Well while we don't need to state reasons, there is also the risk that all proprietary software is less productive for some reason.
How do both of them weight?
The one thing that is certain is that administrative costs of prorpietary software do reduce the softwre availability, as spodek said.
Only from simple empirical studies of a few software packages (OO vs MS Office, Gimp vs PS, Eclipse vs IDEA, Blender vs. many) I think it's fairly obvious that the "normal" open source model doesn't match the megacorp development model for complex desktop software. My best guess at the reason is that 1) Ivory Tower is better than committee design for user interfaces 2) you need a LOT of expensive non dev resources such as designers and focus groups which just don't seem to materialize for the open source projects like they do when Adobe or Microsoft waves a pay check.
I think there may be lots to save in administration, servers etc when moving to Linux, but 2014 isn't the year of desktop Linux, far from it. You really can't motivate not buying office for a few bucks per month and expect to save money.
You CAN probably save a ton by ditching exchange/SQL server and so on, where there are plenty of good alternatives. But Ubuntu/OpenOffice instead of Win/Office? I doubt it, given reasonably low volume license costs.
(Average gross salary in Germany was €3,391 in 3Q2013 so the cost of employing someone would be higher than that.)
http://en.wikipedia.org/wiki/Usage_share_of_operating_system...
Nobody cites Windows or Office as an impediment to growth. It is very unlikely that the Windows Web client share decline has ever hit a "productivity" speed bump.
Another way to look at it is that mobility turned out to be much more highly valued than Office or Windows compatibility.
I agree on OO. The risk in my eyes here is that OSS (desktop) software is almost invariably less productive than proprietary software for some reason. Switching that way can make sense if you save a lot on licenses, administration etc., but if you have to pay once for a switch AND then pay continuously by using less productive software you are taking a much higher risk. It may give a warm fluffy feeling to be using open standards, but the problem is that the only standard that exists is a de-facto proprietary standard set by Microsoft. It may be noble to try to change that, but I certainly wouldn't want to spend tax money being the first major city to do so.