J 2

The Bayou City Symphony accepts season ticket subscriptions during an interval (0,t) starting at time 0. We assume that each subscription entails the purchase of one season ticket costing c dollars payable at the time of purchase. Assume that the arrivals of subscription orders follow a Poisson process with a rate of , and that the symphony is able to accommodate all purchase requests. Let be the discount factor. A dollar received s time units from now will have the present value of e^(-s).

a) Compute the expected present value at time 0 of all revenues received from the ticket sales in (0, t).

b) Consider a variant of the problem. All assumptions remain unchanged except that with probability pa subscription is for i tickets, where i = 1, ... , 4. Compute the expected present value at time 0 of all revenues received from the ticket sales in (0, t).