How to get AJAX script to post - ajax

Question

I am trying to get this AJAX script to post, but it is doing nothing. I am trying to get it to work on my development pc (localhost). See the AJAX script below. The HTML/Velocity is also shown below.
<script type="text/javascript">
$(document).ready(function() {
$("select.country").change(function(){
var selectedCountry = $(".country option:selected").val();
$.ajax({
type: "POST",
url: "$core_v2_page.Url",
data: { country : selectedCountry }
}).done(function(data){
$("#response").html(data);
});
});
});
</script>
And the HTML/Velocity is as follows:
#set($countries = false)
#set($countries = $Ibby_v1_LocationData.GetAllCountries())
<form>
<div>
#if ($countries)
<label>Country:</label>
<select class="country">
<option>Select</option>
#foreach ($country in $countries)
<option value="$country.iso2">$country.country</option>
#end
</select>
#else
#end
</div>
<div>
#if ($core_v2_page.IsPost)
#set($country = false)
#set($country = $core_v2_page.GetFormValue('country'))
#if ($country)
#set($regions = $Ibby_v1_LocationData.GetRegionsInCountry($country))
#if($country != 'Select')
<label>Region:</label
<select>
#foreach($region in $regions)
<option>$region</option>
#end
</select>
#end
#end
#end
</div>
</form>
<div id="response"></div>
</div>