## Why Bill Gates quit Facebook?

Bill Gates told guests at a forum held in New Delhi that he quit facebook. People may think that that is because Bill Gates hates Facebook as a dangerous competitor against Microsoft. However, this is not the reason that he quit facebook. He quit it because he was overwhelmed by the number of friend requests coming to him.

In class, we learned that the value of a certain network increases with the number of people who are using it. For example, the cell phone network will not have a great value to a consumer if there is only one consumer who is using that cell phone network. However, if a million people joined to that network, there will be a great value added to that network because now a consumer will be added and can interact with million other people. So, Metcalfe’s law states that the value of a telecommunication network is proportional to the square of the number of connected users of the system.(n^2)

However, as we can see in Bill Gate’s case, there is a certain tipping point where too many users in the network gives negative effect to the user in it. Inspired from this phenomenon, economist Beckstrom, former director of US National Cyber security Center, proposed “Beckstrom’s Law, which proposes a new way of making a valuation of networks. It states that the value of a network is the net value of each user’s transaction summed up for all users. Basically, the value for the users is the sum of benefits from all transactions minus the cost of all transactions. For example, let’s say one person decides to buy books from Amazon.com worth \$100 every months. He can buy the same stuff at offline stores but then his time to visit bookstore and gas he had to pay to get to the bookstore should be added to the cost as an economic cost. So, using a network generates a value to him. However, there is a related cost of using a network like internet connection fee and computer hardware. Thus, to calculate the total value of the network, we need to add up the value generated by using it minus the cost related to it.

Beckstrom uses the transactions that a user performs when using the network to make a valuation of it “The net present value (V) of any network (j) to any individual (i) is equal to the sum of the net present value of the benefit of all transactions less the net present value of the costs of all transactions on the network over any given period of time (t)”

$V_{i,j} = \sum_{k=1}^n \frac{B_{i,k}}{(1+r_k)^{t_k}} - \sum_{l=1}^n \frac{C_{i,l}}{(1+r_l)^{t_l}}$

Beckstrom’s law can also applied to making valuations of social networks. For instance, having a lot of users will benefit people who join Facebook, but there will be a certain tipping point where having too many number of people harass some people. For example, having too much friend on Facebook floods my news-feed window, thus making me hard to look for certain people’s news feeds that I always want to look at. Bill Gates’ value of using facebook decreases as the number of people using facebook increases. This clearly contrasts Metcalfe’s law that value monotonically increase as the number of people using it increases.

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