Is it literally a brand new iMac on which you haven't done anything, or did it start happening after you did something? That's definitely not normal, but it's hard to say exactly what's wrong without any information.
Just as one test, though, can you click on the Library folder in your home folder and choose "Get Info" from the File menu? In the info window that comes up, there should be a permissions section. That section should say "Read & Write." If it says something else, that would cause what you're seeing.