Suppose First Main Street bank, Second Republic Bank, and Third Fidelity Bank al

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 $100,000 from Akshay, a client of First Main Street Bank. He deposits the money into his account at First Main Street Bank.

On the Assets side of First Main Street Bank's T-Account (before the bank makes any new loans), this (increases/decreases) First Main Street Bank's (Demand deposits/net worth/ reserves/ building and furniture/ loans) by (100k/5k/200k/95k). On the liabilities side of First Main Street Bank's T-account, this(increases/decreases) First Main Street Bank's (Demand deposits/net worth/ reserves/ building and furniture/ loans) by(100k/5k/200k/95k).

Because the required reserve ratio is 5%, the $100,000 deposit (increases/decreases) First Main Street Bank's excess reserves by (90k/95k/75k/zero) and (increases/decreases) First Main Street Bank's required reserves by (100k/10k/25k/5k).

Now, suppose First Main Street Bank loans out all of its new excess reserves to Beth, who then uses the funds to write a check to Jamal. Jamal immediately deposits the check into his account at Second Republic Bank. Then Second Republic Bank lends out all of its new excess reserves to Patrick, who writes a check to Saunita, who deposits the money into her account at Third Fidelity Bank. Third Fidelity Bank lends out all of its new excess reserves as well.

Find Increase in Demand Deposits, Increase in Required Reserves AND Increase in loans for each of the three banks.

First Main Street Bank:

Second Republic Bank:

Third Fidelity Bank:

Assume this process continues, with each successive loan deposited in a checking account and no banks keeping excess reserves. Under these assumptions, the $100,000 injection into the money supply allows banks to make (200k/500k/1,900k/2million), resulting in overall increase of (500k/190k/2million/1,900k) in demand deposits.

Explanation / Answer

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 $100,000 from Akshay, a client of First Main Street Bank. He deposits the money into his account at First Main Street Bank.

On the Assets side of First Main Street Bank's T-Account (before the bank makes any new loans), this increases First Main Street Bank's reserves by 100k. On the liabilities side of First Main Street Bank's T-account, this increases First Main Street Bank's Demand deposit by 100k.

Because the required reserve ratio is 5%, the $100,000 deposit increases First Main Street Bank's excess reserves by 95k [=Actual %u2013 Required reserves = 100-5 =95] First Main Street Bank's required reserves by 5k[=5% of $100,000 = 5k].

Now, suppose First Main Street Bank loans out all of its new excess reserves to Beth, who then uses the funds to write a check to Jamal. Jamal immediately deposits the check into his account at Second Republic Bank. Then Second Republic Bank lends out all of its new excess reserves to Patrick, who writes a check to Saunita, who deposits the money into her account at Third Fidelity Bank. Third Fidelity Bank lends out all of its new excess reserves as well.

Find Increase in Demand Deposits, Increase in Required Reserves AND Increase in loans for each of the three banks.

First Main Street Bank: There is no change in demand deposits and required reserve ratio since further transactions are between other banks. However the loans increase by $95k which is the amount of excess reserves held after the initial deposit by Akshay.

Second Republic Bank: There is an increase in deposit of $95,000 as Jamal deposits the check. The required increase in reserves is $4750 [=5% 0f 95000 = $4750]. The rest is loaned out. Hence loans increase by $90,250.

Third Fidelity Bank: There is an increase in deposit of $90,250 as Jamal deposits the check. The required increase in reserves is $4512.5 [=5% 0f 90250 = $4512.5]. The rest is loaned out. Hence loans increase by $85737.50.

Assume this process continues, with each successive loan deposited in a checking account and no banks keeping excess reserves. Under these assumptions, the $100,000 injection into the money supply allows banks to make 2million [=money multiplier*initial deposit = 20*100,000 = $2,000,000; money multiplier =1/reserve ratio =1/0.05 =20], resulting in overall increase of 2million in demand deposits.

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