# Explain The Relationship Between Mpc And Multiplier With The Help Of An Example

MPC – Marginal propensity to consume

It is defined as the change in consumption per unit change in income.

MPC is denoted by C and is equal to $$\frac{\Delta C}{\Delta Y}$$

The maximum value which MPC can take is 1.

Investment multiplier refers to the ratio of the total increment in equilibrium value of final goods output to the initial increment in autonomous expenditure and is denoted by K.

The investment multiplier = $$\frac{\Delta Y}{\Delta A} = \frac{l}{l – c} = \frac{l}{S}$$

The Relationship between MPC and Multiplier

When MPC = 0, the value of the investment multiplier will be equal to unity.

For a maximum value of MPC, there is a maximum value of multiplier (infinity)

For a minimum value of MPC (0), there is a minimum value of multiplier (1).

As the MPC increases, there is also an increase in the multiplier and vice-versa

Therefore, there is a positive relationship between MPC and multiplier.

For example,

If MPC = 0.8 then

Multiplier(K) = $$\frac{1}{1 -0.8} = 1 / \frac{1}{1 – 8 / 10}$$

=$$\frac{10}{10 – 8}$$

= $$\frac{10}{8}$$ = change in income/ change in investment

= 5 times

Therefore, Change in income = 10 and change in investment = 2

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