Question

1. The Fed pays 2% on reserves of the commercial banks. It also offers to give loans to banks at 4%. There is currently the supply of $300 billion in the market of overnight funds in the federal funds market. The demand for the funds from the banks that “need liquidity” is given by Qd = 1000 − 200if f , where if f is the rate in %.

a. What is the equilibrium federal funds rate? Suppose the federal funds rate is at the level targeted by the Fed.

b. It’s 4:30 pm on Friday. Suddenly a big commercial bank needs to pay a fine for deceiving its consumers. This increases the demand for overnight fines to Qd = 1300 − 200if f . What happens to the equilibrium funds rate?

c. It’s 4:40 pm, the markets close in 20 minutes. The Fed has to respond to the increase in the funds rate (in the previous part) by buying a certain amount of (mostly government-issued) securities, thus increasing the supply. Why should it buy securities rather than sell? How much should the Fed buy given the new demand and the existing supply?

d. The Fed is offering to buy the securities, but nobody wants to sell. Should the Fed offer a higher or lower price for the bonds? What happens to the interest rate on bonds? Note that the Fed wants the federal funds rate to go down. Does the rate on bonds go down or up?

Answer 1

Answer a

Supply = $300 billion

Qd = 1000 − 200f

At equilibrium, quantity demanded = Quantity supplied

hence, 300= 1000-200f

or, 200f = 1000-300

or, f = 700/200 = 3.5%

Hence federal funds rate =3.5%

Answer b

At new demand at Qd = 1300 − 200f

Hence, 300= 1300-200f

or, 200f = 1300-300

or, f =1000/200= 5%

Hence new federal funds rate =5%

Answer c

Since the demand for funds is high and supply is same, federal funds rate is increasing, to maintain the federal funds rate, Fed will need to increase the supply. When Fed will buy the securities, Fed will make payments to Banks, thus the funds supply in market will increase hence federal funds rate will come down.

The new demand at 3.5% rate will be Qd = 1300-200*3.5 = 1300-700 = $600 billion

Hence Additional supply required = 600-300 = $300 billion

Hence Fed needs to buy bonds worth $300 billion

Answer d

If Banks are not willing to sell means the price offered is less, hence Fed will need to increase the offer price for Bonds

Since Fed is buying the bonds and Banks are paying the interest, and Fed wants to buy the Bonds to control the Federal funds rate, hence Banks will decrease the Bonds interest rate because of high demand of bonds by Fed. Hence Bonds interest rate will go down.