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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

The Equilibrium level of income
The level of consumption
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

Average Propensity to Consume
Average Propensity to Save
Marginal Propensity to Consume and
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

Equilibrium level of income
Equilibrium level of consumption
Equilibrium level of saving
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

Determine the equation for the equilibrium level of productivity
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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