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

Two firms in a Cournot duopoly face market demand P = 100 − Q, where Q is total output, and each has zero marginal cost. What is the equilibrium price?

The equilibrium price is Rs 33.33. Each firm's reaction function gives symmetric output of 33.33, total output 66.67, so price is 100 − 66.67 = 33.33, between the monopoly price of Rs 50 and the competitive price of zero.

  1. ARs 25
  2. BRs 50
  3. CRs 33.33Correct
  4. DRs 0
  5. Rs 66.67

Explanation

Firm 1 maximises q1(100 − q1 − q2); the reaction function is q1 = (100 − q2)/2. By symmetry q = (100 − q)/2, so q = 33.33 each. Total Q = 66.67 and P = 100 − 66.67 = 33.33. Rs 50 is the monopoly price and Rs 0 the competitive price.

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