A $4k billable week is incredibly cheap, so much so that I'd worry about the team delivering it. Our rates are high because big firms bid them up. Why are the cheap teams turning down free money?
If someone offers you a $4k week, make sure they know they're cutting you a deal.
Hey, just to be clear: I don't think it's wrong to charge less than the market rate, and while I'm more likely to do a project gratis than at 1/2 or 1/3 my rate, we've given people breaks before.