The marginal propensity to consume is 0.8 and the government collects a proportional income tax at the rate of 0.25 (no other taxes). Government purchases rise by Rs 40 crore, and nothing else changes. By how much does the budget deficit change once the multiplier process is complete?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → It rises by Rs 15 crore.
With a proportional tax, consumption rises by only c(1 − t) of each extra rupee of income, so the multiplier is 1 ÷ [1 − c(1 − t)]. As income rises, tax revenue tY also rises, and this pays for part of the extra spending.
Given:
c = 0.8
t = 0.25
ΔG = Rs 40 crore
\( \displaystyle k = \frac{1}{1 - 0.8 \times 0.75} = \frac{1}{0.4} = 2.5 \)
\( \displaystyle \Delta Y = 2.5 \times 40 = 100 \)
\( \displaystyle \Delta T = 0.25 \times 100 = 25 \)
\( \displaystyle \Delta \text{Deficit} = 40 - 25 = 15 \)
The deficit rises by Rs 15 crore.
Option (1) It rises by Rs 40 crore. — this forgets that tax revenue rises with income.
NCERT (2026-27): “Box 5.1: Fiscal Policy … Case of Proportional Taxes: A more realistic assumption would be that the government collects a constant fraction, t, of income in the form of taxes so that T = tY. …” “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. … If government expenditure rises by 100, output will rise by the multiplier times the rise in government expenditure, that is, by 2.5 × 100 = 250. …” |