    # 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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