Babysitting wages depend on the sitter's age and experience, the area you live in, how many kids you have, etc.
I babysat all through my teen years, and received about $7/hr, on average. After I had been caring for one family's children consistently for a couple years, they gave me a raise, to $10/hr.
I still babysit occasionally, in addition to working full-time elsewhere, and receive $10/hr on average, although some families give me $12-15, and I do accept less from families who can't afford my usual rates. When babysitting is not my main source of income, I can be flexible about rates. When asked what I charge, I say that the general range is $8-12, but that I leave it up to the parents to decide.
If a teenager is old enough to make minimum wage at a job elsewhere, she should earn at least that much for babysitting.
I believe that when you are literally entrusting a person with your children's lives, she should be compensated at the highest rate that you can afford, regardless of her age. It doesn't make sense to pay someone more money to cut your hair or mow your lawn, when the services they are performing are so unimportant in comparison. JMO.
For many years during my teens and early 20s, babysitting was my main source of income. Usually I pieced together several part-time sitting jobs, to total 30-40 hrs/wk. Babysitting was my JOB job, not just something on the side, and I took it very seriously. I am grateful to the families for paying me enough money so that it was *possible* for me to have that be my main source of income.