Question

Ryan Cozzens withdraws \(\$ 400\) from his checking account at the local bank and keeps it in his wallet. a. How will the withdrawal change the T-account of the local bank and the money supply? b. If the bank maintains a reserve ratio of \(10 \%\), how will it respond to the withdrawal? Assume that the bank responds to insufficient reserves by reducing the amount of deposits it holds until its level of reserves satisfies its required reserve ratio. The bank reduces its deposits by calling in some of its loans, forcing borrowers to pay back these loans by taking cash from their checking deposits (at the same bank) to make repayment. c. If every time the bank decreases its loans, checkable bank deposits fall by the amount of the loan, by how much will the money supply in the economy contract in response to Ryan's withdrawal of \(\$ 400 ?\) d. If every time the bank decreases its loans, checkable bank deposits fall by the amount of the loan and the bank maintains a reserve ratio of \(20 \%\), by how much will the money supply contract in response to a withdrawal of \(\$ 400 ?\)

Short answer

Answer: Ryan's $400 withdrawal decreases the bank's demand deposits and reserves by $400, with no net change in the money supply. The bank responds to maintain its reserve ratio (10% or 20%) by calling in loans and reducing demand deposits. The money supply contracts by $4000 with a 10% reserve ratio, and by $2000 with a 20% reserve ratio.

Step-by-step solution

a. Withdrawal's changes to the T-account and money supply

When Ryan withdraws \(400 from his account, the local bank's T-account will be affected by a decrease in demand deposits by \)400. This will also reduce the bank's reserves by $400. The money supply will decrease as well since currency held by the public (Ryan's wallet) increases by \(400, but checkable deposits (bank account) decrease by \)400, with the net change being zero.

b. Bank's response to withdrawal with a \(10 \%\) reserve ratio

The bank will aim to maintain its reserve ratio after the withdrawal, which was given as \(10 \%\). Since reserves have decreased by $400, it will need to reduce its demand deposits until it reaches a level where its remaining reserves satisfy the required reserve ratio. To achieve this, the bank will call in some of its loans, resulting in borrowers repaying by withdrawing cash from their checking deposits at the same bank. The bank's reserves will not change because borrowers are paying off loans using the bank's own deposits.

c. Money supply contraction in response to the withdrawal of $400

The money supply will contract as a result of the loan repayments. When borrowers repay their loans, checkable bank deposits decrease by the amount of the loan repaid. The money multiplier (using a reserve ratio of \(10 \%\)) is: Multiplier = \(\frac{1}{Reserve\;Ratio} = \frac{1}{0.1} = 10\) Hence, the money supply, using the money multiplier, will contract by: Contraction = Withdrawal × Multiplier = \(400 × 10 = \$ 4000\)

d. Money supply contraction with a \(20 \%\) reserve ratio

If the bank maintains a reserve ratio of \(20 \%\), the money multiplier will be: Multiplier = \(\frac{1}{Reserve\;Ratio} = \frac{1}{0.2} = 5\) In this case, the money supply will contract by: Contraction = Withdrawal × Multiplier = \(400 × 5 = \$ 2000\) So, with a reserve ratio of \(20 \%\), the money supply will contract by \(2000 in response to Ryan's withdrawal of \)400.

Key concepts

T-Account

A T-account is a simple tool used by banks to keep track of their financial position. It shows the changes in assets and liabilities in a visual way that looks like the letter 'T'. On the left side of the T-account, we list the assets, which are the things a bank owns. For example, loans made to customers can be seen as assets. On the right side, we list liabilities, which are the things a bank owes. A common liability for a bank is the deposits made by its customers. When Ryan withdraws $400, the bank's T-account reflects this by showing a $400 decrease in demand deposits on the liabilities side and a $400 decrease in cash reserves on the assets side. By understanding T-accounts, you can see how monetary activities affect a bank's financial setup.

Reserve Ratio

The reserve ratio is crucial for banks as it represents the portion of depositor's balances that banks must have on hand as cash. It's a safety measure, ensuring banks always have some funds available if customers withdraw money. When the reserve ratio is 10%, this means for every $100 in deposits, the bank must keep $10 in reserves. When Ryan takes out $400, the bank needs to adjust its reserves to remain compliant. If reserves drop due to withdrawals, banks might reduce their overall deposits by a similar amount to restore this ratio. This often involves calling in loans, meaning borrowers might be asked to repay sooner, thus affecting the bank's overall balance.

Demand Deposits

Demand deposits are funds held in bank accounts that can be withdrawn at any time without prior notice. Examples include checking accounts from which people can freely transfer money or withdraw cash using checkbooks or debit cards. When Ryan withdraws $400 from his checking account, this directly decreases the bank's demand deposits. Demand deposits play a central role in determining the money supply in an economy, as they contribute to the available cash flow. Each alteration in demand deposits can influence the broader economic landscape due to such withdrawals and deposits getting recorded in the bank's T-account, impacting reserve requirements and the money supply.

Money Multiplier

The money multiplier illustrates how an initial deposit can lead to a greater increase in the total money supply due to banks' actions with their deposits and reserves. It is calculated using the formula: \[\text{Money Multiplier} = \frac{1}{\text{Reserve Ratio}}\]This concept depends on the reserve ratio. For example, with a reserve ratio of 10%, the multiplier is 10, indicating each dollar deposited allows the bank to lend out \(9, significantly enlarging the money supply through the banking system. Using the multiplier, Ryan's \)400 withdrawal will lead to a contraction in the money supply by \(4000 with a 10% reserve ratio. If the reserve ratio is 20%, the multiplier is 5, leading to a \)2000 contraction. Thus, the reserve ratio crucially determines how an isolated withdrawal affects the economy on a grand scale.