Proportional taxes, stabilisers and transfers

Most taxes rise with income. With a proportional tax T = tY, people keep only (1 − t) of each extra rupee, so they consume only c(1 − t) of it. The AD line becomes flatter, and the multiplier smaller:

Multiplier = 1 ÷ [1 − c(1 − t)]

Example: c = 0.9 and t = 0.2. Then c(1 − t) = 0.72, and the multiplier = 1 ÷ 0.28 ≈ 3.6, much less than the 10 it would be without the tax.

This makes proportional taxes an automatic stabiliser: when GDP falls, tax payments fall too, so disposable income falls by less than GDP, and the fall in demand is softened. It works by itself, with no decision needed. Unemployment benefits work the same way.

Discretionary fiscal policy, by contrast, is a deliberate decision, such as raising G to make up for a fall in investment.

Transfers (such as pensions) raise income too, but less than an equal rise in G. Their multiplier is c ÷ (1 − c), because households save part of a transfer. With c = 0.6, a rise of 40 in transfers raises Y by 0.6 ÷ 0.4 × 40 = 60, while a rise of 40 in G raises it by 100.