I imagine the moon will be given something like the Antarctic Treaty System declaring it for research, at-least for the next 50 - 100 years (possibly longer but I feel as if space exploration...or rather mining...will 'take off' within it's first 25 - 50 years).
In terms of the asteroids, I'm expecting massive government intervention (interference) on which asteroids they can mine, where, when, and what. I'm not familiar enough with current mining laws / regulations to speculate whether any of those will be applicable in a space-mining environment.
On another note, imagine the fun in dealing with unions in 50 - 150 years. All I can think about is one of the opening scenes from Titan A.E.