Set The Width Of A Div To Be The Same Width Of The Image Inside The Div

I want to set the width of a div to be the same width of the image inside the div.The following code works great. But...The images are different widths, so both wrappers are set to the width of the first image. Without having to add an ID to each wrapper or image, can the wrapper width be set to the image width using the name of the image as the unique identifier?

jQuery:
$(document).ready(function(){
var newWidth = $('div.wrapper img').attr('width');
$('div.wrapper').width(newWidth);
});

HTML:

<div class="wrapper">
<p><img src="image1.jpg" width="200" /><br />
Caption</p>
</div>

[code].....