Consider a third-degree price discriminating monopolist operating in two separate markets with demand functions P1 = 100 - q1 and P2 = 80 - 2q2. The constant marginal cost of production is MC = 20. What is the ratio of optimal output sold in Market 1 to Market 2 (q1* / q2*)?

In third-degree price discrimination the monopolist equates the marginal revenue of each market with the common marginal cost: MR1 = MR2 = MC. Market 1: TR1 = (100 - q1)q1 = 100q1 - q1² MR1 = 100 - 2q1 100 - 2q1 = 20, so q1* = 40 and P1 = 100 - 40 = ₹60. Market 2: TR2 = (80 - 2q2)q2 = 80q2 - 2q2² MR2 = 80 - 4q2 80 - 4q2 = 20, so q2* = 15 and P2 = 80 - 30 = ₹50. Ratio q1* : q2* = 40 : 15 = 8 : 3. We can verify with the Lerner index. In Market 1, |e| = P/(100 - P) = 60/40 = 1.5 and (P - MC)/P = 40/60 = 1/1.5. In Market 2, |e| = P/(80 - P) = 50/30 = 1.67 and (P - MC)/P = 30/50 = 1/1.67. The market with the more elastic demand (Market 2) is charged the lower price, as the theory says it should be. Hence the correct option is (D).