Actually cutting hair I don't think one can do cheap enough, even if the only hairstyle it can do is a bowl cut. The human head is not uniform, and the actual surface is obscured so you have to find where it is by physical touch, which is not easy for a robot. You might be able to build a prototype for a few million, but the production units I can't see being done for less than $50k (you could spend crazy amounts in R&D to get it lower, but I doubt one can drive it down to less than $10k).
Main killer is the number of degrees of freedom the robot would need to cut the hair and the sensitivity in movement so it doesn't injure someone. If someone figured out how to do that, they could make boatloads of money applying it to other problems (eg: non-fun nursing tasks, like replacing bedpans or washing patents of which there is a endless list of complications stemming from them not getting done often enough).