OK -- this is a fun topic. The AIR we breathe consists of approximately 78% nitrogen, 21% oxygen and 1% "other" stuff. So, paying $10 per tire for nitrogen is, shall we say, "extravegant".
Since there's no way to effectively "purge" your tires of the air in them when mounted and filled at the dealer (short of sending them up on the space shuttle and having them filled while out on a space walk) my guess is that you still have a decent percentage of Oxygen mixed in with the added nitrogen.
Unless you are racing F1 or IndyCar, or have a Gulfsteam jet, nitrogen is of little to no benefit, especially true for street driving.
Here's another link (below) that offers more insight. It's your $40 (dealers seem to offer this at $10/tire), so spend it as you wish. I'll just keep topping of with an 80/20 mix (air) and use the $40 for lunch.
http://www.straightdope.com/co...f-air