Effects of Testoserone on Female Deer

So this was a thought I had just now. Apparently testosterone can make female whitetail deer grow antlers but not european deer for some reason. I been thinking, would female deer antlers be worth more than male deer antlers since the female ones are rarer? Or are they worth less because they are man made (Or very rare in nature).  Would it even be ethical to inject female deer with testosterone? Just some cool thoughts I had.