Question 6 (c)(ii)
Profit-maximising output at a price of ₹60 when MC = 0.3Q
1 mark
- Time to write
- About 2 minutes
Question
Question 6 (c)(ii) · 1 marksIn a perfectly competitive market the price of a good is ₹60. A producer has the total cost and marginal cost functions given below.
TC(Q) = 400 + 0.2 Q^2^ MC(Q) = 0.3 Q
- Calculate the output (Q) that the firm will produce in order to maximize profit.
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
As printed, the marginal cost function given is not the slope of the total cost function given; this copy keeps both as printed and the part is answered with the functions as given.
Write it in this order
- 1 Price equals marginal cost for a competitive firm, solved for Q 1 mark 2 min
Try it first. About 2 minutes for 1 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
The profit-maximising rule. A firm in perfect competition takes the market price as given, so the extra revenue from one more unit is the price itself, MR = p. Profit rises while MR is above MC and falls once it is below, so profit is greatest where p = MC, on a rising part of the MC curve.
Output. With p = ₹60 and MC(Q) = 0.3Q as given:
60 = 0.3Q, so Q = 200 units.
MC = 0.3Q rises with output, so this is a maximum, not a minimum.
The other reading. As the paper note says, 0.3Q is not the slope of the total cost function printed; the slope of TC = 400 + 0.2Q² is 0.4Q. With MC = 0.4Q the rule would give 60 = 0.4Q, Q = 150. The question gives MC directly, so the answer uses it.
Answer. The firm maximises profit at Q = 200 units, where the price of ₹60 equals the marginal cost 0.3 × 200 = ₹60.
Where the 1 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Price equals marginal cost for a competitive firm, solved for Q | 1 |
| Total | 1 |
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