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Consumption Function

 Consumption Function

Meaning of Consumption Function

            The consumption function or inclination to consume refers to income-consumption relationship. It is a “functional relationship between two aggregates, i.e. total consumption and gross national income.” Metaphorically, the relationship is represented as C = f (Y),, where C is consumption, Y is income and f is the functional relationship. Thus the consumption function indicates a functional relationship between C and Y, where C is he dependant by Y is the independent variable, i.e. C is determined by Y.

Let us see few illustrations which explain the consumption function.

Illustration 7

Given the tablet below, you have to ascertain the average and marginal propensity to consume.

Income Y
Value in $ ten thousand

Consumption C
Value in $ ten thousand

2000

1900

2200

2080

2400

2240

2600

2380

2800

2500

3000

2600

3200

2680

Solution

Income Y
Value in $ ten thousand

Consumption C
Value in $ ten thousand

Average Propensity to Consume
APC

Marginal Propensity to Consume
MPC

   

C / Y

Δ C / Δ Y

2000

1900

1900 / 2000 = 0.95

-

2200

2080

2080 / 2200 = 0.94

180 / 200 = 0.9

2400

2240

2240 / 2400 = 0.93

160 / 200 = 0.8

2600

2380

2380 / 2600 = 0.91

140 / 200 = 0.7

2800

2500

2500 / 2800 = 0.89

120 / 200 = 0.6

3000

2600

2600 / 3000 = 0.86

100 / 200 = 0.5

3200

2680

2680 / 3200 = 0.83

80 / 200 = 0.4

Illustration 8

Given the saving function S = - 20 + 0.2Y and autonomous investment, I = $100 million. You are required to ascertain

  1. The Equilibrium level of income
  2. The level of consumption
  3. If investment increases permanently by $10 millions, what will be the new levels of income and consumption

Solution

According to saving investment approach, equilibrium level of national income is ascertained by equalling saving and investment, thus

                                                S          =          I
Hence,
                                    - 20 + 0.2Y      =          100
                                                0.2Y    =          120

                                                Y         =          120 / 0.2

(i)         Hence equilibrium of Income (Y)                =          600

According to consumption function, Consumption equals income over savings, thus

                                                C         =          Y – S                           …..Equation (2)
Hence,
                                                S          =          - 20 + 0.2Y                  …..Equation (1)

Substituting the value of Y in the Equation (1), we get the following

                                                S          =          - 20 + 0.2 (600)
                                                            =          - 20 + 120

Hence Saving (S)                               =          100

Substituting the value of S and I in the Equation (2), we obtain the following

                                                C         =          600 – 100

(ii)        Hence the level of consumption (C)             =          500

With the increase in investment by $10 millions, the new investment will be equal to $110 millions

                                                S          =          I
Hence,

                                    - 20 + 0.2 Y     =          110

                                                0.2 Y   =          110 +20

                                                Y         =          130 / 0.2

(iii)       Hence, the new level of income would be (Y)         =          $650 millions

Now, Saving                                       =          - 20 + 0.2 Y

                                                            =          - 20 + 0.2 (650)

                                                            =          -20 + 130

Hence Saving (S)                                =          110

Substituting the new values of S and Y, the new consumption (C) would be computed as below

                                                C         =          Y - S

                                                            =          650 – 110

(iii)       Hence, the new level of consumption would be (C)            =          $540 millions

Illustration 9

Given in the below tablet, Income and Consumption based on which you are required to ascertain the following

  1. Average Propensity to Consume
  2. Average Propensity to Save
  3. Marginal Propensity to Consume and
  4. Marginal Propensity to Save

Income Y
Value in $

Consumption C
Value in $ ten thousand

240

240

360

340

480

440

600

540

720

640

840

740

Solution

Income Y
Value in $ ten thousand

Consumption C
Value in $ ten thousand

Average Propensity to Consume
APC

Average Propensity to Save
APS

Marginal Propensity to Consume
MPC

Marginal Propensity to Save
MPS

   

APC = C / Y

APS = S / Y
(1 – APC)

MPC = Δ C / Δ Y

MPS = Δ S / Δ Y (1 - MPC)

240

240

240 / 240
= 1 or 100%

0

-

-

360

340

340 / 360 = 0.94 0r 94%

0.06

100 / 120 = 0.83

0.167

480

440

440 / 480 = 0.91 or 91%

0.09

100 / 120 = 0.83

0.167

600

540

540 / 600 = 0.9 or 90%

0.10

100 / 120 = 0.83

0.167

720

640

640 / 720 = 0.88 or 88%

0.12

100 / 120 = 0.83

0.167

840

740

740 / 840 = 0.88 or 88%

0.12

100 / 120 = 0.83

0.167

Illustration 10

In an economy, the basic equations are as follows:

The consumption function is C           =          240 + 0.8Y and

Investment function is Ī                      =          500

You are required to ascertain the following

  1. Equilibrium level of income
  2. Equilibrium level of consumption
  3. Equilibrium level of saving
  4. Equilibrium level, aggregate demand equals aggregate supply and saving leakages equals investment injections

Solution

The equilibrium condition is given as Y         =          C + I

Thus,
Y                     =          240 + 0.8Y + 500

Y – 0.8 Y        =          740

Y (1 – 0.8)       =          740

0.2Y                =          740

Y                     =          740 / 0.2

(a)        Hence, the equilibrium level of income (Y) =          3,700

The consumption function is C = 240 + 0.8Y

When Y = 3,700,
                                    C         =          240 + 0.8 (3700)

                                    C         =          240 + 2,960

(b)       Hence, the equilibrium level of consumption (C)   =          3,200

The saving equation is             S          =          Y – C

When Y = 3,700 and C = 3,200, we have

                                                S          =          3,700 – 3,200

(c)        Hence, the equilibrium level of saving (S)               =          500

(d) Now the aggregate demand and aggregate supply has to be equal for equilibrium level which equals saving leakages and investment injections.

Hence,
                                                         C + I    =          C + S

                                3,200 + 500                 =          3,200 + 500

                                                        3,700   =          3,700

(Or) Saving equals investment         S          =          I

                                                        500      =          500

Illustration 11

Presume the consumption function is C = Ca + b Y and investment is I = Ī, then

  1. Determine the equation for the equilibrium level of productivity
  2. Determine the equilibrium level of productivity when Ca = 300, b = 0.8 and Ī = 500

Solution

The equilibrium condition is given as Y = C + I.

                      Y         =          Ca + b Y + Ī

            Y – b Y           =          Ca + Ī

          Y (1 – b)          =          Ca + I
           
(a)                Y         =          Ca + Ī                         ……..Derivative (1)
                                              (1 – b)

Substituting the values in the Derivative (1), we obtain the following

                        Y         =          300 + 500
                                                1     -   0.8

                        Y         =          800 / 0.2

(b)       Hence, the equilibrium productivity level is 4,000

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