Is it Greedy In this Market to Ask for a Raise?

So here's the scoop, I'm in my first management job and I know I'm being drastically underpaid. I know that others in similar positions in my area are earning about $15K-20K more than I am. I love my job despite the stress and responsibility, the commute is great, I'm happy and I wouldn't necessarily leave the job if I didn't get a raise because I value the experience I'm getting. However I can't help feeling slightly taken advantage of. What is the best way to go about asking for a raise? Should I just be grateful that I'm employed at all and live with it?
Since you're in management, what is the staff under you being paid? Is their pay on par with what others in similar positions in your area are getting? If not, first advocate for them to get a pay raise and then I'd say you have fully earned the right to ask for a pay raise of your own.
I agree with PP. Also, you may want to consider whether you, a brand new manager, are comparing your salary to individuals with more experience.Some of the most valuable management advice I have ever received: "always do your homework before taking a stand about anything... your perceptions may be waaaay out of whack and you will save yourself from major embarrassement at the very least."
I don't think it's greedy to ask for a raise: after all, the worst that can happen is that they'll say no In addition to the above advice, you should be realistic and accept that there's a chance you may not get all (or any) of the raise that you're asking for. Also, don't go in threatening to leave if you don't get a raise, unless you are actually prepared to walk away from the job.
I've always been lowballed when it comes to salary. I accept it for the most part. The one time that I spoke up for myself, I was prepared to leave, but I was going to leave anyway. I make my schedule available to more than one employer. The employer who pays me better gets more of my time, if possible.