How to know when to negotiate?

Thanks to self coaching scholars, I have shown up at work 110% or better every day and am so much happier than I have been in a long time. It has not gone unnoticed. In fact, I recently applied for a manager position and got the job! I am very excited.

They offered me a 10% increase in salary and I am wondering should I negotiate for more? I have read that you should always ask for more, and that we as women, rarely do, which is in part why there is a pay wage gap. Lots of other reasons for those pay gaps, but I digress. I feel like if I ask for more, that I will look ungrateful for this opportunity.

However, I am joining a brand new team, launching a brand new system. There were going to be 2 new managers, but instead only decided to go for 1. So, I will be managing 8 people, 6 of which I have to hire, all while launching a brand new system. Just seems that I should get more than 10%. I am also new to management, previous 7 years were as individual contributor. So, this will be an amazing growth/learning opportunity. I guess what I want to know, is how to you put a dollar value on the value I bring to any work I do? Appreciate your help, here and over the last 6 months. PS – I am also down 25 pounds!! Woot!