Ms. Aura is a psychic. The demand for her services is given by Q = 2,000 - 10P, where Q is the number of one-hour sessions per year and P is the price of each session. Her marginal revenue is MR = 200 - 0.2Q. Ms. Aura's operation has no fixed costs, but she incurs a cost of $150 per session (going to the client's house).
(a) What is Ms. Aura's yearly profit?
(b) Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2500 - 5P. Her new marginal revenue is MR = 500 - 0.4Q. What is her profit now?
(c) Advances in telecommunications and information technology revolutionize the way Ms. Aura does business. She begins to use the Internet to find all relevant information about clients and meets many clients through teleconferencing. The new technology introduces an annual fixed cost of $1,000, but the marginal cost is only $20 per session. What is Ms. Aura's profit? Assume the demand curve is still given by Q = 2500 - 5P.
(d) Summarize the lesson of this problem for the superstar phenomenon.