You are the sales manager of an Airline. There is a flight that will take off in

Question

You are the sales manager of an Airline. There is a flight that will take off in six days and there are still two available seats. Therefore, there are five days for you to sell them. Assume that in each day there will be a potential customer browsing your airline’s booking website. The customer’s valuation is random and is described by a uniform distribution. That is, if you price the ticket at p [0, 1], a customer has 1 p chance to purchase the ticket. Unsold tickets generate no profit and overbooking is not allowed. Please find the optimal first-day price of a ticket.

Explanation / Answer

The expected revenue is probability of buying multiplied by price of ticket

Revenue = p(1-p) = p-p^2

We maximise revenue by differentiating it with price,

d(Revenue)/dP= 1-2p=0

or p = 1/2=0.5

Ticket should be prices ar 0.5

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