I seem to recall reading of a design by Robert Heinlein (but maybe Sheffield, Clarke or another scientific writer), where the energy cost of a space elevator was virtually nil, as descending loads were used to recoup the energy cost of the lift.
Looking for the story,author and if possible the quote where it is described.
Answer
If you think it might have been Clarke, I would try The Fountains of Paradise. I don't remember the specific passage you're talking about, but it predates (and in fact probably caused) the era of science fiction in which space elevators are a common trope, so as I recall it spends more time describing them than most.
Edit
Chapter 10 "The Ultimate Bridge"
Quote delivered by the hologram of Vannevar Morgan, Chief Engineer of Terran Construction's Land Division.
"Capsules for passengers, freight, fuel would ride up and down the tubes, at several thousand kilometers an hour. Fusion power stations at intervals would provide all the energy needed: since ninety percent of it would be recovered, the net cost per passenger would be only a few dollars. As the capsules fall earthward again, their motors will act as magnetic brakes, generating electricity. Unlike re-entering spacecraft, they won't waste all their energy heating up the atmosphere and making sonic booms, it will be pumped back into the system. You could say that the down trains will power the up ones. So even at the most conservative estimate, the Space Elevator will be a hundred times more efficient than any rocket."
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