A key notion: The Expected Marginal Seat Revenue (EMSR)
The \(EMSR\) for the seat \(s\) is defined as the price multiplied by the probability of selling an additional seat. We can also understand the \(EMSR(s)\) as the expected value of the current seat \(s\).


To find that optimal quota graphically, we use a simple trick and flip the curve representing the \(EMSR_L\) at the lower price horizontally. So, for the \(EMSR_L\), the horizontal axis starts on the right, as presented below.\(Q\) should be such that the expected value of the last seat sold at the higher price is (nearly) equal to the corresponding expected value for the remaining seats at the lower price.

To sum up
Even in this simple setting with only two prices, the decision on the number of seats to protect at the higher price depends on a precise knowledge of each demand.Knowing the average demand is not sufficient. What is important to know is not the average number of seats one sells, but the probability of selling more than a threshold (whether that’s 50 seats, 60 or even 70 seats). If the company has collected data on past bookings, those probabilities are quite easy to calculate, and so is the \(EMSR\)!This calculation has to be done for both demands such that the optimal quota can be determined, either graphically or analytically.An Introduction to Pricing Strategy and Revenue Management

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