Demand forecast for full-price tickets

(Annenberg) Ron, the director at the Annenberg Center, is planning his pricing strategy for a musical to be held in a 100-seat theater. He sets the full price at $80 and estimates demand at this price to be normally distributed with mean 40 and standard deviation 30. Ron also decides to offer student-only advance sale tickets discounted 50 percent off the full price. Demand for the discounted student-only tickets is usually abundant and occurs well before full-price ticket sales.

a. Suppose Ron sets a 50-seat booking limit for the student-only tickets. What is the number of full-price tickets that Ron expects to sell? [18.2]

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b. Based on a review of the show in another city, Ron updates his demand forecast for full-price tickets to be normal with mean 60 and standard deviation 40, but he does not change the prices. What is the optimal protection level for full-price seats? [18.2]

c. Ron realizes that having many empty seats negatively affects the attendees’ value from the show. Hence, he decides to change the discount given on student-only tickets from 50 percent off the full price to 55 percent off the full price and he continues to set his protection level optimally. (The demand forecast for full-price tickets remains as in b, normal with mean 60 and standard deviation 40.) How will this change in the studentonly discount price affect the expected number of empty seats? (Will they increase, decrease, or remain the same, or is it not possible to determine what will happen?) [18.2]

d. Ron knows that on average eight seats (Poisson distributed) remain empty due to noshows. Ron also estimates that it is 10 times more costly for him to have one more attendee than seats relative to having one empty seat in the theater. What is the maximum number of seats to sell in excess of capacity?

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