you should use Htmlhiddeninput which contain your selected value of the dropdown than render the div

  $(document).ready(function(){

   $('.box').hide();
  // First Way :

   $('#HiddenInput').empty();
   $('#HiddenInput').val($('#dropdown').val());
   var value =  $('#HiddenInput').val();
   $('#dropdown').val(value);
   $('#div' + value).show();


   $('#dropdown').change(function() {
      $('.box').hide();
      $('#HiddenInput').val($(this).val());
      $('#div' + $(this).val()).show();
  }); 
});

Here See DEMO : http://jsfiddle.net/pXdS6/16/