Question

If consumption function is given as c= $25+0.8Y where yd=y-t ,tax rate=10% investment=$50 calculate equilibrium level of income as well as the government expenditure multiplier.

Answer 1

At equilibrium, Y=C+I. Therefore, we have

$Y=25+0.8(Y-0.1Y)+50\\[0.3cm] Y=75+0.64Y\\[0.3cm] Y-0.64Y=75\\[0.3cm] 0.36Y=75\\[0.3cm] Y^*=\boxed{\$208.33}$

The government expenditure multiplier is equal to

$\dfrac{\Delta Y}{\Delta G}=\dfrac{1}{1-mpc}\\[0.3cm] \dfrac{\Delta Y}{\Delta G}=\dfrac{1}{1-0.8}\\[0.3cm] \dfrac{\Delta Y}{\Delta G}=\boxed{5}$