How to Calculate the Balanced Budget Multiplier
The balanced budget multiplier equals 1: raising government spending and taxes by the same amount raises GDP by exactly that amount.
Formula
Steps
- 1Write the spending multiplier. Spending multiplier = 1 ÷ (1 − MPC), which also equals 1 ÷ MPS.
- 2Write the tax multiplier. Tax multiplier = −MPC ÷ (1 − MPC), which also equals −MPC ÷ MPS. It is negative because taxes and GDP move in opposite directions.
- 3Add them because spending and taxes change by the same amount. Set Δspending = Δtaxes and add the two multipliers: 1 ÷ (1 − MPC) + (−MPC ÷ (1 − MPC)).
- 4Combine over the common denominator. The two terms share the denominator (1 − MPC), so the sum is (1 − MPC) ÷ (1 − MPC) = 1. The MPC cancels out entirely.
- 5Apply the result. Because the multiplier is 1, ΔGDP equals the size of the equal spending-and-tax change: GDP rises by exactly the amount the government spends.
Worked example
Suppose MPC = 0.8 (so MPS = 0.2) and the government raises both spending and taxes by $50B. Spending multiplier = 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5, so spending adds 5 × $50B = +$250B. Tax multiplier = −0.8 ÷ 0.2 = −4, so the tax hike subtracts −4 × $50B = −$200B. Net effect: $250B − $200B = +$50B. The balanced budget multiplier = 5 + (−4) = 1, and GDP rises by exactly the $50B that was spent.
Frequently asked questions
What does the balanced budget multiplier tell you?
It tells you that a government can expand GDP even while keeping its budget balanced. Because the spending multiplier is larger than the (negative) tax multiplier by exactly 1, an equal rise in spending and taxes still boosts GDP by the amount spent, so fiscal policy is not neutralized by paying for it with taxes.
Why does the balanced budget multiplier equal 1 regardless of MPC?
The spending and tax multipliers share the same denominator (1 − MPC), and their numerators are 1 and −MPC. Adding them gives (1 − MPC) ÷ (1 − MPC) = 1, so the MPC cancels. The result is always exactly 1 for any MPC between 0 and 1.
Why is government spending more powerful than an equal tax change?
Government spending enters aggregate demand dollar-for-dollar in the first round, but a tax increase first reduces disposable income and households cut saving by the MPS share, so only the MPC share is pulled out of spending initially. That one-round head start is exactly the difference of 1 between the two multipliers.
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