A small correction to bigbears: You cannot consider the gravitic acceleration of the baloon since we’re talking about a gas. Its “upthruast” ("lol") is due to its density being smaller than the air density.
But yeah, I don’t understand what’s the big deal. It’s simple physics.

@ downy bill: There’s one subtle point you’re missing. The balloon only goes up due to its density being smaller than air’s. Period. No gravity acting on the air inside the elevator? OMG, IT’S A SPACE ELEVATOR! Yeah, if we were in space, that would be a completely different story. But it has nothing to do with “outside air friction”.

@ acepincter: Heavier air forced to the top of the elevator by inertia? What inertia, dude? Let’s consider the elevator is completely sealed from the exterior (the possible openings in the door don’t influence that much). What makes the air move? Someone moving their arms, for example (lets not consider breathing). Denser air stays on the bottom, less dense gases move top. Think of a hot air balloon.