[dahfizz]

Assuming that a person will always be productive for X hours a day, regardless of how long they are in the office, is naive.

The reality is that people spend some percentage of their time being productive. During the day they take coffee breaks, chat with coworkers, check Twitter, etc.

Assume people are productive for 20 hours now. If you reduced the work week to be 20 hours, productivity would go down. There would still be meetings, coffee breaks, etc that eat into those 20 hours. Now people are only productive for, say, 15 hours a week.