I. Consider the following model and answer related questions. Y = C + I + G + X
ID: 1195516 • Letter: I
Question
I. Consider the following model and answer related questions.
Y = C + I + G + X - IM
C = 49 + 0.9DI
I = 300 - 2000r
G = 800
T = 10 + 1/3(Y)
X - IM = 60
a. If fed decides to set the interest rate at r = 0.05, how much will be the
equilibrium GDP?
b. At that rate how much is budget deficit or surplus?
c. By how much GDP will change if government cuts tax rate from 1/3 to
0.20 and at the same time the Fed raises the interest rate from 0.05 to 0.06?
d. Now suppose net exports drops by 20. In order to offset its contractionary impact
on GDP, Fed decides to lower the rate of interest from 0.05 to 0.04 (just like
during Asian crisis). How much is your prediction for a change in GDP?
Explanation / Answer
(a)
Y = C + I + G + X - M
DI = Y - T = Y - 10 - (Y/3) = (2Y / 3) - 10
C = 49 + 0.9DI = 49 + 0.9[(2Y / 3) - 10]
= 49 + 0.6Y - 9
C = 40 + 0.6Y
So,
Y = 40 + 0.6Y + 300 - 2,000r + 800 + 60
(1 - 0.6)Y = 1,200 - 2,000r
0.4Y = 1,200 - 2,000r
Y = 3,000 - 5,000r
When r = 0.05,
Y = 3,000 - (5,000 x 0.05) = 3,000 - 250 = 2,750
(b)
T = 10 + (Y/3) = 10 + (2,750 / 3) = 10 + 917 = 927
G = 800
Budget surplus = T - G = 927 - 800 = 127
(c)
New T = 10 + 0.2Y
New r = 0.06
DI = Y - T = Y - 10 - 0.2Y = 0.8Y + 10
C = 49 + 0.9DI = 49 + 0.9(0.8Y - 10)
C = 49 + 0.72Y - 9
C = 40 + 0.72Y
Y = 40 + 0.72Y + 300 - 2,000r + 800 + 60
(1 - 0.72)Y = 1,200 - 2,000r
0.28Y = 1,200 - 2,000r = 1,200 - (2,000 x 0.06) = 1,200 - 120 = 1,080
Y = 1,080 / 0.28 = 3,857
So, change in GDP = 3,857 - 2,750 = 1,107
(d)
If NX decreases by 20, from part 9a):
0.4Y = 1,200 - 20 - 2,000r = 1,180 - 2,000r
Y = 2,950 - 5,000r
When r = 0.04,
Y = 2,950 - (5,000 x 0.04) = 2,950 - 200 = 2,750
Change in GDP = 2,750 - 2,750 = 0
So GDP remains unchanged.
Note: It has been assumed that each sub-question is independent.