You're right, it is self-evident to me that group productivity is not the aggregate of individual productivity. We have companies and teams for a reason.

Secondly, the goal of a company is rarely to maximize aggregate employee productivity. If you can realize the same profits with fewer LOF, stories delivered, or whatever your employees "produce", why not?

Economic productivity is usually defined as the value of what is produced. Again, my point was that if you have some measure of productivity P such that decreasing sum(P(employees)) increases P(sum(employees)), your P is not a good measure.

It's good to be explicit like this. Probably we agree more than I realized, because what I'm trying to get at is that so many of these blog posts complaining about open offices use the wrong P by focusing on a subset what they produce on a daily basis. In fact, I'm suggesting that the employee is using a different P than the employer, and that it's plausible that the employee is the using the wrong P (whether the employer is or not).

Then again, where we might disagree is to what degree the same P can and should be applied to both individual employees and to companies. So often individuals project what they (like to) do onto the team as its primary purpose. "I make widgets, and there are less widgets at the end of the day than there could be, so the company must not be optimized." It might be, or you may overvalue widgets.