3.1

## École Nationale de l'Aviation Civile

Skip to 0 minutes and 8 secondsNicodorus van Ryzin is a great magician! He performs a show every night in his own theatre, showcasing all sorts of tricks, for which he has become famous over the years.

Skip to 0 minutes and 22 secondsHe loves having a diverse audience at his shows: young or old; working class or wealthy. Well, in reality, he loves to make money, and this diversity is a good way to do so. Not only is van Ryzin a great magician, he is also quite good at economics, and he created his own pricing strategy in order to optimize his profit. His theatre has two doors, which open onto two different streets. People arriving from Downtown Boulevard through the main entrance (door A) are asked to pay a price of €100, whereas people coming from Diagon Alley through the side entrance (door B) have a special discount price of €10.

Skip to 1 minute and 11 secondsDoor A or door B, van Ryzin always opens only one door at a time. Here we are! The show is about to begin, and the theatre is almost full. In fact, there is only one free seat remaining. In order to try and sell this last seat, as a matter of course, a theatre door remains open until the show begins, but which door should van Ryzin keep open? Door A or door B? To solve this problem, van Ryzin will not call on his magic skills, but rather on some simple maths and his knowledge of the audience attending his shows.

Skip to 1 minute and 57 secondsOn one hand, he knows by experience that, at the price of €10, there is always someone willing to enter from Diagon Alley through door B. In other words, the demand for a seat at the price of €10 is certain. On the other hand, demand on Downtown Boulevard is more

Skip to 2 minutes and 19 secondsuncertain: there is a chance of one in two that somebody is willing to enter at the price of €100.

Skip to 2 minutes and 28 secondsIn other words, there is a probability of 0.5 to sell a ticket at door A. Equipped with van Ryzin’s secrets about his pricing strategy, you now know what to expect from each entrance. So, which door should van Ryzin open? Door A or door B?

# Case study: van Ryzin's theater

Nicodorus van Ryzin is a great magician, but he is also quite good at economics. He has developed his own pricing strategy in order to optimize his profit.

His theatre has two doors, each with a different price. Tonight, he must decide at which price to sell the last seat for his show…

## Join the discussion

In your opinion, should van Ryzin open door A or door B in order to sell his very last seat?

Discuss why you chose Door A or Door B with your fellow learners in the comments!