply is the total amount of money available in an economy, consisting of currency in circulation and deposits. Banks play a crucial role in money supply creation as they accept deposits and make loans. When a bank receives deposits, it will hold a portion of them as reserves (based on the reserve requirement) and lend the remaining amount to borrowers. These loans then become new deposits in other banks, which again hold a portion as reserves and lend the remaining amount. This process is called the "fractional reserve banking system" and contributes to the expansion of the money supply.

The money multiplier is a measure of the potential maximum amount of money that can be created by banks in a fractional reserve banking system. It is calculated as \(\frac{1}{reserve\; requirement}\). The money multiplier shows how much money can be created through loans given a certain reserve requirement.

When the central bank changes the reserve requirement, it affects the money multiplier and subsequently influences new money creation. If the reserve requirement is decreased, the money multiplier increases, allowing banks to create more money through loans. This expansion of money supply stimulates the economy through increased liquidity. Conversely, if the reserve requirement is increased, the money multiplier decreases, limiting the amount of new money banks can create, thereby contracting the money supply.

Imagine the central bank in an economy sets a reserve requirement of 10%. This means that banks are required to hold 10% of their deposits as reserves and can lend the remaining 90%. The money multiplier in this case would be \(\frac{1}{0.10} = 10\). Suppose there is an initial deposit of \(1,000 at Bank A. Bank A would hold \)100 (10% of \(1,000) as a reserve and lend the remaining \)900 to a borrower. The borrower would then deposit the \(900 in Bank B, which in turn would keep \)90 (10% of \(900) as a reserve and lend out the remaining \)810. This process continues, creating new money and expanding the money supply. Let's now assume the central bank decides to decrease the reserve requirement to 5%. The new money multiplier would be \(\frac{1}{0.05} = 20\). In this case, Bank A would keep \(50 (5% of \)1,000) as reserve and lend out $950. As a result, more money would be created through the lending process, reflecting an expansion in the money supply.