Twitter's Rising Popularity < Twitter's Rising Cost ?

I picked this up on a data mining feed. A really interesting discussion is brewing on how much it costs twitter to maintain it's network. The worry is that users getting SMS messages are going to eat the network out of house and home as the network gets larger. Here is a really simple demonstration of where the worries come from. Say it costs twitter $100 a year to maintain a the correspondence between any two users.



One can see adding a third user increases the overall cost of the network by $200. Adding the fourth will increase the cost by $300. You see where this is going. The fifth member will increase the cost by $400...and the nth member will increase the cost by (n-1)*100.

Now Twitter's actual case is much more complicated. First, each new member doesn't connect with every single old member. Second, some links cost more than others. Third, the more members, the greater twitter's add revenue (I assume they are add-based). This helps offset the greater costs.

Curious? Here is Paul Botin's post that started the discussion.

I came a cross the discussion reading Mathew Hurst's critique of Botin describing the growth of costs as "exponential". The math snark in me also laments the imprecision with which this word is often used.