3.2 Multipliers
The spending multiplier is 1/MPS and the tax multiplier is −MPC/MPS, so a dollar of new spending or tax change moves real GDP by a larger, predictable amount.
One person's spending is another's income, so an initial change in spending re-circulates: households spend the fraction MPC (marginal propensity to consume) of each new dollar and save the fraction MPS, where MPC + MPS = 1. The chain of re-spending multiplies the initial change into a larger total change in real GDP.
The spending multiplier = 1 ÷ MPS = 1 ÷ (1 − MPC). The tax multiplier = −MPC ÷ MPS: it is negative (taxes and GDP move in opposite directions) and one smaller in absolute value, because the first round of a tax cut is partly saved rather than fully spent. With MPC = 0.8, the spending multiplier is 5 and the tax multiplier is −4.
Maximum change in real GDP = initial change × multiplier. So a $20 billion rise in government spending with MPC = 0.8 can raise GDP by up to $100 billion, while a $20 billion tax cut raises it by at most $80 billion — always show the formula and the arithmetic on FRQs.
Key terms for 3.2
Practice the math
Using the spending multiplier for a tax change. The tax multiplier is −MPC/MPS — negative and one smaller in absolute value — because part of any tax cut leaks into saving before it is ever spent.
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