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 andp2 =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) Derive the optimal two-part tariffs (F1, p1; F2, p2) for the two groups.

(b) What is the corresponding optimal block pricing scheme?

(c) Now suppose that the monopolist cannot tell the two consumer groups apart. Define and explain what the term incentive compatible means in this context.

(d) How much surplus does the high type get from buying the low type’s package? Derive a general expression, A(q2), for this surplus in terms of q2.

(e) Will the low type want to buy the high type’s package?