Explain the balanced-budget multiplier in a simple Keynesian framework.

• A. With a one-for-one increase in G financed by a one-for-one tax increase, GDP increases by exactly the same amount as G (multiplier = 1) in the basic model.
• B. GDP increases by twice the change in G.
• C. GDP decreases when funded by taxes.
• D. GDP remains unchanged.

Answer: (A)

The balanced-budget multiplier asks how output responds when the government raises spending and taxes by the same amount. In the simplest Keynesian model with lump-sum taxes, let consumption depend on disposable income as C = a + b(Y − T) and let investment be fixed. The equilibrium is Y = C + I + G, so Y = a + b(Y − T) + I + G. Rearranging gives (1 − b)Y = a − bT + I + G.

Now if G rises by ΔG andTaxes rise by the same amount ΔT = ΔG, the new Y satisfies Y′ − Y = [ΔG − bΔT] / (1 − b) = [ΔG − bΔG] / (1 − b) = ΔG. So output increases by exactly ΔG. The direct boost from higher government spending is offset by higher taxes reducing disposable income through consumption, and in this setup those effects cancel in such a way that the total change in GDP equals the change in G. This is why the multiplier in this simple framework is one.