Eco exam

Problem Set 4 Solutions

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Friday, May 1st

1. (a) The “dual mandate” of the Federal Reserve of the United States is to maximize

employment while maintaining stable inflation.

(b) What are some of the priorities of other central banks? Looking on their websites,

identify the goals of each of the following central banks.

i. The Bank of England has the mission “...to promote the good of the people

by maintaining monetary and financial stability.” The bank does this through

supervision of banks and setting the interest rate through monetary policy.

ii. The Bank of Canada works “...to preserve the value of money by keeping inflation

low and stable.”

iii. The European Central Bank has the mission “...to serve the people of Europe

by safeguarding the value of the euro and maintaining price stability.”

(c) It seems as though the Bank of England has a similar mission in setting monetary

policy to maintain stability in the economy through the interest rate at which banks

can loan. Although it is not said explicitly, this has the effect of balancing employ-

ment and inflation, just like the US Federal Reserve. Although all banks share some

form of the Fed’s “dual mandate,” the Bank of Canada and the European Central

Bank are explicit that price stability is their priority.

(d) San Diego is in Federal Reserve district twelve.

i. The Federal Reserve Bank that supports the twelfth district is located in San

Francisco.

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ii. The twelfth district includes Alaska, Arizona, California, Hawaii, Idaho, Nevada,

Oregon, Utab, and Washington. The territories of American Samoa, Guam, and

the Northern Mariana Islands are also supported by the twelfth district.

2. Suppose the money supply is $2.25 trillion dollars and the reserve ratio is 10%. As a

result of economic trends the, Federal Reserve decides it wants to increase the money

supply to $2.5 trillion.

(a) If the Fed is increasing the money supply, it is doing so in order to stimulate em-

ployment. The increase in the money supply is of course in tension with its other

mandate, which is to control inflation.

(b) The Fed will buy federal bonds in the open market, exchanging currency for financial

assets in order to put more money into the economy.

(c) If banks hold no excess reserves, then every dollar of currency put into the economy

increases money supply by the money multiplier, 1 0.1

= 10. The Fed must then

increase currency by only 10% of the desired increase of money supply. Since the

desired increase is $250 billion, the cash amount of bonds they would buy is $25

billion.

(d) If banks actually hold 25% of deposits in reserves, then then the money multiplier

is 1 0.25

= 4, so that every dollar of bonds sold by the Fed will increase deposits by

4 dollars. The Fed would then buy 250 4

billion in bonds, so the Fed’s open market

operation would be to buy $62.5 billion in bonds.

(e) If the effective reserve ratio is 15%, then the injection of $62.5 by the Fed would

increase money supply (in billions of $) by

62.5 · (

1

0.15

) =

( 1250

3

) ≈ 416.67

Thus the money supply has increased more than the desired $250 billion. The Fed

would like to reduce the money supply by approximately $416.67b−$250b = $166.67b. In order to decrease the money supply, the Fed would sell bonds. With a reserve

ratio of 15%, the Fed would sell (in billions of $)( 1250

3 − 250

) · 0.15 =

( 500

3

) · 0.15 = 25

So the Fed would sell $25 billion of treasury bills.

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(f) If the Fed knew the effective reserve ratio would be 15% upon implementing monetary

policy, it would have only injected $250b · 0.15 = $37.5b. Between (d) and (e), the Fed bought $62.5 billion in bonds and sold $25 billion, with a net result of buying

$37.5 billion. This exactly matches what the Fed would have done had it known the

effective reserve ratio would be 15%.

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