I suspect the answer to the question "why are jet engines more efficient at altitude?" involves a combination of more than one factor.
Looking at it in a simplistic way - the higher up you are, the less dense the atmosphere i.e. atmospheric pressure is lower (yeah yeah, we know!). Assuming the pressure of the exhaust gas is constant throughtout the altitude regime, then this exhaust gas will be allowed to expands more at higher altitude than at lower altitude, as it always expand to ambient pressure. This means more work is done by the gas and, as long as the expansion occurs in the engine nozzle, more thrust is imparted to the aircraft.
This applies very well to rocket engines (which work best in vacuum) and the principle should be equally appicable to the exhaust from a jet engine.
A simple jet engine is more complicated than a simple rocket engine so I'm sure other factors (no doubt mentioned above) come into play...and may be more important.
Regards,
V1R
