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 surplus or deficit in the government budget at equilibrium

Answer 1

C=100+0.75Yd

T=50+0.5Y

X=200

M=50+0.25Y

G=150

I=200.

Now, 

$C = 100+0.75Yd$

$= 100+0.75(Y-T)$

  $= 100+0.75[Y-(50+0.5Y)]$

$=100+0.75(Y-50-0.5Y)$

$= 100+0.75(0.5Y-50)$

  $Y = C+I+G+ (X-M)$

$=> Y = 100+0.75(0.5Y-50) + 200+ 150 + ( 200 - 50 - 0.25Y)$

$=> Y = 100 + 0.375Y - 37.5 + 200+ 150 + 150 - 0.25Y$

$=> Y - 0.375Y + 0.25Y = 562.5$

$=> 0.875Y = 562.5$

$=> Y = 642.86$

Hence $Y = 642.86$

Therefore, $T = 50+0.5Y$

        $T = 50+(0.5\times642.86)$

         $T = 371.43$

Budget$= T - G$

     $= 371.43 - 150$

      $= 221.43$

Hence there is the surplus in the government budget at equilibrium as Government spending is positive.