I have been admitted to a Neuroscience PhD program with a stipend of $21k. This is slightly lower than my current stipend as a Masters student. Moreover, I am currently in a semi-rural setting, and as my new school is in a big city, living expenses there will be twice as much as they are here. Thus, I am effectively taking a major pay cut to go from Masters student to PhD student. I do not have any serious competing offers to use as a bargaining chip.
At my new school, students are funded directly through the department and stipend amounts seem to be fixed. BUT my advisor has tons of grant money under his control (as in, millions; he has 4 full-time RAs). Would it be possible for me to negotiate for a higher stipend? What would be the best way to go about doing this? I get the sense that he really wants me to work with him. How can I bring this up tactfully and professionally? And not be embarrassed if he says no?