Question

Suppose the FED buys \(\$ 100,000\) of government bonds from a commercial bank. What will be the effect of this purchase on the money supply, if the required reserve ratio is \(10 \%\), if banks maintain no excess reserves, and if there is no change in the public's currency holdings?

Short answer

The purchase of \(\$100,000\) worth of government bonds by the FED will have an effect of increasing the money supply by \(\$1,000,000\), assuming banks maintain no excess reserves and the public's currency holdings do not change.

Step-by-step solution

Calculate the change in reserves

Since the FED buys \(\$100,000\) worth of government bonds from the commercial bank, the reserves at the bank will increase by \(\$100,000\).

Find the money multiplier

The money multiplier (M) is given by the formula: \[M = \frac{1}{rr}\] where rr is the required reserve ratio. In this case, rr = \(0.10\). So the money multiplier is: \[M = \frac{1}{0.10} = 10\]

Calculate the change in the money supply

Now that we have the money multiplier and the change in reserves, we can calculate the change in the money supply using the formula: ΔMoney Supply = M × ΔReserves This equals: ΔMoney Supply = 10 × \(100,000 = \)1,000,000

Write the answer

The purchase of \(\$100,000\) worth of government bonds by the FED will have an effect of increasing the money supply by \(\$1,000,000\). This is assuming banks maintain no excess reserves, and the public's currency holdings do not change.

Key concepts

Federal Reserve Operations

The Federal Reserve, often referred to as the Fed, is the central bank of the United States and plays a crucial role in managing the country's monetary policy. One of their main operations is conducting open market operations, which involve the buying and selling of government securities like bonds. When the Fed buys government bonds from commercial banks, as in our example problem, it increases the banks' reserves. This action has a ripple effect on the money supply because it gives banks more funds to lend out to their customers.

In our exercise, the Fed's purchase of \(100,000 in government bonds means that the bank now has an additional \)100,000. This is a strategic move by the Fed to inject more money into the economy. The intention behind such an operation is often to stimulate economic growth by lowering interest rates, which encourages borrowing and investing.

Reserve Requirement Ratio

The reserve requirement ratio is the fraction of deposits which a bank is required to hold in reserve, meaning they cannot lend it out to customers. This ratio is set by the central bank and is a tool used to control the amount of money circulating in the economy.

In our textbook exercise, a reserve requirement ratio of 10% is mentioned. This means for every dollar deposited, the bank must hold 10 cents in reserve and can lend out the remaining 90 cents. The ratio affects how much money a bank can generate through lending, and in turn influences the overall money supply. By setting a higher reserve requirement, the central bank can reduce the amount of money available, and vice versa. It's a balancing act that ensures banks have enough funds to meet withdrawal demands while also not hindering economic growth.

Money Multiplier

The money multiplier concept is an important part of monetary economics. It describes how an initial deposit in a bank can lead to a greater total increase in the overall money supply. This is because the deposited funds are lent out, re-deposited, lent again, and so on.

The formula, as illustrated in the textbook exercise, is simple: \[M = \frac{1}{rr}\] where \(M\) represents the money multiplier and \(rr\) is the reserve ratio. With a 10% reserve requirement, the multiplier is 10. Therefore, an initial increase in reserves of \(100,000 can increase the total money supply by up to \)1,000,000. These steps show the potential for the banking system to expand the money supply through their lending activities.

Banking System

The banking system acts as the backbone of the economy, providing a safe place for people to deposit their money and a source of loans for individuals and businesses. Banks collect deposits and make loans, a process that is intricately tied to the concepts of the reserve requirement and the money multiplier.

At the heart of the banking system is the idea that banks only keep a fraction of deposits as reserves and lend out the majority. This process of lending and re-depositing creates new money in the economy. However, banks need to balance the demand for loans with the necessity to have sufficient reserves on hand to meet withdrawal requests. The central bank supervises this balance by setting regulations like the reserve requirement and influencing it through open market operations. Hence, the interplay between the central bank's policies and commercial banks' operations determines the amount of money in circulation, affecting inflation, interest rates, and economic growth.