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 value of the economy's multiplayer which is applicable to government spending and interpret it.

Answer 1

$Yd = Y - T$

$Y = C + I + G + X - M$

$Y = 100 + 0.75Yd + 200 + 150 + 200 - 50 - 0.25 Y$

$Y = 600 + 0.75(Y - T) - 0.25Y$

$1.25Y = 600 + 0.75(Y - 50 - 0.5Y)$

$1.25Y = 600 - 37.5 + 0.375Y$

$1.25Y - 0.375Y = 562.5$

$0.875Y = 562.5$

$Y = 642.85$

Now suppose government spending increased to 200. 

$Y = 100 + 0.75Yd + 200 + 200 + 200 - 50 - 0.25Y.$

$0.875Y = 612.5$

$Y =\frac{ 612.5}{0.875}$

$Y = 700$

If government spending increases by 50 then the Y have increased by

$(700-642.85) = 57.15$

Government spending multiplier $= \frac{∆Y}{∆G}$  

Government spending multiplier $=\frac{57.15}{50}=1.143$

An increase in one government spending will increase 1.43 of income.