Ask HN: How much should I charge for contract work?

I'm going into my senior year of college and one of the places I'm interviewing with for a full time position out in the bay area asked me if I would be willing to do contract work during the year, and also asked what I thought a fair price would be.

I'm making about ~$50/hr this summer, and a little bit of googling made it seem like contracting jobs usually go for $80-200/hr depending on experience and location. I'm thinking about asking for ~50/hr since that's what I'm getting right now, but is that overvaluing myself since I'm still a student, or is it undervaluing myself since it's a lot lower than what most people charge?

(Note that this place is a small startup - 15ish people).