1) .next is a function not a selector.
2) Your run on onload usage of $('function') is incorrect.
3) The following should work
$(function(){
if($('#page #description + .subdescription').length > 0){
$('#page #description').hide();
}
});
Just going to add a bit of explanation below:
$(function(){
This is equal to $(document).ready(function(){ /* code here */ })
$('#page #description + .subdescription')
Return all elements with class 'subdescription' that are siblings to the div with id of 'description'
$('#page #description').hide();
Shorthand for $('selector').css('display', 'none')