Improving productivity is crucial to profitability. How do you improve employees productivity through working as a team?

Incentify working in teams, reward teamwork, emphasise the importance of collaborating at work, have an event for employees to know each other.
But remember, teams (especially cross functional teams) will go through the FSNP phases, so, it might push your production/service to lower rates for a while, you need to see how long does it take to get to the previous level, if it didn't, you need to introduce some process changes, see the better performing teams, focus on the success factor to those teams.
This will get employees work, and let them have fun every once in a while.

Forget about the team...target each individual within the team on there utilisation and in turn there ouput should increase, thus increasing overall team productivity.
Its very rare to find a team with exactly the same level of skills and more importantly commitment!