Answer to Question #69896 in Macroeconomics for Lesya

Question

Autonomous spending 100mil, Investment spending 200mil, government spending 150mil, and autonomous net exports 150mil. marginal propensity to consume to be 3/5 and proportional tax rate 1/6. the full employment level of income to be 1500mil. calculate the change in government spending required attaining full employment

Answer 1

C0 = 100mil, I = 200mil, government spending 150mil, and NE = 150mil, c = 0.6, t = 1/6, Yp = 1500mil.
Y = C + I + G + NX,
C = C0 + c*(1 - t)*Y = 100 + 3/5*5/6*Y = 100 + 0.5Y,
Y = 100 + 0.5Y + 200 + 150 + 150,
0.5Y = 600,
Y = 1200mil.
Yp - Y = 1500 - 1200 = 300mil.
m = 1/(1 - c) = 1/0.4 = 2.5.
So, the change in government spending required attaining full employment is:
300/2.5 = 120mil.