You're pretty behind-the-scenes by Hollywood standards, but you do have the power to transform the careers and lives of those you represent. You can make Joe Blow a star. (Even though you'll probably have to recommend that he use a stage name.)
You have all kinds of quiet power arrows in your quiver—putting your client together with the right script with the right actor with the right director…. You're a hop, skip, and a jump from being a producer yourself. If you could just get funding from investors and/or a studio, you'd more or less "be there."
Your ultimate power is over the life of your clients—you can have a huge impact on their lives, what they do with their money, spare time, extra efforts outside of acting/writing/directing gigs. And you get to invite yourself to your own parties.
If you represent a major star who is in high demand, you have power up the wazoo. If a producer or director has their heart set on your guy or gal, they'll do just about anything to get their hands on them. It may not even be about offering more money either—your client is Brad Pitt and he’s not going to be hurting for cash any time soon. But maybe he won’t accept the role unless they find a speaking role for his niece. Or maybe they have to agree to cast him as the next Spiderman (you sure you're not a little old for that one, Brad?).
It's up to you to negotiate the terms, to make the power plays that get your clients everything they want and more. You hold all the cards, so to speak, and until you hear an offer that makes you happy, you can just keep telling them to "go fish."