error with submitting a form

i’ve created a plugin (simple form) and this is the shortcode.php file:

<?php
add_shortcode('contact_form','contact_form');

function contact_form(){
    if (isset($_POST['submit'])){
        global $wpdb, $table_prefix;
        $name = $_POST['name'];
        $data = array('name'=>$name,'message'=>'message');
        $wpdb->insert($table_prefix.'contact_form',$data,array('%s','%s'));
        echo 'added';
    }

    ?>
    <form method="POST" action="" id="contact_form">
        Name: <input type="text" name="name">
        <input type="submit" name="submit" value="submit">
    </form>
<?php
}

when I submit the form, if I write sth in the text field, is says ‘The page doesn’t exist’ but if i leave it empty, it submits the form. what is the problem? I have used this shortcode in a page.