Question

a)           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:

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

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

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

 

Answer 1

$Solution$

$1)indogenous \ variables\\ Y=C+I+G\\Y=3000 +0.75 (Y-1000)+4750+1500\\ Y=3000 +0.75 Y-750+4750+1500\\Y=3000 +0.75 Y-750+4750+1500\\Y-0.75Y=8500\\ 0.25Y=8500\\Y=34000\\C=3000+0.75(34000−1000)\\ C =27750\\ Therefore \\ Y=34000\\C=27750$

2)when governments expenditure increases by 50

$Y=C+I+G\\Y=3000 +0.75 (Y-1000)+4750+1550\\Y=3000 +0.75 Y-750+4750+1550\\Y=3000 +0.75 Y-750+4750+1550\\Y-0.75Y=8550\\ 0.25Y=8550\\=\dfrac{8550}{0.25}\\Y=34200\\ C=3000+0.75(34200−1000) C =27900\\ Therefore \\Y=34200\\C=27900$

3)Governments spending multiplier

$The \ multiplier \ is \ calculated \ as\\ \dfrac{\Delta Y}{\Delta G}=\dfrac{1}{1-mpc}\\$

$Mpc =0.75\\Therefore\\ \dfrac{\Delta Y}{\Delta G}=\dfrac{1}{1-0.75}\\ \dfrac{\Delta Y}{\Delta G}=4$

The multiplier is 4