Two-part Tariff

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

(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.