The multiplier

When autonomous spending rises, income rises by more than that amount. Why?

Suppose investment rises by 100 and c = 0.6.

• Round 1: firms produce 100 more, and pay out 100 more as income.
• Round 2: people spend 0.6 of that extra income: demand and output rise by 60.
• Round 3: they spend 0.6 of 60: a rise of 36.
• And so on, each round smaller than the last.

Adding all the rounds: 100 + 60 + 36 + ... = 100 ÷ (1 − 0.6) = 250.

This is the multiplier:

Multiplier = ΔY ÷ ΔA = 1 ÷ (1 − c) = 1 ÷ s

With c = 0.6, the multiplier is 1 ÷ 0.4 = 2.5. With c = 0.9, it would be 1 ÷ 0.1 = 10.

So the larger the MPC, the larger the multiplier: when people spend more of each extra rupee, each round passes more of it on.