Using auth_redirect returns cannot modify header information

It works fine on my localhost as well.

The reason it probably doesn’t work on your server is that it’s not using output buffering. Hooking into wp_head means that the page has already started printing to the client’s screen. Meaning auth_redirect‘s use of wp_redirect will fail: the headers have already been sent and you see the “headers already sent” error.

Try hooking into template_redirect instead of wp_head. I wouldn’t use auth_redirect here either. You’re already checking if the user is logged in (which auth_redirect does as well). Simply sent users to the login page with an appropriate “redirect_to” argument if they aren’t logged in.

<?php
add_action('template_redirect','wpse64899_check_if_logged_in');
function wpse64899_check_if_logged_in()
{
    $pageid = 2; // or whatever you want it to be
    if(!is_user_logged_in() && is_page($pageid))
    {
        $url = add_query_arg(
            'redirect_to',
            get_permalink($pagid),
            site_url('wp-login.php')
        );
        wp_redirect($url);
        exit;
    }
}