IAI Actuarial Core Principles · Business Economics · Profit maximisation under perfect competition and monopoly
A monopolist faces the demand schedule P = 100 − 2Q, where P is in rupees. At Q = 10 units, what are total revenue and marginal revenue (from the MR function derived from the demand curve)?
Total revenue is ₹800 and marginal revenue is ₹60. Price at 10 units is ₹80, giving TR of ₹800. Differentiating TR = 100Q − 2Q² gives MR = 100 − 4Q, which is ₹60 at Q = 10, below price.
- ATR = ₹800; MR = ₹60Correct
- BTR = ₹800; MR = ₹80
- CTR = ₹1,000; MR = ₹60
- DTR = ₹600; MR = ₹80
- TR = ₹800; MR = ₹40
Explanation
At Q = 10, P = 100 − 20 = 80, so TR = 80 × 10 = ₹800. TR = 100Q − 2Q², so MR = 100 − 4Q = 100 − 40 = ₹60. Option B wrongly takes MR equal to price.
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