Let's analyze the given scenario step-by-step:
1. Identifying the Initial and New Legal Reserve Ratios:
- Initial Legal Reserve Ratio: 25% or 0.25
- New Legal Reserve Ratio: 10% or 0.10
2. Checkable Deposits and Actual Reserves:
- Checkable Deposits: [tex]$40,000
- Actual Reserves: $[/tex]10,000
3. Calculating Initial Required Reserves:
[tex]\[
\text{Required Reserves Initial} = \text{Legal Reserve Ratio Initial} \times \text{Checkable Deposits}
\][/tex]
[tex]\[
\text{Required Reserves Initial} = 0.25 \times 40,000 = 10,000
\][/tex]
4. Calculating Initial Excess Reserves:
[tex]\[
\text{Excess Reserves Initial} = \text{Actual Reserves} - \text{Required Reserves Initial}
\][/tex]
[tex]\[
\text{Excess Reserves Initial} = 10,000 - 10,000 = 0
\][/tex]
5. Calculating New Required Reserves After Reduction:
[tex]\[
\text{Required Reserves New} = \text{Legal Reserve Ratio New} \times \text{Checkable Deposits}
\][/tex]
[tex]\[
\text{Required Reserves New} = 0.10 \times 40,000 = 4,000
\][/tex]
6. Calculating New Excess Reserves After Reduction:
[tex]\[
\text{Excess Reserves New} = \text{Actual Reserves} - \text{Required Reserves New}
\][/tex]
[tex]\[
\text{Excess Reserves New} = 10,000 - 4,000 = 6,000
\][/tex]
7. Calculating the Change in Excess Reserves:
[tex]\[
\text{Change in Excess Reserves} = \text{Excess Reserves New} - \text{Excess Reserves Initial}
\][/tex]
[tex]\[
\text{Change in Excess Reserves} = 6,000 - 0 = 6,000
\][/tex]
8. Calculating the Monetary Multiplier Before and After the Change:
[tex]\[
\text{Monetary Multiplier Initial} = \frac{1}{\text{Legal Reserve Ratio Initial}}
\][/tex]
[tex]\[
\text{Monetary Multiplier Initial} = \frac{1}{0.25} = 4
\][/tex]
[tex]\[
\text{Monetary Multiplier New} = \frac{1}{\text{Legal Reserve Ratio New}}
\][/tex]
[tex]\[
\text{Monetary Multiplier New} = \frac{1}{0.10} = 10
\][/tex]
Based on these calculations, the excess reserves will rise by \[tex]$6,000, and the monetary multiplier will increase from 4 to 10. Thus, the correct answer is:
Excess reserves of this single bank will rise by \$[/tex]6,000, and the monetary multiplier will increase from 4 to 10.
