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Saving And Investment Equality

 Saving and Investment Equality

Illustration 44

Presume that the level of self-governing investment in an economy is 400 millions. The saving function is given to be S = - 160 + 0.25 Y. Find the equilibrium level of earnings.

Solution

According to saving – investment approach, the level of earnings is in equilibrium at which S = I.

Given,
                        S          =          -160 + 0.25 Y and

                        I           =          $ 400 millions

Substituting the values of S and I in the equilibrium equation we get,

                        -160 + 0.25Y   =          400

                                    0.25Y  =          400 + 160

                                    Y         =          560 / 0.25

Therefore the equilibrium level of earnings is equal to 2,240 million dollars.

Illustration 45

In an economy the following are the data given:

  1. When the level of the national income is $1000 millions, savings are of $100 millions and
  1. When the national income is $1100 millions, savings are of $140 millions and
  1. If planned investment is $140 millions, what is the equilibrium level of the national income?

Solution

  1. In an economy, equilibrium exists when planned saving equals planned investment.
  1. As planned investment is $140 millions, equilibrium will take place at an earnings level of $1100 millions for the reason that at that income level alone planned investment equals planned savings of $ 140 millions.
  1. Therefore, the equilibrium level of the national income is $ 1100 millions.

Illustration 46

What will be the hike in national income with an initial hike in investment; and is expressed in the form as below:

Increase in Income

ΔY = 200 + 200 * 8 /10 + 200 * (8 / 10) ^ 2 + 200 * (8 / 10) ^ 3 +200 * (8 / 10) ^ 4 ……. + 200 * (8 / 10) ^ n.

Solution

Since the above series is one of geometric progression, increase in income ΔY

                        =          200 *         1               
                                                1 – 8 / 10

                        =          200 *         1               
                                                (10 – 8) / 10

                        =          200 *         1               
                                                    2 / 10

                        =          200 * 5

Therefore ΔY  =          $1,000 millions

  1. Therefore, it is thus clear from above that if the marginal propensity to consume is 8 / 10,
  1. The investment of $ 200 millions tends to a hike in national income by $1000 millions.
  1. Hence the Investment Multiplier is equal to 5.

Illustration 47

Suppose the marginal propensity to consume of a community is equal to 4 / 5, what is the size of multiplier? Also ascertain if the marginal propensity to consume is 1 / 4.

Solution

                        Multiplier        =                1               
                                                            1 – MPC

                                                =                1               
                                                            1 – 4
                                                                  5

                                                =                1               
                                                            (5 – 4) / 5

                                                =          1 / 0.2              =          5

If the marginal propensity to consume is 1 / 4,

                        Multiplier        =               1                
                                                            1 – MPC

                                                =               1                
                                                            1 – 1 / 4

                                                =               1                
                                                            1 – 0.25

                                                =          1 / 0.75            =          1.33.

Hence the size of multipliers are 5 and 1.33 in the above two cases.

Illustration 48

Presume the level of self – governing investment in the economy is $ 600 millions and consumption function of the economy is

                                    C         =          120 + 0.75Y

  1. What will be the equilibrium level of income?
  1. What will be the increase in national income if the investment hikes by $ 40 millions?

Solution

For equilibrium level of income,
Y         =          C + I                            ……….Equation (1)

                                    C         =          120 + 0.60Y

                                    I           =          600 millions

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

                                    Y         =          120 + 0.60 Y + 600

                        Y – 0.60Y       =          120 + 600

                                    0.4Y    =          720

                                    Y         =          720 / 0.4

                                    Y         =          1800

The equilibrium level of income is therefore equal to $1800 millions

The hike in income takes place as a result of hike in investment by 40 millions based on the size of multiplier. The size of multiplier is ascertained by the value of marginal propensity to consume.

In the given consumption function, C = 120 + 0.60 Y and the marginal propensity to consume is equal to 3 / 5.

Therefore,

                        Multiplier K    =               1                
                                                            1 – MPC

                                                =               1                
                                                            1 – 3 /5

                                                =               1                
                                                            (5 – 3) / 5

                                                =               1               
                                                              2 / 5

                                                =          1 / 0.4              =          2.5

                                    ΔY       =          ΔI x k
                                               
                                                =          40 * 2.5

                                                =          100 million dollars

Therefore, the increase in investment by 40 million dollars, national income will rise by $100 millions.

Illustration 49

How much will be the hike in the investment is required to lift the earnings by $5000, if MPC is 0.65.

How much will there be hike in consumption and saving due to this hike in income?

Solution

                        Multiplier K    =          ΔY
                                                          ΔI

                                    ΔI        =          ΔY                   …….Equation (1)
                                                            ΔK

                        Multiplier
                                    K         =               1                
                                                            1 – MPC

                                    MPC    =          0.60

                                    K         =               1                =            2.5    
                                                            1 – 0.60

Given                          ΔY       =          5,000

Substituting the values of ΔY and K in the equation (1), we get

                                    ΔI        =          5,000               =          2,000
                                                              2.5

Thus investment should rise by $2000 to accomplish $ 5000 increment in income.

Now,                           ΔC       =          ΔY x MPC

                                                =          5,000 * 0.60

                                                =          $3,000
                                               
                                    ΔS       =          ΔY – ΔC

                                                =          5,000 – 3,000  =          $2,000

The Functional Equality

The equality amidst saving and investment in the functional or programme sense is brought about by adjusting mechanism of earnings of variations in the cost of interest. In this sense, saving and investment are equal only at equilibrium level of earnings. Revenue is functionally associated to saving and investment. When saving is more than investment, earnings drops and when investment is more than saving, income rises. This dynamic course of variations in earnings, savings and investment will carry on till saving and investment are unequal although are also in equilibrium.

Income - million $

Saving - million $

Investment - million $

Income Shifts

400

0

40



Development

600

30

60

800

60

90

1000

90

100

1200

120

120

Symmetry

1400

150

140


Retrenchment

1600

180

160

1800

210

180

The above table represents that so long as investment is greater than saving earnings prolongs to hike up till it arrives at the earnings level of $ 1200 millions where saving and investment are also in equilibrium at $ 120 millions each. But after this point, saving exceeds investment contracts and again reaches equilibrium level of $ 1200 millions.

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