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### Step-by-step Solution
#### Part (a): Maximum Amount of New Loans
1. Calculation of Required Reserves:
- The required reserves = Checkable deposits Reserve ratio
- Required reserves = \[tex]$100,000 0.10 = \$[/tex]10,000
2. Calculation of Excess Reserves:
- Excess reserves = Total Reserves - Required Reserves
- Excess reserves = \[tex]$22,000 - \$[/tex]10,000 = \[tex]$12,000 3. Maximum Amount of New Loans: - The maximum amount of new loans the bank can make is equal to the excess reserves. - Maximum new loans = Excess reserves = \$[/tex]12,000
So, the maximum amount of new loans that Big Bucks Bank can make is \[tex]$12,000. #### Part (b): Change in the Money Supply - By making the new loans, the money supply increases by the same amount. - The change in the money supply = Maximum new loans = \$[/tex]12,000
So, the money supply has increased by \[tex]$12,000. #### Part (c): Bank's Balance Sheet After Clearing Checks 1. Post-Loan Balance Sheet (Column 1): - Reserves = Initial Reserves - Maximum new loans = \$[/tex]22,000 - \[tex]$12,000 = \$[/tex]10,000
- Loans = Initial Loans + Maximum new loans = \[tex]$40,000 + \$[/tex]12,000 = \[tex]$52,000 The post-loan balance sheet would be: \[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Assets & & & (1) & Liabilities and net worth & & (1) \\ \hline Reserves & $[/tex]\[tex]$ & $10,000$ & & Checkable deposits & \$ 100,000 \\ \hline Securities & & $38,000$ & & \\ \hline Loans & & $52,000$ & & \\ \hline \end{tabular} \] 2. After Checks Cleared (Column 2): - After lending the money, checks drawn for the entire loan amount may be cleared against the bank, decreasing reserves by this amount. - Reserves remain \$10,000 (as no further changes occur after the checks are cleared). - Loans remain \$52,000. The balance sheet after checks have cleared would be: \[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Assets & & & (2) & Liabilities and net worth & & (2) \\ \hline Reserves & $\$[/tex] & [tex]$10,000$[/tex] & & Checkable deposits & \[tex]$ 100,000 \\ \hline Securities & & $[/tex]38,000[tex]$ & & \\ \hline Loans & & $[/tex]52,000[tex]$ & & \\ \hline \end{tabular} \] ### Summary a. Maximum amount of new loans: \$[/tex]12,000
b. Change in the money supply: \[tex]$12,000 c. Bank's balance sheet after checks cleared: \[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Assets & & & (2) & Liabilities and net worth & & (2) \\ \hline Reserves & $[/tex]\[tex]$[/tex] & [tex]$10,000$[/tex] & & Checkable deposits & \[tex]$ 100,000 \\ \hline Securities & & $[/tex]38,000[tex]$ & & \\ \hline Loans & & $[/tex]52,000$ & & \\
\hline
\end{tabular}
\]
### Step-by-step Solution
#### Part (a): Maximum Amount of New Loans
1. Calculation of Required Reserves:
- The required reserves = Checkable deposits Reserve ratio
- Required reserves = \[tex]$100,000 0.10 = \$[/tex]10,000
2. Calculation of Excess Reserves:
- Excess reserves = Total Reserves - Required Reserves
- Excess reserves = \[tex]$22,000 - \$[/tex]10,000 = \[tex]$12,000 3. Maximum Amount of New Loans: - The maximum amount of new loans the bank can make is equal to the excess reserves. - Maximum new loans = Excess reserves = \$[/tex]12,000
So, the maximum amount of new loans that Big Bucks Bank can make is \[tex]$12,000. #### Part (b): Change in the Money Supply - By making the new loans, the money supply increases by the same amount. - The change in the money supply = Maximum new loans = \$[/tex]12,000
So, the money supply has increased by \[tex]$12,000. #### Part (c): Bank's Balance Sheet After Clearing Checks 1. Post-Loan Balance Sheet (Column 1): - Reserves = Initial Reserves - Maximum new loans = \$[/tex]22,000 - \[tex]$12,000 = \$[/tex]10,000
- Loans = Initial Loans + Maximum new loans = \[tex]$40,000 + \$[/tex]12,000 = \[tex]$52,000 The post-loan balance sheet would be: \[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Assets & & & (1) & Liabilities and net worth & & (1) \\ \hline Reserves & $[/tex]\[tex]$ & $10,000$ & & Checkable deposits & \$ 100,000 \\ \hline Securities & & $38,000$ & & \\ \hline Loans & & $52,000$ & & \\ \hline \end{tabular} \] 2. After Checks Cleared (Column 2): - After lending the money, checks drawn for the entire loan amount may be cleared against the bank, decreasing reserves by this amount. - Reserves remain \$10,000 (as no further changes occur after the checks are cleared). - Loans remain \$52,000. The balance sheet after checks have cleared would be: \[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Assets & & & (2) & Liabilities and net worth & & (2) \\ \hline Reserves & $\$[/tex] & [tex]$10,000$[/tex] & & Checkable deposits & \[tex]$ 100,000 \\ \hline Securities & & $[/tex]38,000[tex]$ & & \\ \hline Loans & & $[/tex]52,000[tex]$ & & \\ \hline \end{tabular} \] ### Summary a. Maximum amount of new loans: \$[/tex]12,000
b. Change in the money supply: \[tex]$12,000 c. Bank's balance sheet after checks cleared: \[ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Assets & & & (2) & Liabilities and net worth & & (2) \\ \hline Reserves & $[/tex]\[tex]$[/tex] & [tex]$10,000$[/tex] & & Checkable deposits & \[tex]$ 100,000 \\ \hline Securities & & $[/tex]38,000[tex]$ & & \\ \hline Loans & & $[/tex]52,000$ & & \\
\hline
\end{tabular}
\]
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