What is the marginal propensity to consume?

The marginal propensity to consume (MPC) is the fraction of each extra dollar of income that a household spends rather than saves. If the MPC is 0.8, people spend 80 cents of every additional dollar and save 20 cents. The marginal propensity to save (MPS) is the rest, and $MPC + MPS = 1$.

Why is the spending multiplier 1 divided by (1 minus MPC)?

Each round of spending is the previous round times the MPC, so the total is a geometric series: $1 + MPC + MPC^2 + MPC^3 + \dots$. That series sums to $1 / (1 - MPC)$, which also equals $1 / MPS$. With an MPC of 0.8, the multiplier is $1 / 0.2 = 5$.

Why is the tax multiplier smaller than the spending multiplier?

When the government spends a dollar directly, the full dollar enters the economy in the first round. When it cuts taxes by a dollar, households save part of it immediately — only the MPC portion gets spent in the first round. So the tax multiplier is $-MPC / (1 - MPC)$, smaller in size than the spending multiplier and opposite in sign.

What is the balanced-budget multiplier?

If the government raises spending and taxes by the same amount, real GDP still rises — the balanced-budget multiplier equals 1. The spending injects the full amount, while the tax increase only withdraws the MPC portion of the first round, so the spending effect wins by exactly the original amount.

What makes the real-world multiplier smaller than the textbook value?

Several leakages shrink it: people spend part of their income on imports (which is income abroad, not at home), part goes to taxes, and government borrowing can raise interest rates and crowd out private investment. Time lags and expectations can dampen it further. So real-world estimates are usually well below the simple $1 / (1 - MPC)$ value.

Does the multiplier work in reverse?

Yes. A cut in government spending shrinks GDP by a multiple of the cut, because the lost income reduces the next round of consumption, and so on. This is why austerity during a downturn can deepen a recession more than the headline spending cut suggests.

Why does government spending have a multiplier?

Short answer: every dollar the government spends becomes someone's income. That person spends a fraction of it — the marginal propensity to consume — which becomes the next person's income, and so on. Each round is smaller than the last, but the rounds add up to more than the original dollar. The total rise in GDP is $1/ (1 - M P C)$ times the initial spending.

The mechanism in five steps

The government spends 100 dollars building a bridge. The construction workers earn 100 dollars of new income.
With a marginal propensity to consume of 0.8, those workers spend 80 dollars and save 20. The 80 dollars is new income for shopkeepers.
The shopkeepers spend 80 percent of their 80 dollars — 64 dollars — which becomes income for someone else, who spends 51.20, and so on.
The rounds form a shrinking series: $100 + 80 + 64 + 51.2 + \dots$ Each term is the previous one times the MPC.
That geometric series sums to $100 \times \frac{1}{1 - 0.8} = 100 \times 5 = 500$ dollars. One 100-dollar injection raised total income by 500 dollars. The multiplier is $\frac{1}{1 - M P C} = \frac{1}{M P S}$ .

Worked example

Suppose the marginal propensity to consume is 0.75.

Spending multiplier: $\frac{1}{1 - 0.75} = 4$

A 200-dollar rise in government spending: $Δ Y = 4 \times 200 = 800$ dollars

Tax multiplier: $- \frac{M P C}{1 - M P C} = - \frac{0.75}{0.25} = - 3$

A 200-dollar tax cut (so $Δ T = - 200$ ): $Δ Y = - 3 \times (- 200) = 600$ dollars

The same 200 dollars does more as direct spending (800) than as a tax cut (600), because households save part of a tax cut in the very first round instead of spending all of it.

Common misconception

“The spending multiplier and the tax multiplier are the same size.” No — the tax multiplier is always smaller in magnitude. Government spending injects the full amount in round one; a tax cut only injects the MPC fraction, because households immediately save the rest. That first-round leakage makes the tax multiplier smaller.

Frequently asked questions

What is the marginal propensity to consume?: The marginal propensity to consume (MPC) is the fraction of each extra dollar of income that a household spends rather than saves. If the MPC is 0.8, people spend 80 cents of every additional dollar and save 20 cents. The marginal propensity to save (MPS) is the rest, and $M P C + M P S = 1$ .
Why is the spending multiplier 1 divided by (1 minus MPC)?: Each round of spending is the previous round times the MPC, so the total is a geometric series: $1 + M P C + M P C^{2} + M P C^{3} + \dots$ . That series sums to $1/ (1 - M P C)$ , which also equals $1/ M P S$ . With an MPC of 0.8, the multiplier is $1/0.2 = 5$ .
Why is the tax multiplier smaller than the spending multiplier?: When the government spends a dollar directly, the full dollar enters the economy in the first round. When it cuts taxes by a dollar, households save part of it immediately — only the MPC portion gets spent in the first round. So the tax multiplier is $- M P C / (1 - M P C)$ , smaller in size than the spending multiplier and opposite in sign.
What is the balanced-budget multiplier?: If the government raises spending and taxes by the same amount, real GDP still rises — the balanced-budget multiplier equals 1. The spending injects the full amount, while the tax increase only withdraws the MPC portion of the first round, so the spending effect wins by exactly the original amount.
What makes the real-world multiplier smaller than the textbook value?: Several leakages shrink it: people spend part of their income on imports (which is income abroad, not at home), part goes to taxes, and government borrowing can raise interest rates and crowd out private investment. Time lags and expectations can dampen it further. So real-world estimates are usually well below the simple $1/ (1 - M P C)$ value.
Does the multiplier work in reverse?: Yes. A cut in government spending shrinks GDP by a multiple of the cut, because the lost income reduces the next round of consumption, and so on. This is why austerity during a downturn can deepen a recession more than the headline spending cut suggests.

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The mechanism in five steps

Worked example

Common misconception

Frequently asked questions

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