Dystopia isn’t a frakkin’ system of government, kids. *rolls eyes* Perhaps totalitarian would work better to describe the government in this setting.
Get rid of the ellipsis at the end. It isn’t needed, and there’s no reason for that sentence to trail off.
There’s no noun/pronoun for the adjective each to describe, and not having one could make it appear as if it was intended to describe functions or something, so I added person after each for clarity.
To improve the flow, I broke the second sentence into two and changed the wording.
Add a comma before while in the last sentence. Without the comma, it means literally at the same time, instead of something closer to although or whereas. (After a recent editing job, I’m a bit hypersensitive to while or as being misused. No, strike that — I’m always a bit hypersensitive to some words being misused.)
Biological functions have become the new currency, with the government controlling the amount granted to each person. Sleep is the most prized. The elite regularly experience peaceful rest, while the poor are kept awake for days at a time.
Even compared to most dystopian fiction ideas, this is rather silly. You cannot maintain a society in which most people are severely sleep-deprived. The non-elites are the people you need to do most (or all) of the work, yes? Well, they can’t work if they go for days without sleep. Mistakes would be made, and some of those mistakes would result in bad things happening to the well-rested elites, which the elites would not stand for, so they’d quickly (within a few weeks at most) end up demanding that the workers be allowed to sleep, too… Also, why would “biological functions” become a form of currency? I can see people possibly wanting to purchase/earn artificial emotions or biological improvements, but that doesn’t mean such things would be the sole or even primary means of economic transactions.
In other words, think about what you’re doing before you write a story that doesn’t even have internal logic.