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

A firm has constant marginal cost of Rs 20 and faces demand P = 100 - Q. Which price and quantity maximise its profit?

Profit is maximised at price Rs 60 and quantity 40. Marginal revenue is 100 minus 2Q; equating it to marginal cost of 20 gives Q of 40, and the demand curve then gives a price of 60. Setting price equal to cost would be wrong.

  1. AP = 60, Q = 40Correct
  2. BP = 20, Q = 80
  3. CP = 50, Q = 50
  4. DP = 80, Q = 20
  5. P = 40, Q = 60

Explanation

TR = 100Q - Q^2, so MR = 100 - 2Q. Setting MR = MC: 100 - 2Q = 20, so Q = 40. Price from demand is 100 - 40 = 60. P = 20, Q = 80 is the competitive outcome where P = MC, which wrongly ignores MR lying below price.

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