Expected change in revenue is 1 f 2 b 2 f 1 c b 2 p 2

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expected change in revenue is: (1 – F 2 (b 2 )) × F 1 (C – b 2 ) × p 2 – (1 – F 2 (b 2 )) × (1 - F 1 (C – b 2 )) × (p 1 – p 2 ) Potential revenue increase from booking one more discount passenger Potential revenue decrease from displacing a full fare passenger At the optimal b 2 : (1 – F 2 (b 2 )) × F 1 (C – b 2 ) × p 2 = (1 – F 2 (b 2 )) × (1 – F 1 (C – b 2 )) × (p 1 – p 2 ) F 1 (C – b 2 ) = (p 1 – p 2 ) / p 1 1 – F 1 (C – b 2 ) = p 2 / p 1 (c) Prof Ozge Sahin, JHU Blue Sky Example – Part 1 } BlueSky operates Flight 97, a nonstop flight from JFK to Salt Lake City that departs at 9:30 p.m. For this route they fly an Airbus A320 that can carry 146 passengers. On the airplane, all seats are economy class (there are no business or 1st-class seats), and the marginal cost of each additional passenger in these seats is negligible. BlueSky has constructed a two-tier fare structure: Advance purchase tickets (i.e., non-refundable tickets purchased at least 14 days in advance) cost $114 one-way. Full-fare refundable tickets purchased at any time cost $174. Throughout this case we will focus on a single Flight 97 on a single day. Assume that the demand distributions for this flight have been carefully estimated. In particular, demand for full-fare tickets is normally distributed with a mean of 92 and a standard deviation of 30. Demand for advance purchase ( low-fare ) tickets is normally distributed with a mean of 80 and a standard deviation of 25. } C = 146 } p 2 = 114 } p 1 = 174 } F 1 : normal with mean 92 and standard deviation 30 } b 2 = ? (c) Prof Ozge Sahin, JHU
2/22/17 12 Blue Sky Example – Part 1 1 – F 1 (C – b 2 ) = p 2 / p 1 Þ 1 – F 1 (146 – b 2 ) = 114 / 174 = 0.655 Þ F 1 (146 – b 2 ) = 0.345 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 NORMINV(0.345, 92, 30) = 80 Þ 146 – b 2 = 80 Þ b 2 = 66 We want to find the quantity on the x-axis so that the shaded area is 34.5% of the overall are under the curve. (c) Prof Ozge Sahin, JHU Spotlight on demand assumptions This set-up assumes that customers are neatly divided into two buckets -- leisure vs. business -- and the sizes of these buckets can be estimated as D 2 and D 1 . In reality, the distinction is not so clear, of course. 1. If we reduce the capacity allocated to fare class p 2 , we are likely to see an increase in the demand for the fare class p 1 , as some customers will “buy up.” 2. If we increase the capacity allocated to fare class p 2 , we are likely to see a decrease in the demand for fare class p 1 , because some of the business passengers will “buy down.” 1 2 p 2 p 1 D 2 Demand D 1 Period Fare (c) Prof Ozge Sahin, JHU
2/22/17 13 BlueSky Example Part-2 } Suppose now that the demand for low-fare tickets includes a sub-segment of customers: those who prefer a low-fare ticket but are willing to buy up to a full-fare ticket if a low-fare ticket is not available (think of a price sensitive small business owner who must fly to a meeting).

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