To determine how a change in the required reserve ratio affects the lending capacity of the banking system, follow these steps:
1. Identify the initial parameters:
- Cash held by public: [tex]\( \$120 \)[/tex] billion
- Transactions account balances: [tex]\( \$800 \)[/tex] billion
- Required reserves: [tex]\( \$80 \)[/tex] billion
- Excess reserves: [tex]\( \$0 \)[/tex] billion
- U.S. Treasury bonds held by the public: [tex]\( \$600 \)[/tex] billion
2. Calculate the initial reserve ratio:
This ratio is derived from the required reserves divided by the transactions account balances.
[tex]\[
\text{Initial reserve ratio} = \frac{\$80 \, \text{billion}}{\$800 \, \text{billion}} = 0.1 \, (\text{or 10%})
\][/tex]
3. Determine the new required reserves with the changed reserve ratio:
The new required reserve ratio is given as [tex]\( 5\% \)[/tex].
[tex]\[
\text{New required reserves} = 0.05 \times \$800 \, \text{billion} = \$40 \, \text{billion}
\][/tex]
4. Calculate the change in required reserves:
[tex]\[
\text{Change in required reserves} = \$80 \, \text{billion} - \$40 \, \text{billion} = \$40 \, \text{billion}
\][/tex]
5. Determine the money multiplier:
The money multiplier is the inverse of the new required reserve ratio.
[tex]\[
\text{Money multiplier} = \frac{1}{0.05} = 20
\][/tex]
6. Calculate the change in the lending capacity:
The change in the lending capacity is the change in required reserves multiplied by the money multiplier.
[tex]\[
\text{Change in lending capacity} = \$40 \, \text{billion} \times 20 = \$800 \, \text{billion}
\][/tex]
Thus, with the new required reserve ratio set to 5%, the lending capacity of the banking system will eventually rise by [tex]$800 billion.
So, the correct choice is:
- rise by $[/tex]\[tex]$800$[/tex] billion.
