The market for a monopolist's good consists of two types of consumers: the first has a demand given by PA = 180 5QA and the second has demand given by PB = 130 6QB. To begin with there is one of each type of consumer. The monopolist's cost function is C(Q) = 10Q which means the monopolist has a marginal cost of 10

a. If the monopolist can first degree price discriminate, what is the optimal two part tariff to charge each type of consumer? What are the optimal block pricing bundles to sell to each type of consumer?

b. Suppose that the monopolist cannot tell the two groups apart and can only use second degree price discrimination. What is the optimal menu of bundle(s) to offer to the consumers?

c. Now suppose that the monopolist is still restricted to second degree price discrimination, but instead of having one of each type of consumer, there is one of type B and X of type A. What does X have to be before it's better for the monopolist only to sell to A types. (Note: X is not necessarily an integer)