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.