The marginal propensity to consume is 0.75 and taxes are lump-sum. The government raises lump-sum taxes by 100 and keeps its spending unchanged. By how much does income fall in the first two rounds of the multiplier process taken together, and by how much once all the rounds have worked out?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 131.25 and 300
A tax rise does not cut spending directly. It cuts disposable income, and consumption falls by c times the rise in taxes. That fall in income cuts consumption again in the next round, and so on.
Given:
c = 0.75
ΔT = 100
\( \displaystyle \text{Round 1: } c\,\Delta T = 0.75 \times 100 = 75 \)
\( \displaystyle \text{Round 2: } c^{2}\Delta T = 0.5625 \times 100 = 56.25 \)
\( \displaystyle \text{First two rounds} = 75 + 56.25 = 131.25 \)
\( \displaystyle \text{All rounds} = \frac{c}{1 - c}\,\Delta T = \frac{0.75}{0.25} \times 100 = 300 \)
Income falls by 131.25 in the first two rounds and by 300 in all.
Option (2) 175 and 400 — Incorrect. This treats the tax rise as a direct cut in spending of 100, as if G had fallen.
Option (3) 131.25 and 400 — Incorrect. The first figure is right, but 400 uses the expenditure multiplier 1 ÷ (1 − c) = 4 in place of the tax multiplier.
Option (4) 175 and 300 — Incorrect. The total of 300 is right, but 175 treats the tax rise as a direct cut in spending of 100 in the first round.
NCERT (2026-27): “Box 5.1: Fiscal Policy But the tax increase only enters the multiplier process when the cut in disposable income reduces consumption by c times the reduction in taxes. Thus the effect on income of the tax increase is given by ΔY = – cΔT – c2ΔT + . . . = – ΔT(c + c2 + . . .) (5.11)” “Because a tax cut (increase) will cause an increase (reduction) in consumption and output, the tax multiplier is a negative multiplier. Comparing equation (5.6) and (5.8), we find that the tax multiplier is smaller in absolute value compared to the government spending multiplier. This is because an increase in government spending directly affects total spending whereas taxes enter the multiplier process through their impact on disposable income, which influences household consumption (which is a part of total spending). Thus, with a ΔT reduction in taxes, consumption, and hence total spending, increases in the first instance by cΔT. …” |