I don't think arrangements at the library of Alexandria are known in that kind of detail. (I've read a couple books about it, and most of the sources they use are from much later.) It was founded and funded by the Ptolemies as what you could plausibly call the first research university. Probably it was some combination of knowledge-is-power (it was an era of technical progress -- e.g. you know Eratosthenes and the size of the Earth? Eratosthenes was head of the library, and his work included basically inventing geography https://en.wikipedia.org/wiki/Eratosthenes#.22Father_of_geog... a subject of obvious interest to a new bureaucratic state), prestige, and genuine curiosity/cultivation on the part of the first few Ptolemies.
