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Chapter 29: Problem 6

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

Expert verified
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

01

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.
02

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.
03

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 = \(400 × 10 = \$ 4000\)
04

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.

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Most popular questions from this chapter

The government of Eastlandia uses measures of monetary aggregates similar to those used by the United States, and the central bank of Eastlandia imposes a required reserve ratio of \(10 \% .\) Given the following information, answer the questions below. Bank deposits at the central bank \(=\$ 200\) million Currency held by public \(=\$ 150\) million Currency in bank vaults \(=\$ 100\) million Checkable bank deposits \(=\$ 500\) million Traveler's checks \(=\$ 10\) million a. What is \(\mathrm{M} 1 ?\) b. What is the monetary base? c. Are the commercial banks holding excess reserves? d. Can the commercial banks increase checkable bank deposits? If yes, by how much can checkable bank deposits increase?

In Westlandia, the public holds \(50 \%\) of \(\mathrm{M} 1\) in the form of currency, and the required reserve ratio is \(20 \%\). Estimate how much the money supply will increase in response to a new cash deposit of \(\$ 500\) by completing the accompanying table. (Hint: The first row shows that the bank must hold \(\$ 100\) in minimum reserves \(-20 \%\) of the \(\$ 500\) deposit- against this deposit, leaving \(\$ 400\) in excess reserves that can be loaned out. However, since the public wants to hold \(50 \%\) of the loan in currency, only \(\$ 400 \times 0.5=\$ 200\) of the loan will be deposited in round 2 from the loan granted in round 1.) How does your answer compare to an economy in which the total amount of the loan is deposited in the banking system and the public doesn't hold any of the loan in currency? What does this imply about the relationship between the public's desire for holding currency and the money multiplier?

What will happen to the money supply under the following circumstances in a checkable-deposits-only system? a. The required reserve ratio is \(25 \%,\) and a depositor withdraws \(\$ 700\) from his checkable bank deposit. b. The required reserve ratio is \(5 \%,\) and a depositor withdraws \(\$ 700\) from his checkable bank deposit. c. The required reserve ratio is \(20 \%,\) and a customer deposits \(\$ 750\) to her checkable bank deposit. d. The required reserve ratio is \(10 \%,\) and a customer deposits \(\$ 600\) to her checkable bank deposit.

Although the U.S. Federal Reserve doesn't use changes in reserve requirements to manage the money supply, the central bank of Albernia does. The commercial banks of Albernia have \(\$ 100\) million in reserves and \(\$ 1,000\) million in checkable deposits; the initial required reserve ratio is \(10 \%\). The commercial banks follow a policy of holding no excess reserves. The public holds no currency, only checkable deposits in the banking system. a. How will the money supply change if the required reserve ratio falls to $5 \%$ ? b. How will the money supply change if the required reserve ratio rises to $25 \%$ ?

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 \(\$ 500 ?\)
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