Make dropdown child 100% of container

I have a dropdown inside a black container of 600px and i would like to have the red childrens show in a width of 100% of container instead of 100% of page width as it happens now. I need this to be in % because the website is responsive.

Please take a look at Jsfiddle Demo

<div id="navcontainer">
    <ul>

        <li>
            <a href="#">Eggs</a>

            <ul>
                <li><a href="">sub menu</a></li>

                <li><a href="">sub menu</a></li>

                <li><a href="">sub menu</a></li>

                <li><a href="">sub menu</a></li>
            </ul>
        </li>
    </ul>
</div>