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

Key concepts

T-accounts

T-accounts are a simplified version of accounting statements used to understand the transactions of businesses, such as banks. They visually represent the assets and liabilities of an entity. In banking, the left side of a T-account shows the bank's assets, while the right side shows its liabilities. For example, if a commercial bank holds government securities, these are assets. Similarly, customer deposits in banks are liabilities because they are amounts owed to customers.

A change in the Federal Reserve's actions, such as buying Treasury bills, will impact these T-accounts. When the Fed buys Treasury bills, the reserves—a bank's asset—increase by the purchase amount. This is recorded in the T-account accordingly, showing an equal increase in both the asset and liability sides. The Federal Reserve, by increasing the reserves, enables banks to either hold them or extend new loans.

commercial banks

Commercial banks are financial institutions that provide banking services to individuals and businesses. They play a crucial role in the financial ecosystem by offering services like accepting deposits, providing loans, and facilitating monetary transactions.

When the Federal Reserve engages in activities like purchasing Treasury bills, it directly impacts the commercial banks by increasing their reserves. For instance, when the Fed buys $50 million of Treasury bills, the reserves of commercial banks increase by the same amount. These increased reserves allow banks to lend more money, up to the limits specified by the reserve ratio.

Commercial banks benefit from this activity as they can create additional loans, leading to more deposits within the banking system. Therefore, actions by the Federal Reserve can significantly impact commercial banks' balance sheets and their ability to provide more credit to the economy.

reserve ratio

The reserve ratio is a regulation that sets the minimum amount of reserves a bank must hold against its deposits. This ratio is crucial in ensuring financial stability and controlling the money supply. It is typically set by the central bank, such as the Federal Reserve, and can play a role in monetary policy.

For example, if a bank receives $50 million in new deposits, and the reserve ratio is 10%, the bank must hold at least $5 million in reserve. The remaining $45 million ($50 million - $5 million) is available for new loans. These loans are crucial because they can create new deposits, effectively expanding the money supply.

In the scenario provided, with a reserve ratio of 10%, commercial banks hold exactly the required amount without keeping excess reserves. This means they maximize the money available for lending, contributing to economic expansion. The reserve ratio, therefore, is an essential policy tool used by central banks to influence the economy's credit and liquidity conditions.