This subject has a great deal of misinformation surrounding it, partly due to the rather vague documentation by Google.
There are very many articles about using Google+ authorship for business, but amazingly none of them have this critical piece of information.
After having searched extensively for the answer to this myself for quite some time, and experimenting with the Google Structured Data Testing Tool, I have concluded that you cannot link a Google+ business page to authorship.
Most articles that give examples of how to link your Google+ page for "business marketing" (i.e. not the Google+ business page!) use URL examples that are not business URLs.
Of course, this is one of those under-the-bonnet things that could change with no notice or announcement by Google in the near future.