Equation of Savings Function

(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

(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

We 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

C = 100 + 0.5Y

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

We 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

We 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

We 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

We 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)