Skip to content

IAI Actuarial Core Principles · Business Economics · Profit maximisation under imperfect competition

A monopoly insurer faces the linear demand curve P = 100 - 2Q (P in rupees thousand per policy, Q in thousands of policies) and has constant marginal cost of 20. What profit-maximising price does it charge?

The price is 60. Marginal revenue is 100 - 4Q; equating it to marginal cost of 20 gives Q = 20. Substituting into the demand curve gives P = 100 - 40 = 60. The monopolist prices from the demand curve, not at marginal cost.

  1. A40
  2. B50
  3. C60Correct
  4. D70
  5. 80

Explanation

TR = 100Q - 2Q^2, so MR = 100 - 4Q. Setting MR = MC: 100 - 4Q = 20, so Q = 20. Price = 100 - 2(20) = 60. Choosing 40 comes from setting P = MC (Q = 40 gives P = 20, not 40) or from mistakenly halving; 40 is the quantity where P = MC, not the price.

Did you get it right without looking?

One question tells you little. A timed set on Profit maximisation under imperfect competition shows your real accuracy, how long you take and where you lose marks.

Practise Profit maximisation under imperfect competitionFree diagnostic mock

More Profit maximisation under imperfect competition questions