## Network Effects on Facebook

http://www.kottke.org/09/01/facebooks-valuation-and-the-network-effect

The above blog post applies the idea of network effects to one of the largest “networks” in the world: facebook. Like we learned in class, the author explains that the value of facebook to it’s users depends on the number of people that use it. The post examines a 2009 facebook application released by Burger King which advertised a free whopper for anyone who deleted ten of their facebook friends. As the author explains, this application indirectly gave a way to measure the value and network effects of facebook. It led to some interesting conclusions.

The author of this article refers to Metcalfe’s Law which predicts that the value to a user of a network is equal to n(n-1)/2 where n is the number of connected members of the network. This suggests that the personal value of facebook as a function of the number of users on facebook (the function we called f(z) in class) is asymptotically proportional to z squared. However, in reality, as the author points out, the number of users on facebook (z) is not the only variable in this function. Some connections are worth more than others. For example, many people would delete 10 friends for a whopper, but would hesitate more to delete a second 10 or third 10 for more whoppers. This is because people value certain connections more than others. In other words, the value of facebook to a particular user is not just dependent on how many people are on facebook, but which people are on facebook. Someone is more likely to use facebook if a lot of other people are using it, but more importantly if their friends are using it. According to the theorem we developed in class, a person will use facebook if their value of the function rf is greater than the cost of using facebook. While facebook has no monetary cost associated with it, the author explains that we can view the cost of using facebook as the amount of distractions to the user from things such as advertisements. The amount of distraction that a user is willing to put up with and still use facebook can be viewed as the user’s reservation price. In the end, as we discussed in class, a person will use facebook if the value they receive from using it is greater than their reservation cost.

Interesting post. I’ve been using Facebook for years and never really though about it in mathematical terms. I’ll share this with all of my friends amd I don’t know if I would drop more than 10 of my friends for a whopper though…