In class, we study the two-part tariff question with the following system. Consumer 1 has demand function q1 = 50 − p1 and consumer 2 has q2 = 50 − 2p2 The per-unit cost of the production is mc = 10. Our conclusion is that if we have only one two-part tariff scheme (f, p), it is the best for the monopoly to set f = 800 and p = mc = 10. But it means that we have to exclude consumer 2 from the market as the fee is too expensive. Now suppose that monopoly can design two schemes (f1, p1) (f2, p2) (a) Can the following schemes make the monopoly more profitable? (f1, p1) = (800, 10) (f2, p2) = (225, 10) If so, what’s the new profit? If not, why? (b) What’s the necessary conditions that consumer 1 wants to participate given scheme 1? How about the conditions for consumer 2? (The conditions should be some inequalities.) (c) What’s the necessary conditions that consumer 1 will voluntarily choose scheme 1 and consumer 2 will voluntarily choose scheme 2 if both schemes are available to them? (The conditions should be some inequalities.) (d) Compute the profit maximizing schemes for the monopoly.