The concept of multiplier occupies an important place in Keynesian theory of Income, Output and Employment. It is an important tool to analyze the effect of the changes in planned investment on the level of income. The concept of multiplier was first developed y R.F. Kahn a Cambridge economist in his article.

There are three types of multiplier:

1. Investment Multiplier (Two sector)
2. Balanced Budget Multiplier (Three sector)
3. Foreign Trade Multiplier (Four Sector)

### 1. Investment Multiplier (Multiplier in two sector model)

According to the keynes, “Investment multiplier tells us that when there is an increment of aggregate investment, income will increase by an amount which is K times the increment of investment.”

In the words of Kurihara, “The multiplier is the ratio of change in income to the change in investment.

Formula of Investment Multiplier:

K=∆Y/∆I    (1)

∆Y= K.∆I

Here, K=Multiplier, ∆Y= Change in Income, ∆I= Change in Investment.

### Relation between Investment Multiplier and Marginal Propensity to consume

K=∆Y/∆I

We also know that, Y=C+I

∆Y= ∆C+∆I

∆I= ∆Y-∆C

Here, ∆I= change in Investment, ∆Y=change in Income, ∆C= Change in consumption

Putting the value of ∆I in equation 1

K = ∆Y/∆Y-∆C          ( ∆I =∆Y-∆C) K = ∆Y/∆Y

∆Y/∆Y- ∆C/∆Y        OR

K= 1/1-∆C/∆Y            OR

K= 1/1-MPC             (∆C/∆Y=MPC) OR

K= 1/MPS                 (1-MPC=MPS)