Establishment Of National Earnings By Keynes
Illustration 119
The fundamental equations in a dual sector economy are given as consumption function C = 600 + 0.65 Y, investment Ī = 600. You are required to determine the following.
 Symmetry level of earnings
 Symmetry level of consumption
Solution
In a dual sector economy, the symmetry level of earnings is
Y = 1 (Ca
+ Ī)
1 – b
In the equation, Ca = 600, Ī = 600, b = 0.65
By substituting the above we get
Y = 1 (600
+ 600)
1 – 0.65
Y = 1 / 0.35 (1200)
Y = 2.85 x 1200
(a) Thus, the symmetry level of earnings is 3,429
In a dual sector economy, the consumption function is
C = Ca + b Y
In the above equation, Ca = 600, Ī = 600 and b = 0.65
By substituting the above values we obtain,
C = 600
+ 0.65Y
C = 600
+ 0.65 (3,249)
C = 600
+ 2111.85
C = 2,711.85
(b) Thus the symmetry of level of consumption is 2,711.85
Illustration 120
The fundamental equations in a dual sector economy are given as: Consumption C = 500 + 0.6Y and the investment function Ī = 500.
 Formulate the saving function
 Ascertain the symmetry level of output the equating the saving leakages to the investment injections
Solution
The saving function is given by
S = Y – C
S = Y – 500
+ 0.6Y
S = – 500
+ 1Y – 0.6Y
S = – 500
+ 0.4Y
(a) Hence, the saving function is given by S =  500 + 0.4Y
The symmetry level of output can be ascertained by equating the saving leakages to the investment injections.
Thus,

500 + 0.4Y = 500

500  500 = 
0.4Y
 1000 =  0.4Y
Or 0.4Y = 1000
Y = 1000 / 0.4
Y = 2,500
(b) Thus, the symmetry level of output is 2,500
Illustration 121
For a dual sector economy we have the following equation for consumption function
C = 360 + 0.5Y, ascertain the following
 If investment in a year is $65 millions what will be the symmetry level of earnings or output
 If full employment level of earnings is $860 millions what investment is required to be undertaken to ensure symmetry at full employment
Solution
Y = C + I
Y = 360 + 0.5Y + 65
Y – 0.55Y = 360
+ 65
Y
(1 – 0.5) = 425
0.5Y = 425
Y = 425 / 0.50
Y = 850
(a) Thus, if the investment in a year is $65 millions, then the symmetry
level of
earnings or Output (Y) will be 850
To make sure full employment symmetry investment must parity to the saving gap at full employment earnings. With the given full employment earnings equal to $860 millions,
SF
= YF – CF
Thus,
YF – (360 + 0.50YF)
860 – (360
+ 0.50 (860))
500 – 0.50
(860)
SF = 500 – 425
SF = 75
(b) Thus, investment required for full employment symmetry is S75 millions
Illustration 122
If in a dual sector economy Consumption C = 750 + 0.45Y and Investment I = 1,110 then
 Ascertain the symmetry level of earnings and consumption
 Derive the saving function and ascertain the saving at the symmetry level
 Ascertain the symmetry level of earnings by equating planned investment
Solution
The symmetry condition is given as Y = C + I
Thus,
Y = 750
+ 0.45Y + 1,110
Y = 1,860
+ 0.45Y
Y – 0.45Y = 1,860
0.55Y = 1,860
Y = 1,860 / 0.55
= 3,381
(a) Thus, the symmetry level of
earnings (Y) is 3,381
The consumption function C = 750 + 0.45Y
When Y = 3,381
C = 750
+ 0.45(3,381)
C = 750
+ 1,521
C = 2,272
 Thus, the symmetry level of consumption C is 2,272
The saving function is given by S = Y – C
S = Y – (750
+ 0.45Y)
S = Y – 0.45Y – 750
S = 0.55Y – 750
(b) Thus the saving function is given by S = 0.55Y – 750
At symmetry level,
S = 0.55
(3,381) – 750
S = 1860 – 750
S = 1110
(b) The saving function at Symmetry will be S = 1110
The planned saving is given by S =  750 + 0.55Y
In symmetry, planned saving equals planned investment
Thus,

750 + 0.55Y = 1110
0.55Y = 1110 + 750
0.55Y = 1860
Y = 1860 / 0.55
Y = 3,381
 Thus, the symmetry level of earnings (Y) is 3,381
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