Suppose Disneyland is considering how to price entry into their theme park. They've decided that in addition to charging an entry fee, they will also charge for rides. That is, Disneyland will charge consumers with a two-part tariff T(Q) = a + pQ where a is the entry fee, p is the marginal price of a ride, and Q is the number of rides.
They're facing two types of customers: adults (with children who love rides) with inverse demand function P = 20 - 1/5 Q_A and senior citizens with inverse demand function P = 20 - 2/5 Q_S.
Suppose that the marginal cost of producing rides is constant at 4, so that C(Q) = 4Q.
(a) Assuming that Disneyland wants to serve both types of consumers, find the entry fee and the marginal price under the Oi two-part tariff.
(b) Assuming that Disneyland wants to serve both types of consumers, find the entry fee and the marginal price under the optimal two-part tariff. (Note: be very careful when finding derivatives)
(c) Compare the monopoly profit under the Oi two-part tariff with the profit under the optimal two-part tariff.