Outsourcing sounds like a great idea until you hear the prices. A dedicated team from a company in the US offers support on a 24/7 basis (with a team of 6 people in 4 hour shifts) at around 15.000 USD per month. Now, being just one person per shift, how many tasks can he do simultaneously? And this is just tier 2 support, the most complicated stuff must be done in-house.
So no for outsourcing. Even for big companies, I believe that unless you sell a very expensive product, it is more cheap to grow your own department of support.