Well that is going to be a tough decision for the 14 year old. Firstly, there is nothing wrong with telling her that if she wants to go with her friends she will have to earn the funds to do so. That of course is secondary to discussing the outing and agreeing that it is appropriate for her to do what the other girls are planning to do.
Parents need to come to terms with the concepts of what children are entitled to and what a parent is obligated to do for them, and what WE as parents want to do for them. We need to explain to children the difference between “needs” and “wants”. Especially in these difficult economic times. There are times that parents can give a child what they want and there are times that a parent can’t. There are times when a parent feels that the child doesn’t deserve the privilege. A parent cannot hold back on their obligations to a child and must cover their needs, but wants and privileges are a different ballgame altogether. So each family has to decide what works for them and set up their own set of rules.
In many homes kids get allowance and they buy their nosh with that, they buy their clothes with that, they use it for their entertainment, etc. How ever the family sets it up. In many homes there is no allowance and the kids ask for what they need and want and the parents decide case by case. In many homes kids work for the extras. What ever way works for the family, that is the right way for you and don’t let anyone tell you otherwise. You might use a coupon system for your children to earn things, you might give allowance, you might be well off and generous and not have to worry too much about the extras. Only you know your own value system. Just make sure that what your kids are doing is age appropriate and safe. Know who your kids friends are and who their parents are, make sure that you are all on the same page hashkafa wise. If a group of 14 year olds are planning an outing find out which parent is going with them, how they are traveling, what time they are leaving, what time they are returning, who else will be there, etc. Having her raise her own money is not the only issue of importance.