Let's get right to the point: there is no reason to feel guilty about low-balling when negotiating payment with the babysitter.
When I was a teenager I had no life, and was desperate for cash. I babysat (even though I didn't really like kids) and all my friends babysat. This was twenty years ago and I was paid one-fifty an hour. As soon as I was old enough I got a job at a pizza place (and free pizza when I misread orders and made it wrong) for the lordly sum of $3.35 an hour.
Now, baby-sitters in my neck of the woods charge $8 an hour (I was in my twenties before I made that kind of money - although I am employment-challenged.) I don't know why the price of a teenager's time has gone up so much - they seem about as useless as I was at that age. It probably has something to do with MySpace.
Do the math, a nice dinner for two ($40 and 90 minutes) and a movie ($20 including snacks and two and a half hours), add in transit time and you owe the baby-sitter $40. A modest night out suddenly costs a c-note.
And $8 an hour is not the high end. When we took the kids to an out of town wedding the baby-sitter was $12 an hour.
You have one advantage here, teenagers aren't much for market research. The kids already in the business know the prevailing rates. But the ones who haven't babysat before do not. You need to find fresh meat (bar mitzvahs have been particularly rich veins to mine - although not the kid being honored, he is rolling in gifts that day.)
This is a good start, but it could be counter-productive. If every parent is seeking new blood, soon the kids will get wise. Bidding wars, and possibly fistfights, could ensue. We need to form a cartel, before they start one (possibly through networks of friends on MySpace). As a cartel we can set prices and, if necessary, lobby congress to set a maximum wage for babysitters.
Also, if they are going to charge these prices we should make them take credit cards.
One important note - however desperate you are for a night out, do not compromise on your child's security. One kid told us how smart our son was, explaining, "He even beat me at Connect Four." He won't be back.