1. The Keynesian Model of Income Determination in a Four Sector Economy
Determination of Equilibrium income or output in a Four Sector
The inclusion of the foreign sector in the analysis influences the level of aggregate demand through the export and import of goods and services. Hence it is necessary to understand the factors that influence the exports and imports.

2. The volume of exports in any economy depends on the following factors:
The prices of the exports in any domestic economy relative to the price in the other countries.
The income level in the other economies.
Tastes, Preferences, customs and traditions in the other economies.
The tariff and trade policies between the domestic economy and the other economies.
The domestic economy’s level of imports.

3. Illustration -1
The fundamental equations in an economy are given as:
Consumption Function                  =   Yd
Investment                 =          300
Tax                                                =          120
Government Expenditure             =          200
Exports                                        =          100
Imports                                         =          0.05Y

4. Find the following.
The equilibrium level of income
The net exports
Solution
Here the consumption function is         C         =          Yd
    C         =          (Y – T)
    C         =          (Y – 120)

5. The equilibrium condition is given as
Y         =          C + I + G + X – M Thus,
Y =  (Y – 120) – 0.05Y
Y =  Y – – 0.05Y
Y – 0.8Y+ 0.05Y        =          704
       Y              =          704
                   Y         =          704 / 0.25
The equilibrium level of income is 2,816.

6. There is a deficit in the balance of trade.
        Import M   = 0.05Y = 0.05 (2,816)
                                   =      140.8
Net Exports:     X – M   =        100 – 140.8
                         X - M   =         
There is a deficit in the balance of trade.

7. Illustration- 2
For Credentials of the numerical illustration 1, find the following:
The increase in the income if both government expenditure and tax increased by an amount of 20 each.
The net exports, if exports increased by an amount of 60.
Solution
If both government expenditure and tax increased by an amount of 20 each, G = 220 and Tax = 140

8. The equilibrium condition is given as
Y = C + I + G + X – M
Thus
Y     =   (Y - 140) – 0.05Y
Y         =          Y – – 0.05Y
 Y – 0.8 Y Y      =          708
                  Y  =          708
                  Y       =          708 / 0.25
                  Y =          2,832
The equilibrium level of income is 2,832. Hence, there is an increase in the income by 16.

9. 2. If the exports increased by an amount of 60, X = 160
The equilibrium condition is given as Y = C + I + G + X – M
Thus, Y =  (Y – 120) – 0.05Y
Y         = 700 – Y – 0.05Y
Y         =  Y
Y – 0.75Y       =          764

10. 0.25 Y  =          764
  Y         =          764 / 0.25
The equilibrium level of income is 3,056.
Imports M = 0.05 Y = 0.05 (3,056) = 152.8
Net Exports X – M = 160 – = 7.2
       X – M             =          7.2
There is a surplus in the balance of trade.

11. Illustration-3
The equations in an economy are given as: C = Yd, Investment function I = 320 Tax = 300 Government Expenditure = 300 Exports = 300 – 0.05Y

12. You are required to ascertain the following:
Find the equilibrium level of income
Find the net exports at equilibrium level of income
Find the equilibrium level of income and the net exports when there is an increase in investment from 320 to 340
Find the equilibrium level of income and the net exports when the net export function becomes 280 – 0.05Y

13. Solution
(1) The consumption function is
C = Yd
C = (Y – T)
   C = (Y – 300)
The equilibrium condition is give as Y = C + I + G + X – M
Thus, Y =   (Y – 300) – 0.05Y –0

14. The equilibrium level of income is 3,760.
 Y         =          Y – – 0.05Y
Y – 0.8Y Y          =          940
0.25 Y  =          940
      
 Y         =          940 / 0.25
The equilibrium level of income is 3,760.

15. (2)
Imports M = 0 Net Exports X – M   =  300 – 0.05(3,760) – 0
X – M         =     300 – 188 
       =     112
There is a surplus in the balance of trade.
(3)
 Y =  (Y – 300) – 0.05Y
Y =  Y – – 0.05Y

16. Y – 0.8Y Y       =          960
            0.25 Y             =          960
                        Y         =          960 / 0.25
The equilibrium level of income (Y) is 3,840 which is an increase by 80
Imports M = O,
Net Exports X – M = 300 – 0.05 (3,840) – 0        
=  108
There is a surplus in the balance of trade.

17. (4) 
Y=  (Y – 300) – 0.05Y+0
Y         =      Y – – 0.05Y
 Y – 0.8Y Y       =          920
                        0.25Y              =          920
                             Y         =          920 / 0.25
Thus the equilibrium level of income is which is a decrease by 160.           

18. Imports M       =          0
Net Exports X – M = 280 – 0.05(3,680)
                  X – M =          96
There is a surplus in the balance of trade and decrease net exports 12.