Home › Topics › Spending multiplier

The spending multiplier

A change in spending doesn't move output by just its own size. Each dollar spent becomes someone's income, part of which is spent again, so the final change in output is a multiple of the original shock.

The consumption function

Households spend part of every extra dollar of income. The consumption function captures that: C = Ca + MPC × Y. Ca is autonomous consumption, what households spend even at zero income, and Y is income. The marginal propensity to consume (MPC) is the cents spent out of each extra dollar; the marginal propensity to save (MPS) is the rest, so MPC + MPS = 1.

Changing Ca shifts the whole consumption line up or down. Changing the MPC tilts its slope. Knowing which one moved is half the battle.

The multiplier formula

In a simple economy with no taxes or trade, the multiplier = 1 / (1 − MPC) = 1 / MPS. With an MPC of 0.8 the multiplier is 5: every $1 of new autonomous spending raises equilibrium output by $5.

Worked example. Investment falls by $15 billion and the MPC is 0.8. Income falls $15b. Households cut spending by 80% of that, $12b, which becomes the next round's income loss, then $9.6b, then $7.68b, and so on. The rounds add up to 15 ÷ (1 − 0.8) = $75 billion, five times the original shock.

Why real multipliers are smaller

Taxes, imports and saving are leakages: they pull a slice of each round's income out of the spending stream. The more that leaks, the smaller the effective multiplier compared with the textbook 1 / (1 − MPC). The rounds also take time, so the full effect is not instant.

Equilibrium output and gaps

Equilibrium output is where aggregate expenditure equals output. If it falls short of full-employment output, there is a recessionary gap; if it overshoots, an inflationary gap. The spending change needed to close a gap is the gap divided by the multiplier. To close a $50b recessionary gap with a multiplier of 5, spending has to rise by $10b.

Taxes versus spending

A tax cut first raises disposable income, and households save part of it, so it moves output less than an equal rise in government purchases. The tax multiplier is −MPC / (1 − MPC): −4 when MPC = 0.8, versus 5 for spending.

Common exam traps

• Mixing up a shift of the consumption line (Ca changes) with a tilt (MPC changes).
• Applying the multiplier to total spending instead of to the change in autonomous spending.
• Forgetting that 1 / (1 − MPC) is the same thing as 1 / MPS.
• Using the spending multiplier for a tax change, or dropping the minus sign on the tax multiplier.

Keep going