The investment multiplier (k) measures how a change in autonomous investment produces a larger, magnified change in equilibrium national income. It is defined as $k = \dfrac{1}{1 - \text{MPC}} = \dfrac{1}{\text{MPS}}$.

The formula

Since MPC + MPS = 1, $(1 - \text{MPC}) = \text{MPS}$, so the multiplier is simply the reciprocal of the marginal propensity to save.

How and why it works

Suppose the government/firms invest an extra ₹100 and MPC = 0.8. The ₹100 becomes income for the recipients, who spend 80% (₹80); that ₹80 becomes income for others, who spend ₹64; and so on. The rounds form a geometric series: $100 (1 + 0.8 + 0.8^2 + \dots) = 100 \times \frac{1}{1-0.8} = 100 \times 5 = ₹500$.

Worked illustration

With MPC = 0.8: $k = 1/(1-0.8) = 1/0.2 = 5$. A ₹100 crore rise in investment raises national income by $5 \times 100 = ₹500$ crore. If MPC were 0.5, $k = 2$, and the same investment would raise income by only ₹200 crore.

Key relationships

• Higher MPC → higher multiplier (more of each round is re-spent). …