Productivity is not 'demandable', at least not in the long term. Creating a productive team and as a result, a productive organization is about inspiring the best from people.
There are many factors that drive or hinder success as measured by productivity.
Let's talk about your challenges.
Every organization has a culture. Your culture may not be the one you want, but it is likely the one you created.
The first challenge is to recognize the reality. The second is to define the changes required.