Question

In the expenditure–output or Keynesian cross model, the equilibrium occurs where the aggregate expenditure line (AE line) crosses the 45° line. Given algebraic equations for two lines, the point where they cross can be calculated easily. Imagine an economy with the following characteristics.

Y = Real GDP or national income

C = Consumption = 50 + 0.8Y

I = Investment = 200

G = Government spending = 100

1. Calculate the equilibrium level of income (Y)
2. Suppose G increases to 125 what is the new equilibrium level of income?
3. What level of G is needed to achieve a target income of 2150?
4. Given an MPC of 0.56 and there was an increase in autonomous government spending by $400 Million. How will this affect the equilibrium national income?

Answer 1

i) In equilibrium

Y = C + I + G

Y = 50 + 0.8Y + 200 + 100

Y = 350 + 0.8Y

Y - 0.8Y = 350

0.2Y = 350

Y = 1750

iI) Now G = 125

Again Y = C + I + G

Y = 50 + 0.8Y + 200 +125

= 375 + 0.8Y

Y - 0.8Y = 375

0.2Y = 375

Y = 1875

So new equilibrium level of income Y = 1875

The initial equilibrium level of income Y = 1750 when G = 100

Now targeted level of income is 2150

so change in income i.e. Y = 2150 - 1750

= 400

MPC = 0.8

Y/G = 1/(1 - MPC)  

400/G = 1/(1- 0.8)

400/G = 1/0.2

400/G = 5

5G = 400

G = 400/5

= 80

SO to achieve a target level of income 2150 , we need to increase government spending by 80 million

iv)

MPC = 0.56  

G = 400

Y/G = 1/(1 - MPC)

  Y/400 = 1/(1 - 0.56)

= 1/0.44

Y = 400/0.44

Y = 909.09

so an increase in government spending will increase equilibrium level of income by 909.09 million.