Homework Exercises – 5
Chapter 10 problems
1. “Unemployment us a bad thing, and the government should make every
effort to eliminate it.” Do you agree or disagree? Explain your answer.
Disagree. Some unemployment is beneficial to the economy because
the availability of vacant jobs makes it more likely that a worker will
find the right job and that the employer will find the right worker for
the job.
2. Which goals of the Fed frequently conflict?
The goal of price stability often conflicts with the goal of high
economic growth and employment and interest-rate stability. When
the economy is expanding along with employment, inflation may rise.
In order to pursue the goal of price stability, the Fed may have to
pursue a contractionary and anti-inflationary policy that conflicts with
the goal of high employment and economic growth. Similarly when
the central bank wants to pursue tight monetary policy and raise
interest rates in order to contain inflation, this pursuit of the goal of
price stability may conflict with the goal of interest-rate stability.
3. “If the demand for reserves did not fluctuate, the Fed could pursue both a
non-borrowed reserves target and an interest-rate target at the same time.”
Is this statement true, false or uncertain? Explain your answer.
True. In such a world, hitting a nonborrowed reserves target would
mean that the Fed would also hit its interest rate target, or vice versa.
Thus the Fed could pursue both a nonborrowed reserves target and
an interest rate target at the same time.
4. Classify each of the following as either an operating target or an intermediate
target, and explain why.
a. The three-month Treasury bill rate.
The three-month Treasury bill rate can be thought of as either
an operating target or an intermediate target. It can be an
operating target because it is a variable that can be affected
directly by the tools of the Fed (open market operations, in
particular). It can be an intermediate target because it has
some direct effect on economic activity.
b. The monetary base
The monetary base is an operating target because it can be
directly affected by the tools of the Fed and is only linked to
economic activity through its effect on the money supply.
c. M2
M2 is an intermediate target because it is not directly affected
by the tools of the Fed and has some direct effect on economic
activity.
5. Which procedures can the Fed use to control the three-month Treasury bill
rate? Why does control of this interest rate imply that the Fed will lose
control of the money supply?
The Fed can control the interest rate on three-month Treasury bills by
buying and selling them on the open market. When the bill rate rises
above the target level, the Fed would buy bills, which would bid up
their price and lower the interest rate to its target level. Similarly,
when the bill rate falls below the target level, the Fed would sell bills
to raise the interest rate to the target level. The resulting open market
operations would of course affect the money supply and cause it to
change. The Fed would be giving up control of the money supply to
pursue an interest-rate target.
6. If the Fed has an interest-rate target, why will an increase in the demand for
reserves lead to a rise in the money supply?
The increase in the demand for reserves shifts the reserves demand
curve to the right would raise interest rates. In order to prevent this,
the Fed will buy bonds to increase the supply of reserves. The open
market purchase will then cause the monetary base and the money
supply to rise.
7. “Interest rates can be measured more accurately and more quickly than the
money supply. Hence an interest rate is preferred over the money supply as
an intermediate target.” Do you agree or disagree? Explain your answer.
Disagree. Although nominal interest rates are measured more
accurately and more quickly than the money supply, the interest rate
variable that is of more concern to policymakers is the real interest
rate. Because the measurement of real interest rates requires
estimates of inflation, it is not true that real interest rates are
necessarily measured more accurately and more quickly than the
money supply. Interest-rate targets are therefore not necessarily
better than money supply targets.
8. Compare the monetary base to M2 on the grounds of controllability and
measurability. Which to do you prefer as an intermediate target? Why?
The monetary base is more controllable than M2 because it is directly
controlled by the tools of the Fed. It is measured more accurately and
quickly than M2 because the Fed can calculate the base from its own
balance sheet data, while it constructs M2 numbers from surveys of
banks, which takes some time to collect and are not always that
accurate. Even though the base is a better intermediate target on the
grounds of measurability and controllability, it is not necessarily a
better intermediate target because its link to economic activity may
be weaker than that between M2 and economic activity.
9. “Discounting is no longer needed because the presence of the FDIC
eliminates the possibility of bank panics.” Is this statement true, false or
uncertain? Explain your answer.
False. The FDIC would not be effective in eliminating bank panics
without Fed discounting to troubled banks in order to keep bank
failures from spreading. In addition the FDIC only has approximately
1% of the total deposits in its insurance fund. Significant issues across
banks might deplete this fund. Finally not all deposit accounts are
insured.
10. The benefits of using Fed discount operations to prevent bank panics are
straightforward. What are the costs?
The costs are that banks that deserve to go out of business because of
poor management may survive because of Fed discounting to prevent
panics. This might lead to an inefficient banking system with many
poorly run banks.
11. What are the benefits of using a nominal anchor for the conduct of monetary
policy?
A nominal anchor helps promote price stability by tying inflation
expectations to low levels directly through its constraint on the value
of money. It can also limit the time-inconsistency problem by
providing an expected constraint on monetary policy.
12. Give an example of the time-inconsistency problem that you experience in
your everyday life?
All sorts of answers are possible
13. What incentives arise for a central bank to fall into the time-inconsistency
trap of pursuing overly expansionary monetary policy?
Central bankers might think they can boost output or lower
unemployment by pursuing overly expansionary monetary policy
even though in the long run this just leads to higher inflation and no
gains on the output or unemployment front. Alternatively, politicians
may pressure the central bank to pursue overly expansionary policies.
14. What are the advantages of monetary targeting as a strategy for the conduct
of monetary policy?
Monetary targeting has the advantage that it enables a central bank to
adjust its monetary policy to cope with domestic considerations.
Furthermore, information on whether the central bank is achieving its
target is known almost immediately.
15. What is the big if necessary for the success of monetary targeting? Does the
experience with monetary targeting suggest that the big if is a problem?
Monetary targeting only works well if there is a reliable relationship
between the monetary aggregate and inflation, a relationship that has
often not held in different countries.
16. What methods have inflation-targeting central banks used to increase
communication with the public and increase the transparency of monetary
policy making?
Inflation-targeting central banks engage in extensive public
information campaigns that include the distribution of glossy
brochures, the publication of Inflation Report-type documents, making
speeches to the public, and continual communication with the elected
government.
17. Why might inflation targeting increase support for the independence of the
central bank to conduct monetary policy?
Sustained success in the conduct of monetary policy as measured
against a pre-announced and well-defined inflation target can be
instrumental in building public support for a central bank’s
independence and for its policies. Also, inflation targeting is
consistent with democratic principles because the central bank is
more accountable.
18. “Because the public can see whether a central bank hits its monetary targets
almost immediately, whereas it takes time before the public can see whether
an inflation target is achieved, monetary targeting makes central banks more
accountable than inflation targeting does.” Is this statement true, false or
uncertain? Explain your answer.
Uncertain. If the relationship between monetary aggregates and the
goal variable—say, inflation—is unstable, then the signal provided by
the monetary aggregates is not very useful and is not a good indicator
of whether the stance of monetary policy is correct.
19. “Because inflation targeting focuses on achieving the inflation target, it will
lead to excessive output fluctuations.” Is this statement true, false or
uncertain? Explain your answer.
False. Inflation targeting does not imply a sole focus on inflation. In
practice, inflation targeters do worry about output fluctuations, and
inflation targeting may even be able to reduce output fluctuations
because it allows monetary policymakers to respond more
aggressively to declines in demand because they don’t have to worry
that the resulting expansionary monetary policy will
lead to a sharp rise in inflation expectations.
20. “A central bank with a dual mandate will achieve lower unemployment than
a central bank with a hierarchical mandate in which price stability takes
precedence.” Is this statement true, false or uncertain?
False. There is no long-run trade-off between inflation and
unemployment, so in the long run a central bank with a dual mandate
that attempts to promote maximum employment by pursuing
inflationary policies would have no more success at reducing
unemployment than one whose
primary goal is price stability.
Chapter 10 – Quantitative Problems
1. Consider a bank policy to maintain 12% of deposits as reserves. The bank
currently has $10m in deposits and $400,000 in excess reserves. What is the
required reserve on a new deposit of $50,000?
The bank policy is to maintain 12% of deposits as total reserves. The
excess reserves of $400,000 is 4% of 10m. The total reserves is 12%
which equals the required reserves plus the excess reserves. Thus the
required reserves are 8%. Thus the required reserves on a $50,000
deposit is $4,000.
2. Estimates of unemployment for the upcoming year have been developed as
follows. What is the expected unemployment rate? What is the standard
deviation?
Economy
Probability
Unemployment Rate (%)
Bust
.15
20
Average
.5
10
Good
.2
5
Boom
.15
1
One can set up the problem as follows:
Economy
Probability
Bust
Average
Good
Boom
Unemployment
Rate
Expectation
0.15
0.5
0.2
0.15
20%
10%
5%
1%
0.03
0.05
0.01
0.0015
0.0915
Sum
Squared
Deviation
0.001765838
0.000036125
0.000344450
0.000996338
0.00314275
Thus the expected unemployment rate is 9.15% and the standard
deviation is the square root of the squared deviation or 5.6%.
3. The Federal Reserve wants to increase the supply of reserves, so it purchases
1m USD worth of bonds from the public. Show the effect of this open market
operation using T-accounts.
Banking System
Assets
Liabilities
$1 million
Reserves
Checkable Deposits
$1 million
Federal Reserve System
Assets
Liabilities
$1 million
Securities
$1 million
Reserves
4. Use T-accounts to show the effect of the Federal Reserve being paid back a
$500K discount loan from a bank.
Banking System
Assets
Liabilities
$500,000
Reserves
Discount Loans
$500,000
Federal Reserve System
Assets
Discount Loans
$500,000
Liabilities
Reserves
$500,000
5. The short-term nominal interest rate is 5%, with an expected inflation of 2%.
Economists forecast that next year’s nominal rate will increase by 100 basis
points, but inflation will fall to 1.5%. What is the expected change in real
interest rates?
nominal rate = real rate + expected inflation
Year 1: 5% = real rate + 2%, or the real rate = 3%
Year 2: 6% = real rate + 1.5%, or the real rate = 4.5%
Real rates have increased by 150 basis points.
For problems 6-8 recall from introductory macroeconomics that the money
multiplier = 1/(required reserve ratio).
6. If the required reserve ratio is 10%, how much a new $10,000 deposit can a
bank lend? What is the potential impact on the money supply?
The bank must retain $10,000 × 10%, or $1,000 of the new deposit.
The remaining $9,000 can be lent to, for example, mortgage
borrowers, commercial borrowers, etc. Since the reserve requirement
is 10%, the potential money multiplier is 1/0.10 or 10. The $10,000
deposit can potentially increase the money supply by $100,000.
7. A bank currently holds $150,000 in excess reserves. If the current reserve
requirement is 12.5%, how much could the money supply change? How
could this happen?
The money supply could increase if the bank lent its excess reserves.
Since the reserve requirement is 12.5%, the potential money
multiplier is 1/0.125, or 8. If the bank lends all of the excess reserves,
the money supply could increase by $150,000  8  $1,200,000.
8. The trading desk at the Federal Reserve sold $100,000,000 in T-bills to the
public. If the current reserve requirement is 8.0%, how much could the
money supply change?
Since the reserve requirement is 8.0%, the potential money multiplier
is 1/0.08, or 12.5. The sale of T-bills will act to decrease the money
supply. The contraction will be on the order of $100,000,000 × 12.5 =
1,250,000,000. However, if there are excess reserves in the system, it
may not be this high.
Chapter 10 – Additional Problems
1. Define Monetary Base, M1 and M2.
The monetary base is all cash in circulation outside of the Federal
Reserve plus bank reserves held at the Federal Reserve.
M1 is a measure of money supply and includes all cash outside of the
banking industry plus demand deposits/checking accounts/checkable
deposits/”reservable deposits”.
M2 = M1 + savings accounts + money market accounts + small size
time deposits.
2. Assume Fred has $500 in cash and that this is the entire monetary base.
Assume that the reserve requirement for banks is 5% and that reserves are
taken on checking accounts but not money market accounts.
a. What is the current level for M1 and M2?
M1 and M2 are $500.
b. If Fred deposits the $500 into his checking account what happens to
M1 and M2? What are the required reserves? How much of the cash
can the bank leave in its own vault?
M1 and M2 are unchanged at $500. The required reserves are
$25. The bank can leave $475 in its vault.
c. The bank where Fred has a checking account would like to extend a
loan to another customer, Sue. How large a loan can the bank extend?
After the loan what happens to the Monetary Base, M1 and M2? If the
bank deposits the proceeds of the loan into Sue’s checking account
what are the required reserves of the bank?
The bank can lend $475 to Sue. The Monetary base will be
unchanged at $500, M1 will be 975 and M2 will be 975. The
required reserves will be $48.75
d. If both Fred and Sue want to withdraw their money at the same time
this would cause a run on the bank. What options does the bank
have?
The bank can borrow cash from another bank. The bank can
borrow reserves from another bank through the Fed Funds
market. The bank can borrow from the Federal Reserve. The
bank can sell the loan to another bank for cash. The bank can
recall the loan from Sue.
3. If excess reserves have increased by 100,000 dollars and the required
reserve ratio is 5% then what is the most that M1 can increase?
100,000/0.05 = 5,000,000
4. What is the money multiplier? The following graph shows the Monetary
Base, M1 and M2. Given a reason that might explain why M1 and the
Monetary Base lines crossed in 2008.
12000.0
10000.0
8000.0
6000.0
4000.0
BASE
2000.0
M1
0.0
Jan-00
M2
Nov-01
Sep-03
Jul-05
May-07
Mar-09
Jan-11
Source: Federal Reserve Bank of St. Louis/Board of Governors of the Federal Reserve
System/Board of Governors of the Federal Reserve System/FRED
The money multiplier is defined to be M1/MB. The lines crossed in
2008 when the federal reserve started making large scale asset
purchases and started paying interest on reserves. This meant that
banks were incentivized to keep excess reserves at the Fed rather
than lending them out. Another explanation is that even though the
Fed was significantly increasing the Monetary Base banks were risk
adverse and did not want to lend the excess out.
5. Using T-Accounts show the effect of the Fed reserve buying $1,000 of T-bills
from the Fred and Fred depositing the proceeds into his checking account at
Bank A. What effect will this have on reserves – both required and excess
(assume a reserve ratio of 10%)? What effect will this have on the Monetary
Base, M1 and M2?
We can assume that the Fed Reserve had nothing prior to purchasing the Tbills. We can also assume that the banking system had no assets or liabilities
and Fred simply had one asset the T-bill. Thus the before state looks like
Fred
Assets
T-bill
Liabilities
$1,000
Banking System
Assets
Reserves
Liabilities
0
Discount Loans
0
Federal Reserve System
Assets
Discount Loans
Liabilities


Reserves
After the purchase of the T-bill we have required reserves of 10% and excess
reserves of 90%. The check that was deposited into Fred’s checking account
is from the Federal Reserves so all proceeds are deposited into the bank’s
reserve account. The monetary base, M1 and M2 were all zero to begin with.
After the operation they all increase to $1,000.
Fred
Assets
Checking
Liabilities
$1,000
Banking System
Assets
Req. Reserves
$100
Liabilities
Checking
1,000
Exc. Reserves
$900
Federal Reserve System
Assets
T-bills

Liabilities
Reserves

6. In the previous problem if Bank A already had excess reserves at the Fed
would Bank A expect to be able to lend any additional excess reserves to
Bank B at a higher or lower rate than the rate seen before the Fed’s open
market operation?
The Federal Reserve has increased the amount of excess reserves in
the system. This will push the fed funds rate down so Bank A would
have expected to be able to lend excess reserves to Bank B at a higher
rate before the open market operation.