How to Calculate the Spending Change Needed to Close a Gap
The required change in government spending equals the size of the gap divided by the spending multiplier, not multiplied by it.
The Required Spending Change formula
Calculator
Enter both GDP figures and the MPC to get the spending change that closes the gap, with the trap answer shown.
Full-employment output, the level policy is trying to reach.
Current short-run equilibrium output. Below potential means a recessionary gap.
Sets the spending multiplier, 1 divided by (1 minus MPC).
The gap divided by the multiplier gives $30B. Check it by multiplying back: 4 times $30B returns the full $120B gap.
- Gap to close
- $120B
- Spending multiplier
- 4
- Direction
- Increase government spending
- Common mistake: gap multiplied by the multiplier
- $480B
Actual output is $120B below potential, so this is a recessionary gap.
1 divided by (1 minus MPC), the same as 1 divided by MPS.
Raise spending to close a recessionary gap, cut it to close an inflationary one.
Multiplying instead of dividing gives $480B, which is 16 times the correct answer. The multiplier tells you how far each dollar travels, so it belongs in the denominator.
How to calculate Required Spending Change, step by step
- 1Measure the gap. Take potential real GDP minus actual for a recessionary gap, or actual minus potential for an inflationary gap.
- 2Compute the spending multiplier. Spending multiplier = 1 ÷ (1 − MPC), which also equals 1 ÷ MPS.
- 3Divide the gap by the multiplier. Because ΔGDP = multiplier × Δspending, solving for Δspending gives Δspending = gap ÷ multiplier.
- 4Set the direction. Raise spending to close a recessionary gap and cut spending to close an inflationary gap.
- 5Check by multiplying back. Multiply your answer by the multiplier and confirm the product equals the original gap.
Worked example: Required Spending Change
Potential real GDP is $900B, actual real GDP is $780B, and MPC = 0.75. The recessionary gap is 900 − 780 = $120B. The spending multiplier = 1 ÷ (1 − 0.75) = 1 ÷ 0.25 = 4. Required increase in government spending = 120 ÷ 4 = $30B. Check it: 4 × 30 = $120B, which lifts GDP from 780 back to 900. Multiplying instead ($120B × 4 = $480B) would be sixteen times the correct answer.
Required Spending Change questions
Do you multiply or divide the gap by the spending multiplier?
Divide. The multiplier measures how far each dollar of new spending travels, so the government only needs gap ÷ multiplier dollars to fill the gap.
Why does dividing work?
The underlying relationship is ΔGDP = multiplier × Δspending, and solving that equation for Δspending puts the multiplier in the denominator.
Does the same rule apply to transfer payments?
No, transfers work through the smaller transfer multiplier MPC ÷ MPS, so with MPC = 0.75 closing that same $120B gap takes 120 ÷ 3 = $40B in transfers rather than $30B in purchases.
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