Expansionary and Contractionary Fiscal Policy tells you which way to move. The multipliers tell you how far. Because each dollar of new spending is multiplied, the change needed is much smaller than the gap.
Key idea
To close a gap with government purchases: $\Delta G = \dfrac{\text{gap}}{\text{spending multiplier}}$. With taxes: $\Delta T = \dfrac{\text{gap}}{MPC/MPS}$ (a cut for a recessionary gap, a rise for an inflationary gap). This simple rule assumes the price level stays about the same.
Why it works
If the multiplier is 5, every \$1 of new government purchases raises GDP by \$5. To raise GDP by \$100 billion, the government needs only \$20 billion: $20 \times 5 = 100$. Setting the change equal to the whole gap would overshoot. For taxes, the multiplier is smaller ($MPC/MPS$, one less), because households save part of a tax cut before spending, so a larger tax change is needed for the same effect.
Worked examples
Worked example: Using government purchases
A recessionary gap is \$200 billion and the MPC is 0.75. How much should government purchases rise?
- Spending multiplier $= \dfrac{1}{0.25} = 4$.
- $\Delta G = \dfrac{200}{4} = 50$ billion dollars.
- Check: $50 \times 4 = 200$. ✓
Answer: \$50 billion
Worked example: Using taxes
The same \$200 billion gap, MPC 0.75. How much should taxes be cut?
- Tax multiplier (size) $= \dfrac{0.75}{0.25} = 3$.
- Tax cut $= \dfrac{200}{3} \approx 66.7$ billion dollars, more than the \$50 billion of purchases.
Answer: About \$66.7 billion
Worked example: An inflationary gap
An inflationary gap is \$90 billion and the MPC is 0.9. By how much should purchases fall? Or taxes rise?
- Spending multiplier $= 10$: cut purchases by $\dfrac{90}{10} = 9$ billion dollars.
- Tax multiplier $= 9$: raise taxes by $\dfrac{90}{9} = 10$ billion dollars.
Answer: Cut G by \$9 billion, or raise taxes by \$10 billion
Why "about"? With an upward-sloping SRAS, part of an AD shift goes into a higher price level rather than more output, so in practice a somewhat larger change would be needed. Real-world multipliers are also uncertain, which is one reason economists debate how much fiscal policy to use.
Common mistake
Setting the spending change equal to the whole output gap, ignoring the multiplier, or using the spending multiplier for a tax change. Check: multiply your answer by the right multiplier; you should get back the gap.