Question

. [No commas – hint: there is no answer greater than +$999.9, nor less than -$999.9.] All answers are in billions of dollars so there is no need to write that out.

For the following five questions, assume the following characteristics of the monetary transmission mechanism:

The money multiplier is 3.25

Interest rates will change by 2.5% for every $45 billion change in the money supply.

Investment will change by $76 billion for every 1.5% change in the interest rate.

Income will change by $14.3 billion for every $5.7 billion change in investment.

Identify the change in income when the Fed does the following:

1. Buys $35 billion in bonds.

2. Buys $18 billion in bonds.

3. Buys $4 billion in bonds.

4. Sells $12 billion in bonds.

5. Sells $22 billion in bonds.   

Answer 1

When Fed buys (sells) bonds, money supply (MS) (increases) decreases, which decraeses (increases) interest rate (r), thus increasing (decreasing) both investment (I) and GDP (Y).

Increase (decrease) in money supply (MS) = Amount of bond purchase (sell) x Money multiplier

(All numbers below are in $ billion)

(1)

Increase in MS = 25 x 3.25 = 81.25

Decrease in r = (81.25 / 45) x 2.5% = 4.51%

Increase in I = (4.51% / 1.5%) x 76 = 228.51

Increase in Y = (228.51 / 5.7) x 14.3 = 573.28

(2)

Increase in MS = 18 x 3.25 = 58.5

Decrease in r = (58.5 / 45) x 2.5% = 3.25%

Increase in I = (3.25% / 1.5%) x 76 = 164.67

Increase in Y = (164.67 / 5.7) x 14.3 = 413.12

(3)

Increase in MS = 4 x 3.25 = 13

Decrease in r = (13 / 45) x 2.5% = 0.72%

Increase in I = (0.72% / 1.5%) x 76 = 36.59

Increase in Y = (36.59 / 5.7) x 14.3 = 91.80

(4)

Decrease in MS = 12 x 3.25 = 39

Increase in r = (39 / 45) x 2.5% = 2.17%

Decrease in I = (2.17% / 1.5%) x 76 = 109.95

Decrease in Y = (109.95 / 5.7) x 14.3 = 275.84

(5)

Decrease in MS = 22 x 3.25 = 71.5

Increase in r = (71.5 / 45) x 2.5% = 3.97%

Decrease in I = (3.97% / 1.5%) x 76 = 201.15

Decrease in Y = (201.15 / 5.7) x 14.3 = 504.64