Replace your switch with
switch(Page){
        case First:
            alert("First");
            $(".prev").closest('li').hide();
            $(".next").closest('li').show();
            break;
        case Last:
            alert("Last");
            $(".prev").closest('li').show();
            $(".next").closest('li').hide();
            break;
        default:
            alert("Default");
            $(".prev").closest('li').show();
            $(".next").closest('li').show();
    }
switch implicitly checks equality with the specified cases; you yourself do not perform the comparison.