I have three amazing answers that I can't choose between so on the last day (saturday) I will have to decide randomly as I do not want the bounty to not be given but I am providing an overhaul to the question, this is mainly to provide more context in certain areas and such.
For later reference here are some confusing terms or species interpretations that will be used later.
Brownskins: this does not denote a specific race in any way but is a subgroup of intelligent species with human or human-like skin-tones and with hair that doesn't fully envelop the body (those are furskins).
Fairies: in my world tinkerbell would not be classified as a fairy, nor would she be classified even as a pixie, that would just be dumb. Fairies are (on average) seven feet tall and they can't fly naturally, they don't have any special magical powers (but people believe they do) and they live ~350 years on average. They are also brownskins.
Hobgoblins: They seem like a subspecies of goblin from their name but they aren't, goblins would be classified as greenskins while hobgoblins are brownskins. Hobgoblins are about as tall as yoda but with brown skin and hair, they are not inherently evil but are like any other species.
Half-breeds originally only came about by an inter-species romance which (when they happened) were looked down upon, alot. Originally if two members of a different species conceived a child together they would both be tortured and killed because of their truly offensive action, this is the same if they have an affair and are discovered. Now eventually a certain clever man realized that (since this was a "civilized" society) he could try and get as many half-elves as he could and use them as slaves (inter-species romance was most common between these two races), he was able to go around and convince some people to let any man-elve couple to have one child and they can gift that child to him as a slave, afterwards they would not be allowed to see each-other and so-on. Now he wasn't two successful, instead of him getting a whole lot of slaves (like he wanted) the villages decided to force the half-breeding coupled to sell their half-breed children as slaves and so-on.
Now various practices for producing half-elves were made and some of them got codified into law as "legal" practices, these specifically dealt with half-elves and their production and not any other half-breeds. The specific practices don't matter but suffice it to say that there are many different practices for the production of half-elves and these allowances allowed them to become the second largest group of half-breeds.
So eventually fairy women realized the advantages of half-breeding as-well, you see fairies are the longest lived brownskins living for more than 350 years with a period of fertility lasting for most of their life, this is far greater than any other species. The practice that fairies started is where they would marry a person of a different species (generally as one of their wives with them having at-least one of their own species) and produce half-breed children for him, once he died she would then have a small fortune and she would move to a different region and start a new life and find a husband of her own that was a fairy. This eventually became a legal practice and it happens most with giants, men and elves, dwarves and hobgoblins are rare half-breeding partners for fairies.
Now the other types of half-breeds are totally undeveloped and I don't have good reasons for why any other types of half-breeds would come about (at-least as a very large group) but assume that there are other types.
So the question I am asking is this: how might this practice affect their economy? So note, they use the half-breeds for any use that slaves have been used for throughout history (including hard labor) and they are the only source of slave labor for most of history (except debt-servants). The main question is how that fact that these slaves cannot reproduce will affect how they are treated and their value, I don't know how long they live or even their physical appearances so just assume that they live human-length life-spans. If you would like to provide any general ideas on topics related to attribute variations (mainly in the form of lifespan) hose would be very welcome.
Wow, I just realized that I removed any explanation of what a half-breed was! They are simply a person made by NSFW intercourse between members of two different species, they are totally infertile as-well.