Question

Given the following:

C = 2000 + 0.75Yd

T = 300

I = 320

G = 300

X = 300

M=100



a) Determine the equilibrium level of income using expenditure and injection-leakage approach



b) Determine the value of C at equilibrium level of income.


c) Calculate the equilibrium level of income when there is an increase in investment of 100 using expenditure and multiplier approach.

Answer 1

a) Determine the equilibrium level of income using expenditure and injection-leakage approach

We have the data:

$C = 2000 + 0.75Yd\\[0.3cm] T = 300\\[0.3cm] I = 320\\[0.3cm] G = 300\\[0.3cm] X = 300\\[0.3cm] M=100$

The expenditure approach method is:

$$Y= C + I + G + (X - M)\\[0.3cm]$$

Therefore:

$$Y = 2000 + 0.75(Y - 300) + 320 + 300 + (300 - 100)\\[0.3cm] Y = 2820+ 0.75Y - 225 \\[0.3cm] 0.25Y = 2595\\[0.3cm] Y^* = \dfrac{2595}{0.25} = \color{blue}{10,380}$$

b) Determine the value of C at equilibrium level of income.

$$C = 2000 + 0.75(10,380 - 300)\\[0.3cm] \color{red}{C = 9,560}$$

c) Calculate the equilibrium level of income when there is an increase in investment of 100 using expenditure and multiplier approach.

The multiplier is given by:

$$k = \dfrac{\Delta Y}{\Delta I} = \dfrac{1}{1 - MPC}$$

In our question, MPC = 0.75. Therefore:

$$k = \dfrac{1}{1 - 0.75} = 4$$

When the investment increases by 100, the equilibrium income will increase by:

$$\Delta Y = 4\times \Delta 100\\[0.3cm] \Delta Y = 400$$

The new income is:

$$Y^{**} = 10,380 + 400 = \color{blue}{10,780}$$