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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Licensed to:

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