Question

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

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

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.

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.

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.

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