A monopolist has two sets of customers. The inverse demand for Group 1 is described by P1 = 200 – Q1. For Group 2, the inverse demand is P2 = 100 – Q2. The monopolist faces constant marginal cost of 40. Let Q be the aggregate quantity demanded.
a. Show that the monopolist’s total demand, if the two markets are treated as one is: Q = 0; P ≥ 200 Q = 200 − P; 100 < P ≤ 200 Q = 300 − 2P ; 0 < P ≤ 100
b. Show that the monopolist’s profit maximizing price is P = 95 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?
Now suppose that the monopolist can separate the two groups and charge separate, profit-maximizing prices to each group.
c. What will these prices be? What is consumer surplus? What are total profits?
d. If total surplus is consumer surplus plus profit, how has price discrimination affected total surplus?