Question

In a simplified banking system in which all banks are subject to a 20 percent required reserve ratio, a \(\$ 1,000\) open market purchase by the Fed would cause the money supply to a. increase by \(\$ 100\). b. decrease by \(\$ 200\). c. decrease by \(\$ 5,000\). d. increase by \(\$ 5,000\).

Short answer

The money supply would increase by \$5,000. This is calculated using the money multiplier formula, \(Money\,multiplier=\frac{1}{RRR}\), where RRR is the required reserve ratio. With an RRR of 20 percent or 0.20, the money multiplier is 5. When the Fed makes an open-market purchase of \$1,000, this can potentially increase the money supply by \( \$1,000 \times 5 = \$5,000\). So, the correct answer is 'd. increase by \$5,000'.

Step-by-step solution

Calculate the Money Multiplier

First, we need to find out the money multiplier. The required reserve ratio is 20 percent, or 0.20. Using the formula \(Money\,multiplier=\frac{1}{RRR}\), we can calculate the money multiplier: \(Money\,multiplier = \frac{1}{0.20} = 5\)

Calculate the Change in Money Supply

Next, we need to calculate the potential change in the money supply resulting from the \$1,000 open-market purchase by the Fed. To do this, we'll multiply the open-market purchase by the money multiplier: Change in money supply = Open-market purchase × Money multiplier Change in money supply = \$1,000 × 5 Change in money supply = \$5,000

Select the Correct Answer

Now, we can choose the correct answer from the options given: a. increase by \$100 b. decrease by \$200 c. decrease by \$5,000 d. increase by \$5,000 The change in the money supply due to the \$1,000 open-market purchase is an increase of \$5,000. Therefore, the correct answer is: d. increase by \$5,000.

Key concepts

Money Multiplier

The concept of the money multiplier is central to understanding how the banking system can affect the money supply within an economy. Essentially, the money multiplier quantifies the maximum amount of money that banks can generate with each dollar of reserves. It is calculated using the reserve ratio, which is the portion of depositors' balances that banks must have on hand as cash.

The formula for the money multiplier is \( Money\,multiplier = \frac{1}{RRR} \) with RRR standing for the required reserve ratio. In our example, with an RRR of 0.20 or 20%, the money multiplier is \( \frac{1}{0.20} = 5 \) This means that for every dollar the central bank injects into the economy, the money supply can increase up to five times after accounting for the entire banking system’s lending process.

Understanding this concept is crucial because it illustrates the power of fractional-reserve banking and how banks do not simply store money, but actively expand the money supply through lending.

Open-Market Operations

Open-market operations (OMOs) are the activities carried out by central banks to influence the money supply. These operations involve the purchase or sale of government securities, such as bonds, on the open market. When a central bank like the Federal Reserve buys securities, it pays out cash, which increases the reserves of the banking sector. The opposite occurs when it sells securities, therefore decreasing the reserves.

In the given exercise, a \(\$1,000\) open market purchase is conducted by the Fed. This means the Fed is injecting \(\$1,000\) into the banking system. As banks receive these funds, they can lend out a portion and must keep a fraction as reserves depending on the required reserve ratio. This process of lending and redepositing funds creates a multiplier effect on the money supply, demonstrating the impact of OMOs in monetary policy. They are a primary tool for implementing monetary policy and managing economic fluctuations.

Change in Money Supply

The change in money supply refers to the variation in the total amount of monetary assets available in an economy. It's influenced by the central bank's monetary policy actions, such as the open-market operations discussed previously. An increase in money supply can stimulate economic activity by lowering interest rates and making credit more accessible, while a decrease can have the opposite effect, cooling down an overheating economy.

Using our scenario, the \(\$1,000\) open market purchase by the Fed would result in an increase in the money supply. By applying the calculated money multiplier of 5, we find that the potential increase in the money supply would be \(\$5,000\). It's important to note that this is a simplistic view, and in reality, the change could be less due to factors like banks holding excess reserves or individuals holding onto cash. Nonetheless, the basic principle holds true, and central banks can use this tool to target economic stability and growth.