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C 5 0.9(Y 2 T)
The question is: which effect is larger? The answer is
C 5 0.9[Y 2 ( 1„3 )Y]
found by seeing which tax change is larger, since C
depends on DI 5 Y 2 T. At a GDP of Y 5 10,000 billion, a C 5 0.9[( 2„3 )Y]
two percentage point cut in the income-tax rate reduces
C 5 0.6Y
tax receipts by $200 billion, which is larger than the
Y 5 0.6Y 1 100 1 540 2 40
$100 billion fixed-tax increase. So C, and hence equilibrium
Y 5 0.6Y 1 600
GDP on the demand side, rises.
0.4Y 5 600
Answers to Appendix B Questions Y 5 (1/0.4) 3 600
Y 5 2.5 3 600 5 1,500
1. Y 5 C 1 I 1 G 1 (X 2 IM)
Budget deficit 5 G 2 T
C 5 120 1 0.8DI
5 540 2 [( 1„3 ) 3 1500]
DI 5 Y 2 T
5 540 2 500
DI 5 Y 2 (200 1 0.25Y)
5 40
DI 5 0.75Y 2 200
(b) Since the budget deficit in part a is 40, the government
C 5 120 1 0.8(0.75Y 2 200)
would reduce its purchases by 40, to 500. Repeating
C 5 120 1 0.6Y 2 160 the steps above, but now with G 5 500:
C 5 0.6Y 2 40 Y 5 0.6Y 1 100 1 500 2 40
Y 5 0.6Y 2 40 1 320 1 480 2 80 Y 5 0.6Y 1 560
Y 5 0.6Y 1 680 0.4Y 5 560
0.4Y 5 680
Y 5 (1/0.4) 3 560
Y 5 (1/0.4) 3 680
Y 5 2.5 3 560 5 1,400
Y 5 2.5 3 680 5 1,700
Budget deficit 5 G 2 T
Equilibrium GDP is 1,700.
5 500 2 [( 1„3 ) 3 1,400]
There are three different ways to find the multipliers, any
5 500 2 4662„3
one of which is correct.
5 331„3
for government purchases:
GDP falls by 100, to 1,400. That drop reduces tax
1. Note from the preceding equations that equilibrium
receipts, which are one-third of GDP, by 331„3 (to 4662„3).
GDP is 2.5 times all autonomous spending. Since G is
So in the new equilibrium, the deficit has fallen by
autonomous spending, the multiplier for G is 2.5.
only 62„3 (to 331„3), not by the full 40 in lower spending.
2. Raise G from 480 to 481. Working through the algebra
Although G fell by the amount of the deficit, this in
above, this comes to 0.4Y 5 681, which implies that
turn caused Y to fall, which in turn lowered taxes,
Y 5 1,702.5. So the increase in G of 1 has raised Y by
and the deficit persisted.
2.5, and the multiplier is 2.5.
3. From the formula in the appendix, the multiplier is
CHAPTER 12:
1/1 2 b(12 t) 5 1/[1 2 0.8(1 2 0.25)] 5 1/[1 2 0.8(0.75)]
Money and the Banking System
5 1/(1 2 0.6) 5 1/0.4 5 2.5
for fixed taxes: 1. Under those conditions, the money multiplier is 1/.10, or
1. Note that a rise in fixed taxes decreases GDP (so the 10, so an infusion of $12 million into reserves will support
sign of the multiplier is negative) and that it increases an increase in money of $120 million.


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Appendix 401



3.


(c)
(a) (b)
Assets Liabilities
Assets Liabilities Assets Liabilities
HomeTown Bank
Reserves 2100 Deposits 2100 Reserves Deposits
1100 1100
Reserves 2500 Deposits 2500
Big City Bank
Reserves 1500 Deposits 1500
All Banks
Reserves Deposits
no change no change


5. (a) A $5 billion increase in the bank reserves lowers inter-
CHAPTER 13: est rates by 2.5 percentage points.
Managing Aggregate Demand: (b) A reduction in interest rates of 2.5 percentage points
Monetary Policy stimulates $75 billion of new investment spending.
(c) Aggregate demand rises by $150 billion.
1. In each case, there is $60 billion in the form of cash in
circulation, and the rest of the money supply is held in (d) The aggregate supply curve is horizontal, and GDP
bank deposits, backed by $60 billion in reserves. The rises by $150 billion.
total money supply is calculated as follows: 7. There are several ways to solve this problem. Investment
(I ) can be found at the three different interest rates, and
then equilibrium GDP can be calculated three times
Reserve Money Total using the three different values for I. Alternatively, a
Ratio Multiplier Deposits Money Supply more general solution just works with the symbol r for
the interest rate:
10% 10 600 660
Y5C1I
12.5% 8 480 540
16 2/3% 6 360 420 C 5 300 1 0.75Y
I 5 1,000 2 100r
Y 5 300 1 0.75Y 1 1,000 2 100r
The M1 money supply always exceeds total deposits by
Y 5 1,300 1 0.75Y 2 100r
the $60 billion in cash outside banks.
0.25Y 5 1,300 2 100r
3. Note: all figures are in billions of dollars.


Y 5 4(1,300 2 100r)
Bill Gates Bank of America Federal Reserve
Y 5 5,200 2 400r
Assets Liabilities Assets Liabilities Assets Liabilities
Therefore:
Deposit (a) If r 5 0.02, Y 5 5,192.
at B of A 15 no change Reserves 15 Deposits 15 Bonds 15 Bank
(b) If r 5 0.05, Y 5 5,180.
Bonds 25 reserves 15
(c) If r 5 0.1, Y 5 5,160.

The Fed simply creates the $5 billion (in the form of
CHAPTER 14:
bank reserves) to buy the bonds. In the long run, it
The Debate over Monetary and
makes no difference whether the Fed buys the bonds
Fiscal Policy
from a bank or from an individual. In this case, Bank of
America™s $5 billion in new reserves are offset by $5 bil-
1. Based on recent data, the velocity of money in the United
lion in new deposits, so that not all of the new reserves
States, for M1, is about 9.5“10. Students will probably cal-
are excess reserves, whereas if the Fed had bought the
culate a much higher velocity for themselves.
bonds from Bank of America directly there would have
been no change in deposits, and all the new reserves 3. In Figure 1, M0S0 is the initial money supply. The
would have been excess. In the long run, however, the demand for money falls from M0D0 to M1D1; as a conse-
new reserves of $5 billion will support the same increase quence, the quantity of money in the economy falls from
in deposits. Why? Because in this case, the original M0 to M1, and the interest rate falls from r0 to r1. The Fed
transaction between the Fed and Bill Gates already has three choices.
creates $5 billion in new deposits.




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Licensed to:
Appendix
402



(a) It can accept the new money supply and interest rate. public holds in currency (zero in part (a), 0.2D in part
(b)). In part (a), the monetary base (B 5 R 1 C ) and
(b) It can restore the previous interest rate, r0, by lower-
bank reserves are identical because C 5 0. So all $10
ing the money supply curve to M1S1. This will further
billion in new monetary base goes into bank reserves,
reduce the quantity of money to M2.
where it supports $50 billion in new deposits. But in
(c) If it follows a monetarist policy, it can restore the
part (b), half of the new $10 billion in monetary base
original quantity of money, M0, by increasing the sup-
gets absorbed by currency holdings, leaving an
ply curve to M2S2. This will have the effect of reduc-
increase of only $5 billion in bank reserves”which
ing the interest rate still further, to r2.
supports only $25 billion in new deposits.

F I GU R E 1
CHAPTER 15:
Budget Deficits in the Short and
S1 S0 S2
M0
Long Run
M1 1. The budget deficit is an annual-flow concept. It is the
excess of government expenditures over government
revenues in a given year. The national debt is an accu-
r0
mulated stock of debt. It is increased each year by the
Interest Rate




deficit or reduced by the surplus. If the deficit becomes
a surplus, the debt will fall (although the accumulated
r1
debt may still be very large).
r2
3. Expansionary monetary policy will raise GDP, and this
will raise tax receipts. The lower interest rates will also
D0
decrease the government™s interest payments. Both
changes will reduce the government™s budget deficit. If
M1 M0 D1
M2 the government tries to counteract the Fed™s positive
effect on aggregate demand, it will institute a more
M2 M1 M0
contractionary fiscal policy by decreasing government
Money
spending or raising taxes, or both. The deficit will shrink
still more.
5. (a) Since people hold no currency, M 5 D. Both M and D
will therefore be (1/0.2) 3 $50 billion 5 5 3 $50 bil-
CHAPTER 16:
lion 5 $250 billion. If the Fed increases reserves to
The Trade-Off between Inflation
$60 billion, M and D will rise to $300 billion instead.
and Unemployment
The money multiplier is therefore $50/$10 5 5.
(b) Now, since people hold currency, M 5 C 1 D 5 1.2D,
1. Figure 1 shows that when the aggregate supply curve is
because C 5 0.2D. The $50 billion monetary base (B 5
vertical, shifting aggregate demand curves change only
50) must now serve two purposes: bank reserves plus
the price level, not output.
currency, B 5 R 1 C. Since R 5 0.2D (reserve require-
ments) and C 5 0.2D (currency holdings), this means
B 5 0.4D. With B 5 50, D 5 125 now. But now people F I GU R E 1
also hold 0.2 3 $125 5 $25 billion in currency, so the
money supply is M 5 D 1 C 5 $150. Notice that the
D1
money supply is much less than in part (a). The rea-
S
son is that half of the monetary base is now used as
currency rather than as bank reserves. (Notice that D0
required reserves are 0.2 3 $125 5 $25 billion and
cash holdings are also $25 billion.) P1
Price Level




When the Fed increases the monetary base to $60 bil-
lion, the equation B 5 R 1 C now becomes 60 5 .4D,
P0
so deposits rise to D 5 $150 billion ($60/0.4). With
D1
an additional C 5 $30 billion in cash in circulation
(0.2 3 $150), the money supply will rise to M 5 D 1
C 5 $150 1 $30 5 $180. So the money multiplier is
D0
just $30/$10 5 3 now.
S
(c) As the monetary base increases, the money supply M
increases as well. However, the size of the increase in Y0
the money supply depends both on the required GDP
reserve ratio (0.2) in the example and how much the




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Licensed to:

Appendix 403



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