##
**
Relation between Investment Multiplier K and MPC
**

### PRACTICAL QUESTIONS

#### Example 1.

**
Calculate multiplier if MPC is:
**

(i) 0.75;

(ii) 0.90.

View AnswerCalculate K

(i)

MPC = 0.75

K = 1/1 - MPC

K = 1/ 1 - 0.75

K = 1/ 0.25

K = 4

(ii)

MPC = 0.9

K = 1/1 - MPC

K = 1/ 1 - 0.9

K = 1/ 0.1

K = 10

### Example 3.

**
In an economy, income generated is four times the increase in investment expenditure. Calculate the values of MPC and MPS.
**

We know that

K = Investment Multiplier = Change in Income/Change in Investment

In this question,

Income Generated is 4 Times Change in Investment Expenditure

It means

Increase in Income/Change in Investment = 4

K = 4

Now, we know that

Now, these K and MPC are related as follows

K = 1/1-MPC

4 = 1/1-MPC

4 - 4 MPC=1

- 4 MPC=1-4

- 4 MPC=-3

MPC = - 3 / - 4

MPC = 34 = 0.75

Now, we have to calculate MPS

We know that

MPC + MPS = 1

0.75 + MPS = 1

MPS=1-0.75=0.25

### Example 4.

**
In an economy, the marginal propensity to consume is 0.8. If the investment increases by ₹ 1,000 crores, calculate the total increase in income.
**

MPC = 0.8

Change in Investment = 1000

K = 1/1 - MPC

K = 1/1 - 0.8

K = 1/ 0.2

K = 5

Also,

K = Change in Income/ Change in Investment

5 = Change in Income/ 1000

Change in Income = 5000

### Example 5.

**
In an economy, 60% of increased income is spent on consumption. If ₹ 4 crores invested in a project, find out the increase in income and saving.
**

In this question, it is given that

60% of Increased Income is spent on Consumption

It means,

Change in Consumption/Change in Income=60%=0.6

MPC=0.6

Now ,we know that

K = 1/1-MPC

K = 1/1-0.6

K = 1/0.4

K = 1*10/4

K = 2.5

Now, we know that k is Investment Multiplier whose formula is

k = Change in Income/Change in Investment

2.5 = Change in Income/4

Change in Income=2.5*4=10

Now, we need to calculate Change in Savings

For this, we first need to calculate MPS

MPC+MPS=1

MPS + 0.6 = 1

MPS = 0.4

MPS = change in savings/ change in income

0.4 = change in savings/ 10

Change in savings = 4

## Note

Sometimes in Question, it given that

equilibrium level of income falls short by 100

It means, Change in income =100 in following formula

k = Change in Income/Change in Investment

### Example 7.

**
In an economy, the equilibrium level of income falls short by ₹ 500 crores. Calculate he additional investment needed to achieve the equilibrium level of income, if 80% of increased Income is spent on consumption.
**

In this question, we are given that

80% of increases income is spent on Consumption

It means

Change in Consumption/Change in Income =80%

MPC=80%

MPS=0.8

Also, it is given that

equilibrium level of income falls short by 500 crores

It means, Change in income = 500 in following formula

k = Change in Income/Change in Investment

k = 500/Change in Investment

1/1-MPC = 500/Change in Investment

1/1-0.8 = 500/Change in Investment

1/0.2 = 500/Change in Investment

Change in Investment *1=500*0.2

Change in Investment =100

Additional Investment=100

Sometimes in Question2 Equilibrium Level of Income are given

Suppose they are Rs 6000 and Rs 7000

In this case,

Change in Income =7000-6000=1000

This Change in income is to be taken while calculating equilibrium Level

### Example 10.

**
In an economy, marginal propensity to consume is 0.75. If Investment expenditure is increased by ₹ 500 crores, calculate the total increase in income and consumption expenditure.
**

**
MPC = 0.75
**

**
Change in Investment = 500
**

**
Change in Income = ?
**

**
Change in Consumption = ?
**

K = 1/1 - MPC

K = 1/1-0.75 = 1/0.25 = 4

K = Change in Income/ Change in Investment

4 = Change in Income/ 500

Change in Income = 2000

MPC = Change in Consumption/ Change in income

0.75 = Change in consumption/ 2000

Change in Consumption = 1500

### Example 11.

**
An increase of ₹ 200 crore in investment leads to a rise in national income by ₹ 1000 crores. Find out marginal propensity to consume.
**

**
Change in investment = 200
**

**
Change in income = 1000
**

**
MPC =?
**

K = Change in Income/ Change in Investment

K = 1000/ 200

K = 5

K = 1/ 1-MPC

5 = 1/1-MPC

1-MPC =1/5

1-0.2 = MPC

MPC = 0.8

### Example 12.

**
As a result of increase in investment by ₹ 125 crores, national income increase by
**

**
₹500 crores. Calculate marginal propensity to consume.
**

**
Change in Investment = 125
**

**
Change in Income = 500
**

**
MPC = ?
**

K = Change in Income/ Change in Investment

K = 500/ 125

K = 4

K = 1/ 1-MPC

4 = 1/1-MPC

1-MPC =1/4

1-0.25 = MPC

MPC = 0.75

### Example 13.

**
In an economy, investment is increased by Rs 300 crore. If marginal propensity to consume is 2/3, Calculate increase in national income.
**

**
Change in Investment = 300
**

**
MPC = 2/3
**

**
Change in Income = ?
**

K = 1/ 1-MPC

K = 1/1-2/3

K = 3

K = Change in Income/ Change in Investment

3 = Change in Income/ 300

Change in Income = 900

### Example 14.

**
If marginal propensity to consume is 0.9, what is the value of multiplier? How
**

**
much investment is needed, if national income increases by ₹ 5,000 crores?
**

**
MPC = 0.9
**

**
K = ?
**

**
Change in income = 5000
**

**
Change in Investment = ?
**

K = 1/ 1-MPC

K = 1/ 1-0.9

K = 1/0.1

K = 10

K = Change in Income/ Change in Investment

10 = 5000/ Change in Investment

Change in Investment = 5000/10

Change in Investment = 500

### Example 16.

**
In an Investment 75 percent of the increase in income is spent on consumption Investment is increased by Rs 1,000crore. Calculate:(a)total increase in income;(b)total increase in consumption expenditure.
**

**
MPC =0.75
**

**
Change in Investment = 1000
**

**
a) change in income
**

**
b) Change in consumption
**

(a)

K = 1/ 1-MPC

K = 1/ 1-0.75

K = 1/0.25

K = 4

K = Change in Income/ Change in Investment

4 = Change in Income/ 1000

Change in Income = 4000

(b)

MPC = change in consumption/ change in income

0.75 = change in consumption/ 4000

change in consumption = 3000

### Example 17.

**
An increase of ₹ 250 crores in investment in an economy resulted in total increase in income of ₹ 1,000 crores. Calculate the following:
**

**
(a) Marginal propensity to consume (MPC),
**

**
(b) Change in Saving,
**

**
(c) Change in consumption expenditure,
**

**
(d) Value of multiplier.
**

**
Change in investment = 250
**

**
change in income = 1000
**

**
a MPC = ?
**

**
b Change in savings = ?
**

**
c change in consumption = ?
**

**
d K = ?
**

a)

K = 1/ 1- MPC

K = Change in income/ change in investment

1/ 1 - MPC = Change in income/ Change in investment

1/ 1-MPC = 1000/250

1/ 1-MPC = 4

1/4 = 1 - MPC

MPC = 1- 0.25

MPC = 0.75

b)

MPC + MPS = 1

MPS = 1 - 0.75

MPS = 0.25

MPS = change in savings/ change in income

0.25 = change in savings/ 1000

change in savings = 250

c)

MPC = change in consumption/ change in income

0.75 = change in consumption/ 1000

change in consumption = 750

d)

K = Change in income/ change in investment

K = 1000/ 250

K = 4

### Example 18.

**
In an economy, income increases by 10,000 as a result of a rise in investment expenditure by 1,000 calculate;
**

**
(a)Investment Multiplier;
**

**
(b)Marginal Propensity to consume.
**

a)

K = Change in income/ change in investment

K = 10000/ 1000

K = 10

b)

K = 1/ 1-MPC

10 = 1/ 1-MPC

1 - MPC = 1/10

MPC = 1 - 0.1

MPC = 0.9

## Example 19

In an economy, an increase in investment leads to increase in national income which is three times more than the increase in investment. Calculate marginal propensity to consume.

**
**

Suppose Increase in Investment =x

Increase in Income

is 3 times more than increase in investment

= x+3x

=4x

Now, we know that

k=Increase in income/Increase in Investment

K = 4x/x

K = 4

K = 1/ 1-MPC

4 = 1/ 1-MPC

1 - MPC = 1/4

MPC = 1 - 0.25

MPC = 0.75

### NCERT Questions

**
No questions in this part
**

### Other Books

#### Question 1

**
How is Investment Multiplier related to MPC?
**

Investment Multiplier is the ratio of Increase in National Income(Y) due to Increase in Investment (I)

We know that

K = Investment Multiplier = Change in Income/Change in Investment

Also

MPC = Marginal Propensity to Consume = Change in Consumption/Change in income

Y = C + S

Replacing S with I

Y = C + I

Hence

Delta Y = Delta C+ Delta I

Dividing whole equation with Delta Y

#### Question 2

**
Calculate the value of multiplier, if MPC is:
**

**
(i) 0.6
**

**
(ii) 0.5
**

K = 1/1-MPC

(i)

K = 1/ 1 - 0.6

K = 1/ 0.4

K = 2.5

(ii)

K = 1/ 1-0.5

K = 1/0.5

K = 2

### Other Books

#### Question 3

**
How much additional income will be generated in an economy with an additional investment of Rs 100 crores and when half of increase in income is spent on consumption?
**

**
Change in Investment = 100
**

**
MPC = 0.5
**

**
Change in Income = ?
**

K = 1/1 - MPC

K = 1/1 - 0.5

K = 1/0.5

K = 2

K = change in income/ change in investment

2 = change in income/ 100

change in income = 200