Well the page DOES change if you are using the existing header which includes the currently logged in user. If someone is logged in, they have a menu that shows them logged in. This disqualifies it from cache consideration.
You would have to remove everything that is dynamic from the page including indicating they are logged in to do what you want.
By the way… Google is viewing the page as a guest so it should be seeing a cached version of it. So logged in status is irrelevant. Logout, clear ALL cookies for site and reload the page. Look at the cachability headers. Paste a link if you are not sure.