A monopolist has two sets of customers. The inverse demand for one set may be described by P=200-X. For the other set, 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
X=300-(3/2)P; 0≤P≤100
b. Show that when 100P≤200 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 Group 2 ? what is the consumer surplus of each group? What are total profits?
C. suppose the monopolist can separate the to groups and charge separate, profit maximizing prices to each. what will these prices be? what is consumer surplus? what are total profit?
D. if total surplus is defined as consumer surplus plus profits , how has price discrimination affected total surplus?