A live theater is considering what changing their prices for next season's performances and they've hired a consultant. The consultant has determined that the audience is composed of two types of customers. The first are "enthusiasts", who are wealthy and committed theater enthusiasts. By studying past demand the consultant determined that the enthusiasts' demand is described by the equation and marginal revenue equation

P_e= 450 - 0.15Q_e

MR_e= 450 - 0.30Q_e

Where P_eis the price an enthusiast must pay for a subscription and Q_eare the number of enthusiast subscriptions.

The other group of potential subscribers are "students", how are generally less wealthy and less dedicated to theater. Their demand and marginal revenue is given by

P_s= 300 - 0.15Q_s

MR_s= 300 - 0.30Q_s

Where P_sis the price a student must pay for a subscription and Q_sare the number of student subscriptions.

Assume that the theater has unlimited capacity and saw the marginal cost of selling one more subscription is zero.

1.Suppose the theater can charge different prices to the two groups. Calculate the optimal price and quantity to charge each group. (Explain your answer)

2.Discuss the likelihood that the theater will be able to charge different prices for the two groups; making reference to the issues that must be resolved if a firm is to be successful price discriminator.