The table shows a competitive firm’s long run average cost (LRAC) before and after the government imposes a unit tax:
| Output (units) | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| LRAC before the tax (Rs) | 30 | 24 | 20 | 22 | 26 |
| LRAC after the tax (Rs) | 34 | 28 | 24 | 26 | 30 |
What is the unit tax, and what is the firm’s total cost (including the tax) if it produces and sells 30 units?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Unit tax Rs 4; total cost Rs 720
A unit tax of Rs t raises long run average cost by Rs t at every output. Here LRAC rises by Rs 4 at each output.
Given:
LRAC at 30 units before the tax = Rs 20
LRAC at 30 units after the tax = Rs 24
Unit tax = 24 − 20 = Rs 4
Total cost = average cost × quantity = 24 × 30 = Rs 720
Option (2) Unit tax Rs 4; total cost Rs 600 — Rs 600 is the cost before the tax (20 × 30).
Option (3) Unit tax Rs 4; total cost Rs 120 — Rs 120 is the tax alone (4 × 30).
NCERT (2026-27): “Impact of a unit tax on supply A unit tax is a tax that the government imposes per unit sale of output. For example, suppose that the unit tax imposed by the government is Rs 2. Then, if the firm produces and sells 10 units of the good, the total tax that the firm must pay to the government is 10 × Rs 2 = Rs 20. … Now, suppose the government puts in place a unit tax of Rs t. Since the firm must pay an extra Rs t for each unit of the good produced, the firm’s long run average cost and long run marginal cost at any level of output increases by Rs t.” “4.3.3 Condition 3 … Notice that the firm’s total revenue, TR, at q1 is the area of the rectangle OpAq1 (the product of price and quantity) while the firm’s total cost, TC , is the area of the rectangle OEBq1 (the product of average cost and quantity). …” |