Display a code snippet based on a taxonomy term
The value you're looking for would be stored like so

$content["field_authors_type"]["#items"][0]["tid"]


You could, if you wanted to be tidier, put this if statement in your theme's template.php in a template_preprocess_node or template_preprocess_page function (more on that here: https://api.drupal.org/api/drupal/modules%21node%21node.module/function/template_preprocess_node/7.x). 

You would store your boolean value $variables['author_is_expert'] and then in your node.tpl.php, you can just use if ($author_is_expert)