Chapter 13: Problem 480

Suppose the FED buys $\$ 125,000,000$ of government bonds from commercial banks. If currency held by the public remains unchanged, but banks decide to increase their excess reserves by $\$ 50,000,000$, and the required reserve ratio is $20 \%$, what happens to the total money supply?

Short Answer

Expert verified

The total money supply increases by $\$375,000,000$ after the FED buys $\$125,000,000$ of government bonds from commercial banks and the banks decide to increase their excess reserves by $\$50,000,000$ with a required reserve ratio of $20\%$.

Step by step solution

Calculate the Money Multiplier

The first step is to calculate the money multiplier. The formula for the money multiplier (MM) is: $MM = \frac{1}{RRR}$ where RRR is the required reserve ratio. In our case, the required reserve ratio (RRR) is $20\% = 0.2$. So, the money multiplier (MM) will be: $MM = \frac{1}{0.2}$ Now, let's calculate the value of the money multiplier.

Calculate the Value of the Money Multiplier

With RRR as $0.2$, the money multiplier (MM) will be: $MM = \frac{1}{0.2} = 5$ The value of the money multiplier is 5.

Find the Change in Bank Deposits

Now, we'll find the change in bank deposits. The net change in bank deposits will be the FED's purchase of government bonds minus the increase in excess reserves: Change in deposits = FED purchase of government bonds - Increase in excess reserves Using the given values: Change in deposits = $\$125,000,000 - \$50,000,000$ Let's calculate the change in deposits.

Calculate the Change in Bank Deposits

By substituting the given values, we would get the change in bank deposits as: Change in deposits = $\$125,000,000 - \$50,000,000 = \$75,000,000$ The change in bank deposits is $\$75,000,000$.

Calculate the Change in Total Money Supply

Now, we'll calculate the change in total money supply by multiplying the change in bank deposits by the money multiplier: Change in total money supply = Change in bank deposits × Money multiplier Using the calculated values: Change in total money supply = $\$75,000,000 × 5$ Let's calculate the change in total money supply.

Find the Change in Total Money Supply

By substituting the calculated values, we'd get the change in total money supply as: Change in total money supply = $\$75,000,000 × 5 = \$375,000,000$ So, the total money supply increases by $\$375,000,000$.

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Suppose the FED buys \(\$ 125,000,000\) of government bonds from commercial banks. If currency held by the public remains unchanged, but banks decide to increase their excess reserves by \(\$ 50,000,000\), and the required reserve ratio is \(20 \%\), what happens to the total money supply?