Four Sector Economy The Keynesian Model of Income

Four Sector Economy 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.

The volume of exports in any economy depends on the following factors: 1. The prices of the exports in any domestic economy relative to the price in the other countries. 2. The income level in the other economies. 3. Tastes, Preferences, customs and traditions in the other economies. 4. The tariff and trade policies between the domestic economy and the other economies. 5. The domestic economy’s level of imports.

Illustration -1 The fundamental equations in an economy are given as: Consumption Function = 200 + 0. 8 Yd Investment = 300 Tax = 120 = 200 Exports = 100 Imports = 0. 05 Y Government Expenditure

Find the following. 1. The equilibrium level of income 2. The net exports Solution Here the consumption function is C = 200 + 0. 8 Yd C = 200 + 0. 8 (Y – T) C = 200 + 0. 8 (Y – 120)

The Y equilibrium condition is given as = C+I+G+X–M Thus, Y = 200 + 0. 8 (Y – 120) + 300 + 200 +100 – 0. 05 Y Y = 200 + 0. 8 Y – 96 + 600 – 0. 05 Y Y – 0. 8 Y+ 0. 05 Y = 704 0. 25 Y = 704 / 0. 25 The Y equilibrium level of income is 2, 816.

Import M = 0. 05 Y = 0. 05 (2, 816) = Net Exports: There X–M = X-M = 140. 8 100 – 140. 8 - 40. 8 is a deficit in the balance of trade.

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

The equilibrium condition is given as Y=C+I+G+X–M Thus Y Y = 200 + 0. 8 (Y - 140) + 300 + 220 + 100 – 0. 05 Y = 200 + 0. 8 Y – 112 + 620 – 0. 05 Y Y – 0. 8 Y + 0. 05 Y = 708 0. 15 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.

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 = 200 + 0. 8 (Y – 120) + 300 + 200 + 160 – 0. 05 Y Y = 700 – 96 + 160 + 0. 8 Y – 0. 05 Y Y = 764 + 0. 75 Y Y – 0. 75 Y = 764

0. 25 Y = Y The = 764 / 0. 25 equilibrium level of income is 3, 056. Imports Net 764 M = 0. 05 Y = 0. 05 (3, 056) = 152. 8 Exports X – M = 160 – 152. 8 = 7. 2 X–M There = 7. 2 is a surplus in the balance of trade.

Illustration-3 The equations in an economy are given as: C = 260 + 0. 8 Yd, Investment function I = 320 Tax = 300 Government Expenditure = 300 Exports = 300 – 0. 05 Y

You are required to ascertain the following: 1. Find the equilibrium level of income 2. Find the net exports at equilibrium level of income 3. Find the equilibrium level of income and the net exports when there is an increase in investment from 320 to 340 4. Find the equilibrium level of income and the net exports when the net export function becomes 280 – 0. 05 Y

Solution (1) C The consumption function is = 260 + 0. 8 Yd C = 260 + 0. 8 (Y – T) C = 260 + 0. 8 (Y – 300) The equilibrium condition is give as Y = C + I + G +X–M Thus, Y = 260 + 0. 8 (Y – 300) + 320 + 300 – 0. 05 Y – 0

Y Y – 0. 8 Y + 0. 05 Y 0. 25 Y = 940 / 0. 25 The = 260 + 0. 8 Y – 240 + 920 – 0. 05 Y = 940 equilibrium level of income is 3, 760.

(2) Imports M = 0 Net Exports X – M = 300 – 0. 05(3, 760) – 0 X –M There = 300 – 188 = 112 is a surplus in the balance of trade. (3) Y = 260 + 0. 8 (Y – 300) + 340 + 300 – 0. 05 Y Y = 260 + 0. 8 Y – 240 + 300 – 0. 05 Y

Y – 0. 8 Y + 0. 05 Y = 960 0. 25 Y = 960 / 0. 25 Y The equilibrium level of income (Y) is 3, 840 which is an increase by 80 Imports Net M = O, Exports X – M = 300 – 0. 05 (3, 840) – 0 There = 108 is a surplus in the balance of trade.

(4) Y= 260 + 0. 8(Y – 300)+320+300+280 – 0. 05 Y+0 Y = 260 + 0. 8 Y – 240 + 900 – 0. 05 Y Y – 0. 8 Y + 0. 05 Y Thus = 920 0. 25 Y Y = = 920 / 0. 25 the equilibrium level of income is 3680 which is a decrease by 160.

Imports Net M = 0 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.