I recently rewatched Logan's Run. The concept of "Carousel" is explained well. Citizens participate when they turn 30 and believe they will be able to renew (be reborn) and it is shown later that the process is a hoax and no one is actually reborn.
If the point of carousel is population control then how does the city account for births? Early in the film Francis tells Logan that when one completes another is born. We know that there is no renewal, but is the population controlled in such a way that there is approximately a birth for every death? I have not read the novel. Does it explain that there? Does Francis know there is a birth for every death or are we assuming this is another lie the people have been fed and that he has chosen to believe it?