Question

In a simplified banking system in which all banks are subject to a 25 percent required reserve ratio, a \(\$ 1,000\) open market sale by the Fed would cause the money supply to a. increase by \(\$ 1,000\). b. decrease by \(\$ 1,000\). c. decrease by \(\$ 4,000\). d. increase by \(\$ 4,000\).

Short answer

The money supply would decrease by \(\$4,000\).

Step-by-step solution

Understand the Money Multiplier Formula

The money multiplier formula is used to determine the maximum amount of new money that can be created in a fractional reserve banking system. The formula is: Money Multiplier = \(\frac{1}{Required Reserve Ratio}\)

Calculate the Money Multiplier

We are given a 25 percent required reserve ratio, which means banks must hold 25% of all deposits as reserves. Calculate the money multiplier using the formula from Step 1: Money Multiplier = \(\frac{1}{0.25}\) = \(4\)

Understand Open Market Operations

Open market operations are the purchase and sale of government securities by a central bank to control the money supply and interest rates. In this case, the Federal Reserve ("the Fed") sold \(\$1,000\) in securities. When the Fed conducts an open market sale, it sells government securities which reduces banks' excess reserves, ultimately decreasing the money supply.

Calculate the Change in the Money Supply

Since the money multiplier is 4 (from Step 2) and the open market sale is for \(\$1,000\), we can calculate the change in the money supply as follows: Change in Money Supply = (Money Multiplier) × (Open Market Sale) Change in Money Supply = \(4 × (-\$1,000)\) = \(-\$4,000\) Note that the value is negative, which indicates a decrease in the money supply.

Select the Appropriate Option

From the calculated change in the money supply, we can now select the correct option: The money supply would: c. decrease by \(\$4,000\)

Key concepts

Money Multiplier

The money multiplier is a key concept in understanding how banks can create money in a fractional reserve system. It's a measure of the maximum amount of money that banks can theoretically create with each dollar of reserves.

The formula is simple:

• Money Multiplier = \( \frac{1}{\text{Required Reserve Ratio}} \)

In our example, with a required reserve ratio of 25% (or 0.25), the money multiplier becomes \( \frac{1}{0.25} = 4 \). This means that for every dollar held in reserve, banks can create four dollars through lending.

The multiplier effect thrives on the cycle of deposits and loans. When a bank receives a deposit, it keeps a fraction as reserves and loans out the rest. This loan becomes a new deposit in another bank, and the cycle continues, creating more money each time.

Understanding this concept helps us see how changes in banking regulations or practices, like altering the reserve ratio, can significantly impact the overall money supply.

Open Market Operations

Open market operations (OMO) are a powerful tool used by central banks, like the Federal Reserve, to influence the money supply and interest rates. These involve the buying and selling of government securities.

• Open Market Sale: When the Fed sells securities, it takes money out of the banking system, reducing the overall money supply. Banks have fewer reserves to lend, which can lead to higher interest rates.
• Open Market Purchase: Conversely, buying securities adds money to the system, increasing the supply and often lowering interest rates.

In our scenario, the Fed conducted an open market sale of \(1,000 worth of securities. This action decreases the reserves available to banks, and using our calculated money multiplier of 4, the overall money supply decreases by \( 4 \times -\\)1,000 = -\$4,000 \).

Open market operations are a flexible and frequently used method to fine-tune the economy's financial conditions, impacting everything from inflation to economic growth.

Required Reserve Ratio

The required reserve ratio is the fraction of deposits that a bank must hold in reserve and not lend out. This ratio is critical as it controls how much money banks can create through loans.

In our example, the required reserve ratio is 25%, meaning banks must keep 25% of deposits as reserves. The rest can be loaned out and turned into new deposits, contributing to the money multiplier effect.

• Lower Reserve Ratio: A lower ratio allows banks to lend more, increasing the money supply and potentially stimulating economic activity.
• Higher Reserve Ratio: A higher ratio restricts lending, which can decrease the money supply and be used to control inflation.

Understanding the required reserve ratio helps you see how central banks manage economic stability. It plays a crucial part in ensuring liquidity while simultaneously trying to control the levels of inflation and boom in the economy.