How to use different date formats for different date inputs in jquery

Question

I am trying to use multiple date inputs on same page, some must have format yy-mm-dd and others format yy-mm. When I added jquery code for yy-mm format the input with yy-mm-dd format lost dates, only months and years are visible?

$(function() {    
  var currentDate = new Date();  
  $( ".datepicker" ).datepicker({ dateFormat: "yy-mm-dd" }); 
  $( ".datepicker" ).datepicker( "setDate",currentDate );       
});

$(function() {
    $('.month-picker').datepicker( {
        changeMonth: true,
        changeYear: true,
        showButtonPanel: true,
        dateFormat: 'yy-mm',
        onClose: function(dateText, inst) { 
            var month = $("#ui-datepicker-div .ui-datepicker-month :selected").val();
            var year = $("#ui-datepicker-div .ui-datepicker-year :selected").val();
            $(this).datepicker('setDate', new Date(year, month, 1));
        }
    });
});

Answer 1

I don't think that yy-mm and yy-mm-dd has any conflicts.I tried the same check this Fiddle.Both the file formats are on same page