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Multiple Modular Sectors

 Multiple Modular Sectors

Illustration 123

In a nation’s economy, the full employment productivity takes place at 1750 millions. The marginal propensity to consume is 0.7 and the symmetry level of productivity is currently at 1450 millions. Presume the statute seeks to accomplish the full employment productivity, find the variation in

  1. The level of statute outlays
  1. Net lump sum tax
  1. The level of statute outlays and the net lump sum tax when the statute aims at bringing the productivity the full employment while keeping the budget equated.

Solution

We have, GM   =

             Δ Y      =            1       
             Δ G                  1 - b

Where, Δ G     =          Variation in statute outlay

            b          =          Marginal propensity to consume

            Δ Y      =          Variation in earnings

            GM       =          Statute outlay multiplier

For instance,

            b          =          0.70
           
            Δ Y      =          1750 – 1450
           
            Δ Y      =          300

Thus,
                        300 / Δ G         =          1 / 1- 0.7

                                    Δ G      =          300 (0.3)

                                                =          90

Thus, the level of statute outlays required to accomplish the full employment productivity is 90 millions

We have, GF    =

                                    Δ Y      =          - b      
                                    Δ T                  1 – b
Where,

Δ T      =          Variation in tax

b          =          marginal propensity to consume

Δ Y      =          Variation in earnings

GF        =          Statute tax multiplier

As the tax multiplier is negative, an increase in tax leads to a decrease in the symmetry level of earnings.

For instance,
                                                b          =          0.70

                                                Δ Y      =          1750 – 1450 = 300
Thus,
                                                300      =          - 0.70  
                                                Δ T                  1 – 0.70

                                    - 0.7 Δ T          =          300 (0.30)

                                                Δ T      =          90 / -0.7

                                                            =          - 128.57

The net lump sum tax is – 128.57 millions. There should be a decrease in lump sum tax by 128.57 millions

The next equation to solve is

                                                Δ Y      =              1               (-b Δ T + Δ Ḡ)
                                                                          1 – b

But,                                         Δ G      =          Δ T

Thus we can write
                                                Δ Y      =              1               (-b Δ Ḡ + Δ Ḡ)
                                                                          1 – b
Or
                                    Δ Y (1-b)         =          Δ Ḡ (-b +1)

Or                                Δ Y (1-b)         =          Δ Ḡ (1-b)

Or                               

                                                Δ Y      =          1 – b    =          1
                                                Δ G      =          1 – b
                                               
                                                Δ Y      =          Δ G      =          300

The required increase in the level of statute outlays and the net lump sum tax us 300 millions.

Illustration 124

The fundamental equations in a nation’s economy are given as:

Consumption Function           C         =          150 + 0.6Yd

Investment Function               I           =          200

Tax                                          T          =          280

Statute Outlay                         G         =          175

Exports                                    X         =          80

Imports                                    M         =          0.04Y

Find the following.

  1. The symmetry level of earnings
  1. The net exports

The consumption function is
                                                C         =          150 + 0.6Yd
                                               
                                                C         =          150 + 0.6Y (Y – T)
                                               
                                                C         =          150 + 0.6Y (Y – 280)

The symmetry condition is given as

                                    Y         =          C + I + G + X – M
Thus,
                                    Y         =          150 + 0.6 (Y – 280) + 200 + 175 + (80 – 0.04Y)
                                   
                                   Y         =          150 + 0.6 Y – 168 + 455 – 0.04Y

            Y – 0.6Y+ 0.04Y        =          437
                                   
                       0.44Y              =          437

                                    Y         =          437 / 0.44

The symmetry level of earnings is 993.18

Checking the answer

In symmetry in a four sector model, leakages equal injections or

C + I + G + X             =          C + S + T + M

The consumption function is C           =          150 + 0.6Yd

                                                C         =          150 + 0.6 (993.18 – 280)
                                               
                                                C         =          150 + 0.6 (713.18)
                                               
                                                C         =          150 + 427.90

                                                C         =          577.90

The saving function is             S          =          Yd – C

                                                S          =          (Y – 280) – 577.9
                                               
                                                S          =          713.18 – 577.9

                                                S          =          135.28

Thus,
                                    I + G + X        =          S + T + M
                       
                      200 + 175 + 80            =          135.28 + 280 + 0.04Y

                                                455      =          415.28 + 0.04 Y
                       
                                                455      =          415.28 + 0.04 (993.18)
           
                                                455      =          415.28 + 39.72
                       
                                                455      =          455

Imports                                    M         =          0.04Y = 0.04 (993.18)
                                   
                                                            =          39.72

Net Exports:                X – M              =          80 – 39.72

                                    X - M              =          40.28

There is a surplus in the balance of trade.

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