Economics – Monopoly

A monopolist has two sets of customers. The inverse demand for Group 1 is described by P = 200 − X. For Group 2, the inverse demand is P = 100 − 2X. The monopolist faces constant marginal cost of 40

(a) Show that the monopolist’s total demand, if the two markets are treated as one is: X = 0;P ≥ 200 X = 200 − P ; 100 < P ≤ 200 X = 250 − (3/2)P ; 0 < P ≤ 100

(b) Show that the monopolist’s profit maximizing price is P = 120 if both groups are to be charged the same price. At this price, how much is sold to members of Group 1 and how much to members of Group 2? What is the consumer surplus of each group? What are total profits?