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

A monopolist faces the demand curve P = 100 - Q (P in rupees) and has constant marginal cost of Rs 20 and no fixed cost. A perfectly competitive industry has the same marginal cost. What is the monopolist's profit-maximising price, and how does it compare with the competitive price?

The monopoly price is Rs 60, which is Rs 40 above the competitive price of Rs 20. MR is 100 - 2Q; equating it to MC of 20 gives Q of 40, and the demand curve gives a price of Rs 60.

  1. ARs 60, which is Rs 40 above the competitive price of Rs 20Correct
  2. BRs 80, which is Rs 60 above the competitive price of Rs 20
  3. CRs 50, which is Rs 30 above the competitive price of Rs 20
  4. DRs 60, which is Rs 20 above the competitive price of Rs 40
  5. Rs 20, which equals the competitive price

Explanation

Total revenue is 100Q - Q^2, so MR = 100 - 2Q. Setting MR = 20 gives Q = 40, and P = 100 - 40 = Rs 60. The competitive price equals MC = Rs 20, so the monopoly price is Rs 40 higher. Rs 80 comes from wrongly setting P = MC for Q then doubling.

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