Is there any legal force behind MPAA ratings ans age restrictions?

As I understand it the MPAA is self-regulated. Am I correct in thinking this or not?

Are Theatre owners compelled by law to enforce Movie Ratings age restrictions? Are Theatre owners within their rights to sell a ticket to an “R” rated movie to an unaccompanied child?

MPAA ratings are only enforced by the theaters, not the law. There may be laws against providing obscene material to minors, which the theaters can avoid by enforcing ratings (assuming the MPAA is also rating the movies appropriately), but the ratings themselves are voluntary.

We just did this one.