Question

Consider the following information (amounts in Kshs. Billions)

 

C = 30 + 0.75Y

R = 20

T = 0.4Y

Z = 65

G = 45

 

Determine:

 

a) Equilibrium National Income (6 Marks)

 

b) Government deficit/surplus (7 Marks)

 

c) Additional government expenditure required to raise equilibrium national income by Kshs. 50 billion. (7 Marks)

 

Answer 1

$a)\\Given,\\C=30+0.75Y\\I=20\\T=0.4Y\\N_X=65\\G=45\\ Y=C+I+G+N_X\\Y=30+0.75Y+20+45+65\\Y-0.75Y=160\\0.25Y=160\\Y=\frac{160}{0.25}\\Y=640\\$

Equilibrium national income Y=640 kshs billion

b)

$Tax\space revenue\space T=0.4Y\\0.4(640)\\=256\space kshs\space billion$

$Government\space surplus=revenue-expenditure\\$

$=256-45\\=211\space kshs \space billion$

C)

In the consumption function, $C=30+0.75Y\\mpc=0.75Y\\multiplier\space R=\frac{1}{1-mpc}\\=\frac{1}{1-0.75}\\=\frac{1}{0.25}\\=4$

Also,

$Multiplier\space R=\frac{change\space in\space income}{change\space in\space expenditure}\\\implies R=\frac{\Delta Y}{\Delta G}\\4=\frac{50}{∆G}\\∆G=\frac{50}{4}\\∆G=12.5\space kshs\space billion.$

Additional government expenditure required to raise equilibrium income by kshs 50 billion is kshs12.5 billion