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Saving - Investment Parity

 Saving - Investment Parity

       It facilitates in fetching the impartiality amidst saving and investment. If there is a deviation amidst saving and investment and hike in investment tends to a hike in earnings via the multiplier process by more than the hike in initial investment. Consequently, the hike in earnings, saving also hikes and equals investment.

Let us work out few illustrations which explains us the concept of multiplier.

Illustration 29

With the following information you are required to ascertain the equilibrium income of the economy and the value of the multiplier.

C         =          100 + 0.8Yd

I           =          200

G & T  =          150 each

Where, C, I and Yd are consumption, investment and disposable income respectively.

Solution

  1. Since G = T, budget of the government is balanced.

Y         =          C + I + G

C         =          a + bYd           =          a + b (Y – T)

Substituting the values of C, I and G we have:

            Y         =          100 + 0.8(Y – 150) + 200 + 150

                        =          100 + 0.8Y – 120 + 200 + 150

                        =          330 + 0.8Y

Y – 0.8Y         =          330

0.2Y    =          330

Y         =          330 / 0.2

Thus, equilibrium level of income is 1,650

Value of Multiplier is

               1       =              1     
            1 – b                1 – mpc

                        =              1     
                                    1 – 0.8

                        =          1 / 0.2

Hence the value of multiplier is 5

Illustration 30

In an economy, the marginal propensity to consume is 0.80. the tax is a lump sum tax or, in other words, not related to income level. Find the change in the equilibrium output for the following:

  1. Increase in government expenditure by $20 millions
  2. Increase in taxes by $30 millions
  3. Increase in transfers by $20 millions

Solution

We have

                        GM      =          Δ Y      =            1       
                                                Δ G                  1 – b

And b = 0.80 and Δ G = 20

Thus,
                        Δ Y      =              1                 =          100
                        20                    1 – 0.80

Thus, for a $20 million increase in the level of increase of government expenditures, the equilibrium output increases by $100 millions.

We have

                        GT       =          ΔY       =            -b      
                                                Δ T                  1 – b

And b = 0.80 and Δ T = 30

Thus,

                        ΔY       =          - 0.80               =          -120
                        30                    1 – 0.8

Thus for a $30 million increase in taxes, the equilibrium output decreases by 120 millions.

When transfers are at $20 millions

                        ΔY       =           0.80               =          80
                        20                    1- 0.80

Thus a 20 million increase in transfers increases the equilibrium output by $80 millions.

Illustration 31

Presume the level of autonomous investment in an economy is $ 400 millions and consumption function of the economy is C = 160 + 0.75Y. Ascertain the following.

  1. The Equilibrium level of income
  1. The increase in national income if investment increases by $50 millions

Solution

For equilibrium level of income

                                    Y         =          C + I

Where                          C         =          160 + 0.75Y                …..Equation (1)

                                    I           =          400 millions

Substituting the values of C and I in Equation (1) we have

                                    Y         =          160 + 0.75Y + 400

                        Y – 0.75Y       =          160 + 400

                                    0.25Y  =          560

                                    Y         =          560 / 0.25

Equilibrium level of income is therefore equal to $2,240 millions.

The next condition to be satisfied is an increase in investment with 50 millions and it depends on the size of multiplier. The size of multiplier is determined by the value of marginal propensity to consumer.

In the given consumption function C = 160 + 0.75Y marginal propensity to consume is equal to 0.75 or fractionally ¾.

Thus multiplier is equal to            1    
                                                1 – mpc

                                    =             1                   =          4
                                                1 – ¾
Thus with increase in investment by 50 millions, national income will hike by 50 x 4 = 200 millions.

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