How Multiplier Mechanism Works

Let us understand the logic behind the direct relationship between MPC and multiplier through Multiplier Mechanism. It runs like this:

1) Suppose AB industry limited spends Rs. 100 crore in setting up a new plant i.e  ∆I = Rs. 100 crore.

This will lead to creating more demand for goods and services required for the setting up of this new plant. There will more demand for machinery, raw materials, labour etc.

This will generate income for all those people who are associated with the setting up this plant and leading to more output and income.

As a result national income in the first will increase by an amount equal to amount of investment i.e  ∆Y = Rs. 100 crore

2) This ∆Y = Rs. 100 crore would be split into ∆C and ∆S as a part of income is spent and a part of it is saved.

3) In round – 2, ∆C would be converted  into ∆Y as people who receive this new income (Rs. 100 crore) directly from the building of the factory will spend some of it on consumer goods like food, clothing, TV, cars, etc.

Here comes an important point:

The exact amount of additional consumption expenditure depend on the MPC(c).

Suppose MPC is 0.8, then 

MPC = ∆C / ∆Y (as discussed in consumption function)

∆C = MPC (∆Y)

∆C = 0.5(100)

     = Rs. 50 crore

If  MPC is 0.4, then

∆C = 0.4(100)

     = Rs. 40 crore

Thus higher the value of MPC would mean higher ∆C

Accordingly, ∆Y in round - 2 (which is equal to ∆C) would depend on the value of MPC. Higher MPC would mean higher ∆Y.

If we take MPC = 0.5 and move ahead our Multiplier mechanism.

When output and employment increase to meet this demand (income earned to factors of production by AB industry) for consumer goods like food, clothing, TV, cars, etc. further income will be created for firms and workers producing these consumer goods.

Therefore, income of these people will increase by Rs. 50 crore.

4) This increased income of Rs. 50 crore leads to a further income due to increase in the consumption expenditure in the third round equal to:

 MPC is 0.5, then

∆C = 0.5(50)

      = Rs. 25 crore

This will generate an income of equal amount i.e. Rs. 25 crore. 

The reason is that expenditure by one person becomes the income of another person.

This process of increase in income will continue to be repeated in subsequent rounds with income in each round of spending MPC( c) times the increase in income in the previous round.

The below table illustrates the Multiplier Mechanism.

It is based on the assumption that MPC = 0.5 

Round	Increase in Investment Expenditure(∆I) (Rs. Crore)	Change in Income(∆Y) (Rs. Crore)	Increase in Consumption(∆C) (Rs. Crore)	Savings (Rs. Crore) S = Y- C
1 2 3 4 5 6 7 8 9 10	100 - - - - - - - - -	100 50 25 12.50 6.25 3.12 1.56 0.78 0.39 0.20	50 25 12.50 6.25 3.12 1.56 0.78 0.39 0.20 0.10	50 25 12.50 6.25 3.12 1.56 0.78 0.39 0.20 0.10
	100	200	100	100

In different time periods, as shown in the table, income will go on increasing as a result of increase in consumption expenditure.

Total increase in income = Rs. 200 crore

Since increase in investment = Rs. 100 crore

Multiplier:

K =  ∆Y / ∆I

    = 200 / 100      

K = 2 

Or 

K = 1 / 1-MPC

    = 1 / 1-0.5

    = 1 / 0.5

 K = 2 

With a change in investment of Rs. 100 Crore, total income in the economy doubles to Rs. 200 crore which explains that investment had a multiplier effect in the economy.