Question

Given are the following information for the three sector economy,

C = 600 + 0.8Yd

I = 400

G = 200

T = 300

All values are in RM million.

A) Derive the:

i) consumption function after the tax. [2 marks]

ii) saving function after the tax. [2 marks]

B) Calculate the equilibrium income level for the above economy.

C) If the full employment level of income is RM6, 400 million, calculate the:

i) inflationary gap or deflationary gap.

ii) required tax changes to achieve a full employment level of national income.

D) If the government increases the government spending of RM80 million and reduces the tax by RM80 million at the same time, calculate the new equilibrium level for the above economy.

Answer 1

A)i) we will find it by the formula:

$C=C+mpc\times Yd$

Yd=Y-T

$Y=C+I+G$

$Y=C+mpc(Y-T)+I+G$

$Y=600+0.8Yd+400+200$

$Y=1200+0.8(Y-300)$

$Y-0.8Y=1200-240$

$0.2Y=960$

Y=4800

$C=C+mpc\times Yd=600+0.2(4800-300)=4200$

ii)

$Yd=Y-T=4800-300=4500$

$S=-C+(1-mpc)\times Yd=-600+(1-0.8)\times4500=300$

B)Yd=Y-T

$Y=C+I+G$

$Y=C+mpc(Y-T)+I+G$

$Y=600+0.8Yd+400+200$

$Y=1200+0.8(Y-300)$

$Y-0.8Y=1200-240$

$0.2Y=960$

Y=4800

C) i) deflationary gap=6400-4800=1600

ii)you need to find a tax multiplier

$mt=\frac{\Delta Y}{\Delta T}=\frac{6400-4800}{T-300}$

$-4=\frac{\Delta Y}{\Delta T}=\frac{6400-4800}{T-300}=\frac{1600}{T-300}$

$-4T+1200=1600$

T=-100

$mt=-\frac{mpc}{1-mpc}=-\frac{0.8}{1-0.8}=-4$

D) G=200+80=280

T=300-80=220

$Y=C+I+G$

$Y=C+mpc(Y-T)+I+G$

$Y=600+0.8Yd+400+280$

$Y=1200+0.8(Y-220)$

$Y-0.8Y=1200-176$

$0.2Y=1024$

Y=5120