Question

Suppose First Main Street Bank, Second Republic Bank, and Third Fidelity Bank all have zero excess reserves. The required reserve ratio is 5%. The Federal Reserve buys a government bond worth $200,000 from Paolo, a customer of First Main Street Bank. He deposits the money into his checking account at First Main Street Bank. Now, suppose First Main Street Bank loans out all of its new excess reserves to Lucia, who immediately writes a check for the full amount to Kenji. Kenji then immediately deposits the funds in his checking account at Second Republic Bank. Then Second Republic Bank lends out all of its new excess reserves to Van, who writes a check to Sharon, who deposits the money in her account at Third Fidelity Bank. Finally, Third Fidelity lends out all of its new excess reserves to Amy. Find increase in checkable deposits, increase in required reserves, and increase in loans for first main street bank, second republic bank, and third fidelity bank.

Answer 1

After the Federal Reserve purchases a bond, First Main Street Bank's checkable deposits increase by $200,000, required reserves increase by $10,000, and loans increase by $190,000. Similar increases in deposits, reserves, and loans occur at Second Republic Bank and Third Fidelity Bank as the initial excess reserves are loaned out and redeposited.

Step-by-step explanation:

When the Federal Reserve buys a government bond worth $200,000 from Paolo and he deposits this into First Main Street Bank, the bank's reserves increase by $200,000. With a required reserve ratio of 5%, this means First Main Street Bank needs to keep $10,000 (5% of $200,000) as required reserves and can lend out the remaining $190,000 as excess reserves.

After lending $190,000 to Lucia, the checkable deposits at First Main Street Bank increase by $200,000, the required reserves by $10,000, and loans by $190,000. When Lucia writes a check to Kenji, who then deposits the funds into Second Republic Bank, Second Republic Bank then has to hold 5% of the $190,000, which is $9,500, in required reserves, and it can lend out the remaining $180,500. The pattern continues with Third Fidelity Bank, which must hold 5% of $180,500 ($9,025) and can lend out $171,475.

Therefore, the increase in checkable deposits at First Main Street Bank is $200,000, at Second Republic Bank is $190,000, and at Third Fidelity Bank is $180,500. The increase in required reserves is $10,000 at First Main Street Bank, $9,500 at Second Republic Bank, and $9,025 at Third Fidelity Bank. The increase in loans is $190,000 at First Main Street Bank, $180,500 at Second Republic Bank, and $171,475 at Third Fidelity Bank respectively.

Answer 2

The Federal Reserve's bond purchase results in a cascading effect through the banking system: checkable deposits and excess reserves increase, which are then loaned out, while required reserves are maintained at 5% of deposits for each bank.

Step-by-step explanation:

To calculate the increase in checkable deposits, required reserves, and loans for each of the three banks involved, we will follow the money through the banking system after the Federal Reserve's purchase of government bonds.

First Main Street Bank:

• Increases checkable deposits by $200,000 after Paolo deposits the money from the bond sale.

• Required reserves increase by 5% of $200,000, which is $10,000.

• Loans out all its new excess reserves: $200,000 - $10,000 (required reserves) = $190,000.

Second Republic Bank:

• Receives a deposit of $190,000, which is loaned from the First Main Street Bank to Lucia and then given to Kenji.

• Required reserves increase by 5% of $190,000, which is $9,500.

• Loans out its new excess reserves: $190,000 - $9,500 = $180,500.

Third Fidelity Bank:

• Receives a deposit of $180,500, which is loaned from the Second Republic Bank to Van and then given to Sharon.

• Required reserves increase by 5% of $180,500, which is $9,025.

• Loans out its new excess reserves: $180,500 - $9,025 = $171,475.

The overall effect of the Federal Reserve's open market operation is an increase in checkable deposits and loans in the banking system, with each bank holding the required percentage of reserves.