Innovation happens because people are curious and want to make their (or other's) lives easier, this has nothing to do with patents, or if it's private or government run.

Want to see real innovation? See for example the home made radio receivers people made in WWII, that fit in a small tin can, or visit an Amish settlement (http://kk.org/thetechnium/amish-hackers-a/). Not to mention hacker/maker spaces and fablabs, which all work on open source principles and sustain themselves through donations or member fees.