Just parse the JSON object one more time for the value you need.
JSONArray jsonArray = new JSONArray(ResponseString);
for (int i = 0; i < jsonArray.length(); i++) {
JSONObject currentObject = jsonArray.getJSONObject(i);
String local_parameter = currentObject.getString("LOCAL_PARAMETER");
String tmp = local_parameter.get("Cost").toString(); // this gets the value of Cost
}