Question

Suppose that for a particular economy and period, investment was equal to 100, consumption (C) was given by the consumption function. C = 25 + 0.8YD Where YD is disposable income and Y is GDP. a) What is the level of equilibrium income (Y)? b) What is the value of the government expenditure multiplier (ΔY/ ΔG)? Of the tax multiplier (ΔY/ ΔT)? c) Suppose that investment declined by 40 units to a level of 60. What will be the new level of equilibrium income? 

Answer 1

Solution:

a.). At equilibrium income: Y = AE

YD = Y - T

Y = C + I + G            

Y = 25 + 0.8 $(Y-T)$ + 100 + 75

Y = 25 + 0.8 $(Y-100)$ + 100 + 75

Y = 25 + 0.8Y – 80 + 100 + 75

Y = 25 + 100 + 75 – 80 + 0.8Y

Y = 120 + 0.8Y

Y – 0.8Y = 120

0.2Y = 120

Y = $\frac{120}{0.2}$ = 600

The level of equilibrium income = 600

ii.). Government expenditure multiplier = $\frac{1}{1-MPC}$

MPC = 0.8

Multiplier = $\frac{1}{1-0.8}$ =$\frac{1}{0.2}$ = 5

The value of the government expenditure multiplier = 5

The tax multiplier = $\frac{-MPC}{1-MPC}$

$\frac{-0.8}{1-0.8} = \frac{-0.8}{0.2} = -4$ -0.8/1 – 0.8 = -4

The value of the tax multiplier = -4

b.). The new level of equilibrium income:

Y = C + I + G            

Y = 25 + 0.8 $(Y-T)$ + 60 + 75

Y = 25 + 0.8 $(Y-100)$ + 60 + 75

Y = 25 + 0.8Y – 80 + 60 + 75

Y = 25 + 60 + 75 – 80 + 0.8Y

Y = 80 + 0.8Y

Y – 0.8Y = 80

0.2Y = 80

Y = $\frac{80}{0.2} = 400$

The new level of equilibrium income = 400