Question

Show the changes to the T-accounts for the Federal Reserve and for commercial banks when the Federal Reserve sells \(\$ 30\) million in U.S. Treasury bills. If the public holds a fixed amount of currency (so that all new loans create an equal amount of checkable bank deposits in the banking system) and the minimum reserve ratio is \(5 \%\), by how much will checkable bank deposits in the commercial banks change? By how much will the money supply change? Show the final changes to the T-account for the commercial banks when the money supply changes by this amount.

Short answer

A: Checkable bank deposits and the money supply will both decrease by \$600 million.

Step-by-step solution

Initial T-account Changes for Federal Reserve and Commercial Banks

Present the initial T-account changes for both the Federal Reserve and the commercial banks after the Federal Reserve sells the Treasury bills: Federal Reserve: - Assets: U.S. Treasury bills decrease by \$30 million - Liabilities: Reserves held by commercial banks decrease by \$30 million Commercial Banks: - Assets: Reserves held at the Federal Reserve decrease by \$30 million - Liabilities: Deposits remain unchanged

Calculate Changes in Checkable Bank Deposits and Money Supply

To calculate the change in checkable bank deposits in commercial banks, we first need to calculate the money multiplier, which can be given as: Money multiplier = \(\frac{1}{reserve\;ratio} = \frac{1}{0.05} = 20\) Now, we can calculate the change in checkable bank deposits by multiplying the decrease in reserves by the money multiplier: Change in checkable bank deposits = 20 x (-\$30 million) = -\$600 million Since the money supply includes checkable bank deposits, the money supply will decrease by the same amount: Change in money supply = -\$600 million

Final Changes to the T-Account for Commercial Banks

Show the final changes in the T-account for the commercial banks after the money supply changes by the calculated amount: Assets: - Reserves held at the Federal Reserve: Decrease by \$30 million - Loans: Increase by \$570 million (because the banks have used the excess reserves to create new loans) Liabilities: - Deposits: Decrease by \$600 million (this represents the new checkable bank deposits after the money multiplier effect) In conclusion, the T-account for commercial banks will show a decrease of \$30 million in reserves held at the Federal Reserve, an increase of \$570 million in loans, and a decrease of \$600 million in deposits after the Federal Reserve sells \$30 million in U.S. Treasury bills, assuming a minimum reserve ratio of \(5 \%\) and the public holding a fixed amount of currency. The money supply will decrease by \$600 million as a result of this action.

Key concepts

Federal Reserve

The Federal Reserve plays a pivotal role in maintaining the stability of the financial system. As the central bank of the United States, it is responsible for managing the nation's monetary policy. It does so by influencing interest rates and controlling the money supply. These actions help to keep inflation at bay and promote stable economic growth.

The Federal Reserve can affect money supply by buying or selling U.S. Treasury bills. When it sells Treasury bills, it reduces the reserves of commercial banks, thereby affecting their ability to create money. This is a key lever used by the Federal Reserve to maintain economic equilibrium.

Commercial Banks

Commercial banks are financial institutions that play a crucial role in the economy by accepting deposits and making loans. They act as intermediaries between depositors who want to save their money and borrowers seeking funds for various purposes.

When banks receive deposits, they can use a portion of these funds to create new loans, which in return increase checkable bank deposits—a substantial component of the money supply. However, their ability to create loans is directly affected by the actions of the Federal Reserve and its requirements, such as the reserve ratio.

• Deposits: Customers' funds kept in various accounts.
• Loans: Money lent out to individuals and businesses.
• Reserves: The portion of deposits kept on hold, usually at the Federal Reserve.

Reserve Ratio

The reserve ratio is a regulatory requirement set by the Federal Reserve that determines the minimum amount of reserves a bank must hold relative to its deposits. This ratio ensures that banks have enough reserves to meet the withdrawal demands of their customers and maintain stability within the banking system.

The reserve ratio is essential in determining the potential for money creation via lending. Given a reserve ratio of 5%, as in this exercise, banks need to hold 5% of their deposits and can lend out the remaining 95%. The money multiplier, which we will explain next, is heavily influenced by this ratio.

Money Multiplier

The money multiplier is a concept that explains how an initial deposit can lead to a greater final increase in the total money supply. It is determined by the reserve ratio and shows the potential of banks to create money through lending.

Calculated as the inverse of the reserve ratio, the money multiplier amplifies the effect of changes in bank reserves on the money supply. For instance, with a reserve ratio of 5%, the money multiplier is \(\frac{1}{0.05} = 20\). This indicates that a change in bank reserves leads to a 20 times larger change in the money supply.

This powerful mechanism allows banks to extend substantial credit with relatively small initial reserves, playing a crucial role in economic dynamics and influencing monetary policy.