How to Calculate the Tax Change Needed to Close a Gap
The required tax change equals the gap divided by the tax multiplier (−MPC ÷ MPS), and it is always larger in size than the required spending change.
The Required Tax Change formula
Calculator
Enter both GDP figures and the MPC to get the tax change that closes the gap, next to the smaller spending route.
Full-employment output, the target level.
Current output. Below potential means a recessionary gap and calls for a tax cut.
Drives both multipliers. MPS is 1 minus this.
A negative answer is a tax cut, so closing this gap takes a $25B cut in taxes.
- Gap to close
- $100B
- Tax multiplier
- -4
- Direction
- Tax cut
- Spending route for the same gap
- $20B
- How much larger the tax change is
- $5B
Actual output is $100B below potential, a recessionary gap.
Minus MPC divided by MPS. It is negative, and always one unit smaller in size than the spending multiplier.
Government purchases enter aggregate demand dollar for dollar, so only $20B of spending does the job the tax change needs more dollars to do.
The tax route is $5B bigger, because a tax cut first becomes disposable income and households save the MPS share of it. The gap between the routes is a factor of 1 divided by the MPC.
How to calculate Required Tax Change, step by step
- 1Measure the gap. Potential real GDP minus actual for a recessionary gap, actual minus potential for an inflationary gap.
- 2Compute the tax multiplier. Tax multiplier = −MPC ÷ MPS, which is negative and exactly one unit smaller in size than the spending multiplier.
- 3Divide the gap by the tax multiplier. Δtaxes = gap ÷ tax multiplier, the rearrangement of ΔGDP = tax multiplier × Δtaxes.
- 4Read the sign. A negative answer is a tax cut, the fix for a recessionary gap, while a positive answer is a tax increase for an inflationary gap.
- 5Compare with the spending route. The required tax change is always larger in size than the required spending change, by a factor of 1 ÷ MPC.
Worked example: Required Tax Change
Potential real GDP is $900B, actual real GDP is $800B, and MPC = 0.8, so MPS = 0.2. The recessionary gap is 900 − 800 = $100B. The tax multiplier = −0.8 ÷ 0.2 = −4, so Δtaxes = 100 ÷ (−4) = −$25B, meaning a $25B tax cut. Check it: −4 × (−25) = +$100B. The spending route needs less: the spending multiplier is 1 ÷ 0.2 = 5, so 100 ÷ 5 = $20B of added spending closes the same gap. The tax cut must be $5B larger because households save part of it.
Required Tax Change questions
Why is the required tax cut larger than the required spending increase?
Government purchases enter aggregate demand dollar for dollar, but a tax cut first becomes disposable income and households save the MPS share of it. The tax change is larger by a factor of 1 ÷ MPC.
Do you multiply or divide by the tax multiplier?
Divide, exactly as with spending: Δtaxes = gap ÷ tax multiplier.
What does a negative answer mean?
A negative Δtaxes is a tax cut, which is what you should expect whenever you are closing a recessionary gap.
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