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Establishment Of National Earnings By Keynes

 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.

  1. Symmetry level of earnings
  2. 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.

  1. Formulate the saving function
  2. 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

  1. If investment in a year is $65 millions what will be the symmetry level of earnings or output
  2. 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

  1. Ascertain the symmetry level of earnings and consumption
  2. Derive the saving function and ascertain the saving at the symmetry level
  3. 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
           

  1. 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

  1. Thus, the symmetry level of earnings (Y) is 3,381

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