A firm in a perfectly competitive market earns a total revenue of Rs 96 from selling 8 units. Its SMC of the 9th, 10th, 11th and 12th units is Rs 10, Rs 11, Rs 13 and Rs 15. Its total cost at 10 units is Rs 110, and price is above AVC at these outputs. What output maximises its profit, and what is that profit?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10 units; profit of Rs 10
A price-taker sells every unit at the same price, so price = TR ÷ quantity. It keeps adding units while each one costs less than the price.
Given:
TR from 8 units = Rs 96
SMC of the 9th to 12th units = Rs 10, 11, 13, 15
TC at 10 units = Rs 110
\( \displaystyle p = \frac{96}{8} = 12 \)
The 9th unit (Rs 10) and the 10th unit (Rs 11) cost less than Rs 12, so they add to profit. The 11th unit costs Rs 13, more than Rs 12, so it lowers profit. The firm produces 10 units.
\( \text{TR} = 12 \times 10 = 120 \)
\( \text{Profit} = 120 - 110 = 10 \)
Profit is Rs 10.
NCERT (2026-27): “4.3.1 Condition 1 … Notice that as long as the change in total revenue is greater than the change in total cost, profits will continue to increase. Recall that change in total revenue per unit increase in output is the marginal revenue; and the change in total cost per unit increase in output is the marginal cost. Therefore, we can conclude that as long as marginal revenue is greater than marginal cost, profits are increasing. By the same logic, as long as marginal revenue is less than marginal cost, profits will fall. It follows that for profits to be maximum, marginal revenue should equal marginal cost. In other words, profits are maximum at the level of output (which we have called q0) for which MR = MC For the perfectly competitive firm, we have established that the MR = P. So the firm’s profit maximizing output becomes the level of output at which P=MC.” |