A firm’s long run total cost is Rs 40 for 1 unit, Rs 70 for 2 units and Rs 90 for 3 units of output. Which chain is correct when output rises from 2 to 3 units?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → LRMC of the 3rd unit is Rs 20 → it is less than LRAC at 2 units (Rs 35) → LRAC falls to Rs 30
Given:
Long run TC = Rs 40, 70, 90 for 1, 2, 3 units
LRMC is the change in TC for one more unit, and LRAC = TC/q.
\( LRMC_3 = 90 - 70 = 20 \)
\( LRAC_2 = 70/2 = 35 \)
\( LRAC_3 = 90/3 = 30 \)
A marginal cost below the average pulls the average down, so LRAC falls from Rs 35 to Rs 30.
Option (1) LRMC of the 3rd unit is Rs 20 → it is less than LRAC at 2 units (Rs 35) → LRAC falls to Rs 30 — Correct. Each link holds.
Option (2) LRMC of the 3rd unit is Rs 90 → it is more than LRAC at 2 units (Rs 35) → LRAC rises — Incorrect. Rs 90 is the total cost of 3 units, not the extra cost of the 3rd unit.
Option (3) LRMC of the 3rd unit is Rs 20 → it is less than LRAC at 2 units (Rs 35) → LRAC rises to Rs 45 — Incorrect. An LRMC below LRAC makes LRAC fall, not rise.
Option (4) LRMC of the 3rd unit is Rs 30 → it is less than LRAC at 2 units (Rs 35) → LRAC falls to Rs 30 — Incorrect. Rs 30 is LRAC at 3 units. LRMC of the 3rd unit is Rs 20.
NCERT (2026-27): “3.7.2 Long Run Costs In the long run, all inputs are variable. There are no fixed costs. The total cost and the total variable cost therefore, coincide in the long run. Long run average cost (LRAC) is defined as cost per unit of output, i.e. …” “3.7.2 Long Run Costs … Long run marginal cost (LRMC) is the change in total cost per unit of change in output. When output changes in discrete units, then, if we increase production from q1–1 to q1 units of output, the marginal cost of producing …” “Shapes of the Long Run Cost Curves … Let us check how the LRMC curve looks like. For the first unit of output, both LRMC and LRAC are the same. Then, as output increases, LRAC initially falls, and then, after a certain point, it rises. As long as average cost is falling, marginal cost must be less than the average cost. When the average cost is rising, marginal cost must be greater than the average cost. LRMC curve is therefore a ‘U’-shaped curve. It cuts the LRAC curve from below at the minimum point of the LRAC.” |