The balanced budget multiplier is the change in output (Y) caused by a fiscal package where government spending and taxes rise by the same amount ((\Delta G = \Delta T)). In a simple Keynesian model, that package raises output by exactly the spending increase, so the multiplier is 1.
Model Logic (A Simple Derivation)
In a stripped-down goods-market model:
[ Y = C + I + G ]
with a consumption function:
[ C = a + b(Y - T) ]
where (b) is the marginal propensity to consume (MPC), (0 < b < 1).
Holding (I) fixed and taking changes:
[ \Delta Y = \Delta C + \Delta G ]
and
[ \Delta C = b(\Delta Y - \Delta T) ]
Substitute:
[ \Delta Y = b(\Delta Y - \Delta T) + \Delta G ]
Solve for (\Delta Y):
[ \Delta Y = \frac{1}{1-b}(\Delta G - b\Delta T) ]
If (\Delta G = \Delta T), then:
[ \Delta Y = \Delta G ]
So the balanced budget multiplier is 1 under these assumptions.
When The Multiplier Is Not 1
The “equals 1” result is model-dependent. In practice, it can be smaller (or even ambiguous) if:
- taxes are distortionary (so (\Delta T) changes behavior more than the simple MPC channel),
- imports rise with income (leakage from domestic demand),
- interest rates rise and crowd out private spending,
- the economy is supply constrained (higher demand becomes inflation instead of output).
Policy Context
Balanced-budget expansions sometimes appear in debates about fiscal discipline: they promise stimulus without a larger deficit. But they can still redistribute resources and may be harder to implement politically because they combine spending increases with tax increases.