Question 6 (c)(iii)
Profit at the profit-maximising output, and whether the firm keeps operating
4 marks
- Time to write
- About 8 minutes
Question
Question 6 (c)(iii) · 4 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
- Compute the profit the firm makes if it produces the profit maximizing quantity. Will the firm keep operating, or will it shut down?
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
- Compute…Will…?Two asks in one question: answer both.
- Will the firm…?A yes-or-no question: answer it in your first line, then explain why.
- ComputeFormula 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
- Read the data; note exactly what is asked 1 min
- 1 Total revenue and total cost at the chosen output 1½ marks 3 min
- 2 Profit 1 mark 2 min
- 3 Shut-down rule applied, price against average variable cost 1½ marks 2 min
Try it first. About 8 minutes for 4 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.
Revenue and cost at Q = 200. Profit is total revenue minus total cost, π = TR − TC. At the output found in (ii), Q = 200, with p = ₹60:
| Item | Working | ₹ |
|---|---|---|
| Total revenue | 60 × 200 | 12,000 |
| Fixed cost | 400 | 400 |
| Variable cost | 0.2 × 200² | 8,000 |
| Total cost | 400 + 8,000 | 8,400 |
| Profit | 12,000 − 8,400 | 3,600 |
Profit. The firm earns a profit of ₹3,600. Average cost is 8,400 ÷ 200 = ₹42, so each unit sold at ₹60 earns ₹18 above average cost (18 × 200 = 3,600).
Operate or shut down? In the short run a firm keeps producing as long as the price is at least its average variable cost; it stops only when the price falls below the minimum of AVC, since then it would lose more by producing than by shutting down. Here AVC = 0.2 × 200 = ₹40, below the price of ₹60, so revenue covers all the variable cost (₹8,000) and leaves ₹4,000, more than the fixed cost of ₹400. The firm also covers its total cost, so it would stay even in the long run, where the price must cover average cost.
The other reading. If marginal cost is taken as the slope of the printed total cost, 0.4Q, output would be 150 and profit 9,000 − (400 + 0.2 × 150²) = 9,000 − 4,900 = ₹4,100, with AVC ₹30; the firm would again keep operating. The answer follows the MC function the question gives.
Answer. At Q = 200 the firm's profit is ₹3,600 (TR ₹12,000 − TC ₹8,400). The price of ₹60 is above its average variable cost of ₹40, so the firm keeps operating; it would shut down only if the price fell below the minimum of its AVC.
Where the 4 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Total revenue and total cost at the chosen output | 1.5 |
| 2 | Profit | 1 |
| 3 | Shut-down rule applied, price against average variable cost | 1.5 |
| Total | 4 |
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