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Aggregate Demand Multipler

 Shifts In The Aggregate Demand and The Multiplier

Introduction

            A change in the equilibrium income or output is the result of a shift in the aggregate demand function or the C + I curve. The aggregate demand curve can either shift upwards or downwards. The amount of the change in the income will be a multiple of the amount of the shift in the aggregate demand curve. The multiplier is the amount by which there is a change in equilibrium income or output when autonomous aggregate expenditure increases by one unit. It is this condition necessary for the multiplier to work.

Shifts in the Aggregate Demand and the Multiplier

In a two sector economy, the aggregate demand is a sum of consumption and investment expenditures. It is generally agreed that though both consumption and investment functions undergo a change from one period to another, the consumption function is relatively more stable than the investment function. Thus, the initial changes in income occur more due to the shifts in the investment function.

A few illustrations could explain us clearly the shifts in the aggregate demand as well as the multiplier.

Illustration 16

In an economy, the basic equations are as follows: the consumption function is C = 300 + 0.8Y and investment is Ī = $ 360 millions. You are required to ascertain the following

  1. The equilibrium level of income
  2. The equilibrium level of income when planned investment increases from 360 to 400 millions, a total increases of 40 millions
  3. The multiplier effect of the 40 millions increases in planned investment.

Solution

The equilibrium condition is given as Y = C + I

                                                Y         =          300 + 0.8Y + 360

                                    Y – 0.8Y         =          300 + 360

                                   0.2Y                =          660

                                               Y         =          3,300

1.         The equilibrium level of income is Y           =          3,300

The equilibrium condition is given as Y = C + I

Thus,
                                               Y         =          300 + 0.8Y + 400

                                    Y – 0.8Y         =          300 + 400

                                   0.2Y                =          700

                                               Y         =          700 / 0.2

2.         Hence, the equilibrium level of income is 3,500

The equilibrium level of income increases from 3,300 to 3,500crores when planned investment increases from 360 to 400 millions. There is an increase in income by 200 millions. Hence the multiplier effect is

                                    M         =              1                 
                                                              1 – b

                                                =              1     
                                                            1 – 0.8

                                                =              1     
                                                               0.2

3.         The multiplier effect is m is  5

Illustration 17

Presume in an economy the marginal propensity to consume is 0.75 and the level of autonomous investment decreases by 40 millions. Find,

  1. The change in the equilibrium level of income
  2. The change in consumption expenditures

Solution

                        Δ Y      =          m
                        Δ I

Also,
                        m         =              1                 
                                                1 – mpc

Thus, Δ Y = Δ I

m         =          Δ I     1           
                                                       1 – b

                                    =          -40 x         1    
                                                            1 – 0.75

                                    =          -160

(1)        Thus, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 160 millions. This effect occurs due to the reverse multiplier.

                                    Y         =          C + I

            Therefore,       ΔY       =          Δ C + Δ S

                                   -160     =          Δ C – 40

The autonomous investment decreases by 40 millions, the saving will also decrease by 40 millions

                                    Δ C      =          - 160 + 40

                                    Δ C      =          - 120

(2)        The consumption expenditure decreases by 120 millions

Illustration 18

Compute the value of the investment multiplier when the marginal propensity to continue is

(1) 0.80, (2) 0.65, (3) 0.40 and (4) 0.25

Find the effect of a decrease in the equilibrium income when autonomous investment decreases by 60 millions when the marginal propensity to consume is (1) 0.80, (2) 0.65, (3) 0.40 and (4) 0.25

Solution

The value of m, the investment multiplier is

                                    m         =              1     
                                                            1 – mpc

Hence,

                        (1)        m         =              1     
                                                            1 – 0.8
           
                                    =          1 / 0.2              =          m         =          5

                        (2)        m         =              1     
                                                            1 – 0.65

                                    =          1 / 0.35            =          m         =          2.87
                       
                        (3)        m         =              1     
                                                            1 – 0.4

                                    =          1 / 0.2              =          m         =          1.67

                        (4)        m         =              1     
                                                            1 – 0.25

                                    =          1 / 0.75                        =          m         =          1.33

Thus, the decrease in the equilibrium income when autonomous investment decreases by 60 millions is

                        Δ Y      =          Δ Im              =          60 x 5              =          300

                                                                        =          60 x 2.87         =          172.2

                                                                        =          60 x 1.67         =          100.2

                                                                        =          60 x 1.33         =          79.8

Illustration 19

In an economy the marginal propensity to consume is 0.50. the level of autonomous investment decreases by 60 millions. Find the following

  1. The change in the equilibrium level of income
  2. The change in autonomous demand
  3. The induced change in the consumption expenditure

Solution

                        Δ Y                  =          m
                        Δ Ȳ

But, m is the investment multiplier

Also,
                        m         =               1    
                                                1 – mpc

Thus,
                        Δ Y      =          ΔIm     =               ΔI                   1     
                                                                                    1 – mpc

                                                            =          - 60 x       1     
                                                                                    1 – 0.50

                                                            =          - 120

  1. Hence, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 120 millions.
  2. The decrease in investment by 60 millions is the change in the level of autonomous demand.
  3. Y         =          C         +          I

    Therefore,
                                        Δ Y      =          Δ C + ΔS

                                       -120     =          ΔC – 60

                                       Δ C      =          -120 + 60

  4. The Consumption expenditure falls by 60 millions

Illustration 20

Presume that in two sector economy, the income is $ 1000 million while the marginal propensity to consume is 0.40.

Suppose the government wants to increase the income to $ 1600 million, by an amount of $ 600 million.

By how much should the autonomous investment be increased?

Solution

The income level         =          $1000 millions

The planned income level is $1600 millions

Change in income       =          Δ Y      =          1600 – 1000

                                                            =          $600 millions

But
                                                Δ Y      =          m         =          m ΔI      1       
                                                Δ I                                                       1 – b

                                                Δ Y      =          Δ I         1       
                                                                                    1 – b

                                                600      =          Δ I         1       
                                                                                    1 – b

                                                            =          Δ I       1 / 1-0.4

                                                            =          Δ I       1 / 0.6

                                                600      =          Δ I       1.67

                                                Δ I       =          600 / 1.67

Thus, the autonomous investment should be increased by $360 millions for the income to increase to $ 1600 millions

An increase in income by $ 600 millions

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