Go to Yelp and search for places that do the same thing. Google that business and find their prices for comparison. Make a business plan, do calculations to find which price will likely attract customers and will help you gain money.
I have no fucking clue, but I would call around and make your prices competitive to others in the area. Because you're just starting out you'll want to go a bit cheaper while you build a portfolio.
Check out the prices of other makeup artists and go lower. I say go lower because you are just starting out so you are unheard of? So start low then when you start getting busy and well known you can decide whether or not to up the price. Don't go too low though just a little lower than the others... sorry I can't give you a popper price. I don't live in new york or anywhere in the US even.. so "/