Money and Banking
Fall 2009
Homework assignment #4
1. Answer the following questions with a graph and explain the graph a written explanation that
explicitly includes what happens to the equilibrium Federal Funds rate and the quantity of
reserves in the banking system. Also show what will happen to the Fed balance sheet and the
banking systems balance sheet. Assume for each question that initially the Fed Funds rate is at
4% the discount rate is set at 5% and the Fed pays an interest rate of 1% on reserves held at the
Fed. Assume that it takes a $1 billion change in new reserves to change the Fed funds rate one
percentage point. Also calculate the increase in the money supply assuming our simple money
multiplier applies and that required reserves are set at 5%. (there is no need to trace the
change in the money supply through several banks)
a. Suppose the Fed is worried that the economy is under producing. What happens if there is
an open market purchase from banks of $1 billion treasury bonds.
b. Suppose the Fed finds that the economy is really in crisis and wants to lower interest rates
to zero. How much in reserves would they have to pump into the system? What does the
fed need to to do lower the rate to zero besides open market operations?
c. If the discount rate is lowered to 3% what happens to the Federal funds rate? Where do the
new reserves come from?
2 Many people are worried about the potential consequences of the Fed printing so much money to
deal with the “Great Recession”. For the following questions assume the fed funds rate is at 1%, the
interest rate that the Fed pays on reserves is 1% and the discount rate is set at 1.50%. There are
$2trillion dollars in reserves in the Federal Funds market. Also assume that the “kink” in the demand for
reserves is at $1 trillion. That is, banks are willing to pay more than the rate the Fed pays on reserves to
borrow reserves when there are only $1 trillion in reserves available in the Fed Funds market.
a. Is it possible to lower the Fed Funds rate further with open market operations? Why? Show
this with a graph.
b. If the Fed sells $100 billion in treasury bonds to the banking system will this change the Fed
Funds rate? Show this with a graph.
c. Will the open market sale in question 1b change the amount of deposits in the banking
system? Bear in mind that an open market sale changes the monetary base in exactly the opposite way
as an open market purchase. Trace the change of the monetary base and the money supply on both the
Fed’s balance sheet and the balance sheet of three banks: Bank A, Bank B and Bank C. Assume that the
Fed sells the $100 billion in treasury bonds to Bank A. Also assume that required reserves are 5% of
deposits and that banks hold no excess reserves and that no one holds currency.
d. Given the assumptions of 1c what would be the total change in the money supply and the
monetary base be after the change in reserves worked its way through the entire banking system?
Again, keep in mind that an open market sale takes reserves out of the banking system in exactly the
same way that an open market purchase adds reserves to the banking system.
e. If Bank A had been holding $100billion in excess reserves at the time of the open market sale
what would have happened to the money supply? Why is this important to think about when talking
about current monetary policy?
3.
Captain Morgan Chase.
Assets (billions)
Liabilities (billions)
Reserves
50 Deposits
500
Loans
400 Bank Capital
50
Securities
100 Borrowing
0
a. If there is a run on deposits of $50 and required reserves are 10% of deposits what problem is CMC
facing? Show—using a separate balance sheet for each example—4 different ways this problem can be
solved. What are the most desirable ways to deal with this problem? The least desirable?
b. If CMC is forced to write down $60 billion in mortgage loans what problem are the facing? Also, show
this with a balance sheet. Who will solve this problem?
4. Assume that the Fed has decided to increase reserves in the banking system by $200 billion. Also
assume that reserve requirements are 10% of deposits and assume that banks do not hold excess
reserves. Answer the following questions.
a. What happens to the Fed’s balance sheet?
b. What happens to the balance sheet of the banking system?
c. What are some factors that may make the increase in reserves cause a smaller increase in the
money supply?
5. Quantitative Easing 3 (QE3) is the Federal Reserve’s latest attempt to push the economic recovery
forward. The following questions relate to QE3.
a. Show on the Fed’s balance sheet one month’s open market purchases of $85 billion
b. Show the change on the banking system’s balance sheet if banks do not hold excess reserves
and reserve requirements are 2% of deposits.
c. Show what happens in the market for bonds if instead of making loans banks simply buy more
bonds (You need a graph).
d. Does b or c have a larger economic impact? Why?
e. Do we see the kind of economic impact implied by change in the banking systems balance sheet
in part b? Why might we see something different?