Creating author Specific page URL

Your example works if I delete the newline.

So this should work:

function add_my_rule() {    
    add_rewrite_tag("%args%", '([^/]*)', 'args=");
    add_rewrite_rule("writer/([^/]*)','index.php?pagename=writer&args=$matches[1]','top'); 
}
add_action('init', 'add_my_rule');