I haven't looked at this for a while, but my understanding is that a jet engine is not actually more efficient at high altitude: in fact the opposite applies. Gas turbines work best with dense air. In addition to the higher specific fuel consumption at high altitude, jet engines are also dramatically less powerful at high altitude. However, these effects are more than offset by the massively reduced drag of the aeroplane in thin air, thus aeroplanes as a whole are more efficient at high altitude.