Question

Given the following information

C = 10 + 0.9Yd I* = 25 + 0.8/i G = 25
t = 0.10

Ms = 120
Md = 0.3NP + 2/i
reserve requirement ratio: 0.20

a) State the equilibrium conditions for BOTH the money market and commodity market. b) Solve for the equilibrium rate of interest and NP.
c) What is the level of desired investment?
d) Assuming that banks hold no excess reserves, and that the money supply changes in an amount equal to the maximum possible, what would be the change in the money supply if the Federal reserve bought $20 worth of Treasury notes. (Is this an increase or decrease).

e) Solve for the new equilibrium rate of interest, NP and desired level of investment.

Answer 1

(a)

In money market equilibrium,

Md = Ms

0.3NP + (2/i) = 120

NP = [120 - (2/i)] / 0.3..........(1)

In commodity market equilibrium,

NP = C + I + G

NP = 10 + 0.9 x (NP - 0.1NP) + 25 + (0.8/i) + 25 [since Yd = NP - T = NP - 0.1NP because T = t x NP]

NP = 60 + 0.9 x 0.9NP + (0.8/i)

NP = 60 + 0.81NP + (0.8/i)

0.19NP = 60 + (0.8/i)

NP = [60 + (0.8/i)] / 0.19.........(2)

(b)

Equating (1) and (2):

[120 - (2/i)] / 0.3 = [60 + (0.8/i)] / 0.19

19 x [120 - (2/i)] = 3 x [60 + (0.8/i)]

2280 - (38/i) = 180 + (2.4/i)

40.4/i = 2100

i = 0.0192

NP = [120 - (2/0.0192)] / 0.3 = (120 - 103.96)/0.3 = 16.04/0.3 = 53.47

(c)

I = 25 + (0.8/0.0192) = 25 + 41.67 = 66.67

(d)

Fed's purchase of bonds will increase money supply.

Increase in money supply = Bond purchase / Reserve ratio = 20/0.2 = 100

(e)

New Ms = 120 + 100 = 220

Setting Md = New Ms

0.3NP + (2/i) = 220

NP = [220 - (2/i)] / 0.3..........(3)

Equating (2) and (3),

[220 - (2/i)] / 0.3 = [60 + (0.8/i)] / 0.19

19 x [220 - (2/i)] = 3 x [60 + (0.8/i)]

4180 - (38/i) = 180 + (2.4/i)

40.4/i = 4000

i = 0.0101

NP = [220 - (2/0.0101)] / 0.3 = (220 - 198.02)/0.3 = 21.98/0.3 = 73.27

I = 25 + (0.8/0.0101) = 25 + 79.21 = 104.21