### One item

You have one item to sell and you need to post a price for it. There is a single potential buyer and the value of the item for the buyer is distributed according to a known probability distribution.

It is quite easy to compute which posted price will maximize your revenues. You need to maximize the price multiplied by the probability that the value of the item is greater or equal to that price.

Examples:

1) When the value of the item for the buyer is 10 with probability 1/2 and 15 with probability 1/2. The optimal price is 10 and the expected revenue is 10.

2) When the value of the item for the buyer is 10 with probability 1/2 and 40 with probability 1/2. The optimal price is 40 and the expected revenue is 20.

### Two items

Now you have two items to sell and as before a single potential buyer. For each of the items, the buyer’s value behaves according to a known probability distribution. And these distributions are statistically independent**.** The value for the buyer of having the two items is simply the sum of the individual values.

Now we allow the seller to post a price for the **bundle** of two items and he posts the price that maximizes his revenues.

In summary: The values are additive, the distributions are independent.

*Test your intuition*:

1) Can the revenues of a seller for selling the two items be* larger* than the sum of the revenues when they are sold separately?

2) Can the revenues of a seller for selling the two items be *smaller* than the sum of the revenues when they are sold separately?

PS: there is a new post by Tim Gowers on the cost of Elseviers journals in England. Elsevier (and other publishers) are famous (or infamous) for their bundling policy. The movement towards cheaper journal prices, and open access to scientific papers that Gowers largly initialted two years ago is now referred to as the “academic spring.”

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