The concept of multiplier is an important contribution of Keynes to the theory of income and employment. Hi Friends, in today’s article we are going to know about the relationship between MPC and Multiplier**.** So let’s discuss in details.

## Relationship between MPC and Multiplier

The value of multiplier depends upon the size of MPC. This two concept is closely related to each other. When there is an initial increase in investment, income level will also increase equal to the increment in investment.

Due to this change in income, definitely consumption expenditure will go up depending on the size of MPC. Increased consumption expenditure becomes additional income to factors of production who are engaged in the production of consumer goods.

This increase in income will turn lead to further increase in consumption and so on. Thus higher the value of MPC, higher will be the value of investment.

The investment multiplier is thus a direct function of MPC.

K = 1/1 – MPC

Algebraically, the relationship between multiplier (K) and MPC can be derived as follows through the income expenditure equation.

Y = C + I

ΔY = ΔC + ΔI

Dividing both side by ΔY, we get-

ΔY/ΔY = ΔC/ΔY + ΔI/ΔY

or ΔC/ΔY = 1 – ΔI/ΔY

Where,

C = Consumption,

Y = National Income,

I = Investment.

or ΔI/ΔY = 1 – ΔC/ΔY = 1 – MPC

or ΔY/ΔI = 1/ 1 – MPC

∴ K = 1/1 – MPC

The equation follows that there is a direct relationship between MPC and Multiplier. This relationship can be explain through the table given below-

MPC |
Investment Multiplier (k) |

0 | K = 1/1 – MPC = 1/1 – 0 = 1 |

0.25 | K = 1/1 – MPC = 1/1 – 0.25 = 1.33 |

0.50 | K = 1/1 – MPC = 1/1 – 0.50 = 2 |

0.75 | K = 1/1 – MPC = 1/1 – 0.75 = 4 |

1.00 | K = 1/1 – MPC = 1/1 – 1 = ∝ |

As MPC varies between 0 and 1 (i.e. 0<MPC<1) value of multiplier will lie between one and infinity i.e. 1<K<∝. If we know the value of multiplier can be easily calculated.

**Conclusion**

So friends, this was the concept of the relationship between MPC and Multiplier**.** Hope you get the full details about it and hope you like this article.

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