Question

Suppose that the public wishes to hold $0.35 in pocket money (currency and coin) and $0.25 in time and savings deposits. Suppose that banks wish to hold $0.20 for each new dollar of transaction money received. Suppose that $0.05 finds its way outside of the domestic banking system. Suppose the reserve requirement on transaction deposits is 3 percent and that on time and savings deposits is 4%. (20 points)

a. What is the size of the transaction deposit multiplier? Make sure to show your work.

b. What is the size of the money multiplier? Make sure to show your work.

c. Suppose $5 million in new excess reserves appear in the banking system. How much will be created in the form of deposits and loans? Make sure to show your work.

d. By how much did the leakages of funds from the banking system reduce the size of the transaction deposit multiplier? (Hint: compute the simple transaction deposit multiplier). Make sure to show your work.

e. If the Fed purchases $175 billion worth of government securities on the open market, what is the effect on the money supply?

Answer 1

Solution:-

(A).The transaction deposit multiplier is the given as:

Transaction Deposit Multiplier = 1/ (RR + LA + EX)

Where RR = Reserve requirement, LA = percentage of currency or cash held by public and EX is the percentage of excess reserves banks wish to hold.

Given that public wishes to hold $0.35 in pocket money (currency and coin) and $0.25 in time and savings deposits. The reserve requirement on deposits on time and saving deposits is 4%. So LA = 0.35 + 0.04*0.25 = 0.36

Now banks wish to hold $0.20 for each new dollar of transaction money received. So EX = 0.20. RR is given on deposits as 4% so RR = 0.03. Also note that $0.05 finds its way outside of the domestic banking system. So this reduces the multiplier effect.

Hence Transaction Deposit Multiplier is 1/ (0.03 + 0.36 + 0.20 + 0.05) = 1/0.5625 = 1.5625

(B). Money multiplier = (1 + LA)/(RR + EX + LA) = (1 + 0.36)/(0.03 + 0.36 + 0.20 + 0.05) = 2.125

(C). When $5 million in new excess reserves appear in the banking system, compute the amount of new deposits and loans using transaction deposit multiplier as $5 million * 1.5625 = $7.8125 million

(D). Simple transaction deposit multiplier is given by 1/ (LA + RR + EX) = 1/(0.36 + 0.03 + 0.20) = 1.70. So leakages reduces the multiplier from 1.85 to 1.5625

(E). With Fed's action, money supply increases by $175 billion * 2.125 = $371.875 billion.