Private jets don't really fly at 50k that often but I'm sure there are some that can. 40-42k is pretty common though. There are a handful of reasons. In no particular order: 1) additional separation between recreational private flights and scheduled commercial flights 2) higher performance in small private jets with typically less than 1k lbs of people and cargo 3) winds are generally faster the higher you go so you'll usually go about at high as you're able, at least in one direction.
Most private jets aren't someone flying a billionaire around in a $60M Gulfstream, they're $3M toys being flown around by the owner to go to their ski trip.
> 3) winds are generally faster the higher you go so you'll usually go about at high as you're able, at least in one direction.
I recently flew from NYC to Lisbon, Portugal and it was 6.5 hours there (flying east) and 7.5 hours back (flying west) because you go with and against the jet stream.
I wonder if there's a noticeable difference if you fly at a lower altitude against the wind. It didn't seem like the plane adjusted for that, it cruised at the same altitude both ways from what I remember. Both flights used the same exact plane type (A330neo).
Airlines have dispatch folks that spend a lot of time deciding what altitude and route to file. Yes there are defaults so it's certainly possible they were busy and just filed the same but especially days apart it's likely that was the optimal altitude.
They're also looking at fuel economy so even if it takes longer if the air is thinner and they burn less fuel they may still save money. I imagine there's a certain distance where those two lines cross that is probably baked into the dispatch software for each plane model.
Note also that at higher altitudes the air is less dense, but the plane should fly at the same indicated/calibrated airspeed to generate the same lift, which means that it flies faster (at higher true airspeed).
Basically, with aircraft mass and angle of attack unchanged, \rho v^2 must be constant, so smaller density \rho -> higher air speed.
Most private jets aren't someone flying a billionaire around in a $60M Gulfstream, they're $3M toys being flown around by the owner to go to their ski trip.