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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
 Investment
Function
Function
= 200 + 0.8Yd
=
300
=
120
=
200
 Exports
=
100
 Imports
=
0.05Y
 Tax
 Government
Expenditure
 Find
the following.
1.
The equilibrium level of income
2.
The net exports
 Solution

Here the consumption function is
C
=
200 + 0.8Yd

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 – 0.05Y
Y=
200 + 0.8 Y – 96 + 600 – 0.05Y
Y–
0.8Y+ 0.05Y
=
704
0.25Y
=
704
=
704 / 0.25


 The
Y
equilibrium level of income is 2,816.

Import M = 0.05Y = 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

Y – 0.8 Y + 0.05Y

= 200 + 0.8 (Y - 140) + 300 + 220 + 100 – 0.05Y
=
200 + 0.8Y – 112 + 620 – 0.05Y
=
708
0.15Y =
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.

 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 – 0.05Y
Y
= 700 – 96 + 160 + 0.8Y – 0.05Y
Y
= 764 + 0.75Y
Y–
0.75Y
=
764
 0.25 Y
=
764
Y
=
764 / 0.25

 The
equilibrium level of income is 3,056.
 Imports
 Net

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 – 0.05Y
 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 – 0.05Y
 Solution
 (1)
C


The consumption function is
= 260 + 0.8Yd
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 =
– 0.05Y –0
260 + 0.8 (Y – 300) + 320 + 300 + 300
Y

Y – 0.8Y + 0.05Y

0.25 Y
=
940

Y
=
940 / 0.25
 The
=
260 + 0.8Y – 240 + 920 – 0.05Y

=
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 + 300 – 0.05Y
Y=
260 + 0.8Y – 240 + 340 + 300 + 300 – 0.05Y
Y–
0.8Y + 0.05Y
=
960
0.25 Y
=
960
=
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)
260 + 0.8(Y – 300)+320+300+280 –
0.05Y+0
 Y=
Y

=
260 + 0.8Y – 240 + 900 – 0.05Y
Y – 0.8Y + 0.05Y


 Thus
=
920
0.25Y
Y
=
=
920
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.