Answer to Question #190886 in Macroeconomics for Julia

Question

If consumption is C=100+0.75Yd

Taxes is T=50+0.5Y

Export is X=200

Import is M=50+0.25Y

Government spending is G=150

Investment is I=200. Y is domestic income and Y is private disposable income. Determine the equilibrium level of output/income.

Answer 1

Solution:

At equilibrium: Y = AD

Y = C + I + G + X – M

C = 100+0.75Yd = 100+0.75(Y – T) = 100+0.75(Y – (50+0.5Y)

 

Y = 100+0.75(Y – (50+0.5Y) + 200 + 150 + 200 – (50+0.25Y)

Y = 100 + 0.75Y – 37.5 – 0.375Y + 200 + 150 + 150 – 0.25Y

Y = 100 + 200 + 150 + 150 – 37.5 + 0.75Y – 0.375Y – 0.25Y

Y = 562.5 + 0.13Y

Y – 0.13Y = 562.5

0.88Y = 562.5

Y = $\frac{562.5}{0.88}$

Y = 642.86

The equilibrium level of output/income = 642.86