Balanced Budget Multiplier
What is Balanced Budget Multiplier?
The balanced budget multiplier equals 1: an equal rise in government spending and taxes raises real GDP by exactly the amount of the spending change.
Government spending enters the economy directly (multiplier = 1/(1-MPC)), but a tax increase only reduces spending indirectly because households cut consumption by just MPC times the tax (multiplier = -MPC/(1-MPC)). Adding the two effects, the larger spending multiplier exactly outweighs the smaller tax multiplier, leaving a net multiplier of 1. So a $100 spending increase fully funded by a $100 tax increase raises GDP by $100. This shows balanced-budget fiscal expansion is still expansionary, contrary to a common intuition that it would be neutral.
Balanced Budget Multiplier: a worked example
Set the MPC at 0.8. The spending multiplier is 1 ÷ (1 - 0.8) = 5 and the tax multiplier is negative 0.8 ÷ 0.2 = negative 4. Raise government purchases by $50 and pay for it with a $50 tax increase. The spending side adds 5 × $50 = $250 to real GDP. The tax side subtracts 4 × $50 = $200. The net effect is $250 - $200 = $50, exactly the size of the spending change, so the combined multiplier is 50 ÷ 50 = 1. Change the MPC to 0.9 and the answer holds. The spending multiplier becomes 10 and the tax multiplier negative 9, so the same $50 pair gives $500 - $450 = $50. The two multipliers always differ in magnitude by exactly 1, which is why the balanced budget result never depends on the MPC.
The mistake students make with balanced budget multiplier
The shortcut gets used where it does not apply. Seeing any spending increase paired with any tax increase, students report a net effect equal to the spending change, but the result needs the two amounts to match. With an MPC of 0.8, purchases up $100 against taxes up only $60 is not a balanced budget: work the sides separately, 5 × $100 = $500 up and 4 × $60 = $240 down, a net of $260 rather than $100. A related slip is adding 5 and 4 to get 9. The tax multiplier carries a minus sign, so the two effects subtract.
Balanced Budget Multiplier questions
Why is the balanced budget multiplier equal to 1?
The spending multiplier exceeds the tax multiplier in magnitude by exactly one. Government purchases add the full amount to spending before any multiplying happens, while an equal tax rise removes only the marginal propensity to consume times that amount, because households cover part of the tax by saving less. Written out, 1 ÷ (1 - MPC) minus MPC ÷ (1 - MPC) equals (1 - MPC) ÷ (1 - MPC), which is 1. The survivor is that first dollar of purchases no tax offset ever touches.
Does the balanced budget multiplier change with the MPC?
The balanced budget multiplier stays at 1 for every value of the MPC. At an MPC of 0.5 the two multipliers are 2 and negative 1; at 0.8 they are 5 and negative 4; at 0.9 they are 10 and negative 9. Each pair differs by exactly one, so an equal rise in spending and taxes always changes real GDP by the size of the spending change. A higher MPC enlarges both individual multipliers without touching the gap between them.
What happens if the government cuts spending and taxes by the same amount?
Real GDP falls by the size of the spending cut. The result runs symmetrically. With an MPC of 0.75, cutting purchases by $100 lowers GDP by $400 while cutting taxes by $100 raises GDP by $300, for a net decline of $100. A balanced shrinking of the budget is therefore contractionary rather than neutral, which surprises students who expect the two halves to cancel out.
Formula / Example
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