I think people will still trade bitcoins long after all are mined, I mean everyone wouldn't just hold all of their Bitcoin, so there will still be much transaction going on, much like how gold isn't mined as much today but still has value due to fixed supply and dynamics of demand. But just because supply is fixed doesn't mean prices will only go up, demand for Bitcoin will be the key factor I think, also governments regulation across the globe will also has some influence toward Bitcoin price even after all Bitcoin is mined.