A monopolist faces two consumer groups: old and young. The inverse demand of old clients for the output of the monopolist is P_o = 100 - 2Q_o. The inverse demand of young clients for the output of the monopolist is P_y = 80 - Q_y. The marginal cost of supplying any type of client is MC = 10. If the monopolist can price discriminate between the two groups (i.e., charge a different uniform price to each group), what price will old and young clients be charged? A) P_o = $45; P_y = $55 B) P_o = $55; P_y = $45 C) P_o = $50; P_y = $50 D) P_o = $40; P_y = $60

Question

Quizplus · Accepted Answer

To maximize profits, the monopolist should set the MR for each group equal to MC and then solve for the corresponding prices. For old clients: TR1 = (100 - 2Q1)Q1 = 100Q1 - 2Q1^2 MR1 = 100 - 4Q1 When MR1 = MC = 10: 100 - 4Q1 = 10 Q1 = 22.5 P_o = 100 - 2Q1 = $55 For young clients: TR2 = (80 - Q2)Q2 = 80Q2 - Q2^2 MR2 = 80 - 2Q2 When MR2 = MC = 10: 80 - 2Q2 = 10 Q2 = 35 P_y = 80 - Q2 = $45

A Monopolist Faces Two Consumer Groups: Old and Young