Ms. Aura is a psychic. The demand for her services is given by Q = 2,000 - 10P, where Qis the number of one-hour sessions per year and Pis 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? Find the number of sessions that Ms. Aura will provide by equating the marginal revenue to the marginal cost of a session: setting MR = MC yields 200 - 0.2Q = 150 which solves as Q = 250. The price that would generate demand for 250 sessions is $175 as 2,000 - 10 (175) = 250. Thus, her annual profit is 175 (250) - 150 (250) = $6,250 per year.
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