Here's my take on it:
"You might as well take the money"
"You should just take the money"
But replacing might as well with should doesn't exactly do the job.
You use "might as well" when you're in a situation where you're not getting what you wanted. It's an expression to encourage someone to make the best out of his situation.
Suppose you want to go outside for a run but it starts to rain. You could say something along the line of:
"I might as well study for my exam."
In other words, you try to make the most of the outcome of a situation you didn't want in the first place.
I hope this helps.