We know that
Savings = Income - Consumption
S = Y - C
But we know that C = Ĉ + b(Y)
Putting this value of C, we get
S = Y - C
S = Y - (Ĉ + b(Y))
S = Y - Ĉ - b(Y)
S = -Ĉ + Y - b(Y)
S = -Ĉ + (1-b)Y
Example 1
Income | Consumption Expenditure | Savings |
0 | 4000 | -4000 |
10000 | 12000 | -2000 |
20000 | 20000 | 0 |
30000 | 28000 | 2000 |
40000 | 36000 | 4000 |
50000 | 44000 | 6000 |
60000 | 52000 | 8000 |
Calculating Savings at 50000 Income level
S = -Ĉ + (1-b)Y
= -4000 + (1 - 0.8)*50000
= -4000 + 0.2*50000
= -4000 + 10000
= 6000
Calculating Savings at 20000 Income level
S = -Ĉ + (1-b)Y
= -4000 + (1 - 0.8)*20000
= -4000 + 0.2*20000
= -4000 + 4000
= 0
Example 17
On the basis of consumption function: C = 120 + 0.40 Y; answer the following
questions:
(i) Derive the saving function.
(ii) Determine the saving at the income level of ₹ 500 crores.
(iii) At what level of income, saving becomes zero?
View Answer(i)
We know that
Consumption Function equation is represented by equation
C = Ĉ +b(Y)
where
C = Total Consumption
Ĉ = Autonomous Consumption
Y = Income
b = MPC
In our case, given equaton is
C = 120 +0.4Y
Hence
Ĉ = Autonomous Consumption = 120
b = MPC = 0.4
Now, we know that Saving Function is given by formula
S = -Ĉ + (1-b)Y
= -120 + (1-0.4)Y
= -120+0.6Y
(ii)
Income = 500
S = ?
S = -Ĉ + (1-b)Y
= -120 + (1-0.4)Y
= -120+0.6*500
= -120 + 300
= 180
(iii)
Now we know that
Income - Consumption = Savings
Now, we have to calculate income where Savings are 0
it means
Income - Consumption = 0
Income = Consumption
Y = C
C = Y
Now, coming back to equation
C = 120 + 0.4Y
Y = 120 + 0.4Y
Y - 0.4Y = 120
0.6Y = 120
Y = 120/0.6 = 120/6*10 = 200
Saving will be 0 at level Income is 200
Example 22
If a consumption function of a hypothetical economy is given as:
C = 100 + 0.6 Y; then
(i) What will be the values of marginal propensity to consume and marginal propensity to save for the economy?
(ii) Write the corresponding saving function.
View Answer(i)
We know that
Consumption Function equation is represent by equation
C = Ĉ +b(Y)
where
C = Total Consumption
Ĉ = Autonomous Consumption
Y = Income
b = MPC
In our case, given equation is
C = 100 + 0.6Y
Hence
Ĉ = Autonomous Consumption = 100
b = MPC = 0.6
Hence Marginal Propensity to Consume (MPC)=0.6
Now we know that
MPC+MPS=1
0.6+MPS=1
MPS=1-0.6
MPS=0.4
(ii)
S = -Ĉ + (1-b)Y
S = -100 + 0.4Y
Example 19
The consumption function for an economy is: C = 20 + 0.8Y (assuming amount in ₹ crores). Determine the level of income when average propensity to consume will be one,
View AnswerWe need to Calculate level of income where
APC =1
Consumption/Income=1
Consumption = Income
C=Y
Y=C
Now coming back to our equation
C =20 +0.8Y
Putting C=Y
Y =20 +0.8Y
Y -0.8Y=20
0.2Y=20
2/10*Y=20
Y=20*10/2
Y=100
Example 21
Given below is the consumption function of an economy:
C=100+0.5Y.
With the help of a numerical example, show that in this economy, as income increases, APC will decrease.
View AnswerC = 100 + 0.5Y
Income | Consumption | APC |
50 | 125 | 2.5 |
100 | 150 | 1.5 |
150 | 175 | 1.166667 |
200 | 200 | 1 |
250 | 225 | 0.9 |
300 | 250 | 0.833333 |
In this case, we can clearly see that as the income rises, the value of APC is decreasing.
When income increases from Rs50 to Rs100 and then to Rs150, APC decreases from 2.5 to 1.5 and to 1.16
Therefore, with increase in income, APC decreases
Example 16
With the help of saving function: S = - 20 + 0.3 (Y), calculate consumption expenditure at the income level of ₹ 1,000 crores.
View AnswerWe know that Saving function equation is represented by
S=-Ĉ +(1-b)Y
Now we are given in Question that
S =-20 +0.3Y
Comparing both equations
-Ĉ = -20
Ĉ = 20
Hence Autonomous Consumption Exp =20
Also
0.3Y=(1-b)Y
0.3=(1-b)
b=1-0.3
b=0.7
Hence Marginal Propensity to Consume=0.7
Now we have calculate Consumption at Income level of 1000 Crores
For this, we will take Consumption Function
C = Ĉ +bY
C = 20 + 0.7(1000)
C = 20 + 700
C = 720
Example 18
If MPC is one-third of MPS and consumption at zero level of national income is ₹ 40 crores, derive the consumption and saving function.
View AnswerWe are given that
MPC = 1/3MPS
Also We know that
MPC+MPS=1
1/3MPS+MPS=1
4/3MPS=1
MPS=1*3/4
MPS=3/4=0.75
MPC =1-MPC =1-0.75=0.25
b= 0.25
Also it is given in question that
Consumption at 0 level of income =40 Crores
It means Autonomous Consumption = 40 Crores
Ĉ = 40 Crores
Now ,we know that
Equation for Consumption Function is
C = Ĉ +bY
C = 40 + 0.25Y
Equation for Savings Function is
S = -Ĉ +(1-b)Y
S = -40 + 0.75Y
What is Slope and Intercept of Savings Equation?
We have studied in Math's that
Slope of line is
y=mx + c
where
m is slope of line
c is y intercept
Now, Savings Equation is
S=-Ĉ +(1-b)Y
S=(1-b)Y -Ĉ
Comparing [1] and ]2]
Slope of line is 1-b (1-mpc)
Intercept is -Ĉ (Autonomous Consumption)
Example 15
The saving curve of an economy makes a negative intercept of ₹ 50 crores and 20% of additional income is saved. Derive the saving and consumption function.
View AnswerWe have studied in Math's that
Slope of line is
y=mx + c [1]
where
m is slope of line
c is y intercept
Now, Savings Equation is
S=-Ĉ +(1-b)Y
S=(1-b)Y -Ĉ [2]
Comparing [1] and ]2]
Slope of line is 1-b (1-mpc)
Intercept is -Ĉ (Autonomous Consumption)
Now, it is given in question that
Saving curve makes negative intercept of 50
it means
Intercept =-50
-Ĉ =-50
Ĉ =50
Autonomous Consumption =50
Also it is given that
20% of additional income is saved
It means
MPS=20%=0.2
Now we know that
MPS+ MPC=1
0.2+MPC=1
MPC=1-0.2
MPC=0.8
Now, Savings function is given by equation
S = -Ĉ +(1-b)Y
S = -50 + 0.2Y
Now, Consumption function is given by equation
C = Ĉ +bY
C = 50 + 0.8Y
NCERT Questions
No questions in this part
Other Books
Question 1
What is Slope and Intercept of Savings Equation?
View AnswerWe have studied in Math's that
Slope of line is
y=mx + c [1]
where
m is slope of line
c is y intercept
Now, Savings Equation is
S=-Ĉ +(1-b)Y
S=(1-b)Y -Ĉ [2]
Comparing [1] and ]2]
Slope of line is 1-b (1-mpc)
Intercept is -Ĉ (Autonomous Consumption)