Question 1. (76 pts) Assume that there is only one private bank whose equity or

Question

Question 1. (76 pts) Assume that there is only one private bank whose equity or net worth is always zero. Also maintain the following assumptions:

(A1) The ratio of cash holdings by the non-bank public to demand deposits is 0.05, and all bank liabilities are demand deposits;

(A2) The bank keeps the reserve/deposit ratio at 0.1;
(A3) Demand deposits, bank loans and Treasury securities bear zero net interest.

Use the notation for the non-bank public’s cash holdings, for demand deposits, for bank reserves, and for bank loans. Round up all dollar amounts to 0.01 billion.

(1) (20 pts) Assume that the initial monetary base is = $15 billion and that the bank holds $20 billion Treasury securities. In addition to the Treasuries, the bank’s assets are loans to the private sector and bank reserves. Suppose that the cash/deposit ratio has reached 0.05 and the reserve ratio has reached 0.1. Calculate the non-bank public’s cash holdings, deposits, bank reserves, bank loans, and the money stock 1. Fill in the bank’s balance sheet with the corresponding items.

(2) (15 pts) Suppose that the government increases the reserve requirement to 0.15. After the cash/deposit ratio has reached 0.05 and the reserve ratio has reached 0.15, recal- culate the non-bank public’s cash holdings, deposits, bank reserves, and bank loans. By how much does 1 fall?

For the remainder of Question 1, go back to the assumption that the reserve requirement is 0.1. Start in the situation reached in (1) above. Consider an open market operation in which the bank sells $20 billion Treasuries to the Federal Reserve and lends the proceeds of the sale to the private sector.

(3) (5 pts) Fill in the bank’s balance sheet at the time before the private sector deposits any part of the money from the $20 billion loans back in the bank.

(4) (21 pts) The private sector deposits part of the $20 billion loans back to the bank following the rule (A1). In turn, the bank lends out part of the new deposits and keeps the reserve ratio at 0.1. After this new round of bank lending but before any of the new loans in this round are deposited back in the bank, calculate demand deposits, bank reserves, bank loans, the public’s cash holdings, and the money stock M1. Fill in the bank’s balance sheet after this round of activities.

(5) (15 pts) Suppose that the cash/deposit ratio finally settles at 0.05 and the reserve ratio settles at 0.1. Calculate demand deposits, bank reserves, bank loans, and the public’s cash holdings. By how much has the open market operation increased the money stock M1?

Explanation / Answer

Cash holdings to demand deposits= .05

Reserve /deposit ratio= 0.1

Treasury securities=$2 0 billion

Total of Asset side= $35 billion

Since only deposits are there on the liability side, deposits= $ 35 billion

Cash holdings/35= .05

Cash holdings= $1.75 billion

Rserve/35=.1

Reserves =$3.5 billion

Particulars

Amount(Billion &)

Deposits

35

35

Reserves

3.5

Loans

11.5

Cash holdings

1.75

Other Treasury Securities

18.25

35

Reserve /deposit ratio increased to .15

New reserves= 35*.15= $5.25 billion

Loans will get reduced by $ 1.7 billion and new loans will be $9.75 billions

For the 2nd part, now All the Treasury securities are sold and the receipts lend to public

Now we have deposits on the liability side and Reserves and loans on the Asset side.

Particulars

Amount(Billion &)

Deposits

35

35

Reserves

3.5

Loans

31.5

35

Deposits will be 20/1.05= $19.05billions

New Deposits= $54.05 billions

New Reserves= 54.05*.1= $ 5.41 billion

Deposit in Treasury= 19.05-1.91= 17.14 billion

Particulars

Amount(Billion &)

Deposits

54.05

54.05

Reserves

5.41

Loans

31.5

Other Treasury Securities

17.14

54.05

Particulars

Amount(Billion &)

Deposits

54.05

54.05

Reserves

5.41

Loans

31.5

Cash holdings

2.7

Other Treasury Securities

14.44

54.05

Particulars

Amount(Billion &)

Deposits

35

35

Reserves

3.5

Loans

11.5

Cash holdings

1.75

Other Treasury Securities

18.25

35

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