Principles Of Macroeconomics ECO 102 Problem 1

Problem: Take a closed economy having the consumption function: C = 100 + 0.8(Y - T) and a planned investment of 500.The government's expenditure and tax revenue are both equal to 200.Assuming there are no imports or exports,

Calculate the equilibrium level of national income.

Solution:

To find the equilibrium level of national income, we need to use the Keynesian Cross method. The Keynesian Cross is a graphical tool used to determine the equilibrium level of national income in an economy by showing the intersection of aggregate expenditures and production. 

Step 1: 

Write out the equation for planned expenditure (PE):

PE = C + I + G where C is consumption, I is investment, and G is government expenditure. 

Substituting in the values given in the problem, we have: PE = (100 + 0.8(Y - T)) + 500 + 200 Simplifying the equation, we get: PE = 800 + 0.8Y - 0.8T

 Step 2: 

Write out the equation for actual expenditure (AE): AE = Y where Y is national income. 

Step 3: 

Set PE equal to AE and solve for Y: AE = PE 

Y = 800 + 0.8Y - 0.8T Y - 0.8Y = 800 - 0.8T 0.2Y = 800 - 0.8T Y = (800 - 0.8T)÷0.2

Step 4:

Substitute in the values given in the problem: 

Y or Equilibrium national income =

(800 - (0.8×200)÷0.2 Y = (800 - 160)÷0.2 Y = 3200 

Therefore, the equilibrium level of national income for this closed economy is 3200.