A monopolist produces gizmos at constant marginal cost of 4 and no fixed cost. It recognizes that it has two types of customers. The demand curve of each type of customer is given by:

Type 1 Customer: p1(q1) = 18 - 2q1

Type 2 Customer: P2(q2) = 15 - q2

Where qi (i=1,2) are the quantity demanded of type i consumer per period. While the monopolist knows the demand curves, it cannot identify the type of a given consumer. It is assumed that it has 10 customers in total per period, and five of them are of Type 1.

A) The monopolist wishes to sell both types of customers. Assuming it charges the same two-part tariff schedule to both types of consumers: derive the optimal two part tariff schedule. What would be the resulting profit?

B) Suppose that the monopolist engages in second-degree price discrimination. Derive the two part tariff schedules that are incentive compatible for both types, and the resulting profit in this case.