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Chapter 29: Problem 16

Show the changes to the T-accounts for the Federal Reserve and for commercial banks when the Federal Reserve buys \(\$ 50\) million in U.S. Treasury bills. If the public holds a fixed amount of currency (so that all loans create an equal amount of deposits in the banking system), the minimum reserve ratio is $10 \%$, and banks hold no excess reserves, by how much will deposits in the commercial banks change? By how much will the money supply change? Show the final changes to the T-account for commercial banks when the money supply changes by this amount.

Short Answer

Expert verified
Answer: The change in deposits in commercial banks is $45 million, and the change in the money supply is also $45 million.

Step by step solution

01

Understand the transaction

When the Federal Reserve buys \(50\) million in U.S. Treasury bills, it will "pay" by increasing the reserve accounts of the commercial banks by \(50\) million. The commercial banks, in turn, will give up their \(50\) million in U.S. Treasury bills to the Federal Reserve.
02

Calculate the total change in deposits

Since the banks are holding no excess reserves, and the minimum reserve ratio is \(10 \%\), the banking system must hold \(50\) million × \(0.10 = \$ 5\) million in reserves. The remaining \(50\) million - \(5\) million = \(45\) million can be loaned out. As we are given that the public holds a fixed amount of currency, the banks will loan out the entire \(45\) million, which will create an equal amount of deposits in the banking system. So, the total change in deposits in commercial banks is \(45\) million.
03

Calculate the change in the money supply

The money supply consists of both currency and deposits. In this case, as mentioned earlier, the public holds a fixed amount of currency. So, the change in the money supply will be equal to the change in deposits in the commercial banks, which is \(45\) million.
04

Show the final changes to the T-account for commercial banks

Initially, the T-account for commercial banks looks like this: Assets: Reserves: \(0\) U.S. Treasury bills: \(50\) million Liabilities: Deposits: \(0\) After the transaction: Assets: Reserves: \(50\) million U.S. Treasury bills: \(0\) Liabilities: Deposits: \(45\) million (total change in deposits) Loans: \(45\) million The final T-account for the commercial banks, after the money supply changes by \(45\) million, will be: Assets: Reserves: \(5\) million (required reserves) Loans: \(45\) million Liabilities: Deposits: \(45\) million

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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?

For each of the following transactions, what is the initial effect (increase or decrease) on M1? On M2? a. You sell a few shares of stock and put the proceeds into your savings account. b. You sell a few shares of stock and put the proceeds into your checking account. c. You transfer money from your savings account to your checking account. d. You discover \(\$ 0.25\) under the floor mat in your car and deposit it in your checking account. e. You discover \(\$ 0.25\) under the floor mat in your car and deposit it in your savings account.

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 $\$ 400 ?$

The Congressional Research Service estimates that at least \(\$ 45\) million of counterfeit U.S. \(\$ 100\) notes produced by the North Korean government are in circulation. a. Why do U.S. taxpayers lose because of North Korea's counterfeiting? b. As of December 2014 , the interest rate earned on one-year U.S. Treasury bills was \(0.13 \%\). At a \(0.13 \%\) rate of interest, what is the amount of money U.S. taxpayers are losing per year because of these \(\$ 45\) million in counterfeit notes?
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