Question

Consider the following model of National Income determination

              C= 3000 +0.75 (Y-T)

              T=1000

               I= 4750

              G=1500

              Y=E=C+I+G

Required:

Solve for the equilibrium values for all the endogenous variables              (4 mks)

Suppose government expenditure increases by 50 find the new equilibrium values of the endogenous variables                                                (4 mks)

Calculate the value of the government spending multiplier                   (2 mks)

Answer 1

Solve for the equilibrium values for all the endogenous variables

 $Y=C+I+G\\[0.4cm] Y=3000 +0.75 (Y-1000)+4750+1500\\[0.4cm] Y=3000 +0.75 Y-750+4750+1500\\[0.4cm] Y=3000 +0.75 Y-750+4750+1500\\[0.4cm] Y-0.75Y=8500\\[0.4cm] 0.25Y=8500\\[0.4cm] Y^*=\dfrac{8500}{0.25}\\[0.4cm] Y^*=34000$

$C= 3000 +0.75 (34000-1000)\\[0.4cm] C^*=27750$

Calculate the value of the government spending multiplier 

The multiplier is calculated as

$\dfrac{\Delta Y}{\Delta G}=\dfrac{1}{1-mpc}\\[0.4cm]$

From the consumption function, $mpc=0.75$ . Therefore

$\dfrac{\Delta Y}{\Delta G}=\dfrac{1}{1-0.75}\\[0.4cm] \dfrac{\Delta Y}{\Delta G}=4$