What is the balanced-budget multiplier and under what conditions is it positive?

• A. It is the GDP change from simultaneous increase in government spending and taxes by the same amount.
• B. It is the GDP change from simultaneous increase in government spending and taxes by the same amount. In a simple model with lump-sum taxes, the multiplier is positive (GDP rises) and typically less than the spending multiplier.
• C. It is the change in GDP from a tax cut alone.
• D. It is always larger than the spending multiplier.

Answer: (B)

The balanced-budget multiplier captures how much GDP changes when government spending and taxes are increased by the same amount. In a simple model where taxes are lump-sum (taxes do not depend on income), the direct boost to demand from higher G is only partially offset by the rise in taxes, and the net effect is positive. You can see this by writing Y = C(Y - T) + I + G with C = a + c(Y - T). If we raise G and T by the same amount, ΔT = ΔG, and solving for the change in Y gives ΔY = ΔG. So the GDP increase is equal to the size of the initial spending increase—a positive effect. Since the pure spending multiplier is 1/(1 - c) > 1, the balanced-budget multiplier is typically smaller than the spending multiplier, yet still positive.

This is why the option that defines the balanced-budget multiplier as the GDP change from equal rises in G and T and notes that it’s positive under lump-sum taxes (and usually smaller than the spending multiplier) is the best choice.