Question

Tracy Williams deposits \(\$ 500\) that was in her sock drawer into a checking account at the local bank. a. How does the deposit initially change the T-account of the local bank? How does it change the money supply? b. If the bank maintains a reserve ratio of \(10 \%\), how will it respond to the new deposit? c. If every time the bank makes a loan, the loan results in a new checkable bank deposit in a different bank equal to the amount of the loan, by how much could the total money supply in the economy expand in response to Tracy's initial cash deposit of \(\$ 500 ?\) d. If every time the bank makes a loan, the loan results in a new checkable bank deposit in a different bank equal to the amount of the loan and the bank maintains a reserve ratio of \(5 \%,\) by how much could the money supply expand in response to Tracy's initial cash deposit of \(\$ 500 ?\)

Short answer

Answer: A decrease in the reserve ratio, such as from 10% to 5%, leads to a greater total possible money supply expansion in the banking system. As the reserve ratio decreases, the money multiplier increases, resulting in more potential money being created through the process of lending and redepositing.

Step-by-step solution

Analyze the initial deposit's impact on the T-account and money supply

Tracy deposits $500 into her checking account. This increases the bank's assets (cash) and liabilities (customer deposits). The money supply M1 (which includes cash and checkable deposits) doesn't change, as cash is converted into checkable deposits.

Determine the bank's response to the new deposit based on the reserve ratio

The bank has a reserve ratio of \(10\%\), which means it must hold \(10\%\) of its deposits as reserves. With the new deposit of \(500, the bank will keep \)50 (10\% \times 500)\( as reserves and can potentially lend out the remaining \)\$450$.

Calculate the total possible money supply expansion using the money multiplier

The money multiplier for a reserve ratio of \(10\%\) is \(\frac{1}{0.10}=10\). Tracy's \(\$500\) deposit can potentially create \(500\times 10 = \$ 5,000\) of additional money in the economy through the process of lending and redepositing in different banks.

Calculate the total possible money supply expansion with a reserve ratio of \(5\%\)

The money multiplier for a reserve ratio of \(5\%\) is \(\frac{1}{0.05}=20\). Tracy's \(\$500\) deposit can potentially create \(500\times 20 = \$ 10,000\) of additional money in the economy with a \(5\%\) reserve requirement. This demonstrates how a lower reserve ratio leads to greater potential money supply expansion.

Key concepts

Reserve Ratio

The reserve ratio is a crucial concept in understanding how banks operate. It represents the portion of depositors' balances that banks must have on hand as reserves. In other words, it is the fraction of deposits that banks are required to keep and not lend out. This is determined by regulatory authorities to ensure that banks have enough funds to meet withdrawal demands.

• When the reserve ratio is high, banks can lend out less money, meaning there is a slower expansion of the money supply.
• Conversely, a lower reserve ratio allows banks to lend out more money, increasing the potential for money supply expansion.

For example, if the reserve ratio is set at 10%, it means that for every $100 deposited, the bank must keep $10 in reserve and can lend out $90. In the context of Tracy Williams's deposit, a reserve ratio of 10% allows the bank to keep $50 of her $500 deposit as reserves and use the remaining $450 for loans.

Money Multiplier

The money multiplier is a key concept that illustrates how money can expand in the banking system. It's a way to understand the potential impact of a single deposit through the lending activities of banks. The money multiplier is inversely related to the reserve ratio. The formula for calculating the money multiplier is \( \frac{1}{\text{Reserve Ratio}} \).

• This multiplier effect shows how an initial deposit can lead to a greater increase in the total money supply in the economy.
• The larger the reserve ratio, the smaller the multiplier effect, and vice versa.

In Tracy's case, with a reserve ratio of 10%, the money multiplier is 10 (\( \frac{1}{0.10} \)). This means that her \(500 deposit could potentially increase the total money supply by \)5,000. With a lower reserve ratio of 5%, the multiplier becomes 20 (\( \frac{1}{0.05} \)), indicating a possible $10,000 expansion. This highlights how regulatory requirements influence the liquidity and money supply in the economy.

Checkable Bank Deposits

Checkable bank deposits are a fundamental component of the money supply and play a critical role in the functioning of modern economies. These accounts allow holders to deposit or withdraw funds easily and are accessible via checks or electronic transfers.

• When individuals deposit cash into a checking account, it transitions from physical currency to part of the banking system's deposit liabilities.
• This transformation doesn't initially change the total money supply, as the cash moves from the public to the banks.

For Tracy, her deposit of $500 into a checkable deposit account does not immediately alter the money supply, because the cash simply becomes a checkable deposit. However, the deposit serves as a basis for banks to extend loans, which can then be redeposited in other banks, creating additional checkable deposits. Through such a process, the money supply in the economy can increase significantly, illustrating the importance of deposit accounts in financial systems.