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

Two firms, A and B, form a Cournot duopoly with inverse market demand P = 100 − Q, where Q = qA + qB, and zero marginal cost. Each chooses output taking the other's output as given. What is the equilibrium market price?

The equilibrium price is 33.33. Each firm's reaction function is q = (100 − other's output)/2. With symmetry, each produces 33.33, total output is 66.67, and price is 100 − 66.67 = 33.33, between the monopoly price of 50 and the competitive price of 0.

  1. A25
  2. B33.33Correct
  3. C50
  4. D20
  5. 0

Explanation

Firm A maximises (100 − qA − qB)qA, giving the first-order condition 100 − 2qA − qB = 0, so qA = (100 − qB)/2. By symmetry qA = qB = q, so 3q = 100 and q = 33.33. Q = 66.67 and P = 100 − 66.67 = 33.33. Price 50 is the monopoly price and 0 is the perfectly competitive price at zero cost.

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