In an economy, C = 50 + 0.8YD, I = 70 and G = 80. The government collects a proportional income tax, T = 0.25Y, and makes no transfers. What is the state of the government budget at equilibrium income?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A surplus of 45
First find equilibrium income with the proportional-tax multiplier. Then compare the tax collected at that income with government purchases.
Given:
C = 50 + 0.8YD
I = 70, G = 80
T = 0.25Y
\( \displaystyle A = 50 + 70 + 80 = 200 \)
\( \displaystyle Y^{*} = \frac{200}{1 - 0.8 \times 0.75} = \frac{200}{0.4} = 500 \)
\( \displaystyle T = 0.25 \times 500 = 125 \)
\( \displaystyle T - G = 125 - 80 = 45 \)
Tax revenue is larger than government spending by 45, so the budget shows a surplus of 45.
Option (1) A surplus of 170 — Incorrect. This takes Y = 200 ÷ 0.2 = 1,000, leaving the tax out of the multiplier. Tax would then be 250.
Option (2) A deficit of 45 — Incorrect. This reverses the sign. Revenue (125) is larger than spending (80).
Option (3) A balanced budget — Incorrect. Revenue and spending are not equal at Y = 500.
NCERT (2026-27): “5.2 Balanced, Surplus and Deficit Budget The government may spend an amount equal to the revenue it collects. This is known as a balanced budget. If it needs to incur higher expenditure, it will have … When tax collection exceeds the required expenditure, the budget is said to be in surplus. However, the most common feature is the situation when expenditure exceeds revenue. This is when the government runs a budget deficit.” “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. … 2.5 which is smaller than that obtained with lump-sum taxes. …” |