Question

Autonomous Consumption Spending: R110 million
Investment Spending: R160 million
Government Spending R360 million
Exports R260 million
Autonomous Imports R210 million
Marginal Propensity to Consume 4/5
Marginal Propensity to Import 1/10
Proportional Tax Rate 1/4
Full Employment Level of Income 1660

a) What is the Marginal Propensity to Save?
b) What is the value of the multiplier?
c) Calculate Autonomous Spending.
d) Calculate the equilibrium level of Income.
e) How much does Govt have to spend to increase the current equilibrium level of income to Full Employment?

Answer 1

Solution:

a.). Marginal propensity to save:

$MPC+MPS=1$

$MPS=1-MPC$

$MPS=1-0.8$

$MPS=0.2$

b.). Value of the multiplier:

$Multiplier=\frac{1}{1-[MPC \times (1-Tax \;rate)]-MPI }$

$Multiplier=\frac{1}{1-[0.8 \times (1-0.25)]-0.1 }$

$Multiplier=\frac{1}{1-[0.8 \times 0.75]-0.1 }$

$Multiplier=\frac{1}{1-0.6-0.1 }$

$Multiplier = \frac{1}{0.3 }$

$Multiplier = 3.33$

c.). Calculate Autonomous spending:

$A_{O} =C(1-t)+I+G+X-M(1-t)$

 $A_{O} =110(1-0.25)+160+360+[260-[210(1-0.25)]]$

$A_{O} =82.5+160+360+81.5$

$Autonomous \;Spending =R684 \;Million$

d.). Calculate the equilibrium level of income:

$Y=Multiplier\times (C(1-t) +I+G+X-M(1-t) )$

$Y=3.33(684)$

$Y=R2,277.72\;Million$

e.). How much does Govt have to spend to increase the current equilibrium level of income to Full Employment?

Full employment level of income = 1,660

$Y=C(1-t)+I+G+X-M(1-t)$

Interchange Y with the full employment level of income

$1660 = 82.5+160+G+81.5$

$1660=324+G$

$G=1660-324$

$G=R1,336\;Million$

The government have to spend R1,336 Million to increase the current equilibrium level of income to full employment. In other words increasing the government pending by R1,176 Million from its original value of R160 Million would increase the current equilibrium level of income to full employment.