Food additive manufacturers sell farmers aditives to produce yolks with specific hues[1]. There are regional/cultural variations in color preferences, so regional farmers will target different sades.
It's slightly disingenuous to call carotenoids "additives". Although it might technically be true, carotenoids are naturally present in tons of vegetables (hence carrots) and are a good antioxidant with other known health benefits.
So hens don't usually have to be force-fed. Some of that color can come from having a diverse source of proteins--like the bugs and insects that pasture-raised hens get access to--but farmers "in the know" will also add paprika and marigold to the usual soy-and-grain supplemental feed, to try to encourage it to come out a bit more.
A few years back I briefly thought that a rich yolk color was a quality signal, until I found that additives could produce that color cheaply. The color comes from dietary carotenoids [1]. Companies like BASF sell carotenoid feed additives that producers can employ to get a yolk color as rich as desired:
