Question 1. (76 pts) Assume that there is only one private bankwhose equity or net worth is always zero. Also maintain thefollowing assumptions:
(A1) The ratio of cash holdings by the non-bank public to demanddeposits is 0.ïº05, and all bank liabilities are demanddeposits;
(A2) The bank keeps the reserve/deposit ratio at 0ïº.1;
(A3) Demand deposits, bank loans and Treasury securities bear zeronet interest.
Use the notation ï for the non-bank publicâs cash holdings, ïfor demand deposits, ï for bank reserves, and ï for bank loans.Round up all dollar amounts to 0ïº.01 billion.
(1) (20 pts) Assume that the initial monetary base is ïï = $15billion and that the bank holds $20 billion Treasury securities. Inaddition to the Treasuries, the bankâs assets are loans to theprivate sector and bank reserves. Suppose that the cash/depositratio has reached 0ïº.05 and the reserve ratio has reached 0ïº.1.Calculate the non-bank publicâs cash holdings, deposits, bankreserves, bank loans, and the money stock ï1. Fill in the bankâsbalance sheet with the corresponding items.
(2) (15 pts) Suppose that the government increases the reserverequirement to 0ïº.15. After the cash/deposit ratio has reached0ïº.05 and the reserve ratio has reached 0.ïº15, recal- culate thenon-bank publicâs cash holdings, deposits, bank reserves, and bankloans. By how much does ï1 fall?
For the remainder of Question 1, go back to the assumption thatthe reserve requirement is 0.ïº1. Start in the situation reached in(1) above. Consider an open market operation in which the banksells $20 billion Treasuries to the Federal Reserve and lends theproceeds of the sale to the private sector.
(3) (5 pts) Fill in the bankâs balance sheet at the time beforethe private sector deposits any part of the money from the $20billion loans back in the bank.
(4) (21 pts) The private sector deposits part of the $20 billionloans back to the bank following the rule (A1). In turn, the banklends out part of the new deposits and keeps the reserve ratio at0ïº.1. After this new round of bank lending but before any of thenew loans in this round are deposited back in the bank, calculatedemand deposits, bank reserves, bank loans, the publicâs cashholdings, and the money stock M1. Fill in the bankâs balance sheetafter this round of activities.
(5) (15 pts) Suppose that the cash/deposit ratio finally settlesat 0ïº.05 and the reserve ratio settles at 0ïº.1. Calculate demanddeposits, bank reserves, bank loans, and the publicâs cashholdings. By how much has the open market operation increased themoney stock M1?
Question 1. (76 pts) Assume that there is only one private bankwhose equity or net worth is always zero. Also maintain thefollowing assumptions:
(A1) The ratio of cash holdings by the non-bank public to demanddeposits is 0.ïº05, and all bank liabilities are demanddeposits;
(A2) The bank keeps the reserve/deposit ratio at 0ïº.1;
(A3) Demand deposits, bank loans and Treasury securities bear zeronet interest.
Use the notation ï for the non-bank publicâs cash holdings, ïfor demand deposits, ï for bank reserves, and ï for bank loans.Round up all dollar amounts to 0ïº.01 billion.
(1) (20 pts) Assume that the initial monetary base is ïï = $15billion and that the bank holds $20 billion Treasury securities. Inaddition to the Treasuries, the bankâs assets are loans to theprivate sector and bank reserves. Suppose that the cash/depositratio has reached 0ïº.05 and the reserve ratio has reached 0ïº.1.Calculate the non-bank publicâs cash holdings, deposits, bankreserves, bank loans, and the money stock ï1. Fill in the bankâsbalance sheet with the corresponding items.
(2) (15 pts) Suppose that the government increases the reserverequirement to 0ïº.15. After the cash/deposit ratio has reached0ïº.05 and the reserve ratio has reached 0.ïº15, recal- culate thenon-bank publicâs cash holdings, deposits, bank reserves, and bankloans. By how much does ï1 fall?
For the remainder of Question 1, go back to the assumption thatthe reserve requirement is 0.ïº1. Start in the situation reached in(1) above. Consider an open market operation in which the banksells $20 billion Treasuries to the Federal Reserve and lends theproceeds of the sale to the private sector.
(3) (5 pts) Fill in the bankâs balance sheet at the time beforethe private sector deposits any part of the money from the $20billion loans back in the bank.
(4) (21 pts) The private sector deposits part of the $20 billionloans back to the bank following the rule (A1). In turn, the banklends out part of the new deposits and keeps the reserve ratio at0ïº.1. After this new round of bank lending but before any of thenew loans in this round are deposited back in the bank, calculatedemand deposits, bank reserves, bank loans, the publicâs cashholdings, and the money stock M1. Fill in the bankâs balance sheetafter this round of activities.
(5) (15 pts) Suppose that the cash/deposit ratio finally settlesat 0ïº.05 and the reserve ratio settles at 0ïº.1. Calculate demanddeposits, bank reserves, bank loans, and the publicâs cashholdings. By how much has the open market operation increased themoney stock M1?
