Suppose we have two types of consumers (for simplicity we’ll assume that there is one person of each type). They have inverse demand curves given by: p1 =110−2q1 and p2 =70−4q2. Initially, we will assume that the monopolist can tell them apart and that consumers cannot change or fake their type. Let the marginal cost of production be equal to 10. Label group 1 as the “high type” and group 2 as the “low type.”
(A) Solve for the optimal (V1, q1) and (V2, q2) that satisfies the incentive compatibility constraints.
(B) What rents do the low-type consumers earn in any equilibrium? What about the high-type consumers?
(C) How does welfare compare to the case when the monopolist can tell the two groups apart? What drives the difference?