The problem here is that JavaScript does not support associative arrays (scroll down to "Associative arrays, no way!"). It has some internal workarounds which make it appear as if it does, but really all it does is just adding the keys as properties.
So you would most likely be able to access it using Productdata.someid = ....
EDIT:
So assuming you have the following JSON string: {"id":"123"} (which is valid JSON), you can use it like this:
var jsonString = '{"id":"123"}';
var parsedJSON = $.parseJSON(jsonString);
var productID = "product_" + parsedJSON.id;
Does this help?
Some useful links: JSON format checker to make sure the JSON is valid.
Unfortunately I wasn't allowed to add more than 2 links, so the jQuery parseJSON function link is still in the comment below.