Balanced-Budget Multiplier

The G-multiplier (Government Expenditure Multiplier) works when taxes T stay the same. The T-multiplier (Tax Multiplier) works when government spending G stays the same. But what happens when both G and T change at the same time, by the same amount?​

This is exactly what the Balanced Budget Multiplier answers.
When ΔG = ΔT (the increase in government spending equals the increase in taxes), the government budget remains "balanced." The effect of this balanced budget change on national income is measured by the Balanced Budget Multiplier (BBM).

The balanced budget multiplier is always equal to one.

This means: if the government raises both its spending and taxes by the same amount, national income rises by exactly that amount — no more, no less.

The equilibrium level of national income is:

Y = `1/(1−b)`[a − bT + I + G]         ...(1)

By incorporating ΔG and ΔT (when ΔG = ΔT) and the resulting combined change in income (ΔY) in Equation (1) ; the new equilibrium level of the income can be expressed as

Y + ΔY = `1/(1−b)`[a − b(T + ΔT) + I + G + ΔG]    ...(2)

By subtracting Equation 1 from Equation 2, we will get

ΔY = `1/(1−b)`(−bΔT + ΔG)    ...(3)

Since ΔT = ΔG, we can rewrite Eq. (3), by substituting ΔG for ΔT, as

ΔY = `1/(1−b)`(−bΔG + ΔG)

On multiplying both sides by 1−b, we get

ΔY(1 − b) = −bΔG + ΔG

or

ΔY(1 − b) = ΔG(1 − b)

or

ΔY = ΔG

We can obtain the value of balanced budget multiplier (B_m) by dividing both sides of Eq. (4) by ΔG, we shall get as under:

B_m = `(ΔY)/(ΔG)` = `(ΔG)/(ΔG)` (since ΔY = ΔG)

or

`(ΔY)/(ΔG)`=1

• When government expenditure (ΔG) and taxes (ΔT) increase by the same amount, the budget is balanced.
• The Balanced Budget Multiplier (BBM) is always equal to 1.
• This means national income increases by exactly the same amount as ΔG.
• So, ΔY = ΔG, even when taxes rise along with government spending.