Answer to Question #147583 in Macroeconomics for Ahmed Samsodien

Question

Use the information to answer the questions that follow:
C = 450 + 0.4Y
I = 350
G = 150
X = 70
Z = 35 + 0.1Y
T = 0.15Y
Yf = 1550


Q.2.5 Calculate what the new equilibrium income should be if the government of this
country decides to cancel all taxes, implying the tax rate would now be 0%.
(6)
Q.2.6 Before the government decreased the tax rate, how much of government
spending was required to bring the economy to full employment?

Answer 1

Q.2.5

Tax is 0 now. Other components are unchanged.

New aggregate spending = C + I + G + NX

= 450+ 0.4(Y - 0) + 350 + 150 + 70 – 35 - 0.1Y

= 985 + 0.3Y

At equilibrium Y=AE

Y = 985+0.3Y

Y - 0.3Y = 985

Y* $= \frac{985}{0.7} = 1407.14$

Q.2.6

For this we need the initial aggregate spending with taxes.

AE = 450 + 0.4(Y - 0.15Y) + 350 + 150 + 70 - 35 - 0.1Y

= 985 + 0.4×0.85Y - 0.1Y

= 985 + 0.34Y - 0.1Y

= 985 + 0.24Y

So equilibrium

Y = 985 + 0.24Y

0.76Y = 985

Y** = 1296.05

Gap between initial output and full employment output is Yf - Y** = 253.95

Multiplier for the economy $= \frac{1}{leakages} = \frac{1}{0.76} = 1.31$

So a unit change in government spending will raise the output by 1.31 times. In order to close output hole of 253.95 and rise in government spending is needed by the measure of $\frac{253.95}{1.31} = 193.85$ . The absolute government spending should be 343.85.