Fiscal policy and its multipliers

Fiscal policy is the government's use of spending (G), taxes (T) and transfers (TR) to influence income. With a lump-sum tax, households consume out of disposable income Y − T + TR, and equilibrium income becomes:

Y = (C̄ − cT + cTR + I + G) ÷ (1 − c)

• Government spending multiplier = 1 ÷ (1 − c). With c = 0.9, it is 10: a rise of 50 in G raises Y by 500.
• Tax multiplier = −c ÷ (1 − c). With c = 0.9, it is −9: a tax cut of 50 raises Y by 450. It is negative because a tax increase reduces disposable income and so consumption.

The tax multiplier is one less, in absolute value, than the spending multiplier. That is because spending adds to demand directly, while a tax cut works only through consumption: people save part of it first.

A lump-sum tax shifts the AD line down in parallel.

Balanced budget multiplier: if G and T both rise by the same amount, the budget balance does not change, but income still rises, by exactly that amount. The balanced budget multiplier = 1.