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Section: T.A. Name 180.101 ELEMENTS OF MACROECONOMICS Fall, 2011 Problem Set #5 Prof. Louis J. Maccini Answer Key INSTRUCTIONS: Above, write your name, section number and T. A. name. Answer each
question in the Space provided, or on the back of the same sheet. 1. Suppose the Fed purchases $5 billion worth of government bonds from Bill Gates, who
banks at the Bank of America in San Francisco. Show the effects on the balance sheets of the Fed, the Bank of America, and Gates. Does it make any difference if the Fed buys
bonds from a bank or an individual? BILL GATES
Assets Liabilities
Deposit at +5 no change
Bank of America
Bonds —5
BANK OF AMERICA
Assets Liabilities
Reserves +5 Deposits +5
FEDERAL RESERVE
Assets Liabilities Bonds +5 Bank Reserves +5 In the long run, it makes no difference whether the Fed buys bonds from a bank or an
individual. Initially in this case, Bank of America’s new reserves are offset by new
deposits, so that not all of the new reserves are excess, whereas if the Fed had bought the
bonds from Bank of America directly there would have been no change in deposits, and
all the new reserves would have been excess. In the long run, however, the new reserves
of $5 billion will support the same increase in deposits. When the Fed buys bonds from
Bill Gates, deposits increase by $5 billion, and depending on the required reserve ratio
the increase in reserves will create more deposits through the deposit expansion process.
When BOA sells the bond, deposits do not increase initially, but reserves increase by $5
billion, and, since deposits did not increase immediately, all the increase in reserves is
excess reserves. But, BOA will eventually lend out the $5 billion in excess reserves, and
this will result in an increase in deposits through the deposit expansion process. Since in
both cases there is an injection of reserves of $5 billion into the banking system, in the
long~run there will be no difference in the ultimate increase in deposits under the two
assumptions. 2. Explain and show using appropriate diagrams what a $5 billion increase in bank
reserves will do to real GDP under the following set of assumptions: a. Each $1 billion increase in bank reserves reduces the rate of interest by 0.5 percentage
point. b. Each 1 percentage point decline in interest rates stimulates $30 billion worth of new
investment. 0. The multiplier for investment is 2. d. The aggregate supply curve is so ﬂat that prices do not rise noticeably when demand
increases. If each $1 billion increase in bank reserves reduces the rate of interest by 0.5 percentage
point (from assumption a), a $5 billion increase in bank reserves will reduce the interest
rate by 2.5 percentage points. lfeach 1 percentage point decline in interest rates
stimulates $30 billion worth of new investment (from assumption b), the decline in
interest rates of 2.5 percentage points will increase investment by $75 billion. If the
multiplier for investment is 2 (from assumption 0) the increase in investment will
increase aggregate demand by $150 billion. If the aggregate supply curve is horizontal
(from assumption d) the increase in real GDP would equal $150 billion. See the graphs
below for the diagrammatic representation of this process: 3. Consider an economy in which government purchases and taxes are zero, the
consumption function is C = 300 + 0.75 Y
and investment spending (I) depends on the rate of interest (r) in the following way:
I= 1000  1001 Find the equilibrium GDP if the Fed makes the rate of interest (a) 2 percent (1:002),
(b) 5 percent, and (c) 10 percent. Provide an economic explanation of any differences
that arise in the equilibrium GDP at different interest rates. Draw a diagram that
illustrates the results. Since government purchases and taxes are zero we have Y=C+I. We therefore have
Y=300+0.75Y+1000—1 001‘. Collecting all the Y terms on the left hand side of the equation
we get: 0.25Y=l300100r. This implies Y=4(1300—1001‘)=5200—400r
Given this equation we can calculate equilibrium GDP for different values of r.
a) ifr=0.02 we have Y = 5200 ~ 400 x 0.02 = 5192
b) ifr=0.05 we have Y = 5200 — 400 x 0.05 = 5180
c) ifr=0.10 we have Y = 5200— 400 x 0.10 = 5160
Economic explanation: The higher is the interest rate, the lower is the level of investment spending, the lower is the level of aggregate planned expenditure, and therefore the lower
is the equilibrium level of real output and income. , ( \/ l; i I; I ,, \
E7380 (Va.03.
Ex?” (r: .0?) 1’: SL CV”)— . l0) e/‘i’ ...
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 Fall '08
 Maccini
 Macroeconomics

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