How do professors choose their summer salary? In the United States, most professors are paid by the university on a 9 month basis for teaching (Sep - May). During the summer months a professor is typically paid from their grants and other revenue sources. How is the summer salary chosen? E.g. if a professor is paid 10kUSD/month, can (s)he choose to be paid 20kUSD/month during the summer?
I suppose this could depend on the funding agency.  For the NSF, your summer salary is determined by your academic year salary and you cannot receive more than that, although you could receive less if the program officer cuts that part of your budget.  I believe this is standard for U.S. funding agencies.

This situation is of course not fair to those who hold lower-paying jobs that do not reflect their achievements (but rather state budget priorities).  Like many things in grant funding, there's tremendous bureaucratic inertia and no hope of changing this aspect of the system.