With lump-sum taxes, the government expenditure multiplier of an economy is 5. When the government moves to a proportional income tax, this multiplier falls to 2. What is the rate of the proportional income tax?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 37.5 per cent
The lump-sum multiplier, 1 ÷ (1 − c), gives the marginal propensity to consume. The proportional-tax multiplier, 1 ÷ [1 − c(1 − t)], then gives the tax rate.
Given:
Multiplier with lump-sum taxes = 5
Multiplier with the proportional tax = 2
\( \displaystyle \frac{1}{1 - c} = 5 \;\Rightarrow\; c = 0.8 \)
\( \displaystyle \frac{1}{1 - c(1 - t)} = 2 \;\Rightarrow\; c(1 - t) = 0.5 \)
\( \displaystyle 1 - t = \frac{0.5}{0.8} = 0.625 \)
\( \displaystyle t = 0.375 \)
The tax rate is 37.5 per cent. The tax lowers the propensity to consume out of income from 0.8 to 0.5, so the multiplier falls.
Option (1) 50 per cent — Incorrect. This takes c(1 − t) = 0.5 as the tax rate itself.
Option (2) 25 per cent — Incorrect. With c = 0.8 and t = 0.25, the multiplier is 1 ÷ 0.4 = 2.5, not 2.
Option (3) 62.5 per cent — Incorrect. This is 1 − t, the share of each rupee of income left after the tax.
NCERT (2026-27): “Box 5.1: Fiscal Policy We note that proportional taxes not only lower consumption at each level of income but also lower the slope of the consumption function. The mpc out of income falls to c (1 – t). … Comparing this with the value of the multiplier with lump-sum taxes case, we find that the value has become smaller. …” “In Example 5.1, if we take a tax rate of 0.25, we find consumption will now rise by 0.60 (c (1 – t) = 0.8 × 0.75) for every unit increase in income instead of the earlier 0.80. Thus, consumption will increase by less than before. … 2.5 which is smaller than that obtained with lump-sum taxes. …” |