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IAI Actuarial Core Principles · Business Economics · Profit maximisation under perfect competition and monopoly

A monopolist in Pune faces the demand curve P = 100 - 2Q (P in rupees) and has constant marginal cost of Rs 20 per unit and no fixed costs. What is the profit-maximising price?

The price is Rs 60. Marginal revenue is 100 - 4Q; equating it to marginal cost of 20 gives output of 20 units. Substituting into the demand curve gives price 100 - 40 = Rs 60, giving profit of Rs 800.

  1. ARs 20
  2. BRs 40
  3. CRs 50
  4. DRs 60Correct
  5. Rs 80

Explanation

MR = 100 - 4Q. Setting MR = MC: 100 - 4Q = 20, so Q = 20. Price = 100 - 2(20) = Rs 60. Rs 20 is the marginal cost, and Rs 40 is the price from using P = MC (Q = 40 gives P = 20, not 40), so it arises from a slope error; Rs 60 is the correct figure. Check: profit = (60-20)x20 = Rs 800.

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